Essays on unit root tests in time series

Abstract

This dissertation consists of three essays which develop new unit root testing methods in time series. First one is about the effect of the persistent volatility breaks, i.e. non-stationary volatility, on the unit root inference in regulated time series. In this essay, we show that conventional bounded unit root tests become potentially unreliable in the presence of the non-stationary volatility. Then, as a remedy, we propose a new class of unit root tests that are robust to both the range constraints and the permanent volatility shifts present in the time series. While developing our new tests, we also extend the asymptotic theory for integrated time series. The second essay is about testing for seasonal unit roots. In this essay, we first construct a family of nonparametric seasonal unit root tests by utilizing fractional integration operator. Different from the wellknown parametric seasonal unit root tests, the proposed tests are free from tuning parameters. Another contribution of this essay is on the fractional integration literature. We introduce a new fractionally transformed seasonal series. The third essay deals with the effect of the heteroscedastic innovations on the nonparametric seasonal unit root tests. We demonstrate that these tests spuriously reject the true seasonal unit root null hypothesis under the heteroscedasticity. To remove the aforementioned size distortions, we develop nonparametric wild bootstrap seasonal unit root tests. These tests are successful in correcting size problems under a broad class of heteroscedasticity observed in the seasonal time series. Moreover, we show that the proposed tests are asymptotically pivotal.