Oliver Linton
email: o.linton@lse.ac.uk

Alessio Sancetta
email: asancetta@gmail.com.

Brendan Beare

Consistent estimation of a general nonparametric regression function in time series

Keywords: Kernel, Regression, Time Series Classi…cation : C12

We propose an estimator of the conditional distribution of X t jX t 1 ; X t 2 ; : : : ; and the corresponding regression function E(X t jX t 1 ; X t 2 ; : : :); where the conditioning set is of in…nite order. We establish consistency of our estimator under stationarity and ergodicity conditions plus a mild smoothness condition.

Introduction

There are now many papers on nonparametric estimation in time series. Roussas (1967), Rosenblatt (1970Rosenblatt ( ,1971) ) and Pham Dinh Tuan (1981) gave CLT's for kernel density and/or regression function estimators under the Markov hypothesis. [START_REF] Robinson | Nonparametric estimation for time series models[END_REF] relaxed the Markov assumption. He studied the case where a sample fX t ; t = 1; : : : ; ng is observed where (X t ) t2Z is a real-valued stationary and strong mixing stochastic process. The objects of interest were the marginal and conditional density functions as well as the regression function E(Y t jZ t ); where Y t and Z t are (di¤erent) …nite dimensional vectors containing lags of X t : He provided su¢ cient conditions for the pointwise consistency and asymptotic normality of the kernel estimators under weak dependence. As is by now well known, he found that the rate of convergence and the asymptotic distribution were the same as if the variable X t was i.i.d. with the same marginal distribution. Robinson (1986) considered also the case of regression where e¤ectively X t is a vector and Y t ; Z t are functions of different components of X t . These results have recently been generalized to local polynomial estimators in [START_REF] Masry | Local polynomial estimation of regression functions for mixing processes[END_REF] under more or less the same regularity conditions. [START_REF] Lu | Asymptotic Distributions for Local Polynomial Nonparametric Regression Estimators under weak dependence[END_REF] have extended these results to near epoch dependent functions of mixing processes. [START_REF] Collomb | Nonparametric time series analysis and prediction: uniform almost sure convergence[END_REF] and [START_REF] Masry | Multivariate local polynomial regression for time series: Uniform strong consistency and rates[END_REF] have studied uniform strong convergence. When the assumption of stationarity is abandoned one can …nd quite di¤erent results, for example those obtained by [START_REF] Phillips | Nonstationary density estimaiton and kernel autoregression[END_REF] and Karlsen and Tjøstheim (2001) for unit root or null recurrent processes (see also [START_REF] Bandi | On persistence and nonparametric estimation (with an application to stock return predictability)[END_REF], for near-integrated processes) for which the rates of convergence are slower and limiting distributions are non-normal (see also [START_REF] Sancetta | Nearest Neighbor Conditional Estimation for Harris Recurrent Markov Chains[END_REF], for modi…ed estimators that lead to standard inference in some of these situations). As remarked in [START_REF] Gyor… | Limits to consistent on-line forecasting for ergodic time series[END_REF], while many mixing/dependence conditions seem very plausible, there is virtually no literature on inference for mixing parameters estimated from data.

Hence, following a second strand of literature concerned with consistency only (e.g. Ornstein, 1978, Algoet, 1992[START_REF] Morvai | Nonparametric inference for ergodic, stationary time series[END_REF] we maintain the hypothesis that the data are stationary, but only require ergodicity. We generalize the object of interest to allow for in…nitely many conditioning variables. In particular, we study the estimation of the in…nite order regression E(X t jF t 1 );

(1)

where F t 1 = (X s ; s < t) is the sigma algebra generated by the sequence (X s ) s<t : Using the previous notation, we could have X t = (Y t ; Z t ) so that both the regression and autoregression problems are covered. This object is of interest for the following reasons. First, many parametric time series models involve dependence on the in…nite past. For example, the class of linear processes X t = P 1 j=1 c j ( )X t j + " t ; where c j ( ) are coe¢ cients depending on unknown parameters such that P 1 j=1 c 2 j ( ) < 1; while " t is i.i.d. This class contains the stationary and invertible ARMA processes that are widely used in practice. If X t is a GARCH(1,1) process, then X 2 t = P 1 j=1 c j ( )X 2 t j + " t ; although in that case " t is not i.i.d. In the Gaussian linear process case the univariate conditional expectations E(X t jX t j ) are also linear and can be used to identify the process. But in the non-Gaussian case this is no longer true and the univariate conditional expectations can be nonlinear and quite di¤erent from E(X t jF t 1 ); [START_REF] Tong | Non-linear Time Series: A Dynamical System Approach[END_REF], thereby making identi…cation of the correct model from just these univariate quantities impossible. Second, there are some semiparametric time series models that are di¢ cult to estimate without some preliminary estimator of E(X t jF t 1 ): To be speci…c, [START_REF] Linton | The Shape of the Risk Premium: Evidence from a Semiparametric Generalized Autoregressive Conditional Model[END_REF] studied the risk premium model

X t = ( 2 t ) + " t t ; t = 1; 2; : : : ; n; (2)
where " t are i.i.d. with zero mean and variance one, 2 t is a GARCH or EGARCH volatility process, while ( ) is of unknown functional form. The restriction that E(X t jF t 1 ), where F t 1 = (X s ; s < t), only depends on the past through 2 t is quite severe but is a consequence of asset pricing models such as for example [START_REF] Backus | Theoretical Relations Between Risk Premiums and Conditional Variances[END_REF] and [START_REF] Gennotte | Valuations in Economic Uncertainty and Risk Premiums on Capital Assets[END_REF]. To estimate the function (:) and the parameters of 2 t they proposed an iterative procedure whose properties have not been established as yet. If one can obtain consistent estimates of t = E(X t jF t 1 ); one can use these as starting values in that algorithm and straightforward arguments can be used to show consistency of the resulting estimates of the function (:) and the parameters of 2 t : See also [START_REF] Pagan | Nonparametric Estimation and the Risk Premium[END_REF] and [START_REF] Pagan | The econometric analysis of models with risk terms[END_REF]. A third reason for estimating the unrestricted regression E(X t jF t 1 ) is for speci…cation testing of nonparametric, semiparametric or parametric models. For example, the martingale hypothesis is that E(X t jF t 1 ) = 0 a.s.

The closest work to ours is [START_REF] Morvai | Nonparametric inference for ergodic, stationary time series[END_REF]. This paper proposes what amounts to sequential histogram versions of our estimators. Their primary construction is for the case where the series is binary: they average over the random number of cases where an increasing …nite sequence is reproduced. They then generalize to allow for continuous distributions by "quantizing" the sample space, covering it by a partition that re…nes with sample size. Their estimator involves some implicit temporal downweighting but it is not very transparent because of the sequential nature of its construction. In practice, it is likely to require much greater sample sizes than ours for reasonable performance. Furthermore, it is hard to frame the issues of "quantization" selection. They establish strong consistency of their c.d.f. estimator (in the weak topology of distributions) and regression estimator (under an additional condition of boundedness). [START_REF] Morvai | Weakly convergent nonparametric forecasting of stationary time series[END_REF] propose a modi…cation of this estimator that e¤ectively decouples the quantization from the length of history considered. They show weak consistency results.

Our estimator is relatively simple to implement, and it is intuitively connected with the standard kernel regression estimator, and is very explicit in terms of the spatial and temporal downweighting involved in its construction. Our results provide conditions for uniform strong consistency (existing results deal with the nonuniform case) and are applicable to data in arbitrary metric spaces endowed with a bounded metric and with a partial order ( ). This is of interest when we deal with particular data sequences like functional data (e.g. [START_REF] Ferraty | Nonparametric Functional Data Analysis[END_REF][START_REF] Ferraty | Nonparametric Functional Data Analysis[END_REF][START_REF] Masry | Nonparametric regression for dependent functional data: asymptotic normality[END_REF], for results under mixing conditions). An example of such data is when we observe sequences of interest rates term structures and we wish to predict the whole yield curve.

Our theory requires tuning of two parameters and we provide suggestions on how to choose them. One extra condition that we need to impose is some smoothness of the conditional distribution function. This is the price to be paid for using an estimator as simple as the one proposed here and that allows for uniform strong consistency.

In the simplest case, the function E(X t jF t 1 ) is a function from R 1 to R, denote it by f . When X t is weakly dependent, we can expect the in ‡uence of lagged values to decay in terms of the modulus of uniform continuity of f ,

jf (x i ; i 1) f (z i ; i 1)j X i 1 a i jx i z i j b ;
where j j is a suitable norm, b > 0 and a i ! 0 as i ! 1. For geometrically mixing X t we expect that a i c i for some 2 (0; 1) and positive constant c. We do not impose such speci…c assumptions. Here, we shall only assume that (X t ) t2Z is an ergodic and stationary sequence. Additional conditions related to existence of moments and mild smoothness conditions on the conditional distribution function will also be imposed.

The Estimator

We assume that we have a backward expanding sample X 1 n of n observations and we are interested in constructing an estimator of E (X 0 jF 1 ). By stationarity and the shift operator, this is equivalent to …nding an estimator of E (X t jF t 1 ) using X t 1 t n . See Gyor… et al. (2002, Ch.27) for remarks about estimation using a backward expanding sample and the more challenging estimation based on the forward expanding sample X n 1 . Our estimator is a locally weighted average, like classical nonparametric regression estimators. The only di¤erence here is the way we must de…ne local, which must take account of the size of the conditioning set. We require some additional details. We let X t take values in some metric space (X ; d). The product space

X 1 = N 1 s=1 X is equipped with the metric d (x; y) = P 1 s=1 s d (x s ; y s ), x; y 2 X 1
, for some 2 (0; 1). With abuse of notation, the same d is also used on a …nite product space: for x; y 2 X n , d (x; y) = P n s=1 s d (x s ; y s ). De…ne the following set of d radius h around x 1 n as

B h x 1 n := ( y 2 X 1 : n X s=1 s d (x s ; y s ) h ) : (3)
The set B h (x) includes the set Bh= s (x s ) := fy; x 2 X 1 : d(y s ; x s ) h= s ; y t = x t ; t 6 = sg ; which expands as s ! 1 for …xed h: This means that the neighborhood system has a tilted geometry where distant lags (large s) count much less in the determination of whether a vector is close to another one. Then, for x 2 X , we propose the following estimator

P n xjB h X 1 n := P (n m) s=1 fX s xg K d X 1 (n s) ; X (1+s) n =h P (n m) s=1 K d X 1 (n s) ; X (1+s) n =h ; (4)
where the inequality is meant elementwise if required (e.g. X R v , v > 1), and K is a kernel that has support [0; 1]. Throughout the paper, for any set A, the indicator function of the set is written as the set itself: I A = A. The parameter m 1 is …xed and chosen such that enough observations are available for reasonable conditional estimation. This can reduce the bias in …nite samples. Asymptotically, the value of m is irrelevant, hence, for simplicity we just set it equal to one with no further discussion. The parameter h de…nes the size of the local conditioning sets and is such that h := h n ! 0 as n ! 1. Finally, 2 (0; 1) determines the shape and allocation of the local conditioning sets. These quantities will be implicitly speci…ed in our regularity conditions below.

We de…ne the corresponding estimator of the conditional expectation of some function g (X 0 ),

P n g (X 0 ) jB h X 1 n := Z X g (x) P n dxjB h X 1 n (5) = P n 1 s=1 g (X s ) K d X 1 (n s) ; X (1+s) n =h P n 1 s=1 K d X 1 (n s) ; X (1+s) n =h :
This can be seen as a form of the Nadaraya-Watson kernel regression estimator with covariates of increasing dimension, but where the in ‡uence of temporally remote covariates is small.

Main Results

The goal of this section is to state general high level conditions that ensure consistency in a general framework. For simplicity we shall restrict our attention to the uniform kernel case where K(u) = fjuj 1g. For the estimator in (4) we shall show that

sup x2X P n xjB h X 1 n Pr (X 0 xjF 1 ) ! 0;
in probability (a.s.). For the estimator in [START_REF] Dawid | Prequential analysis[END_REF], in the special case g (x) = x p , p 2 N, the previous display together with an additional regularity condition implies

P n X p 0 jB h X 1 n := Z X x p P n dxjB h X 1 n ! E (X p 0 jF 1 ) ;
in probability (a.s.).

