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Marginal analysis of count time series in the presence of missing observations

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  • Simon Nik

    (Helmut Schmidt University)

Abstract

Time series in real-world applications often have missing observations, making typical analytical methods unsuitable. One method for dealing with missing data is the concept of amplitude modulation. While this principle works with any data, here, missing data for unbounded and bounded count time series are investigated, where tailor-made dispersion and skewness statistics are used for model diagnostics. General closed-form asymptotic formulas are derived for such statistics with only weak assumptions on the underlying process. Moreover, closed-form formulas are derived for the popular special cases of Poisson and binomial autoregressive processes, always under the assumption that missingness occurs. The finite-sample performances of the considered asymptotic approximations are analyzed with simulations. The practical application of the corresponding dispersion and skewness tests under missing data is demonstrated with three real data examples.

Suggested Citation

  • Simon Nik, 2024. "Marginal analysis of count time series in the presence of missing observations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(4), pages 1105-1128, December.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:4:d:10.1007_s11749-024-00938-6
    DOI: 10.1007/s11749-024-00938-6
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    References listed on IDEAS

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    1. Fokianos, Konstantinos & Rahbek, Anders & Tjøstheim, Dag, 2009. "Poisson Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1430-1439.
    2. Jonas Andersson & Dimitris Karlis, 2010. "Treating missing values in INAR(1) models: An application to syndromic surveillance data," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 12-19, January.
    3. Schweer, Sebastian & Weiß, Christian H., 2014. "Compound Poisson INAR(1) processes: Stochastic properties and testing for overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 267-284.
    4. Borges, Patrick & Molinares, Fabio Fajardo & Bourguignon, Marcelo, 2016. "A geometric time series model with inflated-parameter Bernoulli counting series," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 264-272.
    5. Christian H. Weiß & Murat Caner Testik, 2015. "On the Phase I analysis for monitoring time-dependent count processes," IISE Transactions, Taylor & Francis Journals, vol. 47(3), pages 294-306, March.
    6. Weiß, Christian H., 2010. "INARCH(1) processes: Higher-order moments and jumps," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1771-1780, December.
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