Forecasting using supervised factor models

This paper examines the theoretical and empirical properties of a supervised factor model based on combining forecasts using principal components (CFPC), in comparison with two other supervised factor models (partial least squares regression, PLS, and principal covariate regression, PCovR) and with the unsupervised principal component regression, PCR. The supervision refers to training the predictors for a variable to forecast. We compare the performance of the three supervised factor models and the unsupervised factor model in forecasting of U.S. CPI inflation. The main finding is that the predictive ability of the supervised factor models is much better than the unsupervised factor model. The computation of the factors can be doubly supervised together with variable selection, which can further improve the forecasting performance of the supervised factor models. Among the three supervised factor models, the CFPC best performs and is also most stable. While PCovR also performs well and is stable, the performance of PLS is less stable over different out-of-sample forecasting periods. The effect of supervision gets even larger as forecast horizon increases. Supervision helps to reduce the number of factors and lags needed in modelling economic structure, achieving more parsimony.     

Sparse estimation of dynamic principal components for forecasting high-dimensional time series

We present the sparse estimation of one-sided dynamic principal components (ODPCs) to forecast high-dimensional time series. The forecast can be made directly with the ODPCs or by using them as estimates of the factors in a generalized dynamic factor model. It is shown that a large reduction in the number of parameters estimated for the ODPCs can be achieved without affecting their forecasting performance.     

Forecast combination through dimension reduction techniques

This paper considers several methods of producing a single forecast from several individual ones. We compare “standard” but hard to beat combination schemes (such as the average of forecasts at each period, or consensus forecast and OLS-based combination schemes) with more sophisticated alternatives that involve dimension reduction techniques. Specifically, we consider principal components, dynamic factor models, partial least squares and sliced inverse regression.Our source of forecasts is the Survey of Professional Forecasters, which provides forecasts for the main US macroeconomic aggregates. The forecasting results show that partial least squares, principal component regression and factor analysis have similar performances (better than the usual benchmark models), but sliced inverse regression shows an extreme behavior (performs either very well or very poorly).     

Factor MIDAS for Nowcasting and Forecasting with Ragged‐Edge Data: A Model Comparison for German GDP*

In this article, we merge two strands from the recent econometric literature. First, factor models based on large sets of macroeconomic variables for forecasting, which have generally proven useful for forecasting. However, there is some disagreement in the literature as to the appropriate method. Second, forecast methods based on mixed‐frequency data sampling (MIDAS). This regression technique can take into account unbalanced datasets that emerge from publication lags of high‐ and low‐frequency indicators, a problem practitioner have to cope with in real time. In this article, we introduce Factor MIDAS, an approach for nowcasting and forecasting low‐frequency variables like gross domestic product (GDP) exploiting information in a large set of higher‐frequency indicators. We consider three alternative MIDAS approaches (basic, smoothed and unrestricted) that provide harmonized projection methods that allow for a comparison of the alternative factor estimation methods with respect to nowcasting and forecasting. Common to all the factor estimation methods employed here is that they can handle unbalanced datasets, as typically faced in real‐time forecast applications owing to publication lags. In particular, we focus on variants of static and dynamic principal components as well as Kalman filter estimates in state‐space factor models. As an empirical illustration of the technique, we use a large monthly dataset of the German economy to nowcast and forecast quarterly GDP growth. We find that the factor estimation methods do not differ substantially, whereas the most parsimonious MIDAS projection performs best overall. Finally, quarterly models are in general outperformed by the Factor MIDAS models, which confirms the usefulness of the mixed‐frequency techniques that can exploit timely information from business cycle indicators.     

Sparse structures with LASSO through principal components: Forecasting GDP components in the short-run

This paper examines the use of sparse methods to forecast the real (in the chain-linked volume sense) expenditure components of the US and EU GDP in the short-run sooner than national statistics institutions officially release the data. We estimate current-quarter nowcasts, along with one- and two-quarter forecasts, by bridging quarterly data with available monthly information announced with a much smaller delay. We solve the high-dimensionality problem of monthly datasets by assuming sparse structures of leading indicators capable of adequately explaining the dynamics of the analyzed data. For variable selection and estimation of the forecasts, we use LASSO together with its recent modifications. We propose an adjustment that combines LASSO cases with principal components analysis to improve the forecasting performance. We evaluated the forecasting performance by conducting pseudo-real-time experiments for gross fixed capital formation, private consumption, imports, and exports over a sample from 2005–2019, compared with benchmark ARMA and factor models. The main results suggest that sparse methods can outperform the benchmarks and identify reasonable subsets of explanatory variables. The proposed combination of LASSO and principal components further improves the forecast accuracy.     

