Detection of Structural Changes in Mean and Variance for Polynomial Regression of Dependent Data

Abstract

In this talk we considered the structural changes in the mean and the variance of segmented polynomial regression models for dependent data. We first introduced the polynomial regression model with no breaks in the mean (denoted by M0), or with one break in the mean, denoted by M2 or M1 if the polynomial regression function is discontinuous or continuous at the break, respectively. We then applied a model-selection procedure for selecting Mk; k=0,1,2, where we derived an efficient algorithm to estimate the parameters of M1 and M2. When the underlying model for the mean of the data exists, we established the selection and estimation consistency under some mild conditions, where the structural breaks in the variance of the data are allowed at any locations. Based on Mk, we treat the corresponding squared residuals as the artificial responses. We further imposed the polynomial regression models for these fitted sqaured residuals (the variance model of the data), denoted by N0, N1 and N2, with no breaks, one continuous break and one discontinuous break in the variance, respectively. We then applied the same selection and estimation algorithm for selecting Nk; k=0,1,2, on the squared residuals to detect the break in the variance of the data. If the underlying model exists, consistency for the selection and estimation for the break in the variance is also established under conditions enhanced from the aforementioned ones.