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This paper offers a new approach to modeling and forecasting of nonstationarytime series with applications to volatility modeling for financial data. Theapproach is based on the assumption of local homogeneity: for every time point,there exists a historical interval of homogeneity, in which the volatilityparameter can be well approximated by a constant. The proposed procedurerecovers this interval from the data using the local change point (LCP)analysis. Afterward, the estimate of the volatility can be simply obtained bylocal averaging. The approach carefully addresses the question of choosing thetuning parameters of the procedure using the so-called ``propagation''condition. The main result claims a new ``oracle'' inequality in terms of themodeling bias which measures the quality of the local constant approximation.This result yields the optimal rate of estimation for smooth and piecewiseconstant volatility functions. Then, the new procedure is applied to some datasets and a comparison with a standard GARCH model is also provided. Finally, wediscuss applications of the new method to the Value at Risk problem. Thenumerical results demonstrate a very reasonable performance of the new method.

Multiscale local change point detection with applications to value-at-risk