Leading Indicators for Euro‐area Inflation and GDP Growth*

In this paper, we evaluate the role of a set of variables as leading indicators for Euro‐area inflation and GDP growth. Our leading indicators are taken from the variables in the European Central Bank's (ECB) Euro‐area‐wide model database, plus a set of similar variables for the US. We compare the forecasting performance of each indicator ex post with that of purely autoregressive models. We also analyse three different approaches to combining the information from several indicators. First, ex post, we discuss the use as indicators of the estimated factors from a dynamic factor model for all the indicators. Secondly, within an ex ante framework, an automated model selection procedure is applied to models with a large set of indicators. No future information is used, future values of the regressors are forecast, and the choice of the indicators is based on their past forecasting records. Finally, we consider the forecasting performance of groups of indicators and factors and methods of pooling the ex ante single‐indicator or factor‐based forecasts. Some sensitivity analyses are also undertaken for different forecasting horizons and weighting schemes of forecasts to assess the robustness of the results.     

A new approach to estimating earnings forecasting models: Robust regression MM-estimation

This study focuses on the impact of model estimation methods on earnings forecast accuracy. Compared with an ordinary least squares (OLS) regression combined with winsorization, robust regression MM-estimation improves the earnings forecast accuracy of all the models examined, especially for those with more variables. My findings indicate that the impact of outliers on the OLS regression increases with the number of variables in the models, alerting researchers who use OLS regressions for forecasting. My findings explain the puzzling negative relationship between earnings forecast accuracy and the number of model variables in prior research. Moreover, I demonstrate the valuation implications of earnings forecasted using robust regression MM-estimation. This study contributes to earnings forecasting, valuation, and influential observation treatment in forecasting.     

Forecasting macroeconomic time series: LASSO-based approaches and their forecast combinations with dynamic factor models

In a data-rich environment, forecasting economic variables amounts to extracting and organizing useful information from a large number of predictors. So far, the dynamic factor model and its variants have been the most successful models for such exercises. In this paper, we investigate a category of LASSO-based approaches and evaluate their predictive abilities for forecasting twenty important macroeconomic variables. These alternative models can handle hundreds of data series simultaneously, and extract useful information for forecasting. We also show, both analytically and empirically, that combing forecasts from LASSO-based models with those from dynamic factor models can reduce the mean square forecast error (MSFE) further. Our three main findings can be summarized as follows. First, for most of the variables under investigation, all of the LASSO-based models outperform dynamic factor models in the out-of-sample forecast evaluations. Second, by extracting information and formulating predictors at economically meaningful block levels, the new methods greatly enhance the interpretability of the models. Third, once forecasts from a LASSO-based approach are combined with those from a dynamic factor model by forecast combination techniques, the combined forecasts are significantly better than either dynamic factor model forecasts or the naïve random walk benchmark.     

Forecasting national activity using lots of international predictors: An application to New Zealand

We assess the marginal predictive content of a large international dataset for forecasting GDP in New Zealand, an archetypal small open economy. We apply “data-rich” factor and shrinkage methods to efficiently handle hundreds of predictor series from many countries. The methods covered are principal components, targeted predictors, weighted principal components, partial least squares, elastic net and ridge regression. We find that exploiting a large international dataset can improve forecasts relative to data-rich approaches based on a large national dataset only, and also relative to more traditional approaches based on small datasets. This is in spite of New Zealand’s business and consumer confidence and expectations data capturing a substantial proportion of the predictive information in the international data. The largest forecasting accuracy gains from including international predictors are at longer forecast horizons. The forecasting performance achievable with the data-rich methods differs widely, with shrinkage methods and partial least squares performing best in handling the international data.     

