Forecasting with Big Data: A Review <s> -Monetary Policy <s> This article considers forecasting a single time series when there are many predictors (N) and time series observations (T). When the data follow an approximate factor model, the predictors can be summarized by a small number of indexes, which we estimate using principal components. Feasible forecasts are shown to be asymptotically efficient in the sense that the difference between the feasible forecasts and the infeasible forecasts constructed using the actual values of the factors converges in probability to 0 as both N and T grow large. The estimated factors are shown to be consistent, even in the presence of time variation in the factor model. <s> BIB001 </s> Forecasting with Big Data: A Review <s> -Monetary Policy <s> Time varying correlations are often estimated with multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two-step methods based on the likelihood function. It is shown that they perform well in a variety of situations and provide sensible empirical results. <s> BIB002 </s> Forecasting with Big Data: A Review <s> -Monetary Policy <s> Structural vector autoregressions (VARs) are widely used to trace out the effect of monetary policy innovations on the economy. However, the sparse information sets typically used in these empirical models lead to at least two potential problems with the results. First, to the extent that central banks and the private sector have information not reflected in the VAR, the measurement of policy innovations is likely to be contaminated. A second problem is that impulse responses can be observed only for the included variables, which generally constitute only a small subset of the variables that the researcher and policymaker care about. In this paper we investigate one potential solution to this limited information problem, which combines the standard structural VAR analysis with recent developments in factor analysis for large data sets. We find that the information that our factor-augmented VAR (FAVAR) methodology exploits is indeed important to properly identify the monetary transmission mechanism. Overall, our results provide a comprehensive and coherent picture of the effect of monetary policy on the economy. <s> BIB003 </s> Forecasting with Big Data: A Review <s> -Monetary Policy <s> Historically, time series forecasts of economic variables have used only a handful of predictor variables, while forecasts based on a large number of predictors have been the province of judgmental forecasts and large structural econometric models. The past decade, however, has seen considerable progress in the development of time series forecasting methods that exploit many predictors, and this chapter surveys these methods. The first group of methods considered is forecast combination (forecast pooling), in which a single forecast is produced from a panel of many forecasts. The second group of methods is based on dynamic factor models, in which the comovements among a large number of economic variables are treated as arising from a small number of unobserved sources, or factors. In a dynamic factor model, estimates of the factors (which become increasingly precise as the number of series increases) can be used to forecast individual economic variables. The third group of methods is Bayesian model averaging, in which the forecasts from very many models, which differ in their constituent variables, are averaged based on the posterior probability assigned to each model. The chapter also discusses empirical Bayes methods, in which the hyperparameters of the priors are estimated. An empirical illustration applies these different methods to the problem of forecasting the growth rate of the U.S. index of industrial production with 130 predictor variables. <s> BIB004 </s> Forecasting with Big Data: A Review <s> -Monetary Policy <s> We propose a new method for multivariate forecasting which combines Dynamic Factor and multivariate GARCH models. We call the model Dynamic Factor GARCH, as the information contained in large macroeconomic or financial datasets is captured by a few dynamic common factors, which we assume being conditionally heteroskedastic. After describing the estimation of the model, we present simulation results and carry out two empirical applications on financial asset returns and macroeconomic series, with a particular focus on different measures of inflation. Our proposed model outperforms the benchmarks in forecasting the conditional volatility of returns and the inflation level. Moreover, it allows to predict conditional covariances of all the time series in the panel. <s> BIB005 </s> Forecasting with Big Data: A Review <s> -Monetary Policy <s> As a generalization of the factor-augmented VAR (FAVAR) and of the Error Correction Model (ECM), Banerjee and Marcellino (2009) introduced the Factor-augmented Error Correction Model (FECM). The FECM combines error-correction, cointegration and dynamic factor models, and has several conceptual advantages over the standard ECM and FAVAR models. In particular, it uses a larger dataset than the ECM and incorporates the long-run information which the FAVAR is missing because of its specification in differences. In this paper, we examine the forecasting performance of the FECM by means of an analytical example, Monte Carlo simulations and several empirical applications. We show that FECM generally offers a higher forecasting precision relative to the FAVAR, and marks a useful step forward for forecasting with large datasets. <s> BIB006 </s> Forecasting with Big Data: A Review <s> -Monetary Policy <s> This paper is motivated by the recent interest in the use of Bayesian VARs for forecasting, even in cases where the number of dependent variables is large. In such cases, factor methods have been traditionally used but recent work using a particular prior suggests that Bayesian VAR methods can forecast better. In this paper, we consider a range of alternative priors which have been used with small VARs, discuss the issues which arise when they are used with medium and large VARs and examine their forecast performance using a US macroeconomic data set containing 168 variables. We ?nd that Bayesian VARs do tend to forecast better than factor methods and provide an extensive comparison of the strengths and weaknesses of various approaches. Our empirical results show the importance of using forecast metrics which use the entire predictive density, instead of using only point forecasts. <s> BIB007 </s> Forecasting with Big Data: A Review <s> -Monetary Policy <s> The primary objective of this paper is to propose two nonlinear extensions for macroeconomic forecasting using large datasets. First, we propose an alternative technique for factor estimation, i.e., kernel principal component analysis, which allows the factors to have a nonlinear relationship to the input variables. Second, we propose artificial neural networks as an alternative to the factor augmented linear forecasting equation. These two extensions allow us to determine whether, in general, there is empirical evidence in favor of nonlinear methods and, in particular, to verify whether the nonlinearity occurs in the estimation