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On Edgeworth models for count time series

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  • Weiß, Christian H.

Abstract

Inspired by the Edgeworth–Portnoy model for Gaussian time series, a family of randomized moving window (RMW) and randomized moving sum (RMS) models for stationary count time series is proposed. For the RMW process, we derive Markov properties which, in turn, allow to conclude on a connection of the RMS model to the Hidden-Markov model. This connection is used to develop an efficient scheme for maximum likelihood estimation. Then, we derive marginal and serial moment properties of the RMS process. It commonly exhibits an autoregressive autocorrelation structure, but also forms of a long memory are possible. The latter holds in particular for the proposed extended RMS model, which also satisfies certain Markov properties.

Suggested Citation

  • Weiß, Christian H., 2021. "On Edgeworth models for count time series," Statistics & Probability Letters, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:stapro:v:171:y:2021:i:c:s0167715220302972
    DOI: 10.1016/j.spl.2020.108994
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    References listed on IDEAS

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    1. P. A. Jacobs & P. A. W. Lewis, 1983. "Stationary Discrete Autoregressive‐Moving Average Time Series Generated By Mixtures," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(1), pages 19-36, January.
    2. Portnoy, Stephen, 2019. "Edgeworth’s time series model: Not AR(1) but same covariance structure," Journal of Econometrics, Elsevier, vol. 213(1), pages 281-288.
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