Tests For Seasonal Unit Roots In Periodical Heteroscedastic Time Series

Unit root tests in economic time series has been paid more and more attention in recent years, and seasonal periodicity is one of an important characteristics in economic time series. Thus, testing unit root in seasonal time series is necessary. In this paper, we mainly study that testing seasonal unit root which has periodical heteroscedastic shocks. We introduce different parameter estimators, construct test statistics, and obtain some results as follows:In chapter 2, periodical heteroscedastic seasonal unit root model is proposed. Test statistics and their limit distributions are obtained based on least square estimation. Simulate calculations give that empirical critical values under same variances and periodical heteroscedasticity has effect to the test size.In chapter 3, a Cauchy estimator based on instrument variable is proposed. Then, the test statistic is constructed and the limit distribution is standard normal regardless of period of seasonality. Simulations show that different periodical heteroscedasticity has no influence to the test size.In chapter 4, weighed least square estimation is introduced in the test model and then periodical heteroscedasticity is removed. The limit distributions of statistics which are functional of standard Wiener process and don't have variance of errors are gained.