Statistical Inference for Multivariate Linear Regression Models with Stochastic Volatility

• Activity Number: 279 - Temporal and Spatial Models in Business and Economics
• Type: Contributed
• Date/Time: Tuesday, August 9, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): WenJing Cai* and Jean-Marie Dufour
• Companies: McGill University and McGill University
• Keywords: Simple estimators; regularization; stochastic covariance; asymptotic distribution

Abstract

This paper extends the Multivariate Linear Regression (MLR) model by assuming the correlated high-order stochastic volatility p order (SV(p)) structure for the disturbance term. We propose the Regression-based Simple Moment based estimation and Regression-based ARMA-based estimation. All of them can be easily applied to a multivariate case with less computational time and simpler computational procedures. We impose two regularizations: alternating projection and Winsorization to improve the efficiency of our estimators. We derive the asymptotic properties for our estimators. The simulation study shows that the proposed estimators perform well in terms of lower bias and root mean square error(RMSE) compared with generalized method of moment (GMM) estimators and Bayesian MCMC estimators. We apply the proposed estimators to monthly securities returns of CRSP to construct the prediction intervals from 1987 to 2021 by the rolling window. We find that the prediction intervals constructed based on our estimators are most reliable and have the shortest interval width compared to the intervals constructed by Bayesian MCMC estimators or by regardless of correlated SV(p) structure.