Statistical analysis of financial time series under the assumption of local stationarity

The aim of this paper is to apply a nonparametric methodology developed by Donoho et al(2003 IEEE Trans. Signal Processing53614-27) for estimating an autocovariance sequence to the statistical analysis of the return of securities and discuss the advantages offered by this approach over other existing methods such as fixed-window-length segmentation procedures. Theoretical properties of adaptivity of this estimation method have been proved for a specific class of time series, namely the class of locally stationary processes, with an autocovariance structure which varies slowly over time in most cases but might exhibit abrupt changes of regime. This method is based on an algorithm that selects empirically from the data the tiling of the time-frequency plane which exposes best in the least-squares sense the underlying second-order time-varying structure of the time series, and so may properly describe the time-inhomogeneous variations of speculative prices. The applications we consider here mainly concern the analysis of structural changes occurring in stock market returns, VaR estimation and the comparison between the variation structure of stock index returns in developed markets and in developing markets.