POOLING VERSUS MODEL SELECTION FOR NOWCASTING GDP WITH MANY PREDICTORS: EMPIRICAL EVIDENCE FOR SIX INDUSTRIALIZED COUNTRIES

This paper discusses pooling versus model selection for nowcasting with large datasets in the presence of model uncertainty. In practice, nowcasting a low‐frequency variable with a large number of high‐frequency indicators should account for at least two data irregularities: (i) unbalanced data with missing observations at the end of the sample due to publication delays; and (ii) different sampling frequencies of the data. Two model classes suited in this context are factor models based on large datasets and mixed‐data sampling (MIDAS) regressions with few predictors. The specification of these models requires several choices related to, amongst other things, the factor estimation method and the number of factors, lag length and indicator selection. Thus there are many sources of misspecification when selecting a particular model, and an alternative would be pooling over a large set of different model specifications. We evaluate the relative performance of pooling and model selection for nowcasting quarterly GDP for six large industrialized countries. We find that the nowcast performance of single models varies considerably over time, in line with the forecasting literature. Model selection based on sequential application of information criteria can outperform benchmarks. However, the results highly depend on the selection method chosen. In contrast, pooling of nowcast models provides an overall very stable nowcast performance over time. Copyright © 2012 John Wiley & Sons, Ltd.     

Macroeconomic forecasting using structural factor analysis

The use of a small number of underlying factors to summarize the information from a much larger set of information variables is one of the new frontiers in forecasting. In prior work, the estimated factors have not usually had a structural interpretation and the factors have not been chosen on a theoretical basis. In this paper we propose several variants of a general structural factor forecasting model, and use these to forecast certain key macroeconomic variables. We make the choice of factors more structurally meaningful by estimating factors from subsets of information variables, where these variables can be assigned to subsets on the basis of economic theory. We compare the forecasting performance of the structural factor forecasting model with that of a univariate AR model, a standard VAR model, and some non-structural factor forecasting models. The results suggest that our structural factor forecasting model performs significantly better in forecasting real activity variables, especially at short horizons.     

Forecasting with approximate dynamic factor models: The role of non-pervasive shocks

This paper studies the role of non-pervasive shocks when forecasting with factor models. To this end, we first introduce a new model that incorporates the effects of non-pervasive shocks, an Approximate Dynamic Factor Model with a sparse model for the idiosyncratic component. Then, we test the forecasting performance of this model both in simulations, and on a large panel of US quarterly data. We find that, when the goal is to forecast a disaggregated variable, which is usually affected by regional or sectorial shocks, it is useful to capture the dynamics generated by non-pervasive shocks; however, when the goal is to forecast an aggregate variable, which responds primarily to macroeconomic, i.e. pervasive, shocks, accounting for non-pervasive shocks is not useful.     

Real-time forecasting of German GDP based on a large factor model with monthly and quarterly data

This paper discusses a factor model for short-term forecasting of GDP growth 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 some in-sample properties of the estimator in a real-time environment and propose alternative methods for forecasting quarterly GDP with monthly factors. In the empirical application, we use a novel real-time dataset for the German economy. Employing a recursive forecast experiment, we evaluate the forecast accuracy of the factor model with respect to German GDP. Furthermore, we investigate the role of revisions in forecast accuracy and assess the contribution of timely monthly observations to the forecast performance. Finally, we compare the performance of the mixed-frequency model with that of a factor model, based on time-aggregated quarterly data.     

Statistical inference on seemingly unrelated varying coefficient partially linear models

This paper is concerned with the statistical inference on seemingly unrelated varying coefficient partially linear models. By combining the local polynomial and profile least squares techniques, and estimating the contemporaneous correlation, we propose a class of weighted profile least squares estimators (WPLSEs) for the parametric components. It is shown that the WPLSEs achieve the semiparametric efficiency bound and are asymptotically normal. For the non‐parametric components, by applying the undersmoothing technique, and taking the contemporaneous correlation into account, we propose an efficient local polynomial estimation. The resulting estimators are shown to have mean‐squared errors smaller than those estimators that neglect the contemporaneous correlation. In addition, a class of variable selection procedures is developed for simultaneously selecting significant variables and estimating unknown parameters, based on the non‐concave penalized and weighted profile least squares techniques. With a proper choice of regularization parameters and penalty functions, the proposed variable selection procedures perform as efficiently as if one knew the true submodels. The proposed methods are evaluated using wide simulation studies and applied to a set of real data.     

