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

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  • La Vecchia, Davide
  • Ronchetti, Elvezio

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.

Suggested Citation

  • La Vecchia, Davide & Ronchetti, Elvezio, 2019. "Saddlepoint approximations for short and long memory time series: A frequency domain approach," Journal of Econometrics, Elsevier, vol. 213(2), pages 578-592.
    • Handle: RePEc:eee:econom:v:213:y:2019:i:2:p:578-592
    DOI: 10.1016/j.jeconom.2018.10.009
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    Cited by:

    1. Chaonan Jiang & Davide La Vecchia & Elvezio Ronchetti & Olivier Scaillet, 2023. "Saddlepoint Approximations for Spatial Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(542), pages 1164-1175, April.
    2. Alfonso García-Pérez, 2022. "On Robustness for Spatio-Temporal Data," Mathematics, MDPI, vol. 10(10), pages 1-17, May.
    3. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.

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    More about this item

    Keywords

    Periodogram; Tilted edgeworth expansion; Macroeconomic time series; Relative error; Whittle’s estimator;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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