Macroeconomic Forecasting Using Approximate Factor Models with Outliers

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 those 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 simultaneously disentangle and estimate the sharp spikes from the common components. Numerical values of the estimates can be obtained by iteratively solving a principal component analysis (PCA) problem and a one dimensional shrinkage estimation problem. In addition, it is easy to incorporate methods for selecting the number of common components in the iterations. We then compare our method and PCA method by conducting simulation experiments to examine their finite-sample performances. We also apply our method to predict important macroeconomic indicators in the U.S. and find that it can deliver comparable performances as PCA method