This thesis is concerned with various non- and semiparametric estimation problems in a locally stationary time series setting. It consists of three essays that are self-contained and can be read separately. The first essay studies a nonparametric regression model which allows for locally stationary regressors and a regression function that changes smoothly over time. The second essay provides testing theory in this framework. The third essay deals with a semiparametric multiplicative volatility model in a locally stationary setting.
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