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On the Optimal Segment Length for Parameter Estimates for Locally Stationary Time Series

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  • Rainer Dahlhaus
  • Liudas Giraitis

Abstract

We discuss the behaviour of parameter estimates when stationary time series models are fitted locally to non‐stationary processes which have an evolutionary spectral representation. A particular example is the estimation for an autoregressive process with time‐varying coefficients by local Yule–Walker estimates. The bias and the mean squared error for the parameter estimates are calculated and the optimal length of the data segment is determined.

Suggested Citation

  • Rainer Dahlhaus & Liudas Giraitis, 1998. "On the Optimal Segment Length for Parameter Estimates for Locally Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(6), pages 629-655, November.
    • Handle: RePEc:bla:jtsera:v:19:y:1998:i:6:p:629-655
    DOI: 10.1111/1467-9892.00114
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    Cited by:

    1. Schnaubelt, Matthias, 2019. "A comparison of machine learning model validation schemes for non-stationary time series data," FAU Discussion Papers in Economics 11/2019, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    2. Beran, Jan, 2007. "On parameter estimation for locally stationary long-memory processes," CoFE Discussion Papers 07/13, University of Konstanz, Center of Finance and Econometrics (CoFE).
    3. Federico Belotti & Alessandro Casini & Leopoldo Catania & Stefano Grassi & Pierre Perron, 2023. "Simultaneous bandwidths determination for DK-HAC estimators and long-run variance estimation in nonparametric settings," Econometric Reviews, Taylor & Francis Journals, vol. 42(3), pages 281-306, February.
    4. Alessandro Casini, 2021. "Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models," Papers 2103.02981, arXiv.org.
    5. Casini, Alessandro, 2023. "Theory of evolutionary spectra for heteroskedasticity and autocorrelation robust inference in possibly misspecified and nonstationary models," Journal of Econometrics, Elsevier, vol. 235(2), pages 372-392.
    6. Zani, Marguerite, 2002. "Large Deviations for Quadratic Forms of Locally Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 205-228, May.
    7. Alessandro Casini, 2022. "Theory of Evolutionary Spectra for Heteroskedasticity and Autocorrelation Robust Inference in Possibly Misspecified and Nonstationary Models," CEIS Research Paper 539, Tor Vergata University, CEIS.
    8. Alessandro Casini & Pierre Perron, 2021. "Change-Point Analysis of Time Series with Evolutionary Spectra," Papers 2106.02031, arXiv.org, revised Jun 2021.
    9. Tsukasa Hokimoto & Kunio Shimizu, 2008. "An angular–linear time series model for waveheight prediction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 781-800, December.
    10. Giraitis, L. & Kapetanios, G. & Yates, T., 2014. "Inference on stochastic time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 179(1), pages 46-65.
    11. Kley, Tobias & Preuss, Philip & Fryzlewicz, Piotr, 2019. "Predictive, finite-sample model choice for time series under stationarity and non-stationarity," LSE Research Online Documents on Economics 101748, London School of Economics and Political Science, LSE Library.

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