Modeling and forecasting realized portfolio weights

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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.