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On the cumulated periodogram goodness-of-fit test in ARMA models

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  • Velilla Cerdan, Santiago

Abstract

The asymptotic distribution of the cumulated periodogram goodness-of-fit test statistic for ARMA models is obtained, and is shown to be different from the limiting distribution of the standard Kolmogorov-Smirnov test statistic for probability distributions. The implications of this anomaly for inference purposes are analyzed. A modified cumulated periodogram goodness-of-fit test statistic is suggested, and its properties are studied and compared with other goodness-of-fit criteria proposed in the literature.

Suggested Citation

  • Velilla Cerdan, Santiago, 1996. "On the cumulated periodogram goodness-of-fit test in ARMA models," DES - Working Papers. Statistics and Econometrics. WS 10721, Universidad Carlos III de Madrid. Departamento de Estadística.
    • Handle: RePEc:cte:wsrepe:10721
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    References listed on IDEAS

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    1. Durlauf, Steven N., 1991. "Spectral based testing of the martingale hypothesis," Journal of Econometrics, Elsevier, vol. 50(3), pages 355-376, December.
    2. Santiago Velilla, 1994. "A Goodness‐Of‐Fit Test For Autoregressive Moving‐Average Models Based On The Standardized Sample Spectral Distribution Of The Residuals," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(6), pages 637-647, November.
    3. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-421, May.
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    Keywords

    Autocorrelation function;

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