Shrinkage and noniterative estimation for moving average models with structural breaks

This article considers the break detection and parameter estimation problem in moving average models with structural breaks. The moving average process is first approximated by an autoregressive process, then the breakpoint detection problem is reformulated as a high-dimensional variable selection one, which could be solved by a group Lasso- based shrinkage estimation procedure. Finally, the moving average parameters are estimated within each segment separated by the estimated break points through a simple noniterative method. 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 a set of simulated examples. Our empirical analysis shows that for stock returns and retail inventory data, our proposed procedure successfully detects structural breaks and delivers more accurate forecasts compared to autoregressive models.