Empirical Processes Techniques for the Spectral Estimation of Fractional Processes

Abstract

Empirical processes techniques have only recently been applied to the spectral analysis of time series. Dahlhaus (1988) and Mikosch and Norvaiša (1997) proved a functional central limit theorem for the empirical spectral measure under weak dependence assumptions. This paper presents new applications of empirical processes techniques to the spectral analysis of time series. Different empirical contrast functions are considered, and applied to strongly dependent processes. Statistical applications are presented, including parametric estimation, goodness-of fit tests and adaptive estimation.KeywordsSpectral DensityCentral Limit TheoremGaussian ProcessSpectral EstimationEdgeworth ExpansionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.