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Contiguity of the Whittle measure for a Gaussian time series

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  • Nidhan Choudhuri

Abstract

For a stationary time series, Whittle constructed a likelihood for the spectral density based on the approximate independence of the discrete Fourier transforms of the data at certain frequencies. Whittle's likelihood has been widely used in the literature for constructing estimators. In this paper, we show that, for a Gaussian time series, the Whittle measure is mutually contiguous with the actual distribution of the data. As a consequence, most asymptotic properties of estimators and test statistics derived under the Whittle measure can be carried over to the actual distribution. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Nidhan Choudhuri, 2004. "Contiguity of the Whittle measure for a Gaussian time series," Biometrika, Biometrika Trust, vol. 91(1), pages 211-218, March.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:1:p:211-218
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    Cited by:

    1. Fiorentini, Gabriele & Galesi, Alessandro & Sentana, Enrique, 2018. "A spectral EM algorithm for dynamic factor models," Journal of Econometrics, Elsevier, vol. 205(1), pages 249-279.
    2. Gabriele Fiorentini & Enrique Sentana, 2019. "Dynamic specification tests for dynamic factor models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(3), pages 325-346, April.
    3. Meier, Alexander & Kirch, Claudia & Meyer, Renate, 2020. "Bayesian nonparametric analysis of multivariate time series: A matrix Gamma Process approach," Journal of Multivariate Analysis, Elsevier, vol. 175(C).

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