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A Note on a Specification Test for Time Series Models Based on Spectral Density Estimation

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  • Holger Dette
  • Ingrid Spreckelsen

Abstract

In a recent paper, Paparoditis [Scand. J. Statist. 27 (2000) 143] proposed a new goodness‐of‐fit test for time series models based on spectral density estimation. The test statistic is based on the distance between a kernel estimator of the ratio of the true and the hypothesized spectral density and the expected value of the estimator under the null and provides a quantification of how well the parametric density fits the sample spectral density. In this paper, we give a detailed asymptotic analysis of the corresponding procedure under fixed alternatives.

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  • Holger Dette & Ingrid Spreckelsen, 2003. "A Note on a Specification Test for Time Series Models Based on Spectral Density Estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(3), pages 481-491, September.
    • Handle: RePEc:bla:scjsta:v:30:y:2003:i:3:p:481-491
    DOI: 10.1111/1467-9469.00343
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    Cited by:

    1. Jensen, D.R., 2006. "Gauss inequalities on ordered linear spaces," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 985-998, April.
    2. Holger Dette & Efstathios Paparoditis, 2009. "Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 831-857, September.
    3. Xu Guo & Wangli Xu & Lixing Zhu, 2015. "Model checking for parametric regressions with response missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(2), pages 229-259, April.
    4. Dette, Holger & Paroditis, Efstathios, 2007. "Testing equality of spectral densities," Technical Reports 2007,29, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    5. Dette, Holger & Hildebrandt, Thimo, 2012. "A note on testing hypotheses for stationary processes in the frequency domain," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 101-114, February.
    6. Dette, Holger & Paparoditis, Efstathios, 2008. "Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities," Technical Reports 2008,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Philip Preuss & Mathias Vetter & Holger Dette, 2013. "Testing Semiparametric Hypotheses in Locally Stationary Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 417-437, September.

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