A Flexible Model for Time Series of Counts with Overdispersion or Underdispersion, Zero-Inflation and Heavy-Tailedness

Abstract

Time series of counts observed in practice often exhibit overdispersion or underdispersion, zero inflation and even heavy-tailedness (the tail probabilities are non-negligible or decrease very slowly). In this article, we propose a more flexible integer-valued GARCH model based on the generalized Conway–Maxwell–Poisson distribution to model time series of counts, which offers a unified framework to deal with overdispersed or underdispersed, zero-inflated and heavy-tailed time series of counts. This distribution generalizes the Conway–Maxwell–Poisson distribution by adding a parameter, which plays the role of controlling the length of the tail. We investigate basic properties of the proposed model and obtain estimators of parameters via the conditional maximum likelihood method. The numerical results with both simulated and real data confirm the good performance of the proposed model.

Keywords

Conditional maximum likelihood / Heavy-tailedness / Integer-valued GARCH / Overdispersion / Underdispersion / Zero inflation

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Funding

National Natural Science Foundation of China(11871027)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature