Modeling and forecasting realized portfolio weights

We propose direct multiple time series models for predicting high dimensional vectors of observable realized global minimum variance portfolio (GMVP) weights computed based on high-frequency intraday returns. We apply Lasso regression techniques, develop a class of multiple AR(FI)MA models for realized GMVP weights, suggest suitable model restrictions, propose M-type estimators and derive the statistical properties of these estimators. In the empirical analysis for portfolios of 225 stocks from the S&P 500 we find that our direct models effectively minimize either statistical or economic forecasting losses both in- and out-of-sample as compared to relevant alternative approaches.