We formally state the conditions that imply consistency of the estimator.

Condition 1 (X t ) t2Z is a stationary and ergodic sequence of random variables with law P and values in X endowed with a partial order .

We impose smoothness on the joint distribution function.

Condition 2

The conditional probability Pr X 0 jX 1 1 = x 1 1 is P a.s. continuous in x 1 1 with respect to the topology generated by d .

The next is the crucial condition for consistency.

Condition 3 For P-almost all x 1 n , choose h n ! 0 such that lim n!1 n 1 X s=1 n d x 1 (n s) ; X (1+s) n h n o = 1 in probability (a:s:):
In Section 4.1 we provide a simple condition on the metric d that is su¢ cient for Condition 3 to be non-vacuous. Hence, we have the following.

Theorem 1 Suppose that the family of sets ffs 2 X : s xg ; x 2 X g has …nite bracketing number. Under Conditions 1, 2 and 3,

sup x2X P n xjB h X 1 n
Pr (X 0 xjF 1 ) ! 0 in probability (a:s:):

If X R v
, the left open intervals ffs 2 X : s xg ; x 2 X g have …nite bracketing numbers for v bounded (van der Vaart and Wellner, 2000). We can use a uniform integrability condition to show a related uniform convergence result for classes of functions which we denote by G.

Condition 4 G is a family of functions with envelope function G (x) = sup g2G jg (x)j such that

sup 1 i n<1 E h G (X i+1 ) p j n d X 1 (n i+1) ; X i n h n oi < 1; for some p > 1:
Condition 4 makes sure that the terms in the summation de…ning (5) are uniformly integrable. (Note that summation is over the X i 's satisfying fd (X 1 (n i+1) ; X i n ) h n g). We now state two corollaries to Theorem 1 that follow by use of Condition 4.

Corollary 1 Let G be the family of equicontinuous functions satisfying Condition 4. Then, under Conditions 1, 2 and 3,

sup g2G Z X g (x) P n dxjB h X 1 n E (g (X 0 ) jF 1 ) ! 0 in probability (a:s:):
For example, a family of functions is equicontinuous if it contains functions that are Lipschitz under some metric or if it comprises of a …nite arbitrary collection of continuous functions.

Remark 1 Clearly, when G comprises of the single function x p , p 2 N, which is continuous, Corollary 1 implies consistency for conditional moment estimators, i.e. E (X p 0 jF 1 ).

In some circumstances, we are interested in G whose elements are not necessarily continuous. If we restrict attention to functions with domain in a Euclidean space X R v (v a …nite integer), the elements in G can be replaced by functions of Hardy bounded variation. We brie ‡y recall the de…nition before stating the result.

De…nition 1 A function g : R v ! R is of Hardy bounded variation (BV) if it can be written as g (x) = g 1 (x) g 2 (x) where g j (j = 1; 2) are coordinatewise increasing functions, …nite on any compact subset of X .

Note that for v = 1 all de…nitions of bounded variation are the same and they di¤er for v > 1 (e.g. [START_REF] Clarkson | On De…nitions of Bounded Variation for Functions of Two Variables[END_REF]. Hence, we have the following.

Corollary 2 Suppose that G is a class of BV functions satisfying Condition 4. Then, under Conditions 1, 2 and 3,

sup g2G Z X g (x) P n dxjB h X 1 n E (g (X 0 ) jF 1 ) ! 0 in probability (a:s:):
Note that continuous functions are not necessarily BV function, e.g. g (x) = x sin (1=x) for x > 0, and zero elsewhere, is continuous, but not of bounded variation. Basically, functions of Hardy bounded variation are functions having a.e. the derivative D v g, where (D v g) (x) = @ v g (x) = (@x 1 @x v ), x = (x 1 ; : : : ; x v ). We now turn to some further discussion.

Discussion

Remarks on Condition 3

While we do not impose dependence conditions, veri…cation of Condition 3 is a major di¢ culty, but it is exactly what is required for consistency. If Condition 3 holds, there is no need to require the data sequence to be ergodic. Nevertheless, ergodicity appears to be needed in order to verify Condition 3. Recall that Condition 3 relates to the way the bandwidth needs to be chosen. Condition 1 does not seem to imply that there exists a bandwidth for which Condition 3 holds. For stationary ergodic processes, recurrence to some set is implied by the Poincare Recurrence Theorem (e.g. Theorem 6.4.1 in Gray 1998). In our case, the set is expanding and we cannot make direct use of this result. However, under an additional mild technical condition we can show that Condition 1 is su¢ cient to ensure that Condition 3 can be satis…ed.

Condition 5

The metric d is bounded, i.e. max x;y2X d (x; y) C, where C is a …nite absolute constant.

This condition has minor practical consequences. Indeed we can easily turn any metric d 0 on X into a bounded one, e.g. d := d 0 = (1 + d 0 ). Then, we have the following.

Lemma 1 Under Conditions 1 and 5, there is a sequence h n ! 0 such that, for P almost all x 1 1 ,

lim n!1 n X s=1 n d x 1 (n s) ; X (1+s) n h n o = 1 a:s:
In the proof of Lemma 1, it is shown that

B a h x 1 I := d x i ; X (s+i) a i h i ; i = 1; : : : ; I n d x 1 (n s) ; X (1 s) n h o
for any sequence a := (a i ) i>0 such that a i a i+1 , P i>0 a i 1 and

I = inf i 2 N : a i h= i 1 :
Clearly, I depends on h and a. Hence, to check Condition 3 we can check that

n I X s=1 n X (s+1) (s+I) 2 B a h x 1 I o ! 1 (6)
in probability (a.s.). Then, ( 6) is similar in spirit to standard conditions used to show convergence of kernel regression estimators (e.g. Devroye, 1981, Theorem 4.1). It would be conceptually useful to relate h n ! 0 directly to n. Suppose that for P almost all

x 1 I , 1 R n n X s=1 n X (s+1) (s+I) 2 B a h x 1 I o n X s=1 Pr X (s+1) (s+I) 2 B a h x 1 I ! 0 (7)
in probability (a.s.) for some sequence

R n = R n (h) = o n Pr X (1+1) (1+I) 2 B a h x 1 I
. By recurrence, the sequence R n ! 1 only when I = o (n) implying ( 6), hence Condition (3). To show [START_REF] Dudley | Real analysis and probability[END_REF] we would need regularity conditions on Pr X

(1+1) (1+I) 2 B a h x 1 I
in order to …nd its rate of decay as well as suitable mixing conditions (e.g. Rio, 2000, for a review). Given that x 1 I expands as n ! 1 the resulting conditions on h n are very complex and can be only stated as the solution of some nonlinear equation. Hence, for the sake of simplicity (and generality) our results are presented under Condition 3 only without using mixing conditions. Nevertheless, having established that Condition 3 is not void, it is necessary to choose h n in some reasonable way. We discuss this issue next.

Remarks on Parameter Selection

Estimators (4) and ( 5) depend on parameters h ! 0 and 2 (0; 1) and it is not obvious a priori what are good choices of them. The weak conditions used here make the direct application of classical cross-validation procedures di¢ cult and possibly dubious. In fact, while cross-validation for time series has been considered in the literature (Härdle and Vieu, 1992), the conditions required are too strict for the present context. In particular, the proof for the consistency of crossvalidation in Härdle and Vieu (1992) relies on inequalities for moments of partial sums (i.e. Marcinkiewicz-Zygmund kind of inequalities; e.g. see their Lemmata 3 and 4). Related moment inequalities are also used to derive the rate of convergence of the nonparametric estimator to the true regression function (their Lemma 1). None of these results is applicable here. Hence, we are only left with the choice of splitting the sample into an estimation sample and a validation sample over which to evaluate the performance of di¤erent bandwidths. Clearly, the splitting could be done recursively leading to a procedure that is amenable to standard analysis. For the sake of clarity we outline the procedure. Let P n ( jB h (X n 1 )) be ( 4) where we have shifted forward the segment of observations (X 1 ; : : : ; X n ) used to construct the estimator. Parametrize the possible sequence of smoothing parameters, i.e. h = h n ( ). Then, the problem reduces to optimal choice of := ( ; ) with 2 R 2 . The problem reduces to forecast validation as done in the prequential statistical literature [START_REF] Dawid | Prequential analysis[END_REF], for a review and references). The estimators discussed in this paper are functions of P n ( j ) =

P n ( jB h (X n 1
)) (emphasizing dependence on ). We only discuss the regression problem

P n (X n+1 j ) = R X xP n (dxj ). Let E n be expectation conditioning on F n . De…ne L N ( ) = N X n=m E n X (n+1) P n X (n+1) j
2 so that minimization of L N ( ) with respect to delivers the forecast closest to the conditional mean, say (N ) . Since L N ( ) is unknown, we minimize the empirical criterion

L N ( ) := N X n=m X (n+1) P n X (n+1) j 2 ^ (N ) := arg min 2 L N ( ) :
By the martingale structure of L N ( ) L N ( ), under regularity conditions, the empirical optimal choice ^ (N ) can be shown to be close to (N ) in probability, using standard martingale arguments (e.g. Seillier-Moiseiwitsch and Dawid, 1993).

5 Numerical Work

Simulation

In this section we discuss some Monte Carlo results whose aim is to verify the consistency of a simple implementation of our procedure. We suppose that

X t = 1 + " t " t 1 ;
where " t is either N (0; 2 ) or U [ =2; =2]: When " t is Gaussian, the conditional expectation E(X t jX t 1 ) = 1 (X t 1 1)=(1 + 2 ) is linear, but when " t is uniform, it can be nonlinear, see Tong (1990, pp 13-14). But in either case, E(X t jX t 1 ; : : :) = 1 1L) (L is the lag operator), which depends linearly on all past values of X: This is assuming invertibility, i.e., j j < 1:

" t 1 = 1 (X t 1 1)=(
We consider a …xed sample size n = 1000 and change the parameter 2 f0:01; 0:1; 0:3; 1g: The e¤ect of decreasing error scale should be similar to that of increasing sample size. We consider 2 f0:0; 0:33; 0:66; 1:0g:

We have used d(x; y) = jx yj:

We set = b = P t (X t X)(X t 1 X)= P t (X t 1 X) 2 :
This seems to capture the idea that the more dependent X t is, the larger we should set : We have tried other, …xed, values of and found similar results. To choose the value of h we have just taken h such that two hundred neighbors are included. Let

g = P X 0 jB h X 1 n and b g = P n X 0 jB h X 1 n
; and de…ne also the one dimensional estimators b g 1 = P n X 0 jB h X 1 1 : In Table 1 below we report the bias Eb g g and standard deviation std(b g) for the uniform error case, where both moments are computed by averaging across the one thousand simulations. The results improve as decreases and as decreases, but even when = 1; the estimator appears consistent. Note that b g 1 is inconsistent in this case. The results for the normal distribution are similar and not shown. Table 1 = 0:0 0:33 0:66 1:0 bias std bias std bias std bias std 1.0 0.0055 0.2732 0.0008 0.2884 -0.0081 0.3400 0.0060 0.4226 0.3 -0.0027 0.0823 -0.0008 0.0855 -0.0028 0.1005 -0.0038 0.1336 0.1 0.0001 0.0273 0.0012 0.0278 0.0002 0.0329 -0.0016 0.0439 0.01 0.0001 0.0027 0.0001 0.0028 0.0000 0.0034 0.0002 0.0043

The distribution of the estimator appears approximately normal according to Figure 1.

Figure 1. This shows the case where = 1 and = 1: Solid line is the standard normal pdf, dashed line is the estimated density of b g g (standardized to have mean zero and variance one).

In Table 2 we show the case where = 0:3 for sample sizes n 2 f100; 400; 1600; 6400g: This shows that consistency (as n ! 1) is achieved but the convergence is rather slow.

