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Autoregressive conditional proportion: A multiplicative-error model for (0,1)-valued time series

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  • Aknouche, Abdelhakim
  • Dimitrakopoulos, Stefanos

Abstract

We propose a multiplicative autoregressive conditional proportion (ARCP) model for (0,1)-valued time series, in the spirit of GARCH (generalized autoregressive conditional heteroscedastic) and ACD (autoregressive conditional duration) models. In particular, our underlying process is defined as the product of a (0,1)-valued iid sequence and the inverted conditional mean, which, in turn, depends on past reciprocal observations in such a way that is larger than unity. The probability structure of the model is studied in the context of the stochastic recurrence equation theory, while estimation of the model parameters is performed by the exponential quasi-maximum likelihood estimator (EQMLE). The consistency and asymptotic normality of the EQMLE are both established under general regularity assumptions. Finally, the usefulness of our proposed model is illustrated with simulated and two real datasets.

Suggested Citation

  • Aknouche, Abdelhakim & Dimitrakopoulos, Stefanos, 2021. "Autoregressive conditional proportion: A multiplicative-error model for (0,1)-valued time series," MPRA Paper 110954, University Library of Munich, Germany, revised 06 Dec 2021.
    • Handle: RePEc:pra:mprapa:110954
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    References listed on IDEAS

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    1. Zhang, Peng & Qiu, Zhenguo & Shi, Chengchun, 2016. "simplexreg: an R package for regression analysis of proportional data using the simplex distribution," LSE Research Online Documents on Economics 102115, London School of Economics and Political Science, LSE Library.
    2. Pablo Mitnik & Sunyoung Baek, 2013. "The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation," Statistical Papers, Springer, vol. 54(1), pages 177-192, February.
    3. Andréa Rocha & Francisco Cribari-Neto, 2009. "Beta autoregressive moving average models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 529-545, November.
    4. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    5. Heejoon Han & Dennis Kristensen, 2014. "Asymptotic Theory for the QMLE in GARCH-X Models With Stationary and Nonstationary Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(3), pages 416-429, July.
    6. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    7. Scott R. Baker & Nicholas Bloom & Steven J. Davis & Kyle J. Kost, 2019. "Policy News and Stock Market Volatility," NBER Working Papers 25720, National Bureau of Economic Research, Inc.
    8. Zheng, Tingguo & Xiao, Han & Chen, Rong, 2015. "Generalized ARMA models with martingale difference errors," Journal of Econometrics, Elsevier, vol. 189(2), pages 492-506.
    9. Barndorff-Nielsen, O. E. & Jørgensen, B., 1991. "Some parametric models on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 106-116, October.
    10. Fabrizio Cipollini & Giampiero M. Gallo, 2021. "Multiplicative Error Models: 20 years on," Papers 2107.05923, arXiv.org.
    11. Nikolaus Hautsch, 2012. "Econometrics of Financial High-Frequency Data," Springer Books, Springer, number 978-3-642-21925-2, December.
    12. 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.
    13. 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.
    14. Paolino, Philip, 2001. "Maximum Likelihood Estimation of Models with Beta-Distributed Dependent Variables," Political Analysis, Cambridge University Press, vol. 9(4), pages 325-346, January.
    15. Drew Creal & Siem Jan Koopman & André Lucas, 2013. "Generalized Autoregressive Score Models With Applications," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 777-795, August.
    16. 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.
    17. Benjamin M.A. & Rigby R.A. & Stasinopoulos D.M., 2003. "Generalized Autoregressive Moving Average Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 214-223, January.
    18. Robert Engle, 2002. "New frontiers for arch models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 425-446.
    19. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    20. Francq, Christian & Thieu, Le Quyen, 2019. "Qml Inference For Volatility Models With Covariates," Econometric Theory, Cambridge University Press, vol. 35(1), pages 37-72, February.
    21. Patrícia L. Espinheira & Alisson Oliveira Silva, 2020. "Residual and influence analysis to a general class of simplex regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 523-552, June.
    22. Heinen, Andreas, 2003. "Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model," MPRA Paper 8113, University Library of Munich, Germany.
    23. Ed McKenzie, 1985. "An Autoregressive Process for Beta Random Variables," Management Science, INFORMS, vol. 31(8), pages 988-997, August.
    24. René Ferland & Alain Latour & Driss Oraichi, 2006. "Integer‐Valued GARCH Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 923-942, November.
    25. HEINEN, Andreas & RENGIFO, Erick, 2003. "Multivariate modelling of time series count data: an autoregressive conditional Poisson model," LIDAM Discussion Papers CORE 2003025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    26. Zhang, Peng & Qiu, Zhenguo & Shi, Chengchun, 2016. "simplexreg: An R Package for Regression Analysis of Proportional Data Using the Simplex Distribution," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i11).
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    More about this item

    Keywords

    Proportional time series data; Beta-ARMA model; Simplex ARMA; Autoregressive conditional duration; Exponential QMLE.;
    All these keywords.

    JEL classification:

    • 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
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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