Detection Of Structural Breaks In Time Series Model Based On Adaptive Group Lasso

Detection of structural breaks in Time Series Model has always been an important research field of statistics and econometrics.In this paper,we propose a method to detect structural breaks in the variance structure of time series.We focus on the situations where the number of structural breaks is unknown.Based on ARCH models and GARCH models,we first transform the problem of estimating structural breaks in time series into the variable selection issue in the high dimensional linear regression framework.Then we adopt the Adaptive Group Lasso method to perform the detection of possible structural breaks and estimation of parameters simultaneously.Further,we consider more complex cases,where both mean and variance structures have structural breaks,and formulate the corresponding high dimensional linear regression models to address these issues.Simulations are conducted to illustrate the finite-sample performance of estimation procedure respectively in the setting of short and long time series.We also compare our method with the classical Binary Segmentation method and find that the former one has better performance in terms of estimation accuracy and precision.The empirical analyses are carried out by using the Shanghai 50 stock index and Brent oil prices to verify the effectiveness of our method.