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Mixture periodic autoregressive conditional heteroskedastic models

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  • Bentarzi, M.
  • Hamdi, F.

Abstract

Mixture Periodically Correlated Autoregressive Conditionally Heteroskedastic (MPARCH) model, which extends the ARCH model, is proposed. The primary motivation behind this extension is to make the model consistent with high kurtosis, outliers and extreme events, and at the same time, able to capture the periodicity feature exhibited by the autocovariance structure. The second and the fourth moment periodically stationary conditions and their closed-forms are derived. Maximum likelihood estimation is obtained via the iterative Expectation Maximization algorithm and the performance of this algorithm is shown via a simulation studies and the MPARCH models are fitted to a real data set.

Suggested Citation

  • Bentarzi, M. & Hamdi, F., 2008. "Mixture periodic autoregressive conditional heteroskedastic models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 1-16, September.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:1:p:1-16
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    References listed on IDEAS

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    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Shao, Q., 2006. "Mixture periodic autoregressive time series models," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 609-618, March.
    7. C. S. Wong & W. K. Li, 2000. "On a mixture autoregressive model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 95-115.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Nadia Boussaha & Faycal Hamdi & Saïd Souam, 2018. "Multivariate Periodic Stochastic Volatility Models: Applications to Algerian dinar exchange rates and oil prices modeling," Working Papers hal-04141780, HAL.
    2. Abdelhakim Aknouche & Nadia Rabehi, 2010. "On an independent and identically distributed mixture bilinear time‐series model," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 113-131, March.
    3. Nadia Boussaha & Faycal Hamdi & Saïd Souam, 2018. "Multivariate Periodic Stochastic Volatility Models: Applications to Algerian dinar exchange rates and oil prices modeling," EconomiX Working Papers 2018-14, University of Paris Nanterre, EconomiX.

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