of the factors or in the functional form that links the target variable to the factors. In an effort to verify the empirical performances of the methods proposed, we conducted several pseudo forecasting exercises on the industrial production index and consumer price index for the Euro area and US economies. These methods were employed to construct the forecasts at 1-, 3-, 6-, and 12-month horizons using a large dataset containing 259 predictors for the Euro area and 131 predictors for the US economy. The results obtained from the empirical study suggest that the estimation of nonlinear factors, using kernel principal components, significantly improves the quality of forecasts compared to the linear method, while the results for artificial neural networks have the same forecasting ability as the factor augmented linear forecasting equation. <s> BIB008 </s> Forecasting with Big Data: A Review <s> -Monetary Policy <s> We propose a new approach to forecasting the term structure of interest rates, which allows to efficiently extract the information contained in a large panel of yields. In particular, we use a large Bayesian Vector Autoregression (BVAR) with an optimal amount of shrinkage towards univariate AR models. The optimal shrinkage is chosen by maximizing the Marginal Likelihood of the model. Focusing on the US, we provide an extensive study on the forecasting performance of the proposed model relative to most of the existing alternative specifications. While most of the existing evidence focuses on statistical measures of forecast accuracy, we also consider alternative measures based on trading schemes and portfolio allocation. We extensively check the robustness of our results, using different datasets and Monte Carlo simulations. We find that the proposed BVAR approach produces competitive forecasts, systematically more accurate than random walk forecasts, even though the gains are small. <s> BIB009 </s> Forecasting with Big Data: A Review <s> -Monetary Policy <s> We study the performance of Bayesian model averaging as a forecasting method for a large panel of time series and compare its performance to principal components regression (PCR). We show empirically that these forecasts are highly correlated implying similar mean-square forecast errors. Applied to forecasting Industrial production and in ation in the United States, we find that the set of variables deemed informative changes over time which suggest temporal instability due to collinearity and to the of Bayesian variable selection method to minor perturbations of the data. In terms of mean-squared forecast error, principal components based forecasts have a slight marginal advantage over BMA. However, this marginal edge of PCR in the average global out-of-sample performance hides important changes in the local forecasting power of the two approaches. An analysis of the Theil index indicates that the loss of performance of PCR is due mainly to its exuberant biases in matching the mean of the two series especially the in ation series. BMA forecasts series matches the first and second moments of the GDP and in ation series very well with practically zero biases and very low volatility. The fluctuation statistic that measures the relative local performance shows that BMA performed consistently better than PCR and the naive benchmark (random walk) over the period prior to 1985. Thereafter, the performance of both BMA and PCR was relatively modest compared to the naive benchmark. <s> BIB010
In BIB003 , a Factor-augmented Vector Autoregressive (FAVAR) model was used for Big Data forecasting and structural analysis in order to accurately identify the monetary policy transmission mechanism so that the exact impact of monetary policy on the economy could be ascertained. They find the proposed FAVAR model outperforming the Structural VAR model by exploiting far more informative content for assessing the monetary policy transmission mechanism. De  use a Bayesian regression model with macroeconomic Big Data which includes real and nominal variables, asset prices, surveys and yield curves for forecasting the industrial production and consumer price indices. They find the results from the Bayesian regression are highly correlated with forecasts from principal components. BIB005 exploits a monthly panel dataset comprising of 130 U.S. macroeconomic time series and four price indexes (PCE, PCE core, CPI and CPI core) for forecasting inflation and its volatility using a DFM in combination with multivariate GARCH models (DF-GARCH). They find the DF-GARCH model outperforming GARCH, AR(p) and AR(p) -GARCH(1,1) BIB004 along with a Bayesian Reduced Rank multivariate model for forecasting industrial production and consumer price indices and the federal funds rate. Their results are compared against models based on Rank Reduction, which include Bayesian VAR models, Multivariate Boosting and the Factor model from BIB001 . They find that combining Rank Reduction with Shrinkage can improve forecasts attained when applied to Big Data. BIB008 proposes the use of Kernel Principal Component Analysis (PCA) (as this enables factors to take a nonlinear relationship to the input variables) and an Artificial Neural Networks (ANN) model on Big Data containing 259 predictors for the Euro area, and 131 predictors for the U.S. economy for forecasting the industrial production and consumer prices indices. The author finds that using the Kernel PCA approach for predicting nonlinear factors yield results of better quality in comparison to the linear method, and that the ANN method reports a similar forecast to that obtained via the Factor Augmented Linear forecasting equation. In BIB009 a large BVAR model coupled with optimised shrinkage towards univariate AR models are used to forecast interest rates. The authors find the BVAR model showing small gains over random walk forecasts. BIB006 used a FECM and showed that FECM can outperform a FAVAR model at forecasting; U.S. inflation using a large panel of 132 U.S. macroeconomic variables, and German inflation and interest rate using 90 monthly series for the German economy. BIB010 compared Bayesian Model Averaging (BMA) and Principal Component Regression (PCR) on a large panel data set for forecasting U.S. inflation and industrial production. Based on the Root Mean Squared Error the author concludes that in general, PCR can provide more accurate forecasts than BMA. BIB007 exploits the U.S. macroeconomic data set found in  which includes 168 variables along with BVAR model for forecasting inflation and interest rates. They find that BVAR models can provide better forecasts than those attainable via Factor methods. Using the U.S. Treasury zero coupon yield curve estimates, BIB006 showed that a FECM model can outperform a FAVAR model at forecasting interest rates at different maturities. BIB005 use their DF-GARCH model for forecasting financial asset returns using Big Data relating to transaction prices of stocks traded on the London Stock Exchange after cleaning the data for outliers. They find the DF-GARCH model outperforming a GARCH (1,1) model and that the full BEKK specification  provides better forecasts in comparison to the DCC specification BIB002 .