Essays on time series econometrics

This thesis explores the asymptotic distribution theory of maximum likelihood estimation in nonstationary time series econometric models.;The first chapter aims to extend the cointegration rank test to error correction models with exogenous stationary covariates. The distribution of the likelihood ratio statistic is a function of the canonical correlations between the equation errors with and without the covariates. The distribution approaches the chi-squared distribution as the stationary covariates lower the canonical correlations. This enables more powerful inference concerning the determination of the cointegration rank.;The second chapter considers tests for structural change of the cointegrating vector and the adjustment vector in the error correction model with unknown change point. Our tests for structural change of the cointegrating vector have nonstandard asymptotic distributions which are different from those found by Andrews and Ploberger (1994). In contrast, the tests on the adjustment vector have the same asymptotic distributions that have been found for models with stationary variables.;The third chapter explores the asymptotic distribution theory of autoregressive (AR) unit root tests where the error follows an autoregressive conditional heteroskedastic (ARCH) process. The proposed unit root test is based on maximum likelihood estimation, which estimates the AR unit root and the ARCH parameters jointly. The asymptotic distribution of the t-statistic for the AR unit root is a mixture of the Dickey-Fuller t-distribution and the standard normal, with the relative weight depending on the magnitude of the ARCH effect and the fourth moment of the standardized errors. As the ARCH effect increases, the power of the tests improves significantly. These results show that significant power gains emerge from the joint estimation rather than relying on the conventional ADF test which ignores the heteroskedasticity in the data.