A NEGATIVE BINOMIAL AUTOREGRESSION WITH A LINEAR CONDITIONAL VARIANCE-TO-MEAN FUNCTION

Bader S. Almohaimeed ()
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Bader S. Almohaimeed: Department of Mathematics, College of Science, Qassim University, P. O. Box 6644, Buraydah 51452, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-14

Abstract: A general integer-valued time-series model with a conditional variance proportional to the conditional mean is proposed. Specifically, the conditional distribution is a Poisson mixture with a dependent mixing sequence, which results in a negative binomial distribution with a linear conditional variance-to-mean relationship. In addition, the conditional mean is specified as a general parametric function of past observations. We first propose stationarity, ergodicity, and finite moment conditions for the model. Furthermore, the parameters are estimated using the Poisson quasi-maximum likelihood estimate, whose asymptotic properties are studied under weak conditions. Illustrations of the proposed methodology on simulated and actual time series of counts are given.

Keywords: Quasi-Poisson Autoregression; Mixed Poisson Autoregression; Negative Binomial 1 INGARCH; Ergodicity; Poisson Quasi-maximum Likelihood Estimate (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402393

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