Table 2 n= 0:0 0:33 0:66 1:0 bias std bias std bias std bias std 100 0.0000 0.0120 -0.0009 0.0173 0.0006 0.0370 0.0032 0.0697 400 -0.0001 0.0089 0.0000 0.0126 0.0000 0.0337 0.0001 0.0629 1600 0.0001 0.0061 0.0007 0.0107 0.0000 0.0326 -0.0065 0.0627 6400 0.0000 0.0043 0.0002 0.0094 -0.0004 0.0309 -0.0013 0.0615

Application

We apply our theory to the study of the risk return relationship. Modern asset pricing theories imply restrictions on the time series properties of expected returns and conditional variances of market aggregates. These restrictions are generally quite complicated, depending on utility functions as well as on the driving process of the stochastic components of the model. However, in an in ‡uential paper, Merton (1973) obtained very simple restrictions albeit under somewhat drastic assumptions; he showed in the context of a continuous time partial equilibrium model that

t = E[(r mt r f t )jF t 1 ] = var[(r mt r f t )jF t 1 ] = 2 t ; (8)
where r mt , r f t are the returns on the market portfolio and risk-free asset respectively, while F t 1 is the market wide information available at time t 1. The constant is the Arrow-Pratt measure of relative risk aversion. The linear functional form actually only holds when 2 t is constant; otherwise t and 2 t can be nonlinearly related, Gennotte and Marsh (1993). Many previous tests of this restriction imposed parametric speci…cations both in the dynamics of the volatility process 2 t like GARCH-M and in the relationship between risk and return like linearity. Pagan and Hong (1990) argue that the risk premium t and the conditional variance 2 t are highly nonlinear functions of the past whose form is not captured by standard parametric GARCH-M models. They estimate t and 2 t as nonparametric regressions on a …nite dimensional information set …nding evidence of considerable nonlinearity. They then estimated from the regression r mt r f t = 2 t + t ; by least squares and instrumental variables methods with 2 t substituted by the nonparametric estimate, …nding a negative but insigni…cant . [START_REF] Linton | The Shape of the Risk Premium: Evidence from a Semiparametric Generalized Autoregressive Conditional Model[END_REF] considered the model (2), where 2 t was a parametrically speci…ed CH process (with dependence on the in…nite past) but t = '( 2 t ) for some function ' of unknown functional form. They proposed an estimation algorithm but did not establish any statistical properties. They found some evidence of a nonlinear relationship.

We suppose that both functions t and 2 t are unrestricted nonparametric functions of the entire information set F t 1 and they are related in a general way, that is, t = '( 2 t ) for some function ' of unknown functional form, or equivalently X t = '( 2 t ) + t ; where t is a martingale di¤erence sequence satisfying E( t jF t 1 ) = 0: Below we show some preliminary estimation of t = E(X t jF t 1 ) and 2 t = var(X t jF t 1 ) using S&P500 weekly stock returns with n = 2475. We chose = 0:99 and h such that k = 200 lags were included in the weighting. We then estimated the function ' by a univariate local linear kernel estimator with Silverman rule of thumb bandwidth: We show the estimated function ': The relationship is rather weak, i.e., the function ' is close to a constant.

Concluding Remarks

We have established the uniform strong consistency of the conditional distribution function estimator under very weak conditions. It is reasonable to expect that the best rate we can hope for over this very large class of functions is logarithmic in sample size. To formally derive almost sure rates of convergence we would need to impose dependence conditions that allow us to control the bias of the estimator. These dependence conditions would also be needed to establish some exponential inequality to control the estimation error. Exponential inequalities are commonly used in the application of the Borel-Cantelli lemma to ensure that the convergence is almost sure. If rates of convergence were available, then we could also hope to derive a central limit theorem for the estimator.

It is an open question whether one can achieve algebraic rates for some restricted class of functions. For example, suppose that

f (x i ; i 1) = 1 X i=1 f i (x i ); (9)
where the functions f i (:) are such that the sum is well de…ned, which implies some decay in their respective magnitudes. This additive regression model has been well studied in the case where it is known that f i (:) 0 for all i > d for some …nite d. [START_REF] Stone | Additive regression and other nonparametric models[END_REF] showed that the optimal rate for estimation of the components f i (:) and f (:) is the same as for one-dimensional nonparametric regression. Estimation algorithms have been proposed in Linton and Nielsen (1995) and Mammen, Linton, and Nielsen (1999). Linton and Mammen (2005) have considered the case where d = 1 but f i (x i ) = i ( )m(x i ) for some parametric quantities i ( ) that decline suitably fast. It may be possible to adapt the algorithm of Mammen, Linton, and Nielsen (1999) to the general model ( 9) by allowing the number of dimensions iterated over to increase slowly with sample size but such analysis is beyond the scope of this paper.

A Appendix: Proof of Main Results

At …rst we note the following, simple result.

Lemma 2 For any x 1 1 2 X 1 , lim h!0 B h x 1 1 = lim h!0 y 1 1 2 X 1 : d x 1 1 ; y 1 1 h = x 1 1 :
Proof. For any sequence k n ! 1

x 1 1 B h x 1 1 B h x 1 kn :
Hence it is su¢ cient to show that

lim n!1 B hn x 1 kn = x 1 1 : Since B h x 1 k k \ s=1 y 2 X : d (x s ; y s ) h s we choose k = o log 1= (1=h) so that, as h ! 1, h= k ! 0 implying k \ s=1 y 2 X : d (x s ; y s ) h s # 1 \ s=1 fy s 2 X : d (x s ; y s ) = 0g = x 1 1
and the result is proved.

Proof. [Theorem 1] De…ne

in probability (a.s.) for all i I n J n , implying jIIj ! 0 (in 11) in the same mode of convergence because (I n J n ) =I n ! 1. Since the result holds for P-almost all x 1 1 , it holds for X 1 1 as well. Using a …nite number of brackets for ffs 2 X : s xg ; x 2 X g the convergence is also uniform in x 2 X (e.g. see the proof of Theorem 2.4.1 in van der Vaart and Wellner, 2000).

To prove the corollaries we use the following.

Lemma 3 Condition 4 implies lim M !1 lim N !1 sup n>N Z fx2X :G(x)>M g G (x) P n dxjB h X 1 n = 0 a:s: (14)
Proof

i;n + inf n s > 0 : d X 1 (n+1 i;n s) ; X ( i;n +s) n h n o
which is just the sequence of stopping times de…ned in the proof of Theorem using X 1 (n+1 i;n s) instead of x 1 (n+1 i;n s) . Hence, mutatis mutandis, de…ne I n as in [START_REF] Granger | Thick Modeling[END_REF]. Rewrite Z

X G (x) p P n dxjB h X 1 n = 1 I n In X i=1 G X i;n +1 p .
Then, for any I n 0, the above display is a.s. …nite if sup 1 i n<1 EG X i;n +1 p < 1 for some p > 1. By stationarity this is just equal to sup 1 i n<1 EG X i;n +1 p = sup

1 i n<1 E h G X i;n +1 p j n d X 1 (n i;n +1) ; X i;n n h n oi sup 1 i n<1 E h G (X i+1 ) p j n d X 1 (n i+1) ; X i n h n oi < 1;
taking the supremum over all i n rather than i;n n only. ! so that, for n large enough, n I > 0: De…ne Y I s := X (s+1) ; X (s+2) ; : : : ; X (s+I) . Then, the right hand side of ( 16) is the number of times (out of n I steps) the ergodic process Y I s s 0 visits open sets of positive radius, induced by d in each coordinate, and centered at x 1 I . By stationarity and ergodicity the process is recurrent and the number of visits of any open set centered at x 1 I goes to in…nity as n ! 1 for P almost all x 1 I by Poincare Recurrence Theorem (e.g. Theorem 6.4.1 in Gray 1998). Since h is arbitrary we can let h = h n ! 0 slowly enough such that n I (h; ) ! 1 to deduce the …nal result.

Figure 2 .

 2 Figure 2. Weekly returns on the S&P500 Index. On the horizontal axis is shown the square root of the estimated conditional variance of returns given the in…nite past; on the vertical axis is shown the estimated conditional mean of returns given the in…nite past. The dashed line is the one-dimensional smooth of estimated mean on estimated standard deviation.

Proof. [Corollary 1 ]GGP n dxjB h X 1 nP 1 nP 1 nP (dxjF 1 )=P i 1 i 2

 111112 By Lemma 3 we directly work with[START_REF] Hall | Martingale limit theory and its application[END_REF]. Write P (xjF 1 ) = Pr (X 0 xjF 1 ) and de…ne G M (x) := G (x) ^M . For any …nite M ,lim (x) P n dxjB h X 1 n lim n!1 Z X G (x) P n dxjB h X 1 M (x) P n dxjB h X 1 n = Z X G M (x) P (dxjF 1 ) a:s:where the equality follows by weak convergence (Theorem 1) because G M (x) is continuous and bounded. By asymptotic uniform integrability the left hand side of the above display is …nite. Hence, by the monotone convergence theoremZ X G (x) G M (x) P (dxjF 1 ) ! 0:(15)For simplicity assume that G only contains positive functions (otherwise deal with positive and negative part of each function separately). Therefore, for any …nite M , x) ^M ) P n dxjB h X x) (g (x) ^M )] P n dxjB h X I + II: by letting P i 1 a i = h > h =2 and z i = i d x i ; X (s+i) in the …rst two displays. By Condition 5, with no loss of generality assume that d C = 1 so that fy 2 X : d (x; y) 1g = X :Letting I = I (h; ) be the smallest integer such that h= 2I 2 I 1, the previous display impliesd x i ; X (s+i) h 2i 2 i ; i = 1; : : : ; (n s) = d x i ; X (s+i) h 2i2i ; i = 1; : : : ; I and this last display implies n n I (h; ) X s=1 d x i ; X (s+i) h 2i 2 i ; i = 1; : : : ; I :(16) From the de…nition of I, note that for any > 0,

  . [Lemma 3] It is well known that a moment condition implies uniform integrability (e.g. Example 1.11.4 in van der Vaart and Wellner, 2000), i.e.

		Z
	lim N !1	sup n>N	X	G (x) p P n dxjB h X 1 n	< 1 a:s:
	for some p > 1 implies (14). De…ne
	1;n := inf	n s > 1 : d X 1 (n s 1) ; X s n	h n	o
	and, for i 1,

i+1;n :=

A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT

With this notation write, for P-almost all x 1 n ,

Hence,

where E i is expectation conditioning on F i;n . Since, by Condition 3, I n ! 1 in probability (a.s.), jIj ! 0 in probability (a.s.) by the martingale strong law of large numbers. Note that 1 i;n < i+1;n n for i = 1; :::; I n n and I n ! 1. Hence, for any sequence

because the second sum is

, so that we can explicitly write

Let T be the left shift operator, i.e. T X s = X s+1 , T k X s = X s+k . Then, for any i I n J n , using the explicit notation in [START_REF] Gyor… | Limits to consistent on-line forecasting for ergodic time series[END_REF],

because for any i I n J n , (n i;n ) ! 1 implying that for any h > 0

Since h is arbitrary we can choose h = h n ! 0 as in Condition 3 so that, B h x 1 1 ! x 1 1 by Lemma 2. Hence, by Condition 2, the last remark together with (13) implies that for P almost all x 1 1 ,

Therefore, by the triangle inequality, Jensen inequality and then by the above display,

The …rst term can be made arbitrary small for M large enough, by asymptotic uniform integrability and similarly for the second term by [START_REF] Joe | Multivariate Models and Dependence Concepts[END_REF]. Proof. [Lemma 1]Note that for any real variables (z i ) i 1 and summable constants

To see this, consider

))

and proceed by induction. Hence deduce d x i ; X (s+i) h 2i 2 i ; i = 1; : : : ; (n s)


V O E Akpambang A

G Purcaro B

L Lajide A

I A Amoo A

L S Conte

S Moret B

Determination of polycyclic aromatic hydrocarbons (PAHs) in commonly consumed Nigerian smoked/grilled fish and meat

Keywords: Chromatography -HPLC, Clean-up, Extraction Additives/Contaminants: Process contaminants -PAH's Food Types: Fish, Meat polycyclic aromatic hydrocarbons (PAHs), microwave assisted extraction (MAE), HPLC, fish, meat, smoking, grilling, risk assessment

Smoking and/or grilling, when carried out with traditional methods involving direct contact with wood combustion fumes, is responsible for high contamination levels with carcinogenic polycyclic aromatic hydrocarbons (PAHs). The aim of this work was to investigate the PAH content of different smoked or grilled meat and fish products, commonly consumed in Nigeria. A rapid method involving microwave assisted saponification and simultaneous extraction followed by solid phase extraction (SPE), HPLC separation and spectrofluorometric detection was employed. Samples which were smoked or grilled using traditional systems, which use a wood fire, were heavily contaminated with benzo[a]pyrene (BaP) at levels ranging from 2.4 to 31.2 µg kg -1 wet weight. Considerably lower contamination levels were found in samples smoked or grilled in the laboratory using a charcoal fire (BaP from 0.7 to 2.8 µg kg -1 wet weight). The health risk associated to a daily consumption of 100 g of these products was also evaluated using the margin of exposure (MOE) approach. MOE values lower than 10,000 were obtained for all smoked/grilled commercial samples, indicating a potential concern for consumer health.

