| Nowadays, technological innovations have made it possible to collect a massive amount of data with complex structure over a relatively long period of time. For such data, many empirical evidences have shown that the traditional time series analysis tools for stationary processes are insufficient. As a consequence, there have been great demands and interests for theoretical and methodological advancements for non-stationary time series analysis. In this thesis, we shall propose a general class of non-stationary time series models, which we call locally stationary time series, and discuss the consequences of such modelling. In particular, inferences of quantile curves and conditional mean functions of such processes will be discussed in detail. Numerous real data examples shows the applicability of our theory and methodology in fields such as environmental sciences and financial econometrics. |
