In this paper we consider estimating an approximate factor model in which candidate predictors are subject to sharp spikes such as outliers or jumps. Given that these sharp spikes are assumed to be rare, we formulate the estimation problem as a penalized least squares problem by imposing a norm penalty function on those sharp spikes. Such a formulation allows us to disentangle the sharp spikes from the common factors and estimate them simultaneously. Numerical values of the estimates can be obtained by solving a principal component analysis (PCA) problem and a one-dimensional shrinkage estimation problem iteratively. In addition, it is easy to incorporate methods for selecting the number of common factors in the iterations. We compare our method with PCA by conducting simulation experiments in order to examine their finite-sample performances. We also apply our method to the prediction of important macroeconomic indicators in the U.S., and find that it can deliver performances that are comparable to those of the PCA method.
International Journal of Forecasting, Vol.36, No.2, pp.267-291