Introduction

Polycyclic aromatic hydrocarbons (PAHs) are a group of environmental contaminants, originating from incomplete combustion of organic matter, which have received much attention over the years because of their ability to cause cancer. It is well known that raw meat (from mammals) does not contain appreciable levels of carcinogenic PAHs and no accumulation along the food chain has been observed for these contaminants in animal fat tissue [START_REF] Efsa | Polycyclic Aromatic Hydrocarbons in Food. Scientific Opinion of the Panel on Contaminants in the Food Chain (Adopted on 9 June 2008) [Internet][END_REF]. More controversial is the presence of PAHs in vertebrate fish. According to most of the authors, due to their ability to rapidly metabolize PAHs, fish generally contain very low PAH concentrations, even when they come from heavily contaminated areas [START_REF] Van Der Oost | Fish bioaccumulation and biomarkers in environmental risk assessment: a review[END_REF]. Nevertheless, some researchers found high PAH concentrations in raw fish from contaminated waters [START_REF] Visciano | Polycyclic aromatic hydrocarbons in fresh and cold-smoked Atlantic salmon fillets[END_REF]. Some authors [START_REF] Akpan | Polycyclic aromatic hydrocarbons in fresh and smoked fish samples from three Nigerian cities[END_REF] reported benzo[a]pyrene (BaP) concentrations ranging from 5.4 to 44.0 µg kg -1 dry weight for raw fish from 3 Nigerian cities. Amounts found in fish from the same contaminated area showed a correlation with their lipid content indicating the ability to bio-accumulate PAHs in their fatty tissues. More recently, [START_REF] Anyakora | A screen for benzo(a)pyrene in fish samples from crude oil polluted environments[END_REF] reported BaP concentrations between 1.5 and 10.5 µg kg -1 in 4 different fish samples from the Niger delta, a highly contaminated site due to the extensive petroleum production activities.

All food processing involving thermal treatments at high temperature and/or direct contact with combustion gases, such as smoking, toasting, roasting or grilling may be responsible for high PAH levels in processed foodstuffs. The amount of PAHs generated during the thermal food processing depends on several parameters such as temperature, duration of the treatment, distance from the source of heating, oxygen accessibility, fat content, and type of combustible used [START_REF] Alonge | Carcinogenic polycyclic aromatic hydrocarbons (PAH) determined in Nigerian Kundi (smoke-dried meat)[END_REF][START_REF] Visciano | Polycyclic aromatic hydrocarbons in fresh and cold-smoked Atlantic salmon fillets[END_REF]. Very high contamination levels are expected when food is smoked over an open flame, while charcoal grilling usually yields small amounts of PAHs [START_REF] Larsson | Polycyclic aromatic hydrocarbons in grilled food[END_REF].

Smoking is an age-old technique which brings desired flavors, improves color and appearance, has a tenderizing action and preservatives foods [START_REF] Ihekoronye | Integrated Food Science and Technology for the Tropics[END_REF]. Traditional direct smoking, in which the smoke is generated in the same chamber where the product is processed, exposes it to higher PAH content than indirect smoking which uses a separate chamber for smoke generation. In the latter case, it is possible to lower PAH load by passing the smoke through filters and washers or by cooling it before it comes in contact with the food. While in developed countries computerized smoking chambers with external smoke generators, and emission and temperature control systems, able to minimize PAH production, have generally replaced direct smoking systems using traditional kilns [START_REF] Karl | Determination of polycyclic aromatic hydrocarbons in smoked fishery products from different smoking kils[END_REF]Leinemann 1996, Hattula et al., 2001), in other countries such as Nigeria, traditional direct smoking systems are almost exclusively used even today. The most popular fish smoking method in Nigeria utilizes wire gauze on steel drums fuelled by wood.

Different approaches have been proposed s for risk characterization of the PAH mixture in food, the most popular being the use of BaP as a marker and the toxic equivalency factor (TEF) approach. Based on examination of PAH profiles in food and on evaluation of a carcinogenicity study of two coal tar mixtures in mice, both the Scientific Committee on Food [START_REF] Scf | Opinion of the Scientific Committee on Food on the risks to human health of polycyclic aromatic hydrocarbons in food (expressed on 4 December 2002)[END_REF] and the Joint FAO/WHO Expert Committee on Food Additives Expert Committee on Food Additives (JECFA, 2005) suggested that BaP should be used as a marker of the occurrence and effect of PAHs in food. However, latterly the TEF approach was re-assessed and it was deemed as not scientifically valid because of the lack of data from oral carcinogenicity studies on individual PAHs, their different modes of action and the evidence of poor predictivity of the carcinogenic potency of PAH mixtures based on the currently proposed TEF values [START_REF] Scf | Opinion of the Scientific Committee on Food on the risks to human health of polycyclic aromatic hydrocarbons in food (expressed on 4 December 2002)[END_REF][START_REF] Efsa | Polycyclic Aromatic Hydrocarbons in Food. Scientific Opinion of the Panel on Contaminants in the Food Chain (Adopted on 9 June 2008) [Internet][END_REF].

In 2005, the European Commission (EC) introduced for BaP (chosen as a marker of the occurrence and carcinogenic potency of the entire class of carcinogenic and genotoxic PAHs) a maximum levels of 5 µg kg -1 in smoked fish and meat (Commission Regulation 2005/208/EC). Before the introduction of this Regulation, lower legal limits for BaP existed in a number of EU Member States such as Belgium (2 µg kg -1 ), Slovak Republic and Germany (1 µg kg -1 ) [START_REF] Wenzl | Analytical methods for polycyclic aromatic hydrocarbons (PAHs) in food and the environment needed for new food legislation in the European Union[END_REF]. Up to now no maximum allowable levels for PAHs and/or BaP have been established by the government of Nigeria.

Based on new available data, in 2008 the EFSA CONTAM Panel concluded that BaP is not a suitable indicator for the occurrence of PAHs in food and that 8 high molecular weight PAHs (PAH8), and a subgroup of 4 PAHs (PAH4), are the most suitable indicators of PAHs in foods, and suggested to use the margin of exposure (MOE) approach for the risk assessment [START_REF] Efsa | Polycyclic Aromatic Hydrocarbons in Food. Scientific Opinion of the Panel on Contaminants in the Food Chain (Adopted on 9 June 2008) [Internet][END_REF].

According to [START_REF] Kazerouni | Analysis of 200 food items for benzo[a]pyrene and estimation of its intake in an epidemiologic study[END_REF], smoked and grilled foods may contribute significantly to PAH dietary intake if such foods are part of the usual diet. The consumption of traditionally smoked products could be responsible for the higher incidence of primary liver and stomach cancer in Nigeria compared with that in Europe and in the USA [START_REF] Alonge | Carcinogenic polycyclic aromatic hydrocarbons (PAH) determined in Nigerian Kundi (smoke-dried meat)[END_REF]. To our knowledge there are no recent consumption data for fish and meat in Nigeria. [START_REF] Yeh | The role of socioeconomic status and serum fatty acids in the relationship between intake of animal foods and cardiovascular risk factors[END_REF] City) of different socioeconomic status an average daily meat and fish consumption of 43.5 and 70.5 g, respectively.

Limited information on the levels of PAHs in smoked fish and meat in Nigeria is available from the literature. [START_REF] Afolabi | Polynuclear aromatic hydrocarbons in some Nigerian preserved freshwater fish species[END_REF] and [START_REF] Akpan | Polycyclic aromatic hydrocarbons in fresh and smoked fish samples from three Nigerian cities[END_REF] found BaP concentrations ranging from 11.1 to 66.9 and from 35.5 to 139 µg kg -1 dry weight, respectively, in Nigerian traditionally smoked fish. [START_REF] Alonge | Carcinogenic polycyclic aromatic hydrocarbons (PAH) determined in Nigerian Kundi (smoke-dried meat)[END_REF] reported BaP contents from 10.5 to 66.9 µg kg -1 in traditionally smoked meat from Nigeria, while [START_REF] Bababunmi | The role of aflatoxins and other aromatic hydrocarbons in human carcinogenesis. In: Host factors in carcinogenesis[END_REF] reported 8.5 µg kg -1 of BaP in suya meat (a spiced skewered beef very popular in West Africa, usually grilled over an open fire). More recently, [START_REF] Duke | Polynuclear aromatic hydrocarbons concentrations in char-broiled meat suya[END_REF] found BaP contents ranging from 6.5 to 21.5 µg kg -1 in suya meat from 4 different selling points.

PAH determination in meat and fish samples, when carried out by means of traditional sample preparation method, is solvent-and time-consuming and can be cause of analyte losses and source of spurious contamination. To overcome these disadvantages, new extraction techniques, such as microwave assisted extraction (MAE), able to perform simultaneous rapid extraction of a number of samples depending on the kind of apparatus, have been recently introduced and applied by different authors for PAH extraction from food matrices [START_REF] García Falcón | Analysis of benzo[a]pyrene in spiked fatty foods by second derivative synchronous spectrofluorimetry after microwave-assisted treatment of samples[END_REF][START_REF] Hernández-Borges | Optimization of the microwave-assisted saponification and extraction of organic pollutants from marine biota using experimental design and artificial neural networks[END_REF][START_REF] Pena | Optimization of a microwaveassistad extraction method for the analysis of polycyclic aromatic hydrocarbons from fish samples[END_REF].

The aim of this study was to investigate on PAH levels in some smoked/grilled fish and meat products commonly consumed in Nigeria and to estimate the potential risk associated with consumption of such traditionally processed foodstuffs. Unprocessed samples were analyzed, too. For this purpose a quick and efficient microwave assisted extraction (MAE) method, involving simultaneous saponification and solvent extraction, was used for sample preparation before HPLC determination and spectrofluorometric detection of 15 EPA-priority PAHs. The attention was focused on the EPA priority PAHs as they include the 8 PAHs (PAH8) recently indicated (together with a subgroup of 4 PAHs) as the most suitable indicators of the presence of carcinogenic and genotoxic PAHs in foodstuffs [START_REF] Efsa | Polycyclic Aromatic Hydrocarbons in Food. Scientific Opinion of the Panel on Contaminants in the Food Chain (Adopted on 9 June 2008) [Internet][END_REF]. All the solvents used were of HPLC grade (Sigma, St. Louis, MO, USA). Water was purified with a Milli-Q System (Millipore, Bedford, MA, USA). The standard PAH mixture (610M) in 1 ml of methanol/dichlorometane (Supelco, Bellefonte, PA, USA) consisted of: acenaphthene (Ac) (1000 µg/ml), fluoranthene (Fl) (200 µg/ml), naphthalene (Na) (1000 µg/ml), benzo[a]anthracene (BaA) (100 µg/ml), benzo[b]fluoranthene (BbF) (200 µg/ml), BaP (100 µg/ml), benzo[k]fluoranthene (BkF) (100 µg/ml), chrysene (Ch) (100 µg/ml), acenaphthylene (Ap) (2000 µg/ml), anthracene (A) (100 µg/ml), benzo[g,h,i]perylene (BghiP) (200 µg/ml), fluorene (F) (200 µg/ml), phenanthrene (Pa) (100 µg/ml), dibenz[a,h]anthracene (DBahA) (200 µg/ml), indeno[1,2,3-cd]pyrene (IP) (100 µg/ml), pyrene (P) (100 µg/ml). All the glassware was carefully washed and rinsed with distilled solvent (acetone and hexane) before use.

