| This dissertation consists of three essays. In the first essay, entitled "Robust Spectral Analysis," I introduce quantile spectral densities that summarize the cyclical behavior of time series across their whole distribution by analyzing periodicities in quantile crossings. This approach can capture systematic changes in the impact of cycles on the distribution of a time series and allows robust spectral estimation and inference in situations where the dependence structure is not accurately captured by the auto-covariance function. I study the statistical properties of quantile spectral estimators in a large class of nonlinear time series models and discuss inference both at fixed and across all frequencies. Monte Carlo experiments and an empirical example illustrate the advantages of quantile spectral analysis over classical methods when standard assumptions are violated.;In the second essay, "Stochastic Equicontinuity in Nonlinear Time Series Models," I provide simple and easily verifiable conditions under which a strong form of stochastic equicontinuity holds in a wide variety of modern time series models. In contrast to most results currently available in the literature, my methods avoid mixing conditions. I discuss two applications in detail.;In the third essay, "A Simple Test for Regression Specification with Non-Nested Alternatives," I introduce a simple test for the presence of the data-generating process among several non-nested alternatives. The test is an extension of the classical J test for non-nested regression models. I also provide a bootstrap version of the test that avoids possible size distortions inherited from the J test. |
