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Saddlepoint approximations for short and long memory time series: a frequency domain approach

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Published in Journal of Econometrics. 2019, vol. 213, no. 2, p. 578-592
Abstract Saddlepoint techniques provide numerically accurate, 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. Under short or long range serial dependence, for Gaussian and non Gaussian processes, we show how to derive and implement saddlepoint approximations for two relevant classes of frequency domain statistics: ratio statistics and Whittle’s estimator. We compare our new approximations to the ones obtained by the standard asymptotic theory and by two widely-applied bootstrap methods. The numerical exercises for Whittle’s estimator show that our approximations yield accuracy’s improvements, while preserving analytical tractability. A real data example concludes the paper.
Keywords PeriodogramTilted edgeworth expansionMacroeconomic time seriesRelative errorWhittle’s estimator
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LA VECCHIA, Davide, RONCHETTI, Elvezio. Saddlepoint approximations for short and long memory time series: a frequency domain approach. In: Journal of Econometrics, 2019, vol. 213, n° 2, p. 578-592. doi: 10.1016/j.jeconom.2018.10.009 https://archive-ouverte.unige.ch/unige:125551

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Deposited on : 2019-11-04

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