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Title: Saddlepoint approximations for short and long memory time series: A frequency domain approach Authors:  Davide La Vecchia - University of Geneva (Switzerland)
Elvezio Ronchetti - University of Geneva (Switzerland) [presenting]
Abstract: Saddlepoint techniques provide accurate, higher order, small sample approximations to the distribution of estimators and test statistics. Except for a few simple models, these approximations are not available in the framework of stationary time series. We contribute to fill this gap by developing new saddlepoint approximations for frequency domain statistics. Under short or long range serial dependence, for Gaussian and non Gaussian processes, we show how to derive and implement our saddlepoint techniques (density and tail areas approximations and tests in the presence of nuisance parameters) for two relevant classes of statistics: ratio statistics and Whittle's estimator. Extensive Monte Carlo experiments illustrate the theory for widely-applied time series models, comparing our new approximations to the ones obtained by first order asymptotic theory and the frequency domain bootstrap. The numerical exercises for Whittle's estimator show that our approximations yield accuracy's improvements, while preserving analytical tractability. Finally, a real data example about the European Central Bank assets dynamics is shown.