Materials and methods

Reagents and standards

Samples

Raw fish (about 2.5 kg) and commercially smoked fish (about 1.5 kg) of four different species commonly consumed in Nigeria, namely mudfish (Clarias gariepinus, Claridae), croaker (Pseudotolithus senegalensis, Sciaenidae), mackerel (Scomber scombrus, Scombridae) and jackfish (Selar crumenophthalmus, Carangidae), were purchased from 4 different local fish vendors in Akure (Nigeria). The raw fish was gutted, cleaned and a part (about half) was placed over a wire gauze that was on burning hardwood charcoal (15 cm away from the hot hardwood charcoal ember). The mackerel and the jackfish were allowed to cook for 40 min on both sides, while the croaker and the mudfish were cooked for 90 min on both sides to obtain a greater level of drying. The usual way of commercial fish-smoking is done on wire gauze placed over steel drums fuelled by burning wood. This produces a lot of smoke which meets the products directly, without any filtering or washing of the smoke.

About 1 kg of suya meat and 2.5 kg of smoked dried antelope ("bush meat") were purchased from each of three "suya spots" in Akure (Nigeria) and from two local vendors in Oja-Oba (Akure, Nigeria), respectively. Raw beef (about 1 kg) and antelope meat (about 2 kg) were purchased from 3 and 4 vendors in Akure, respectively. About half of the raw antelope meat and of the thinly-sliced raw beef meat (the latter brushed lightly with vegetable oil) was placed on a wire gauze over a hardwood charcoal fire and cooked on both sides slowly for 2 hours and 30 min, respectively. All raw (A), laboratory smoked/grilled (B) and commercially smoked/grilled (C) samples were deboned (if necessary) and cut in small pieces. Samples from different vendors were pooled together to obtain representative samples (for A, B, and C) for each of 4 types of fish and 2 types of meat products analyzed. An aliquot of the sample so obtained (about 100 g) was lyophilized, milled, packed in aluminum foil wraps and stored in the freezer at -20 °C prior to analysis.

Apparatus and HPLC conditions

A microwave extractor (Mars, CEM Corporation, Matthews, North Carolina, USA) able to process up to 14 sample simultaneously was used to extract PAHs from lyophilized samples. A Varian model 9010 HPLC gradient pump (Varian, Palo Alto, CA, USA) equipped with a Rheodyne 7161 injector with a 20 µL loop was used for analytical determination. A mobile phase consisting of acetonitrile and water (flow rate of 1 ml/min) was used for HPLC determination. The gradient elution program started with 40% acetonitrile (isocratic for 5 min), going linearly to 100% acetonitrile (total run time: 40 min).

The column was a C18 reversed phase (Supelcosil LC-PAH), 250 x 3 mm ID, 5µm particle size (Supelco, Bellefonte, PA, USA) thermostatted at 38°C. The detector was a programmable spectrofluorometer (Jasco, model FP 1520, Cremella, Como, Italy) whose wavelength settings are reported elsewhere [START_REF] Moret | A rapid method for polycyclic aromatic hydrocarbons determination in vegetable oils[END_REF]. A second spectrofluorometer set at different wavelengths settings was connected in series with the former and used to confirm analyte identity (Varian spectrofluorometer, model 9070). Quantification was carried out by the external standard method.

Sample preparation

PAH extraction was carried out by applying the method described by [START_REF] Pena | Optimization of a microwaveassistad extraction method for the analysis of polycyclic aromatic hydrocarbons from fish samples[END_REF], with little modifications. Briefly, 400 mg of lyophilized sample were weighed in a teflon lined vessel (Green Chem plus, CEM Corporation), added with 1.6 mL of water, 8 mL of saturated methanolic potassium hydroxide and 20 mL of n-hexane. A microwave assisted saponification/extraction was carried out at 120 °C for 20 min. Once cooled, vessels were opened and a measured amount (15 mL) of the organic extract, corresponding (with a relative uncertainty of less than 2%) to 3/4 th of the added amount of nhexane, was withdrawn with a volumetric pipette and concentrated to a few microlitres using a rotavapor and then a nitrogen flow. In order to minimize volatile PAH losses (which resulted higher when the last portion of solvent was evaporated to dryness under nitrogen flow or under vacuum), the residual solvent was allowed to evaporate spontaneously to dryness at room temperature, and the residue was then dissolved with 400 µL of n-hexane. Sample purification was performed by solid phase extraction (SPE). To speed up sample preparation reducing sample manipulation (avoiding the necessity to wash the test tube with additional solvent in order to realise a quantitative transfer of the sample extract onto the cartridge), a measured part of the sample extract (200 µL) was directly loaded on a 500 mg silica cartridge (Supelco), previously conditioned with 2 mL of dichloromethane and 2 mL of n-hexane. After sample loading, the PAH fraction was eluted with 3 mL of nhexane/dichloromethane (70/30). The fraction so obtained was gently concentrated to a few microlitres under a nitrogen flow and then left to evaporate spontaneously to dryness at room temperature. The sample residue was dissolved in 100 µL of acetonitrile and directly injected into the HLPC apparatus.

Two different aliquots of each sample underwent the entire analytical procedure (two replicates) and each replicate was injected twice. Analytical blanks (prepared in duplicate by subjecting all reagents and solvents, except the sample, to the entire procedure) were analysed (in duplicate) every day together with the samples and average data obtained were subtracted to those obtained from the real sample.

Results and discussion

Microwave assisted saponification and extraction

The method proposed by [START_REF] Pena | Optimization of a microwaveassistad extraction method for the analysis of polycyclic aromatic hydrocarbons from fish samples[END_REF], and applied for this work with little modifications (introduced for practical reasons), allowed us to perform a simultaneous saponification and extraction with minimal sample manipulation and solvent consumption. With respect to the conditions optimised by Pena and co-workers, the amount of sample and all the solvent volumes were doubled in order to assure that the temperature probe was properly dipped into the liquid phase. Extraction temperature and extraction time were also adjusted to avoid that at higher temperature the pressure inside the vessel exceeded the maximum allowable value (when it happens the system is automatically stopped for safety).

Method Performance

Linearity was verified by injecting in duplicate 7 diluted standard solutions in acetonitrile (in the range 0.1-39.6 µg/kg) and plotting the mean peak area against PAH standard concentration. Regression coefficients > 0.998 were obtained for all the PAHs. Limits of detection (LOD, s/n =3) and quantification (LOQ, s/n =10) lower than 0.1 and 0.3 µg/kg dry weight, respectively, were found for all PAHs (which corresponded to lower LOD and LOQ values when expressed on wet weight basis, depending on sample moisture content). The precision of the method was estimated by performing 6 replicate analyses of the same sample for each one of the relevant matrices: fish (laboratory smoked mackerel) and meat (laboratory smoked antelope). Relative standard deviations (RSD%) lower than 10%, except for F and Pa (<23%) were obtained for all PAHs in both matrices.

Since a suitable reference material with certified content of the target analytes (to test the accuracy of the method) was not available for meat and fish products, a spiking procedure was used to calculate recoveries. A 10 g-aliquot of lyophilised raw meat and fish with a low amount of naturally occurring PAHs, was weighed in a round flask and slurred with 20 mL of n-hexane containing a known amount of PAH standard mixture (to obtain a final BaP concentration of 2 µg/kg and other quantified PAH concentrations ranging from 2 to 4 µg/kg). The mixture was efficiently mixed using a rotary evaporator without using the vacuum supply. The solvent was left to evaporate slowly under continuous stirring for 2 hours. After solvent removal the sample was left to age for 3 days in the darkness.

The recoveries (mean of 3 replicate analyses) were calculated by comparing the difference between spiked and unspiked sample with the known amount of PAHs added. Mean recoveries ranging from 78 to 108% (higher than 96% for PAH8) and from 75 to 101% (higher than 93% for PAH8) were found for meat and fish sample, respectively.

PAH content in raw and smoked/grilled samples

Table I reports concentrations (µg kg -1 dry weight) of each single PAH in both raw and processed samples. The dry weight of the samples was determined by oven-drying at 103+2 °C until a constant weight was achieved. PAH amounts are the average of duplicate analyses (two replicates for sample).

Data were not corrected for recoveries. Due to their high volatility with consequent low recoveries and high coefficients of variation, data concerning Na e Ac were not reported. The sum of 5 low molecular weight PAHs (LMW-PAHs) (F, Pa, A, Fl and P), the sum of 8 high molecular weight PAHs (PAH8, including BaA, Ch, BbF, BkF, BaP, DBahA, BghiP and IP), the total PAHs (T-PAHs) and the LMW-PAHs/T-PAHs percentage ratios are reported, too. Results reported in table I are expressed on the basis of dry matter to exclude the diverse concentration effect due to the different loss of water occurring during food processing and to compare the data obtained to those reported by other authors on meat and fish products from the Nigerian market. Raw samples (A) had LMW-PAHs ranging from 20.5 to 84.8 µg kg -1 dry weight (table I). Considering the widespread diffusion of these contaminants in the ambient air, it can not be excluded that, at least part of the contamination originated from food manipulation and processing (cutting, transport and storage) before and after cooking. PAH8 and BaP content varied between 2.1 and 19.3 and 0.1 and 0.7 µg kg -1 dry weight, respectively. Data on fish samples were considerably lower than those reported by other authors for samples from the Nigerian market [START_REF] Akpan | Polycyclic aromatic hydrocarbons in fresh and smoked fish samples from three Nigerian cities[END_REF][START_REF] Anyakora | A screen for benzo(a)pyrene in fish samples from crude oil polluted environments[END_REF].

Anyway our samples did not come from recognized polluted areas such as the Niger delta.

All the fish samples smoked or grilled on hardwood charcoal in the laboratory (B) had LMW-PAHs ranging from 113.5 to 209.3 µg kg -1 dry weight (on average 161.1 µg kg -1 dry weight), while the fish samples smoked by commercial vendors and purchased from the local market (C) had LMW-PAHs comprised between 152.1 and 936.4 µg kg -1 dry weight (on average 603.7 µg kg -1 dry weight). LMW-PAHs accounted for 77.5-90.0% of the total contamination in smoked/grilled products. Pa was found to be the most abundant compound, ranging from 30.9% to 58.5% of LMW-PAHs in all samples. Among PAH8, Ch and BaA, were found to be the most abundant PAH compounds. BaP contents in the range 0.9-3.4 and 3.0-38.0 µg kg -1 dry weight were found in samples B and C, respectively, while PAH8 varied from 15.4 to 43.9 µg kg -1 dry weight for samples B and from 44.1 to 197.2 µg kg -1 dry weight for samples C. Among fish samples, the mudfish and the croaker, which had higher quantities of high molecular weight PAHs, were smoked dried to nearly constant level of moisture, while the mackerel and jackfish were partially dried.

Fish smoked under controlled conditions contains generally about 0.1 µg kg -1 of BaP (Stolyhwo and Sikorsky, 2005). Compared to these data and those obtained from a number of surveys on smoked fish and meat products from the European market [START_REF] Moret | Assessment of polycyclic aromatic hydrocarbon content of smoked fish by means of a fast HPLC/HPLC method[END_REF][START_REF] Storelli | Polycyclic aromatic hydrocarbons, polychlorinated biphenyls, chlorinated pesticides (DDTs), hexachlorocyclohexane, and hexachlorobenzene residues in smoked seafoods[END_REF][START_REF] Watson | PAHs -Report on seafish survey of UK seafood smoking businesses and products[END_REF], Yurchenko & Mölder, 2005[START_REF] Duedahl-Olesen | Polycyclic aromatic hydrocarbons (PAH) in Danish smoked fish and meat products[END_REF][START_REF] Efsa | Polycyclic Aromatic Hydrocarbons in Food. Scientific Opinion of the Panel on Contaminants in the Food Chain (Adopted on 9 June 2008) [Internet][END_REF], which rarely reported BaP concentration exceeding 1 µg kg -1 , samples from the Nigerian market resulted heavily contaminated. Nevertheless, BaP values found in commercial samples resulted in agreement or were slightly lower than those reported by [START_REF] Afolabi | Polynuclear aromatic hydrocarbons in some Nigerian preserved freshwater fish species[END_REF], [START_REF] Alonge | Carcinogenic polycyclic aromatic hydrocarbons (PAH) determined in Nigerian Kundi (smoke-dried meat)[END_REF] and [START_REF] Akpan | Polycyclic aromatic hydrocarbons in fresh and smoked fish samples from three Nigerian cities[END_REF] in Nigerian traditionally smoked fish and meat. Also data on suya meat well agree with those reported by [START_REF] Bababunmi | The role of aflatoxins and other aromatic hydrocarbons in human carcinogenesis. In: Host factors in carcinogenesis[END_REF] and more recently by [START_REF] Duke | Polynuclear aromatic hydrocarbons concentrations in char-broiled meat suya[END_REF].

