2007 ForecastComparisonofPrincipalCo

(Heij et al., 2007) ⇒ Christiaan Heij, Patrick J. F. Groenen, and Dick van Dijk. (2007). “Forecast Comparison of Principal Component Regression and Principal Covariate Regression.” In: Computational Statistics & Data Analysis Journal, 51(7). doi:10.1016/j.csda.2006.10.019

Subject Headings: Conditional Forecasting Algorithm, Multi-Predictor Forecasting.

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Author Keywords

Factor model; Macroeconomic forecasting; Principal components; Principal covariates; Regression model

Abstract

Forecasting with many predictors is of interest, for instance, in macroeconomics and finance. The forecast accuracy of two methods for dealing with many predictors is compared, that is, principal component regression (PCR) and principal covariate regression (PCovR). Simulation experiments with data generated by factor models and regression models indicate that, in general, PCR performs better for the first type of data and PCovR performs better for the second type of data. An empirical application to four key US macroeconomic variables shows that PCovR achieves improved forecast accuracy in some situations.

1. Introduction

In many forecasting applications in macroeconomics and finance, a large number of predictor variables are available that may all help to forecast the variable of interest. In such situations, one should somehow compress the predictor information. For instance, if T observations are available for a set of k predictors, then for k > T it is simply impossible to estimate a multiple regression model that includes all predictors as separate regressors. If k · T but k is large, then it is still not advisable to estimate a regression model with all predictors as regressors because the resulting forecasts will have large variance. The forecasts may improve if the information in the predictors issomehow compressed and a forecast equation containing fewer predictors is used.

Several methods for forecasting with many predictors have been proposed in the literature. We refer to Stock and Watson (2004) for a survey. For example, in ‘Principal Component Regression’ (PCR) the predictor information is first summarized by a (small) number of principal components, which are then used as prediction factors in a low-dimensional multiple regression model. This approach is followed, for instance, by Stock and Watson (1999, 2002a,b) within the context of dynamic factor models to forecast key macroeconomic variables like production and inflation from large sets of economic and financial predictor variables. An essential aspect of PCR and similar methods is that they consist of two stages, as first the factors are constructed and then the forecast equation is estimated. The resulting factors need not necessarily be the ones that forecast best, as the construction of the factors in the first stage is not directly related to their use in forecasting in the second stage.

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	Author	volume	Date Value	title	type	journal	titleUrl	doi	note	year
2007 ForecastComparisonofPrincipalCo	Christiaan Heij Patrick J. F. Groenen Dick van Dijk			Forecast Comparison of Principal Component Regression and Principal Covariate Regression				10.1016/j.csda.2006.10.019