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Goodness-of-Fit Tests for SPARMA Models with Dependent Error Terms

Author

Listed:
  • Boubacar Maïnassara Yacouba
  • Ilmi Amir Abdoulkarim

    (Laboratoire de mathématiques de Besançon, Université Bourgogne Franche-Comté, UMR CNRS 6623, 16 route de Gray, 25030, Besançon, France)

Abstract

In this paper we consider tests for lack of fit in a class of seasonal periodic autoregressive moving average (SPARMA) models under the assumption that the errors are uncorrelated but non-independent (i.e. weak SPARMA models). We derive the asymptotic distributions of residual and normalized residual empirical autocovariances and autocorrelations of these weak SPARMA models. We then deduce the modified portmanteau statistics. We establish the asymptotic behavior of the proposed statistics, which can be quite different from the usual chi-squared approximation used under independent and identically distributed (iid) assumptions on the noise. We also propose another test based on a self-normalization approach to cheek the adequacy of SPARMA models. A set of Monte Carlo experiments and an application to the daily returns of the SP500 are presented.

Suggested Citation

  • Boubacar Maïnassara Yacouba & Ilmi Amir Abdoulkarim, 2022. "Goodness-of-Fit Tests for SPARMA Models with Dependent Error Terms," Journal of Time Series Econometrics, De Gruyter, vol. 14(2), pages 107-140, July.
    • Handle: RePEc:bpj:jtsmet:v:14:y:2022:i:2:p:107-140:n:4
    DOI: 10.1515/jtse-2022-0002
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    Keywords

    quasi-generalized least squares; seasonality; goodness-of-fit test; residual autocorrelations; self-normalization; weak PARMA models; weak SARMA; weak SPARMA models; primary 62M10; 62F03; 62F05; secondary 91B84; 62P05;
    All these keywords.

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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