The samples analyzed had all a similar PAH profile in agreement with the fact that the source of contamination was the same for all the samples. With the exception of jackfish (which had similar PAH content in both commercially and laboratory smoked samples), fish and meat samples from the market (C) had considerably higher PAH load than the corresponding samples smoked or grilled in the laboratory (B). The reason for this could be the food smoking technique utilized for commercial samples which made use of wood fires instead of charcoal fire used for laboratory smoked samples.

According to [START_REF] Larsson | Polycyclic aromatic hydrocarbons in grilled food[END_REF], the combustion of charcoal, being an already pyrolized material, gives a relatively clean smoke and, accordingly, lower PAH levels in the grilled sample.

Furthermore, in order to increase the shelf-life of the product, fish and meat vendors may re-smoke it many times until it is sold, thus contributing to increase PAH formation [START_REF] Afolabi | Polynuclear aromatic hydrocarbons in some Nigerian preserved freshwater fish species[END_REF][START_REF] Alonge | Carcinogenic polycyclic aromatic hydrocarbons (PAH) determined in Nigerian Kundi (smoke-dried meat)[END_REF]. Histograms of figure 1 show average PAH concentrations as well as minimum and maximum values for both laboratory and commercially smoked/grilled fish and meat samples. It is interesting to note that in commercially processed samples PAH amounts vary within a wider range than laboratory processed products. This could be explained with the fact that, while laboratory samples were smoked under standardized conditions aiming to avoid the generation of high amount of PAHs, commercial samples were obtained by different vendors using different conditions which can result in different PAH load. Smoked/grilled samples had fat content, determined by the AOAC method (1990), ranging from 13 to 21%. No evident correlation between fat and PAH content was found, neither for commercial samples (C) nor for samples processed under the same conditions (B).

Figure 2 shows the HPLC traces of a raw fish sample (croaker) and the corresponding sample smoked in the laboratory.

Compliance with the European legal limit and risk assessment

To make a comparison with the legal limit settled for smoked fish and meat by the European Commission in 2005 and to calculate PAH intake, table II reports (for the only smoked/grilled products) BaP and PAH8 contents, expressed in µg kg -1 wet weight. As we can see, 5 of the 6 commercially smoked/grilled samples contained BaP amounts exceeding the 5 µg kg -1 limit, while none of the laboratory smoked samples exceeded it.

Table II reports also the percentage ratio of BaP to PAH8, as well as BaP and PAH8 intake (ng kg -1 bw day -1 ), calculated considering a daily consumption of 100 g of product (fish and/or meat) per person and assuming a reference body weight of 60 kg. We used the amount of 100 g product for risk assessment because it roughly accounts for total meat and fish consumption of Nigerian population [START_REF] Yeh | The role of socioeconomic status and serum fatty acids in the relationship between intake of animal foods and cardiovascular risk factors[END_REF]. Compared to the median European dietary exposure to PAHs for mean and high dietary consumers, which varied between 3.9 and 6.5 ng kg -1 bw day -1 respectively for BaP alone, and between 28.8 and 51.3 ng kg -1 bw day -1 , respectively for PAH8 [START_REF] Efsa | Polycyclic Aromatic Hydrocarbons in Food. Scientific Opinion of the Panel on Contaminants in the Food Chain (Adopted on 9 June 2008) [Internet][END_REF], results obtained for commercially smoked samples always lead to higher dietary exposure (without considering the possible contribution from other food items). Of course, higher health risk is associated to higher consumption levels.

The MOE approach was used for risk assessment. MOE is the ratio between a defined point on the dose-response curve (reference point) for the adverse effect of the compound in the animal carcinogenicity study and the estimated human intake of the compound. The reference point is calculated using the benchmark dose (BMD) approach, based on a mathematical modelling being fitted to the experimental tumour data within the observed range. It estimates the dose that causes a low but measurable response. The use of benchmark dose lower limit (BMDL 10 ) representing the lower bound of a 95% confidence interval on the BMD corresponding to a 10% tumour incidence was chosen as reference point on the dose-response curve [START_REF] Larsen | Risk assessment of chemicals in European traditional foods[END_REF].

The ESFA Contaminant Panel calculated for BaP and PAH8 a BMDL 10 of 0.07 and 0.49 mg kg bw -1 , respectively [START_REF] Efsa | Polycyclic Aromatic Hydrocarbons in Food. Scientific Opinion of the Panel on Contaminants in the Food Chain (Adopted on 9 June 2008) [Internet][END_REF]. As we can see in table II, using these BMDL 10 values (considering a daily consumption of 100 g per person), MOE values lower than 10,000, were found in all commercially smoked samples for both BaP (except for the jackfish sample) and PAH8. The lowest values were found for the mudfish sample which presented MOE of 1,346 and 1,816 for BaP and PAH8, respectively.

Conclusions

Traditionally smoked and/or grilled fish and meat from the Nigerian market was found to be heavily contaminated, with BaP amounts often exceeding by far the limit of 5 µg kg -1 settled in 2005 by the European Commission. MOE values lower than 10,000, which according to EFSA (2008) indicate a potential concern for consumer health, were generally found in commercially smoked samples for both BaP and PAH8. This demonstrates the need for legal limits in traditionally smoked foodstuffs in Nigeria and possible risk management action. In agreement with previous works, it has been demonstrated that, the use of charcoal smoke instead of smoke from burning wood can help in lowering the final PAH load at levels around 2 µg kg -1 . Data are mean of two replicate analyses (each one injected twice). A = raw samples; B = laboratory smoked/grilled samples; C= commercially smoked/grilled samples; n.q. = not quantifiable for the presence of interference. Abbreviations: fluorene (F), phenanthrene (Pa), anthracene (A), fluoranthene (Fl), pyrene (P), benz

Figure 1 .

 1 Figure 1. Average PAH concentration (µg kg -1 ) for laboratory (B) and commercially smoked/grilled (C) fish and meat samples. Bars indicate minimum and maximum values. For abbreviations see table I.

Figure 2 .

 2 Figure2. HPLC traces of a raw sample of croaker and of the corresponding sample smoked in the laboratory (using charcoal fire). For peak abbreviations see tableI.

  [a]anthracene (BaA), chrysene (Ch), benzo[b]fluoranthene (BbF), benzo[k]fluoranthene (BkF), benzo[a]pyrene (BaP), dibenz[a,h]anthracene (DBahA), benzo[g,h,i]perylene (BghiP), indeno[1,2,3-cd]pyrene (IP), LMW-PAHs = low molecular weight PAHs (F+Pa+A+Fl+P), PAH8 = BaA+Ch+BbF+BkF+BaP+DBahA+BghiP+IP, T-PAHs = total PAHs (LMW-PAHs + PAH8).

  Table II reports also BaP and PAH8 concentrations in smoked products on wet weight basis.

Table I .

 I PAH content (µg kg -1 dry weight) in raw, laboratory and commercially smoked/grilled fish and meat samples from the Nigerian market

			Mudfish			Jackfish			Mackerel		Croaker			Suya		Antelope
		A	B	C	A	B	C	A	B	C	A	B	C	A	B	C	A	B	C
	F	7.3	7.1	140.1	0.6	14.0	7.3	2.9	8.6	27.0	0.3	7.1	72.0	1.2	4.2	31.6	0.6 11.1 53.3
	Pa	43.3	96.9 485.1	10.2 104.8 74.9	41.4	60.0 269.4	6.6 56.5 372.0	16.6 61.8 246.9	12.4 94.4 210.6
	A	5.3	15.3	26.5	1.2	5.0	4.7	6.8	4.4	48.0	0.7	6.3	72.6	1.5	8.1	48.8	0.8 13.6 70.0
	Fl	17.3	38.2 115.0	4.0	39.6	39.8	16.4	21.1 100.7	7.0 19.5 169.7	9.7 32.7 122.9	7.9 31.4 121.4
	P	3.5	46.5	63.0	4.5	46.0	25.4	17.3	24.6	94.2	6.8 24.1 250.1	9.7 31.7 125.2	7.0 32.1 134.3
	BaA	0.8	4.2	39.4	0.3	6.9	7.4	0.9	2.5	12.6	0.2	1.8	17.5	0.4	2.5	15.4	0.4	3.6	19.6
	Ch	4.6	7.7	55.2	0.8	15.2	16.3	4.2	5.8	20.0	0.7	3.7	55.4	1.1	4.8	25.6	1.0	7.4	39.6
	BbF	1.1	5.9	23.2	0.7	7.3	5.7	0.8	2.0	10.0	0.2	2.8	21.5	0.3	1.6	12.3	0.1	3.6	15.6
	BkF	0.6	1.8	15.1	0.4	2.7	2.4	0.3	0.9	6.3	0.1	1.2	13.0	0.1	1.2	6.0	0.2	2.0	6.6
	BaP	0.7	2.6	38.0	0.3	3.4	3.0	0.3	0.9	6.6	0.1	1.3	21.5	0.1	1.7	10.1	0.1	2.8	7.9
	DBahA	0.3	1.2	3.4	3.6	1.2	0.9	5.6	0.9	1.3	0.9	0.8	2.5	0.1	0.1	1.5	0.1	2.2	0.9
	BghiP	1.1	3.0	8.5	0.2	6.6	6.6	7.3	1.4	8.9	1.2	2.7	6.9	1.2	2.1	7.8	0.2	3.1	7.5
	IP	0.3	0.4	14.5	n.q.	0.6	1.8	n.q.	1.0	6.4	3.3	1.8	4.6	0.4	1.4	6.5	0.0	3.0	3.8
	LMW-PAHs	76.6 204.0 829.6	20.5 209.3 152.1	84.8 118.6 539.3	21.5 113.5 936.4	38.7 138.5 575.3	28.7 182.5 589.7
	PAH8	9.4	26.7 197.2	6.3	43.9	44.1	19.3	15.4	72.1	6.8 16.1 142.9	3.7 15.4	85.2	2.1 27.7 101.5
	T-PAHs	86.1 230.7 1026.9	26.8 253.2 196.2	104.1 133.9 611.4	28.3 129.6 1079.3	42.4 153.9 660.6	30.9 210.2 691.2
	LMW /T-PAHs (%) 89.0	88.4	80.8	76.4 82.7	77.5	81.4	88.5	88.2	75.9 87.6	86.8	91.2 90.0	87.1	93.2 86.8 85.3

Table II .

 II Risk assessment ,816 8,379 8,437 23,386 5,096 22,867 2,338 21,989 4,177 13,152 3,605 Data are mean of two replicates analyses (each one injected twice). B = laboratory smoked/grilled samples; C= commercially smoked/grilled samples. *Daily human exposure was calculated on the basis of amounts of 100 g fish or meat consumed daily. **Assuming a reference body weight of 60 kg.

