A Note on Adaptive Group Lasso for Structural Break Time Series

Abstract

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.