Time series forecasting by principal covariate regression

This paper is concerned with time series forecasting in the presence of a large number of predictors. The results are of interest, for instance, in macroeconomic and financial forecasting where often many potential predictor variables are available. Most of the current forecast methods with many predictors consist of two steps, where the large set of predictors is first summarized by means of a limited number of factors —for instance, principal components— and, in a second step, these factors and their lags are used for forecasting. A possible disadvantage of these methods is that the construction of the components in the first step is not directly related to their use in forecasting in the second step. This motivates an alternative method, principal covariate regression (PCovR), where the two steps are combined in a single criterion. This method has been analyzed before within the framework of multivariate regression models. Motivated by the needs of macroeconomic time series forecasting, this paper discusses two adjustments of standard PCovR that are necessary to allow for lagged factors and for preferential predictors. The resulting nonlinear estimation problem is solved by means of a method based on iterative majorization. The paper discusses some numerical aspects and analyzes the method by means of simulations. Further, the empirical performance of PCovR is compared with that of the two-step principal component method by applying both methods to forecast four US macroeconomic time series from a set of 132 predictors, using the data set of Stock and Watson (2005).