Adaptive estimation for financial time series

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This thesis develops new locally adaptive methods for estimation and forecasting of financial time series data. These methods are mainly tailored for volatility estimation of financial returns and for regression and autoregression problems. The proposed approaches are defined locally adaptive because instead of imposing a stationary data generating process which can be globally described by a finite number of parameters, they only assume that observations which are chronologically close to each other can be well approximated by a constant process. These procedures are adaptive in the sense that for each observation they choose in a data driven way the interval of time homogeneity, i.e. the number of chronologically close and homogeneous past data where the hypothesis of a constant structure can not be rejected. Nonasymptotic theoretical results are derived, which show the optimality of the suggested algorithms. Comparisons with standard approaches demonstrate that the new procedures behave competitively and offer a valuable alternative, furthermore, intensive simulation studies and applications to real data provide good results, confirming their effectiveness and practical relevance.