		Mudfish	Jackfish	Mackerel	Croaker	Suya	Antelope
		B	C	B	C	B	C	B	C	B	C	B	C
	BaP (µg kg -1 wet weight)	2.1	31.2	2.8	2.4	0.7	5.2	1.1	18.9	1.5	8.4	2.2	6.3
	PAH8 (µg kg -1 wet weight)	22.2 161.9 35.1	34.8	12.6	57.7	12.9 125.8 13.4	70.4	22.4	81.6
	BaP/PAH8 (%)	9.6	19.3	7.8	6.8	5.7	9.1	8.3	15.1	11.0	11.9	10.0	7.7
	Daily human exposure*
	ng BaP kg -1 bw day -1 **	3.6	52.0	4.6	4.0	1.2	8.7	1.8	31.6	2.4	14.0	3.7	10.5
	ng PAH8 kg -1 bw day -1 **	37.0 269.8 58.5	58.1	21.0	96.1	21.4 209.6 22.3 117.3 37.3 135.9
	BaP-MOE	19,698 1,346 15,251 17,722 58,464 8,008 39,200 2,218 28,664 5,015 18,864 6,652
	PAH8-MOE	13,237 1

http://mc.manuscriptcentral.com/tfac Email: fac@tandf.co.ukFood Additives and Contaminants


Keywords: Mycotoxins, Pesticide residues apples, pesticides, patulin, Penicillium expansum, LC-MS/MS

A method for the simultaneous determination of 33 pesticides or degradation products together with patulin in apples by LC-MS/MS was developed. The method involved homogenisation of the apples, extraction with ammonium acetate-acetic acid solution in methanol-water by ultrasonication, filtration and determination by LC-MS/MS. The repeatability and within-laboratory reproducibility for the three spiking levels 0.02, 0.04 and 0.2 mg kg -1 were between 4 and 35%. In general, the repeatability and reproducibility were about 10-20%. The limits of quantification (LOQs) were between 0.01-0.14 mg kg -1 . The method was used on incurred samples from parts of the ISAFRUIT project financed by the European Commission under the 6 th Framework Programme.

Samples were analysed at four different stages, after harvest, after storage (controlled), after water bath and after 28 days at room temperature. Pesticide residues were found at all stages, but no significant differences in the concentration were seen between the stages analysed. The concentration decreased significantly only for tolylfluanid after storage at room temperature for 28 days when only 0-6% of the original amount of tolylfluanid remained in the apples. . No patulin was found in the apples stored for 28 days at room temperature and no growth of P. expansum was observed on these apples. However, when the apples were inoculated with a spore suspension of P. expansum high concentrations of patulin were found.

Introduction

Pesticides are widely used in the production of apples, both pre-and post-harvest to protect the apples from a range of pests and fungi, but also to preserve quality. Food Authorities such as the European Commission (EC) have established Maximum Residue Levels (MRLs) for the majority of the pesticides used in the production of apples (European Community, 2006). Monitoring programmes for pesticides have shown that fungicides and insecticides are often found in apples. In 59% of apple samples analysed in the EC coordinated monitoring programme for 2004 pesticide residues were found (European Commission, 2004). Although, residues above the MRLs were Several fungi can produce mycotoxins either in the field or during storage, and especially for apples Penicillium expansum is by far the most dominant fungal species. P. expansum is a known producer of patulin, and the European Communities (EC), have introduced a maximum limit of 50 µg kg -1 , for patulin content in apple juice and other apple products (European Commission, 2003). Furthermore, P. expansum spoilage of and hence patulin content in apples is a well known problem for the apple juice industry as apples are commonly stored prior to production due to processing capacity limitations. Patulin is therefore often used as an indicator of the use of poor quality raw materials in juice manufacture (Pitt, 2002). The analytical methods for the determination of patulin in fruit and vegetables have often been carried out by methods dedicated to a single analyte, where HPLC with UV detection is commonly employed [START_REF] Iha | Determination of Patulin in applejuice by liqid chromatography[END_REF][START_REF] Macdonald | Liquid chromatography method for determination of patulin in clear and cloudy apple juices and apple puree: Collaborative study[END_REF].

Commonly, pesticide residues have been detected by so called multi-residue methods that cover several hundred compounds. However, risk assessment involving different contaminant groups have necessitated multi-residue methods covering different compound groups. No previous published papers have, to the authors knowledge, described the simultaneously determination of pesticides and mycotoxins in apples.

In the present study an integrated method for sample preparation, extraction and determination was developed for the simultaneous analysis of several pesticides together with patulin. The method was used especially, to identify the critical steps for chemical contaminants in the chain from orchard to consumer. Results from apples analysed after harvest, storage, grading and after shelf life are presented. The study was part of the European Integrated Research Project, ISAFRUIT that focuses on all aspects of fruit. It was financed via the 6 th Framework Programme (Thematic Priority 5 -Food Quality and Safety). For more information on the project see the website, www.isafruit.org

Materials and Methods

Field trials

An experiment with the apple variety Malus Domestica (Golden delicious) to simulate the chain from orchard to consumers was performed at Agroscope Wadenswill (Switzerland). The apples were treated with the fungicides, trifloxystrobin, flusilazole, pirimicarb and thiacloprid at different application times (see Table 1). For the fungicide tolylfluanid four different application times were used in order to achieve different concentrations of the residue. Samples were collected at four 3 critical points to simulate the chain from producer to consumer. The four points were 1) after harvest, 2) after storage for 6 month at 4ºC in controlled atmosphere with low oxygen concentration, 3) after grading (here represented as a warm water bath at 30ºC for 10 min) performed the day that the apples were taken out of storage and 4) after 28 days shelf life at room temperature to simulate the consumers table.

[insert table 1]

Samples of 1 kg and at least 10 apples were collected from each group (1-4) and send to the laboratory at the National Food Institute, Technical University of Denmark, Denmark. Analysis was performed on samples collected at the four above mentioned critical point in the chain. See table 2.

The samples were packed in polyethylene bags and transported as quickly as possible to avoid any degradation during transportation.

[insert table 2]

Incubation of apples with P. expansum

The P. expansum isolate, IBT number 23732, the type culture used in this study, was obtained from the Fungal Culture Collection (IBT collection) at the Department of Systems Biology, Technical University of Denmark, Denmark. The apples were divided into three groups of 10 apples (replicates). Group A was untreated, group B was surface inoculated with P. expansum and group C was inoculated in the core with P. expansum. The surface inoculated apples were stab wounded with a sterilised needle (4-5 mm wound) and 10 µl of spore suspension (>10 6 spores ml -1 ) was put on the wound. Core inoculated apples were inoculated through the flower opening via a syringe and 10 µl of spore suspension (> 10 6 spores ml -1 ) was injected. The apples were incubated at room temperature for 28 days.

Materials and instruments

Chemicals

The pesticide standards (with certified purities >96%) were purchased from Dr. Ehrenstorfer (Augsburg, Germany) and the 13 C 6 -carbaryl (purity 99%) from Cambridge Isotope Labs. (MA, USA). The patulin was purchased from Sigma Aldrich (USA). The methanol p.a. was from Fisher Scientific (Leichestershire, UK). Acetic acid and ammonium acetate were from Merck (Darmstadt, Germany). Mini Uniprep polypropylene filter vials 500 µl, pore size 0.45µm was purchased from Whatman (Kent, UK). The water used was Milli-Q water (Millipore, Bedford, MA, USA). Stock solutions of pesticides and patulin of 1mg ml -1 were prepared in methanol and kept at -18 ºC.

A standard mixture of 10 µg ml -1 in methanol was prepared from the stock solutions. Matrixmatched standards in the concentration range from 0.0015 to 0.05 µg ml -1 (0.007-0.24 mg kg -1 matrix) were prepared by diluting the 10 µg ml -1 mixture with sample extracts of the relevant commodities bought as organically grown. The sample extracts were in the extraction solution: ammonium acetate / acetic acid 20 mM in methanol-water (95:5), which is the same solution as eluent B.

Sample preparation

The apples were homogenised by a chopper (Weisser, Obersasbach, Germany). 10 g of sample was extracted with 40 ml ammonium acetate-acetic acid solution 20mM in methanol-water (95:5) in an ultrasonic bath (Branson 5510, Soest, The Netherlands) for 30 minutes. The samples were centrifuged at 3500 rpm for 10 min (Heraeus Sepatech Megafuge 3.0R, Osterode, Germany).

Extracts, 400 µl, were transferred to Miniprep filter HPLC vials and added 40 µl internal standard: 13 C 6 -carbaryl 0.1 µg ml -1 before filtration.

Instrumentation and chromatographic conditions

The LC system consisted of a HP1100 liquid chromatograph (Agilent Technologies, Palo Alto, CA, USA) equipped with a vacuum degasser, a solvent delivery compartment with high pressure mixing, an autosampler and a column compartment. The injection volume was 10 µl. Separation of pesticides was performed on a Genesis C 18 column, 100mm × 3 mm, 4µm particle size, (Gracevydac, Hengoed, UK). In front of the separation column was a Phenomenex SecurityGuard column, C 18 ODS, 4mm × 2mm (Cheshire, UK). The total flow rate of eluent A (ammonium acetate-acetic acid 20 mM in MilliQ water) and B (ammonium acetate-acetic acid 20 mM in methanol-MilliQ water (95:5)) was 0.3 ml min -1 . The initial gradient was 100% A, decreasing to 50% A after 2 min and 0% A after 20 min. A was held at 0% until 24 min. The total run time was 30 min.

The MS-MS detection was performed on a Quattro Ultima triple quadrupole instrument (Micromass Manchester, UK) equipped with an atmospheric pressure ionisation (API) interface.

The mass spectrometer was operated with electrospray both in the positive and the negative ion mode (ESI+ and ESI-). The capillary voltage was set to 1.0 kV. The source temperature was 120 ºC and the desolvation temperature 350 ºC. Nitrogen was used as desolvation gas (flow 550 l h -1 ) and cone gas (flow 50 l h -1 ), and argon was used as collision gas at a pressure of 1.7 × 10 -3 mbar. 3). The quantification was made using Masslynx software with Quanlynx. The maintenance of the mass spectrometer includes cleaning of the cone.

[Insert table 3]

Results and discussion

Method Validation

The pesticides included in the method was chosen due to the possible use on apples. The accuracy of a method can be estimated from certified reference material, recoveries of spiked samples or from accuracy in proficiency testing. Recoveries were obtained by fortifying blank apple samples with pesticides and patulin. The majority of the pesticides, 30, were validated according to Document SANCO/2007/3131 (European Commission, 2007). The mean recoveries of the pesticides (n = 6) at the spiking levels 0.02, 0.04 and 0.2 mg kg -1 appears from Table 4. For most pesticides recoveries were within 70-110%. For the three pesticides trifloxystrobin, tolylfluanid, thiacloprid and for patulin, the determination of the accuracy consisted in recovery test at the three spiking levels, 0.02, 0.04 and 0.2 mg kg -1 , single determination with three repetitions (four repetitions for patulin). Again the mean recovery was between 69-109%, see table 5.

[insert table 4] [inset table 5]

Precision

For the 30 pesticides or degradation products, the repeatability and within laboratory reproducibility were calculated according to ISO5725-2 [START_REF] Anon | Accuracy (Trueness and Precision) of Measurements Methods and Results-Part[END_REF] using duplicate determinations for calculations of repeatability and the repetitions for calculation of reproducibility. The repeatability, RSD r , and reproducibility, RSD R , for the three spiking levels 0.02, 0.04 and 0.2 mg kg -1 is shown in Table 4. No significant differences were seen between the spiking levels. In general, the repeatability and reproducibility were about 10-20%, which is acceptable for multi-residue methods. For trifloxystrobin, tolylfluanid, thiacloprid the standard deviation between the recovery series were in the range of 4-26% (see table 5). The limit of quantification (LOQ) was calculated as 6 times the standard deviation of the absolute recoveries at the lowest accepted spiking level. The LOQ's are given in table 4 for the 46 pesticides, and table 5 for the three pesticides and patulin.

Limits of quantification.

Quantification was performed for each analytical series using means of two 5-point calibration curves. The matrix matched calibrations standards were of the concentrations 0.0015, 0.003, 0.01, 0.025 and 0.05 µg ml -1 . The linearity of the calibration curves were r2> 0.99.Chromatograms of field treated samples are shown in figure 1.

[insert figure 1]

Result from apples sampled along the artificial chain from producer to consumer.

The validated method was used for the analysis of 64 samples collected from an artificial chain from producer to consumer, described above under Method. Thiacloprid was not found in any of the samples, however this may be due to the fact that thiacloprid was only applied once 90 days before harvest, which may lead to residue content below the detection limit. Patulin was expected only to be present in the samples analysed after 28 days at room temperature and therefore only analysed for in these 16 samples.

