Essays on Time Series Econometrics

Abstract

This dissertation focuses on the construction of statistical tests to differentiate stationary and non-stationary time series. Chapter 1 deals with non-stationarity induced by a broken trend function and considers testing for the presence of a structural break in the trend of a univariate time-series where the date of the break is unknown. The proposed tests are robust as to whether the shocks are generated by a stationary or an integrated process. The simulation results suggest that the robust tests perform well in small samples, showing good size control and displaying very decent power regardless of the degree of persistence of the data. Chapter 2 proposes a bootstrap stationarity test that has good size control and also retains power. The test utilizes a parametric bootstrap re-sampling scheme that can generate independent re-samples and impose the null constraint on the bootstrap samples. The empirical size and power performance of the proposed test is compared with the existing bootstrap and conventional stationarity tests through Monte-Carlo studies. Simulations demonstrate that the proposed bootstrap test controls size better and has higher power than the competing methods. Finally, chapter 3 considers the initial condition problem in unit root testing and develops a powerful unit root test robust to initial condition. The proposed method estimates the trend parameters using indirect inference and results show that the proposed test statistic is robust to initial condition.