Limit Theorems and Applications of Time Series with Varying Coefficients

Abstract

In this thesis, we study the asymptotic behaviour and applications of a class of time series with varying coefficients. More specifically, we establish the large deviation principles and the moderate deviation principles for the first-order autoregressive models. The ADF and KPSS, two different methods, are then used to test the stationarity and conintegration of the annual average temperature series for the hemispheric, continental, and individual cities. We confirm that these series adhere to varying coefficient model. Finally, we examine some regions’ extreme rainfall series and show that they should follow the ARCH model.