Three Essays in Nonparametric Econometrics

Abstract

This thesis consists of three self-contained essays in econometrics and statistics. In these essays, I am interested in the nonparametric regression models and in developing new methods for testing various qualitative hypotheses about the trend functions in these models. Each of the three chapters proposes a novel multiscale testing procedure that is used either for investigating the properties of one time series (Chapter 1), or for comparison of the regression curves between multiple time series (Chapters 2 and 3). The underlying idea of any multiscale test is to consider a number of test statistics (each corresponding to a different set of values of some tuning parameters) simultaneously rather than to perform a separate test for each single test statistics, which leads to a well-known multiple testing problem. All of the proposed tests account for this problem by picking appropriate critical values, and the main methodological contributions of the current thesis are the theoretical results that these test all have (asymptotically) correct size and good power properties. Even though there are many similarities between the chapters, the research questions are quite distinct. In Chapter 1, the method is designed to determine whether the trend in one time series is decreasing or increasing, whereas in Chapters 2 and 3 the testing procedures were designed for comparison of multiple time trends and locating the differences. Moreover, the difference between Chapters 2 and 3 lies in the models under consideration: Chapter 2 deals with epidemic time trends in a simple nonparametric regression and places certain restrictions on the error terms in the observed times series, whereas Chapter 3 considers a very general model that allows for including covariates and fixed effects. The first two chapters are also completed by extensive simulation studies and the applications to the real-life data: temperature time series in Chapter 1 and the data on the new cases of COVID-19 in Chapter 2.