Forecasting High Dimensional Time Series with Dynamic Dimension Reduction

Many dimension reduction techniques have been developed for independent data, and most have also been extended to time series. However, these methods often fail to account for the dynamic dependencies both within and across series. In this work, we propose a general framework for forecasting high-dimensional time series that integrates dynamic dimension reduction with regularization techniques. The effectiveness of the proposed approach is illustrated through a simulated example and a forecasting application using an economic dataset. We show that several specific methods are encompassed within this framework, including Dynamic Principal Components and Reduced Rank Autoregressive Models. Furthermore, time-domain formulations of Dynamic Canonical Correlation and Dynamic Redundancy Analysis are introduced here for the first time as particular instances of the proposed methodology. All of these techniques are analyzed as special cases of a unified procedure, enabling a coherent derivation and interpretation across methods.