Semiparametric estimation of long range dependence

This thesis is concerned with experimental and empirical aspects of long memory in time series. The aim of this dissertation is to further investigate estimating methods for the order of fractional integration by employing Monte Carlo simulations, and to provide empirical evidence of long range dependence in German asset returns. In particular, the performance of a popular semiparametric estimator of long memory, the Local Whittle (LW) estimator, is studied in detail under empirically relevant conditions and compared to modified versions of it. The experimental results shed light on the finite sample performance of the estimators and also address the choice of the number of frequencies to be used in the estimation. It turns out that extended versions of the LW estimator dominate the classical variant given an appropiate choice of the bandwidth, and are clearly needed to ensure consistency in the nonstationarity region or in the presence of an additive noise. The empirical work in this thesis investigates the persistence in volatility measures of the German stock price index DAX. For this purpose, not only semiparametric estimators of long memory are applied to the data, but also possible breaks in mean and persistence are taken into account. The results are highly indicative of the presence of long memory in absolute and logsquared returns, and suggest a significant increase in persistence in the year 2001.