The Ph.D thesis, titled Essays On Diagnostic Testing In Time Series Models, investigates several issues related to inference in time series models. The aim is to develop a deeper understanding of issues involving hypothesis testing and inference in models that exhibit some non-linear dependence or time-varying endogeneity. This thesis is made up of five main chapters, In the first chapter (Chapter 1) we provide a motivation for the thesis. In the second chapter (Chapter 2), we develop a data-driven version of a portmanteau test for detecting nonlinear types of statistical dependence. The test properly controls the type I error without being sensitive with respect to the number of autocorrelations used. In addition, the automatic test is found to have higher power in simulations when compared to the standard portmanteau test, for both raw data and residuals. In the third chapter (Chapter 3), we propose a bootstrap version of a time-varying Hausman test statistic, which compares kernel based time-varying OLS and IV estimators of regression coefficients, allowing for possible
changes in the endogeneity status of the regressors over time. In this chapter, we examine the finite-sample performance of the asymptotic and the bootstrap version of the test by means of Monte Carlo simulations and we establish the asymptotic validity of a simple, easy to use bootstrap procedure. The bootstrap test has more accurate size and higher power than its asymptotic counterpart. What is more, it is demonstrated that the size
and power of the bootstrap test are insensitive with respect to the choice of the bandwidth parameters. This is
of particular importance since in current practice researchers use a variety of ad hoc approaches to bandwidth
selection which are typically based on objective functions that address estimation concerns rather than test accuracy.
In the fourth chapter (Chapter 4), we study the problem of bandwidth choice for non-parametric instrumental variable and least square estimation for econometric models whose coefficients can vary over time either de-terministically or stochastically, under both endogeneity and exogeneity. In this chapter, we compare different data-driven selectors for the smoothing parameter. We find that data-driven methods perform well for both the estimators. Quite interestingly, we find that selecting the bandwidth parameter in a data-driven way for the time-varying least square estimation under endogeneity provides a way to reduce the finite small sample bias of the estimator.
In the last chapter we summarize the results of the thesis.