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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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    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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