Vector-valued multiple regression model with time varying coefficients and its application to predict excess stock returns

We consider a simple application of a Kalman filter to the OLS (cross-sectional regression) framework that produces almost the same result as the OLS estimates without smoothing. That is, simply introducing smoothness priors is not effective for obtaining smooth factor payoffs enough to be used in prediction. After showing that this comes from inadequate modeling of the covariance matrix R_t, we introduce a GLS type specification. Secondly, even if an appropriate GLS type formulation for R_t is given, application of the Kalman filter sometimes encounters a huge computational burden, because, as is often the case, the number of stocks in a model (N, the dimension of observation vector) is much larger than that of explaining factors (K, the dimension of coefficient vector)