A Note on Adaptive Group Lasso for Structural Break Time Series

Abstract Considering structural break autoregressive (SBAR) processes and following recent literature, the problem of estimating the unknown number of change-points is cast as a model selection problem. The adaptive group Lasso is used to select the number of change-points for which parameter estimation consistency, model selection consistency, and asymptotic normality are proven. It is shown in simulation experiments that adaptive group Lasso performs comparably to a state-of-the-art two-step group Lasso procedure with backward elimination and other leading-edge approaches. Moreover, comparing the forecasting performance of both group Lasso procedures in an empirical application to realized variance dynamics, adaptive group Lasso is found to date change-points with equal accuracy. Thus, in practice, adaptive group Lasso can provide an alternative way to consistently select change-points in related applications.