Vector Autoregressive Models with Structural Changes in Regression Coefficients and in Variance-Covariance Matrices

This paper analyzes vector autoregressive models (VAR) with multiple structural changes. One distinct feature of this paper is the explicit consideration of structural changes in the variance-covariance matrix, in addition to changes in the autoregressive coefficients. The model is estimated by the quasi-maximum likelihood method. It is shown that shifts in the covariance matrix help identify the change points. We obtain consistency, rate of convergence, and limiting distributions for the estimated change points and the estimated regression coefficients and variance-covariance matrix. We also show that the number of change points can be consistently estimated via the information criterion approach. The paper provides tools for constructing confidence intervals for change points in multiple time series. The result is also useful for analyzing volatility changes in economic time series.