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Title: Statistical inference for multivariate linear regression models with stochastic volatility Authors:  WenJing Cai - McGill University (Canada) [presenting]
Jean-Marie Dufour - McGill University (Canada)
Abstract: The Multivariate Linear Regression (MLR) model is extended by assuming the correlated high-order stochastic volatility (SV(P)) structure for the disturbance term. The complication of estimation comes from the high dimension variance-covariance matrix of the disturbance term and the estimation of deep parameters in the SV(p) models. There are no existing references to estimate such a model, and the related estimation is sampling algorithms, which are computationally expensive and initial values dependent. We propose the Regression-based Simple Moment based estimation and ARMA-based estimation. All of them are computationally inexpensive and initial values independent. The analysis provides the asymptotic properties of our estimators and imposes two regularizations to improve efficiency. The simulation study shows that the proposed estimators perform well in terms of lower bias and root mean square error (RMSE) compared with the generalized method of moment (GMM) estimators and Bayesian MCMC estimators. We apply the proposed estimators to construct the prediction intervals from 1988 to 2021 for monthly returns of CRSP. We find that the prediction intervals constructed by the proposed estimators are reliable and have shorter interval widths compared to those constructed by Bayesian MCMC estimators or by regardless of correlated SV(p) structure in the error term.