Joint change point estimation in regression coefficients and variances of the errors of a linear model

This dissertation describes how to estimate a linear model that admits multiple breaks in coefficients of a linear regression function and in error variance. We begin by considering a single change point estimation problem and then show a method of a sequential estimation of multiple breaks. Pitarakis (2004) considered one and two change points problem. There always exists a collection of parameters for which change point estimators introduced by the author are inconsistent even in the case of a single change point for regression coefficients and the error variance. This dissertation considers joint and separate testing for and estimation of breaks in regression parameters and error variances depending on whether or not errors and regressors satisfy some moment stationarity conditions. If they then in Chapter II we introduce estimators of a change point which are uniformly consistent with respect to the parameter space in the case of a single break. Our estimation method is based on application of specific objective functions in conjunction with tests of structural change. In particular, sup-Wald test of Andrews (1993) can be used to detect structural breaks. Chapter III of this dissertation describes Wald-type tests of structural breaks in regression parameters and error variances of a linear model when regressors and errors are non-stationary and change points are unknown. Nonstationarity considered here includes time trends and shifts in distributions of errors and regressors. Sup, Ave and Exp tests of Andrews (1993), Andrews and Ploberger (1994) are not applicable in that framework and neither are tests of Bai and Perron (1998) for multiple breaks in regression parameters that also rely on the assumption of second order stationarity in errors and regressors. Hansen (2000) addressed that problem by deriving bootstrap tests for conditional models when regressors may have shifts in their marginal distributions. The errors were assumed to be second order stationary. In autoregressive models distributional breaks in dependent regressors can be caused by distributional breaks in errors. Chapter III introduces a testing procedure that takes into account nonstationarity in errors and regressors. If error variances admit step-like breaks then we sequentially estimate such breaks when regression parameters also break.