Forecasting large datasets with Bayesian reduced rank multivariate models

The paper addresses the issue of forecasting a large set of variables using multivariate models. In particular, we propose three alternative reduced rank forecasting models and compare their predictive performance for US time series with the most promising existing alternatives, namely, factor models, large‐scale Bayesian VARs, and multivariate boosting. Specifically, we focus on classical reduced rank regression, a two‐step procedure that applies, in turn, shrinkage and reduced rank restrictions, and the reduced rank Bayesian VAR of Geweke ( 1996 ). We find that using shrinkage and rank reduction in combination rather than separately improves substantially the accuracy of forecasts, both when the whole set of variables is to be forecast and for key variables such as industrial production growth, inflation, and the federal funds rate. The robustness of this finding is confirmed by a Monte Carlo experiment based on bootstrapped data. We also provide a consistency result for the reduced rank regression valid when the dimension of the system tends to infinity, which opens the way to using large‐scale reduced rank models for empirical analysis. Copyright © 2010 John Wiley & Sons, Ltd.     

基于偏最小二乘的泰国菠萝出口影响因素实证研究

本文采用偏最小二乘回归模型(PLS),以泰国菠萝贸易为例,通过变量投影重要性准则筛选自变量,由交叉有效性提取主成分,进而建立偏最小二乘回归模型。深入分析了各指标对泰国菠萝出口贸易的影响。研究表明泰国菠萝出口与原料价格及工厂生产加工速度密切相关,并且偏最小二乘回归的拟合效果优于普通最小二乘回归。     

The cross section of Chinese commodity futures return

This paper investigates the cross-section of expected commodity futures returns in China using a large panel of 13 individual factors. We find that 6 out of 13 individual factors produce positive and significant returns. To aggregate the information among these factors, we apply not only the traditional Fama-MacBeth regression (FM), but also a set of alternative methods, including the forecast combination method (FC), principal component analysis (PCA), principle component regression (PCR) and partial least squares (PLS). It turns out that PLS outperform other methods in forecasting the cross-section of Chinese expected futures returns. The equally weighted combination of 5 methods produces an even higher annualized return and lower standard deviation compared to each single method. The investigation of factor importance reveals that the skewness (SKEW) factor is more important than other factors in predicting expected futures returns in Chinese markets.     

A UNIFYING VIEW ON MULTI‐STEP FORECASTING USING AN AUTOREGRESSION

Abstract This paper unifies two methodologies for multi‐step forecasting from autoregressive time series models. The first is covered in most of the traditional time series literature and it uses short‐horizon forecasts to compute longer‐horizon forecasts, while the estimation method minimizes one‐step‐ahead forecast errors. The second methodology considers direct multi‐step estimation and forecasting. In this paper, we show that both approaches are special (boundary) cases of a technique called partial least squares (PLS) when this technique is applied to an autoregression. We outline this methodology and show how it unifies the other two. We also illustrate the practical relevance of the resultant PLS autoregression for 17 quarterly, seasonally adjusted, industrial production series. Our main findings are that both boundary models can be improved by including factors indicated from the PLS technique.     

Financial nowcasts and their usefulness in macroeconomic forecasting

Financial data often contain information that is helpful for macroeconomic forecasting, while multi-step forecast accuracy benefits from incorporating good nowcasts of macroeconomic variables. This paper considers the usefulness of financial nowcasts for making conditional forecasts of macroeconomic variables with quarterly Bayesian vector autoregressions (BVARs). When nowcasting quarterly financial variables’ values, we find that taking the average of the available daily data and a daily random walk forecast to complete the quarter typically outperforms other nowcasting approaches. Using real-time data, we find gains in out-of-sample forecast accuracy from the inclusion of financial nowcasts relative to unconditional forecasts, with further gains from the incorporation of nowcasts of macroeconomic variables. Conditional forecasts from quarterly BVARs augmented with financial nowcasts rival the forecast accuracy of mixed-frequency dynamic factor models and mixed-data sampling (MIDAS) models.     

Macroeconomic forecast accuracy in a data‐rich environment

The performance of six classes of models in forecasting different types of economic series is evaluated in an extensive pseudo out‐of‐sample exercise. One of these forecasting models, regularized data‐rich model averaging (RDRMA), is new in the literature. The findings can be summarized in four points. First, RDRMA is difficult to beat in general and generates the best forecasts for real variables. This performance is attributed to the combination of regularization and model averaging, and it confirms that a smart handling of large data sets can lead to substantial improvements over univariate approaches. Second, the ARMA(1,1) model emerges as the best to forecast inflation changes in the short run, while RDRMA dominates at longer horizons. Third, the returns on the S&P 500 index are predictable by RDRMA at short horizons. Finally, the forecast accuracy and the optimal structure of the forecasting equations are quite unstable over time.