Long memory and structural breaks in time series models
This thesis examines structural breaks in time series regressions where both regressors and errors may exhibit long range dependence. Statistical properties of methods for detecting and estimating structural breaks are analysed and asymptotic distribution of estimators and test statistics are obtained. Valid bootstrap methods of approximating the limiting distribution of the relevant statistics are also developed to improve on the asymptotic approximation in finite samples or to deal with the problem of unknown asymptotic distribution. The performance of the asymptotic and bootstrap methods are compared through Monte Carlo experiments. A background of the concepts of structural breaks, long memory and bootstrap is offered in Introduction where the main contribution of the thesis is also outlined. Chapter 1 proposes a fluctuation-type test procedure for detecting instability of slope coefficients. A first-order bootstrap approximation of the distribution of the test statistic is proposed. Chapter 2 considers estimation and testing of the time of the structural break. Statistical properties of the estimator are examined under a range of assumptions on the size of the break. Under the assumption of shrinking break, a bootstrap approximation of the asymptotic test procedure is proposed. Chapter 3 addresses a drawback of the assumption of fixed size of break. Under this assumption, the asymptotic distribution of the estimator of the breakpoint depends on the unknown underlying distribution of data and thus it is not available for inference purposes. The proposed solution is a bootstrap procedure based on a specific type of deconvolution.