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Bayesian Identification Procedure for Triple Seasonal Autoregressive Models

Author

Listed:
  • Ayman A. Amin

    (Department of Statistics, Mathematics, and Insurance, Faculty of Commerce, Menoufia University, Menoufia 32952, Egypt)

  • Saeed A. Alghamdi

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

Triple seasonal autoregressive (TSAR) models have been introduced to model time series date with three layers of seasonality; however, the Bayesian identification problem of these models has not been tackled in the literature. Therefore, in this paper, we have the objective of filling this gap by presenting a Bayesian procedure to identify the best order of TSAR models. Assuming that the TSAR model errors are normally distributed along with employing three priors, i.e., normal-gamma, Jeffreys’ and g priors, on the model parameters, we derive the marginal posterior distributions of the TSAR model parameters. In particular, we show that the marginal posteriors are multivariate t and gamma distributions for the TSAR model coefficients vector and precision, respectively. Using the marginal posterior distribution of the TSAR model coefficients vector, we present an identification procedure for the TSAR models based on a sequence of t-test of significance. We evaluate the accuracy of the proposed Bayesian identification procedure by conducting an extensive simulation study, followed by a real application to hourly electricity load datasets in six European countries.

Suggested Citation

  • Ayman A. Amin & Saeed A. Alghamdi, 2023. "Bayesian Identification Procedure for Triple Seasonal Autoregressive Models," Mathematics, MDPI, vol. 11(18), pages 1-13, September.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3823-:d:1234002
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    References listed on IDEAS

    as
    1. Ayman A. Amin, 2023. "Gibbs sampling for Bayesian estimation of triple seasonal autoregressive models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(20), pages 7303-7322, October.
    2. Taylor, James W. & Snyder, Ralph D., 2012. "Forecasting intraday time series with multiple seasonal cycles using parsimonious seasonal exponential smoothing," Omega, Elsevier, vol. 40(6), pages 748-757.
    3. Taylor, James W., 2010. "Triple seasonal methods for short-term electricity demand forecasting," European Journal of Operational Research, Elsevier, vol. 204(1), pages 139-152, July.
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    7. James W. Taylor, 2008. "A Comparison of Univariate Time Series Methods for Forecasting Intraday Arrivals at a Call Center," Management Science, INFORMS, vol. 54(2), pages 253-265, February.
    8. Taylor, James W., 2008. "An evaluation of methods for very short-term load forecasting using minute-by-minute British data," International Journal of Forecasting, Elsevier, vol. 24(4), pages 645-658.
    9. Taylor, James W., 2010. "Reply to the discussion of: Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles," International Journal of Forecasting, Elsevier, vol. 26(4), pages 658-660, October.
    10. Ayman A. Amin, 2018. "Bayesian inference for double SARMA models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(21), pages 5333-5345, November.
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    13. Ayman A. Amin & Walid Emam & Yusra Tashkandy & Christophe Chesneau, 2023. "Bayesian Subset Selection of Seasonal Autoregressive Models," Mathematics, MDPI, vol. 11(13), pages 1-13, June.
    14. Ayman A. Amin, 2020. "Bayesian Analysis of Double Seasonal Autoregressive Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 328-352, November.
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