Forecasting with Big Data: A Review <s> Forecasting with Big Data in Economics <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> Forecasting with Big Data in Economics <s> The estimation of dynamic factor models for large sets of variables has attracted considerable attention recently, due to the increased availability of large datasets. In this paper we propose a new parametric methodology for estimating factors from large datasets based on state space models and discuss its theoretical properties. In particular, we show that it is possible to estimate consistently the factor space. We also develop a consistent information criterion for the determination of the number of factors to be included in the model. Finally, we conduct a set of simulation experiments that show that our approach compares well with existing alternatives. <s> BIB002 </s> Forecasting with Big Data: A Review <s> Forecasting with Big Data in Economics <s> This Paper proposes a new forecasting method that exploits information from a large panel of time series. The method is based on the generalized dynamic factor model proposed in Forni, Hallin, Lippi, and Reichlin (2000), and takes advantage of the information on the dynamic covariance structure of the whole panel. We first use our previous method to obtain an estimation for the covariance matrices of common and idiosyncratic components. The generalized eigenvectors of this couple of matrices are then used to derive a consistent estimate of the optimal forecast, which is constructed as a linear combination of present and past observations only (one-sided filter). This two-step approach solves the end-of-sample problems caused by two-sided filtering (as in our previous work), while retaining the advantages of an estimator based on dynamic information. Both simulation results and an empirical illustration on the forecast of the Euro area industrial production and inflation, based on a panel of 447 monthly time series show very encouraging results. (This abstract was borrowed from another version of this item.) <s> BIB003 </s> Forecasting with Big Data: A Review <s> Forecasting with Big Data in Economics <s> This paper discusses the forecasting performance of alternative factor models based on a large panel of quarterly time series for the german economy. One model extracts factors by static principals components analysis, the other is based on dynamic principal components obtained using frequency domain methods. The third model is based on subspace algorithm for state space models. Out-of-sample forecasts show that the prediction errors of the factor models are generally smaller than the errors of simple autoregressive benchmark models. Among the factors models, either the dynamic principal component model or the subspace factor model rank highest in terms of forecast accuracy in most cases. However, neither of the dynamic factor models can provide better forecasts than the static model over all forecast horizons and different specifications of the simulation design. Therefore, the application of the dynamic factor models seems to provide only small forecasting improvements over the static factor model for forecasting German GDP. <s> BIB004 </s> Forecasting with Big Data: A Review <s> Forecasting with Big Data in Economics <s> This paper presents ideas and methods underlying the construction of an indicator that tracks the euro area GDP growth, but, unlike GDP growth, (i) is updated monthly and almost in real time; (ii) is free from hort-run dynamics. Removal of short-run dynamics from a time series, to isolate the mediumlong-run component, can be obtained by a band-pass filter. However, it is well known that band-pass filters, being two-sided, perform very poorly at the end of the sample. New Eurocoin is an estimator of the medium- long-run component of the GDP that only uses contemporaneous values of a large panel of macroeconomic time series, so that no end-of-sample deterioration occurs. Moreover, as our dataset is monthly, New Eurocoin can be updated each month and with a very short delay. Our method is based on generalized principal components that are designed to use leading variables in the dataset as proxies for future values of the GDP growth. As the medium- long-run component of the GDP is observable, although with delay, the performance of New Eurocoin at the end of the sample can be measured. <s> BIB005 </s> Forecasting with Big Data: A Review <s> Forecasting with Big Data in Economics <s> This paper discusses a factor model for estimating monthly GDP using a large number of monthly and quarterly time series in real-time. To take into account the different periodicities of the data and missing observations at the end of the sample, the factors are estimated by applying an EM algorithm combined with a principal components estimator. We discuss the in-sample properties of the estimator in real-time environments and methods for out-of-sample forecasting. As an empirical application, we estimate monthly German GDP in real-time, discuss the nowcast and forecast accuracy of the model and the role of revisions. Furthermore, we assess the contribution of timely monthly data to the forecast performance. <s> BIB006 </s> Forecasting with Big Data: A Review <s> Forecasting with Big Data in Economics <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> BIB007 </s> Forecasting with Big Data: A Review <s> Forecasting with Big Data in Economics <s> Is maximum likelihood suitable for factor models in large cross-sections of time series? We answer this question from both an asymptotic and an empirical perspective. We show that estimates of the common factors based on maximum likelihood are consistent