In my dissertation, I consider hypothesis testing with nuisance parameters identified only under the alternative hypothesis in the time series environment. The first chapter proposes tests for cointegrating rank that have power against the trend-break alternative. The conventional testing procedure may mislead one into accepting the null of no cointegration or the null of a cointegrating rank smaller than the true rank when there is a trend break under the alternative hypothesis. The proposed tests are applied to the U.S. money demand function. The results support the Campbell-Perron conjecture: money, income and interest rates are cointegrated around a broken trend. The second chapter proposes nonparametric tests of change in the distribution function of a time series. The limiting null distributions of the test statistics depend on a nuisance parameter, and we cannot tabulate critical values a priori. In order to circumvent this problem, I develop a version of the block bootstrap, the wild block bootstrap, and establish the validity of our bootstrap procedure in terms of size, local power, and test consistency. I examine the distributional stability in financial markets. The empirical results strongly suggests structural change in the distribution of important stock return series. The third chapter proposes a unified approach for consistent testing of linear restrictions on the conditional distribution function of a time series, as well as for testing conditional moment restrictions. A wide variety of interesting hypotheses in economics and finance correspond to such restrictions. I provide bounds tests based on the law of the iterated logarithm for martingales. Crucially, the tests do not require the resampling procedures, such as the bootstrap, despite the presence of nuisance parameters, and I prove that they nevertheless have the desirable property that the probabilities of both type I and type II errors are asymptotically zero. Finally, I investigate finite-sample performance in a set of Monte Carlo experiments using autoregressive, GARCH, and stochastic volatility models.
