High-dimensional banded vector autoregressions subject to structural breaks

This article considers the break point detection and parameter estimation problem in the high-dimensional structural break vector autoregressive models that have banded autoregressive coefficient matrices. The banded structure portrays a type of sparsity in the high-dimensional time series modeling and indicates explicit dependence on neighboring component series, which is often convenient and, more importantly, practically meaningful for empirical analysis. The bandwidth parameter is first assumed to be known, under which scenario the breakpoint detection problem is reformulated as a high-dimensional variable selection one solved by a group Lasso-based procedure. Then a Bayesian information criterion is proposed to determine the bandwidth, and finally, the autoregressive matrices are estimated within each segment separated by the estimated break points. Theoretical properties of the proposed estimators are established, with data-driven choices of tuning parameters in the procedure. The finite sample performance of the procedure is nicely illustrated through several simulated and real data examples. Our empirical analysis shows that the proposed procedure successfully detects structural breaks in the constituent stock return series and delivers more accurate forecasts than existing methods.