Essays on time series econometrics

Chapter 1 develops an asymptotic theory for testing the presence of structural change in a weakly dependent time series regression model. The cases of full structural change and partial structural change are considered. A HAC estimator is involved in the construction of the test statistics. Depending on how the long run variance for pre- and postbreak regimes is estimated, two types of heteroskedasticity and autocorrelation (HAC) robustWald statistics, denoted by Wald(F) and Wald(S) are analyzed. The fixed-b asymptotics established by Kiefer and Vogelsang (2005) is applied to derive the limits of the statistics with the break date being treated as a priori. The fixed-b limits turn out to depend on the location of break fraction and the bandwidth ratio as well as on the kernel being used. For both Wald statistics the limits capture the finite-sample randomness existing in the HAC estimators for the pre- and post-break regimes. The limit of Wald(F) further captures the finite-sample covariance between the pre-break estimators of regression parameters and the post-break estimators of the regression parameters. The fixed-b limit stays the same and is pivotal for Wald(F) irregardless of whether some of the regressors are not subject to structural change. Critical values for the tests are obtained by simulation methods. Monte Carlo simulations compare the finite sample size properties of the two Wald statistics and a local power analysis is conducted to provide guidance on the power properties of the tests. This Chapter extends its analysis to cover the case of the break date being unknown. Supremum, mean and exponential Wald statistics are considered and finite sample size distortions are examined via simulations with newly tabulated fixed- b critical values for these statistics.;Chapter 2 generalizes the structural change test developed in Chapter 1 while allowing for a shift in the mean and(or) variance of the explanatory variable. Chapter 2 assumes the break date for the mean/variance is different from the possible break date for the regression parameters. The test is robust to serial correlation and heteroskedasticity of the error term and the explanatory variables. The fixed-b theory is applied to derive the limits of the statistics. The asymptotic theory in this paper is based on a new set of high level conditions which incorporates the possibility of the moments shift and serves to provide pivotal limits of the test statistics.;Chapter 3 proposes a test of the null hypothesis of integer integration against the alternative of fractional integration. The null of integer integration is satisfied if the series is either I(0) or I(1), while the alternative is that it is I(d) with 0 < d < 1. The test is based on two statistics, the KPSS statistic and a new unit root test statistic. The null is rejected if the KPSS test rejects I(0) and the unit root test rejects I(1). The newly proposed unit root test is a lower-tailed KPSS test based on the first differences of the original data, so the test of the null of integer integration is called the "Double KPSS" test. Chapter 3 shows that the test has asymptotically correct size under the null that the series is either I(0) or I(1) and the test is consistent against I(d) alternatives for all d between zero and one. These statements are true under the assumption that the number of lags used in long-run variance estimation goes to infinity with sample size, but more slowly than sample size. Chapter 3 refers to this as "standard asymptotics". This requires some original asymptotic theory for the new unit root test, and also for the KPSS short memory test for the case that d = 1/2. Chapter 3 also considers "fixed-b asymptotics" as in Kiefer and Vogelsang (2005). Finite-sample size and power of the Double KPSS test is investigated using both the critical values based on standard asymptotics and the critical values based on fixed-b asymptotics. The new test is more accurate when it uses the fixed-b critical values. The conclusion is that one can distinguish integer integration from fractional integration using the Double KPSS test, but it takes a rather large sample size to do so reliably.