Time varying factor models with possibly strongly correlated noises

Abstract

In factor models, noises are often assumed to be weakly correlated; otherwise, separation of factors from noises becomes difficult, if not impossible. This paper will address this problem. We utilize an econometric idea, the so called common correlated effects (CCE) to estimate time varying factor models. We first cross sectionally average the covariates and then project the responses to the space spanned by the averaged covariates. By doing so, noises are diminished while factors are distinguished. The advantages of our new estimators are two folds. First, the convergence rates of estimated factors and loadings are independent of cross sectional dimension. Second, our new estimators are robust to the correlation of noises. Hence our new estimators can, on one hand, separate market factors for the stock data set used in this paper even if noises exhibit strong correlations within industries due to industry-specific factors and on the other hand, avoid inappropriately absorbing industry-specific factors into market factors.