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Some Estimation Methods for a Random Coefficient in the Gegenbauer Autoregressive Moving-Average Model

Author

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  • Oumaima Essefiani

    (Mathematics and Applications Laboratory, Abdelmalek Essaadi University, Tangier 90000, Morocco)

  • Rachid El Halimi

    (Mathematics and Applications Laboratory, Abdelmalek Essaadi University, Tangier 90000, Morocco)

  • Said Hamdoune

    (Mathematics and Applications Laboratory, Abdelmalek Essaadi University, Tangier 90000, Morocco)

Abstract

The Gegenbauer autoregressive moving-average (GARMA) model is pivotal for addressing non-additivity, non-normality, and heteroscedasticity in real-world time-series data. While primarily recognized for its efficacy in various domains, including the health sector for forecasting COVID-19 cases, this study aims to assess its performance using yearly sunspot data. We evaluate the GARMA model’s goodness of fit and parameter estimation specifically within the domain of sunspots. To achieve this, we introduce the random coefficient generalized autoregressive moving-average (RCGARMA) model and develop methodologies utilizing conditional least squares (CLS) and conditional weighted least squares (CWLS) estimators. Employing the ratio of mean squared errors (RMSE) criterion, we compare the efficiency of these methods using simulation data. Notably, our findings highlight the superiority of the conditional weighted least squares method over the conditional least squares method. Finally, we provide an illustrative application using two real data examples, emphasizing the significance of the GARMA model in sunspot research.

Suggested Citation

  • Oumaima Essefiani & Rachid El Halimi & Said Hamdoune, 2024. "Some Estimation Methods for a Random Coefficient in the Gegenbauer Autoregressive Moving-Average Model," Mathematics, MDPI, vol. 12(11), pages 1-16, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1629-:d:1399794
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    References listed on IDEAS

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    1. Marc Hallin & Abdelhadi Akharif, 2003. "Efficient detection of random coefficients in AR(p) models," ULB Institutional Repository 2013/2121, ULB -- Universite Libre de Bruxelles.
    2. Abdelhadi Akharif & Marc Hallin, 2003. "Efficient detection of random coefficients in autoregressive models," ULB Institutional Repository 2013/127956, ULB -- Universite Libre de Bruxelles.
    3. Henry L. Gray & Nien‐Fan Zhang & Wayne A. Woodward, 1989. "On Generalized Fractional Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 10(3), pages 233-257, May.
    4. Wayne A. Woodward & Q. C. Cheng & H. L. Gray, 1998. "A k‐Factor GARMA Long‐memory Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(4), pages 485-504, July.
    5. Richard Hunt & Shelton Peiris & Neville Weber, 2022. "Estimation methods for stationary Gegenbauer processes," Statistical Papers, Springer, vol. 63(6), pages 1707-1741, December.
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