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Fourier--type tests involving martingale difference processes

Author

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  • Zdeněk Hlávka
  • Marie Hušková
  • Claudia Kirch
  • Simos G. Meintanis

Abstract

We develop testing procedures which detect if the observed time series is a martingale difference sequence. Furthermore, tests are developed that detect change--points in the conditional expectation of the series given its past. The test statistics are formulated following the approach of Fourier--type conditional expectations first proposed by Bierens (1982) and have the advantage of computational simplicity. The limit behavior of the test statistics is investigated under the null hypothesis as well as under alternatives. Since the asymptotic null distribution contains unknown parameters, a bootstrap procedure is proposed in order to actually perform the test. The performance of the bootstrap version of the test is compared in finite samples with other methods for the same problem. A real--data application is also included.

Suggested Citation

  • Zdeněk Hlávka & Marie Hušková & Claudia Kirch & Simos G. Meintanis, 2017. "Fourier--type tests involving martingale difference processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 468-492, April.
    • Handle: RePEc:taf:emetrv:v:36:y:2017:i:4:p:468-492
    DOI: 10.1080/07474938.2014.977074
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    References listed on IDEAS

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    Cited by:

    1. Kloodt, Nick & Neumeyer, Natalie, 2020. "Specification tests in semiparametric transformation models — A multiplier bootstrap approach," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    2. J. S. Allison & M. Hušková & S. G. Meintanis, 2018. "Testing the adequacy of semiparametric transformation models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 70-94, March.
    3. Simos G. Meintanis & Joseph Ngatchou-Wandji & James Allison, 2018. "Testing for serial independence in vector autoregressive models," Statistical Papers, Springer, vol. 59(4), pages 1379-1410, December.
    4. M. Dolores Jiménez-Gamero & Sangyeol Lee & Simos G. Meintanis, 2020. "Goodness-of-fit tests for parametric specifications of conditionally heteroscedastic models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 682-703, September.

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