Multiple Change-points Estimation Of The Regressive Model With Dependent Errors

The change-point estimation is used to identify changes at unknown times and estimatethe locations of changes in the processes.Many approaches inuse are assumed that the error term of the model is independent.However,the significant serial correlation might occur when data are collected sequentially in time.In this case,we propose a new approach for dealing with the estimation of the locations of change-points in one-dimensional piecewise constant signals with dependent errors.The main idea of our approach is reframing this task against the variable selection background,and we use a penalized least-square criterion with al₁-type penalty for this purpose.We explain how to implement this method in practice by using least absolute shrinkage and selection operator?LASSO?and adaptive LASSO algorithms.The first is similar to the traditional LASSO estimator with only two tuning parameters?one for regression coefficients and the other for autoregression coefficients?.These tuning parameters can be easily calculated via a data driven method,but the resulting LASSO estimator may not be fully efficient.Hence,our simulation consists in comparing the effect of the two algorithms.Moreover,we also contrast the estimation effect between the model with autoregressive errors and the model with independent errors.An application to a study of the stock market is provided.