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A beta prime ARMA model for positive time series

Author

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  • Aknouche, Abdelhakim
  • Almohaimeed, Bader
  • Dimitrakopoulos, Stefanos

Abstract

A class of generalized ARMA models with an identity link function and a conditional beta prime (BP-ARMA) distribution is proposed for modeling positive time series. Sufficient and necessary conditions for the existence of an ergodic stationary BP-ARMA process having finite moments are first proposed. Then, the parameters are estimated using the geometric quasi-maximum likelihood method, the convergence and asymptotic normality of which are shown under reasonable assumptions. The proposed methodology is illustrated through a simulation study and an application to the S&P 500 volume.

Suggested Citation

  • Aknouche, Abdelhakim & Almohaimeed, Bader & Dimitrakopoulos, Stefanos, 2025. "A beta prime ARMA model for positive time series," MPRA Paper 123873, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:123873
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    References listed on IDEAS

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    1. Saranjeet Kaur Bhogal & Ramanathan Thekke Variyam, 2019. "Conditional Duration Models For High‐Frequency Data: A Review On Recent Developments," Journal of Economic Surveys, Wiley Blackwell, vol. 33(1), pages 252-273, February.
    2. Marcelo Bourguignon & Manoel Santos-Neto & Mário Castro, 2021. "A new regression model for positive random variables with skewed and long tail," METRON, Springer;Sapienza Università di Roma, vol. 79(1), pages 33-55, April.
    3. Aknouche, Abdelhakim & Francq, Christian, 2021. "Count And Duration Time Series With Equal Conditional Stochastic And Mean Orders," Econometric Theory, Cambridge University Press, vol. 37(2), pages 248-280, April.
    4. M. Dashti Moghaddam & Jiong Liu & R. A. Serota, 2021. "Implied and realized volatility: A study of distributions and the distribution of difference," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 2581-2594, April.
    5. Abdelhakim Aknouche & Christian Francq, 2022. "Stationarity and ergodicity of Markov switching positive conditional mean models," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(3), pages 436-459, May.
    6. Aknouche, Abdelhakim & Francq, Christian, 2023. "Two-stage weighted least squares estimator of the conditional mean of observation-driven time series models," Journal of Econometrics, Elsevier, vol. 237(2).
    7. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    8. Engle, Robert F. & Gallo, Giampiero M., 2006. "A multiple indicators model for volatility using intra-daily data," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 3-27.
    9. Chou, Ray Yeutien, 2005. "Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(3), pages 561-582, June.
    10. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    11. Abdelhakim Aknouche & Sara Bendjeddou & Nassim Touche, 2018. "Negative Binomial Quasi†Likelihood Inference for General Integer†Valued Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(2), pages 192-211, March.
    12. Giampiero M. Gallo & Edoardo Otranto, 2018. "Combining sharp and smooth transitions in volatility dynamics: a fuzzy regime approach," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(3), pages 549-573, April.
    13. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    14. Hujer, Reinhard & Vuletic, Sandra, 2007. "Econometric analysis of financial trade processes by discrete mixture duration models," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 635-667, February.
    15. Nikolaus Hautsch, 2012. "Econometrics of Financial High-Frequency Data," Springer Books, Springer, number 978-3-642-21925-2, March.
    16. Qian Li, 2020. "Location Multiplicative Error Models with Quasi Maximum Likelihood Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(3), pages 387-405, May.
    17. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    18. Abdelhakim Aknouche & Stefanos Dimitrakopoulos, 2023. "Autoregressive conditional proportion: A multiplicative‐error model for (0,1)‐valued time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(4), pages 393-417, July.
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    More about this item

    Keywords

    Nonnegative time series data; Beta Prime ARMA; Generalized ARMA; ergodicity; Two-stage weighted least squares; Geometric QMLE.;
    All these keywords.

    JEL classification:

    • 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
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies

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