A note on rank reduction in sparse multivariate regression.

Area of Science:

• Statistics
• Econometrics
• Time Series Analysis

Background:

• Reduced-rank regression with sparse singular value decomposition (RSSVD) facilitates variable selection in reduced-rank models.
• Existing methods efficiently model multivariate responses by creating latent variables from sparse linear combinations of predictors.

Purpose of the Study:

• To generalize the RSSVD approach for rank reduction.
• To apply the generalized method to reduced-rank vector autoregressive (VAR) modeling for automatic rank and order selection.
• To identify the model rank and sparse dependence structure in stationary time-series data.

Main Methods:

• Generalization of the reduced-rank regression with sparse singular value decomposition (RSSVD) approach.
• Application to reduced-rank vector autoregressive (VAR) modeling.
• Asymptotic analysis for stationary time-series data.

Main Results:

• The generalized approach correctly identifies model rank and sparse dependence structure asymptotically.
• Demonstrated efficacy through simulations.
• Successful analysis of a macro-economical multivariate time series.

Conclusions:

• The proposed generalized RSSVD method effectively performs rank reduction and variable selection in VAR models.
• The method enables automatic rank determination and order selection for time-series data.
• Provides a robust framework for analyzing complex multivariate time-series data.