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Estimating SPARMA Models with Dependent Error Terms

Author

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  • 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

We are interested in a class of seasonal autoregressive moving average (SARMA) models with periodically varying parameters, so-called seasonal periodic autoregressive moving average (SPARMA) models under the assumption that the errors are uncorrelated but non-independent (i.e. weak SPARMA models). Relaxing the classical independence assumption on the errors considerably extends the range of application of the SPARMA models, and allows one to cover linear representations of general nonlinear processes. We establish the asymptotic properties of the quasi-generalized least squares (QLS) estimator of these models. Particular attention is given to the estimation of the asymptotic variance matrix of the QLS estimator, which may be very different from that obtained in the standard framework. A set of Monte Carlo experiments are presented.

Suggested Citation

  • Boubacar Maïnassara Yacouba & Ilmi Amir Abdoulkarim, 2022. "Estimating SPARMA Models with Dependent Error Terms," Journal of Time Series Econometrics, De Gruyter, vol. 14(2), pages 141-174, July.
    • Handle: RePEc:bpj:jtsmet:v:14:y:2022:i:2:p:141-174:n:5
    DOI: 10.1515/jtse-2021-0022
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    More about this item

    Keywords

    quasi-generalized least squares; seasonality; weak PARMA models; weak SARMA; weak SPARMA models; Primary 62M10; 62F03; 62F05; secondary 91B84; 62P05;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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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