for the size of the cross-section (n) and the sample size (T) going to infinity along any path of n and T and that therefore maximum likelihood is viable for n large. The estimator is robust to misspecification of the cross-sectional and time series correlation of the the idiosyncratic components. In practice, the estimator can be easily implemented using the Kalman smoother and the EM algorithm as in traditional factor analysis. <s> BIB008 </s> Forecasting with Big Data: A Review <s> Forecasting with Big Data in Economics <s> We assess the contribution of national (country-wide) and international data to the task of forecasting the real GDP of Canadian provinces. Using the targeting predictors approach of Bai and Ng (2008) [Bai, J., Ng, S., 2008. Forecasting economic time series using targeted predictors. Journal of Econometrics 146, 304–317], we find that larger datasets containing regional, national and international data help improve forecasting accuracy for horizons below the one-year-ahead mark, but that beyond that horizon, relying on provincial data alone produces the best forecasts. These results suggest that shocks originating at the national and international levels are transmitted to Canadian regions and reflected in regional timeseries fairly rapidly. <s> BIB009
Researchers in the field of Economics have been major exploiters of Big Data for forecasting various economic variables.  used a Dynamic Factor Model (DFM) based on the methodology presented in BIB001 to forecast a large dataset involving Spanish diffusion indexes which they describe as an exhaustive description of the Spanish economy. DFM models are an extension of BIB001 factor models and are frequently used for forecasting with Big Data. However,  asserted that the use of DFM for macroeconomic Big Data forecasting is flawed as it is based on linear models, and also as Big Data is more likely to be nonlinear. Over time through the work of Stock and Watson (2003) , BIB003 and BIB002 , the DFM technique was improved, thus enabling it to handle Big Data more appropriately. The application of Maximum Likelihood estimates of Factor Models for Big Data forecasting has been evaluated by BIB008 via a simulation study where the authors find this approach to be effective and efficient. A seasonal AR model was used to show how Big Data from the Google search engine can be used to predict economic indicators in  .  used a multivariate factor-augmented Bayesian shrinkage model on Big Data comprising of 143 monthly time series to forecast employment in eight sectors of the U.S. economy. Big Data relating to various exchange rates are used to forecast the Euro, British Pound and Japanese Yen in BIB007 where the authors find their proposed Factor-augmented Error Correction Model (FECM) outperforming a Factor-augmented VAR (FAVAR) model at accurately predicting the three major bilateral exchange rates. Ba bura et al. (2014) proposed an algorithm based on Kalman filtering for large VAR and DFM models to enable obtaining conditional forecasts, and providing a scenario analysis for the European economy using 26 macroeconomic and financial indicators for the Euro area. In what follows, we further group the applications of Data Mining and statistical techniques for forecasting with Big Data in the field of Economics into topics based on the use of Big Data to forecast economic variables. -Gross Domestic Product (GDP) BIB004 evaluated the forecasting performance of Factor models using Static and Dynamic Principal Components and Subspace algorithms for State Space models. He finds Factor models outperforming AR models at forecasting a large panel of quarterly time series relating to German GDP. Moreover, the Subspace Factor Model and Dynamic Principal Component model is seen outperforming the Static Factor Model, but this ranking depends greatly on the correct specification of the model parameters BIB004 . A large factor model which uses an Expectation Maximization (EM) algorithm combined with Principal Components is adopted in BIB006 to forecast a large dataset comprising of German real-time GDP. They find the Mixed Frequency Factor model performing better than simple benchmark models but find meagre differences in forecast accuracy between the Factor models themselves.  apply the ensemble machine learning technique of Random Forests to forecast European Union GDP using large survey datasets. They find Random Forests outperforming the AR model and forecasts from the 'Euro zone economic outlook'.  also note that Random Forests are popular for its ability of not over-fitting when handling a large number of inputs. BIB005 use monthly accumulated Big Data along with a modified DFM to forecast medium-to long run GDP growth in the Euro area and finds their model is able to perform better than Bandpass Filter in terms of fitting and change point detection.  adopted a Bayesian Mixed Frequency model in combination with stochastic volatility for nowcasting with Big Data to obtain real time GDP predictions for the United States. BIB007 used 90 monthly time series for the German economy and showed that a FECM can outperform a FAVAR model at forecasting real GDP in Germany. BIB009 used factor models with national and international Big Data for improving the accuracy of GDP forecasts for Canadian provinces below the one year ahead mark. Beyond the one year ahead horizon they find that relying on the provincial data alone optimizes the forecasts. Ba bura and Modugno (2014) use factor models with maximum likelihood estimation on over 101 series for nowcasting GDP in the Euro area. They find that sectoral information is not mandatory for obtaining accurate GDP predictions in the Euro area.