High Dimensional Factor Models: An Empirical Bayes Approach

We propose an empirical Bayesian implementation of principal components analysis for estimating high dimensional factor models. The method is evaluated in a large Monte Carlo study where we compare the traditional principal components estimator to the our proposed empirical Bayes version. We find that for increasingly weak factor specifications the mean squared error gain that is obtained from the empirical Bayes implementation increases. We further compare the standard and empirical Bayes principal components estimators to their maximum likelihood counterparts and document that in all cases the maximum likelihood estimates remain more accurate. The methodology is illustrated for two empirical applications. One for nowcasting macroeconomic time series and one for portfolio management. We find that the empirical Bayesian principal components estimates outperform the standard principal components estimates when compared the mean squared error for the inner product of the macroeconomic forecast estimates. Second, in the portfolio optimization problem the covariance matrix of the stock returns estimated by empirical Bayes methods achieve, in most cases, the highest Information Ratio and the highest expected return for the portfolio manager.