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Bootstrapping locally stationary processes

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  • Jens-Peter Kreiss
  • Efstathios Paparoditis

Abstract

type="main" xml:id="rssb12068-abs-0001"> We propose a non-parametric method to bootstrap locally stationary processes which combines a time domain wild bootstrap approach with a non-parametric frequency domain approach. The method generates pseudotime series which mimic (asymptotically) correct, the local second- and to the necessary extent the fourth-order moment structure of the underlying process. Thus it can be applied to approximate the distribution of several statistics that are based on observations of the locally stationary process. We prove a bootstrap central limit theorem for a general class of statistics that can be expressed as functionals of the preperiodogram, the latter being a useful tool for inferring properties of locally stationary processes. Some simulations and a real data example shed light on the finite sample properties and illustrate the ability of the bootstrap method proposed.

Suggested Citation

  • Jens-Peter Kreiss & Efstathios Paparoditis, 2015. "Bootstrapping locally stationary processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 267-290, January.
    • Handle: RePEc:bla:jorssb:v:77:y:2015:i:1:p:267-290
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    File URL: http://hdl.handle.net/10.1111/rssb.2014.77.issue-1
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    Cited by:

    1. Carolina Euán & Hernando Ombao & Joaquín Ortega, 2018. "The Hierarchical Spectral Merger Algorithm: A New Time Series Clustering Procedure," Journal of Classification, Springer;The Classification Society, vol. 35(1), pages 71-99, April.
    2. Frazier, David T. & Koo, Bonsoo, 2021. "Indirect inference for locally stationary models," Journal of Econometrics, Elsevier, vol. 223(1), pages 1-27.
    3. Karmakar, Sayar & Richter, Stefan & Wu, Wei Biao, 2022. "Simultaneous inference for time-varying models," Journal of Econometrics, Elsevier, vol. 227(2), pages 408-428.
    4. David T. Frazier & Bonsoo Koo, 2020. "Indirect Inference for Locally Stationary Models," Monash Econometrics and Business Statistics Working Papers 30/20, Monash University, Department of Econometrics and Business Statistics.
    5. Franziska Häfner & Claudia Kirch, 2017. "Moving Fourier Analysis for Locally Stationary Processes with the Bootstrap in View," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 895-922, November.
    6. Rajae Azrak & Guy Mélard, 2022. "Autoregressive Models with Time-Dependent Coefficients—A Comparison between Several Approaches," Stats, MDPI, vol. 5(3), pages 1-21, August.
    7. Efstathios Paparoditis & Philip Preuß, 2016. "On Local Power Properties of Frequency Domain-based Tests for Stationarity," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 664-682, September.
    8. Krampe, J. & Kreiss, J.-P. & Paparoditis, E., 2015. "Hybrid wild bootstrap for nonparametric trend estimation in locally stationary time series," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 54-63.

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