Stationary and trend stationary processes with level and trend breaks: central limit theorems and asymptotic distribution

Abstract

This thesis provides an analytical study of the limiting distribution of the typical statistic employed in the central limit theorem, albeit with a minor twist. An asymptotic theory is developed for the aforementioned statistic involving data generated from stationary and trend stationary processes with level and trend breaks. Four case-specific theorems are proved and Monte Carlo simulation is utilized in order to both confirm empirically that these results hold and to provide evidence of how variations in the parameterization of the underlying data generating processes affect the normality of the central limit theorem statistic. Finally, two possible applications of these theoretical results, pertaining to a context of ordinary least squares linear regression, are presented and discussed in detail. These applications exploit intermediate results obtained in the process of proving the main theorems and the contrapositives of the theorem statements so as to bring about derivations of the limiting distribution of regression coefficients and a potential independent variable exogeneity test statistic.