High-Dimensional Vector Autoregression with Common Response and Predictor Factors
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Reinterpreting the reduced-rank vector autoregressive (VAR) model of order one as a supervised factor model, where two factor modelings are simultaneously conducted to response and predictor spaces, this article introduces a new model, called vector autoregression with common response and predictor factors, to further explore the common structure between the response and predictors of a high-dimensional time series. The new model can provide better physical interpretations and improve estimation efficiency. In conjunction with the tensor operation, the model can easily be extended to any finite-order VAR models. A regularization-based method is considered for the high-dimensional estimation with the gradient descent algorithm, and its computational and statistical convergence guarantees are established. Simulation experiments confirm our theoretical findings, and a macroeconomic application showcases the appealing properties of the proposed model in structural analysis and forecasting.
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