No patulin was found in the apple samples analysed after 28 days at room temperature. But to verify the capability of the method, it was used to analyse samples inoculated with P. expansum. The results of these samples are presented below.

Pesticides

Trifloxystrobin, flusilazole and pirimicarb were found in low concentrations from 0.006-0.024 mg kg -1 . These pesticides were applied more than 50 days before harvest and the low levels were expected. No significant differences in the concentration were seen in the samples after harvest, after storage, after grading and samples after 28 days shelf life, see Figure 2. However, due to the low concentrations it may be difficult to see any decrease in the concentration through the chain.

[insert Figure 2 The concentrations found in the samples sprayed 4 weeks before harvest were at the same levels as the tolylfluanid untreated apples. The reasons for the finding of tolylfluanid residues in the untreated samples are supposed to arise from drift of pesticides during spraying. The concentration of the tolylfluanid residue found in the samples collected after harvest were 4-6 times lower than the concentration after storage. According to the Pesticide Manual (Tomlin, 2006), tolylfluanid is rapidly hydrolysed into dimethylamino sulfotoluidide (DMST). The explanation of the low levels in the apples collected after harvest could be that tolylfluanid in the apples were degraded due to exposure to light, heat and moisture during transportation.. These factors were better controlled by wrapping the apples during transportation.The wrapping was consequently improved when next batch of samples were send to the laboratory and these apples arrived in very good condition. No significant decrease in tolylfluanid residues was seen after water bath. However, storage at room temperature in 28 days decreased the concentration significantly. No residues were found in the 28 days sample that had been sprayed four and two weeks before harvest. The concentration of tolylfluanid in the samples sprayed 1 week before harvest was 0.03 mg kg -1 , which was a reduction of 94%.

[insert Figure 3 here] The results of pesticide residues from the critical point 2, 3 and 4 are in accordance with an investigation done by Rasmussen et al. (2003) on the effects of washing and storing two different sorts of apples. None of the pesticide included in that study was significantly reduced when the apples were subjected to simple washing. However, storing in a refrigerated room at 4 o C for 42-79 day significantly reduced 5 out of 13 pesticide residues, including tolylfluanid, which were reduced by 47-69%.

Patulin

The patulin content and the growth of P. expansum in apples treated with pesticides at different times before harvest was investigated after 28 days of shelf-life (see Table 2 for more details).

As shown in Table 6 no patulin was found in the apple samples stored for 28 days at room temperature. Furthermore no growth of P. expansum was observed on these apples, showing that patulin producing fungi is not a problem in apple samples stored under the present incubation conditions. When the apples were inoculated by a spore suspension of P. expansum patulin had been produced at quite high levels in both core and surface inoculations exceeding the EU maximum limit of 50 µg kg -1 for apple juice with several hundred percent. In accordance with the study of [START_REF] Karlshøj | Prediction of Penicillium expansum spoilage and patulin concentration in apples used for apple juice production by electronic nose analysis[END_REF], the patulin concentrations were 2 -5 times higher in core inoculated apples compared to the surface inoculated apples. This was probably due to the higher degree of spoilage in these apples as the fungus was able to grow spherically in all directions from the core, whereas the surface inoculated colony was limited to hemispherical growth; that is, the patulin to hyphae ratio between the two types of infection is expected to be the same. It was not possible from the present results to evaluate or explain the effects of pesticide treatment carried at different periods before harvest.

[insert table 6 here]

Conclusions

A method for simultaneous determination of 33 pesticides or degradation products together with patulin in apples was developed. The repeatability and within laboratory reproducibility for the three spiking levels 0.02, 0.04 and 0.2 mg kg -1 were between 4-35%. In general, the repeatability and reproducibility were about 10-20%. The limits of detection (LODs) were between 0.01-0.14 mg kg -1 . The method was used for the determination of pesticide residues and patulin in samples from the ISAFRUIT project. Trifloxystrobin, flusilazole and pirimicarb were found in low concentrations from 0.006-0.024 mg kg -1 . No significant differences in the concentration were seen in the samples after harvest, after storage, after grading and samples after 28 days shelf life.

Tolylfluanid was found in concentrations between 0.016-0.488 mg kg -1 . No significant decrease in tolylfluanid residues was seen after water bath. However, the storage in room temperature in 28 days decreased the concentration significantly with 94-100%. No patulin was found in the apple samples stored for 28 days at room temperature and no growth of P. expansum was observed on these apples. However, patulin were produced in levels exceeding the EU maximum limit of 50 µg kg -1 for apple juice, when the apples were inoculated with a spore suspension of P. expansum. The patulin concentrations were 2 -5 times higher in core inoculated apples compared to the surface inoculated apples. 2003): Distribution of multiple pesticide residues in apple segments after home processing. Food Additives andContaminants, 20, No. 11, pp. 1044-1063. Tomlin CDS (ed) (2006)(2007)

  2% of the samples, many consumers are nevertheless concerned about exposure to pesticide residues.

  in multiple reacting monitoring (MRM) mode. The cone voltage and the collision energy were optimized for the different pesticides and patulin (see Table

  here]

  Figure 3. The highest concentrations were found in the samples sprayed seven days before harvest.

  I. (2002). Biology and ecology of toxigenic Penicillium species. In:Mycotoxins and Food Safety, pp 29-41. Eds: DeVries JW, Truckness MW, Jackson LS. Kluwer Academic, New York, USA. Rasmussen, R.R., Poulsen, M.E. and Hansen, H.C.B.(

Table 1 .

 1 The e-Pesticide manual, 14 th ed. British Crop Protection Council, Figure 1. Examples of chromatogrammes of samples containing trifloxystrobin, pirimicarb, flusilazole, tolylfluanid, thiacloprid and patulin.Figure 2. Residues of trifloxystrobin, flusilazole and pirimicarb in apples collected at the critical points along the artificial chain from producer to consumer.Figure 3. Residues of tolylfluanid in apples, applied at different time and collected at the critical points along the artificial chain from producer to consumer. Application dates with the formulations and active substances used, apple group spayed and number of days from spraying to harvest

	London, UK.

Table 2 .

 2 Schedule for sampling at critical point from the chain from orchard to consumer, group samples, number of samples and the analytical program performed

				Number of
	Critical point	Date	Apple group	samples	Analytical profile
	1) After harvest	15 September 2006 Group 1,2,3,4	4	Pesticides
	2) After storage in CA
	Controlled Atmosphere	15 March 2007	Group 1,2,3,4	4	Pesticides
	3) After grading/water bath	15 March 2007	Group 1,2,3,4	4	Pesticides
	4) After 28 days of shelf-life	12 April 2006	Group 1,2,3,4	4	Pesticides and patulin

Table 3 :

 3 Transitions for the validated pesticides and patulin.

	Transition 1	Transition 2

Table 4 .

 4 Repeatability, reproducibility, recovery and limits of detection (LOD) at three spiking levels, for pesticides residues in apple.

					LOQ,				LOQ,
	Spiking concentration, mg/kg	0.02 0.04	0.2	mg/kg	Spiking concentration, mg/kg	0.02 0.04	0.2	mg/kg
	RSD r , %		6%	8%		RSD r , %	14% 16% 12%
	RSD R , %		7%	11%		RSD R , %	14% 22% 12%
	Recovery,%		92% 88%	0.02	Recovery,% 102% 99% 107% 0.02
	RSD r , %		23% 19%		RSD r , %	20% 21% 14%
	RSD R , %		23% 19%		RSD R , %	24% 21% 14%
	Recovery,%		101% 98%	0.06	Recovery,% 101% 70% 107% 0.03
	RSD r , %	17%	7%	11%		RSD r , %	8%	21% 19%
	RSD R , %	22% 26% 11%		RSD R , %	14% 22% 19%
	Recovery,% 128% 105% 107% 0.03	Recovery,% 94% 80% 89%	0.01
	RSD r , %	7%	9%	16%		RSD r , %	21% 12% 3%
	RSD R , %	7%	17% 17%		RSD R , %	21% 20% 8%
	Recovery,% 112% 125% 107% 0.01	Recovery,% 99% 100% 107% 0.02
	RSD r , %		14%	7%		RSD r , %	17% 4% 27%
	RSD R , %		14% 31%		RSD R , %	27% 19% 27%
	Recovery,%		94% 113% 0.03	Recovery,% 109% 99% 98%	0.02
	RSD r , %	21% 21% 14%		RSD r , %		14% 17%
	RSD R , %	26% 26% 14%		RSD R , %		24% 19%
	Recovery,% 89% 103% 117% 0.03	Recovery,%		104% 121% 0.05
	RSD r , %	29% 17% 18%		RSD r , %		5%	4%
	RSD R , %	29% 20% 18%		RSD R , %		17% 25%
	Recovery,% 88% 93% 107% 0.03	Recovery,%		104% 92%	0.04
	RSD r , %		4%	17%		RSD r , %	9%	23% 8%
	RSD R , %		16% 17%		RSD R , %	31% 23% 9%
	Recovery,%		87% 106% 0.03	Recovery,% 107% 96% 108% 0.04
	RSD r , %	11%	8%	18%		RSD r , %	15% 18% 8%
	RSD R , %	14% 19% 18%		RSD R , %	19% 35% 14%
	Recovery,% 85% 91% 90%	0.01	Recovery,% 108% 106% 111% 0.02
	RSD r , %		19% 26%		RSD r , %	12% 7% 11%
	RSD R , %		22% 26%		RSD R , %	19% 23% 14%
	Recovery,%		90% 115% 0.05	Recovery,% 94% 89% 117% 0.02
	RSD r , %	26% 18% 17%		RSD r , %	18% 24% 9%
	RSD R , %	26% 21% 18%		RSD R , %	18% 24% 9%
	Recovery,% 75% 93% 107% 0.02	Recovery,% 109% 105% 112% 0.02
	RSD r , %			8%		RSD r , %	13% 6% 14%
	RSD R , %			11%		RSD R , %	15% 20% 14%
	Recovery,%			99%	0.14	Recovery,% 105% 130% 120% 0.02
	RSD r , %			20%		RSD r , %	16% 16% 16%
	RSD R , %			20%		RSD R , %	17% 25% 16%
	Recovery,%			117% 0.28	Recovery,% 93% 90% 113% 0.02
	RSD r , %	2%	17% 18%		RSD r , %	19% 24% 11%
	RSD R , %	20% 18% 18%		RSD R , %	19% 28% 11%
	Recovery,% 112% 92% 114% 0.02	Recovery,% 65% 96% 103% 0.01
	RSD r , %	19% 28% 16%		RSD r , %	28% 4% 20%
	RSD R , %	19% 28% 16%		RSD R , %	30% 54% 20%
	Recovery,% 104% 99% 110% 0.02	Recovery,% 78% 109% 113% 0.03

Table 5 .

 5 Mean recovery and standard deviation for patulin, trifloxystrobin, tolylfluanid, thiacloprid, flusilazole and pirimicarb in apples.

	LOQ

Table 6 .

 6 Patulin content in apples treated with pesticides at different times before harvest. Both the non-inoculated and the samples inoculated with P. expansum were investigated after 28 days of shelf-life

	Pesticide treatment	Patulin content	Patulin content in core	Patulin content in surface
		(mg/kg) in non	inoculated samples	inculated samples
		inoculated	(mg/kg)	(mg/kg)
		samples
	Untreated	< 0.02	15.4	4.1
		(-)	(+)	(+)
	Treated with pesticides	< 0.02.	not determined	not determined
	4 weeks before harvest	(-)
	Treated with pesticides	< 0.02.	8.7	4.3
	2 weeks before harvest	(-)	(+)	(+)
	Treated with pesticides	< 0.02.	15.2	2.7
	1 week before harvest	(-)	(+)	(+)

http://mc.manuscriptcentral.com/tfac Email: fac@tandf.co.ukFood Additives and Contaminants

Acknowledgement

We would like to thank the European Commission for financing the project (ISAFRUIT). We would also like to thank Merete B. Ludwigsen and Inge Schröder for the excellent technical skills.