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Zero-Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros

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  • Wagner Barreto-Souza

Abstract

type="main" xml:id="jtsa12131-abs-0001"> In this article, we propose a first-order integer-valued autoregressive [INAR(1)] process for dealing with count time series with deflation or inflation of zeros. The proposed process has zero-modified geometric marginals and contains the geometric INAR(1) process as a particular case. The proposed model is also capable of capturing underdispersion and overdispersion, which sometimes are caused by deflation or inflation of zeros. We explore several statistical and mathematical properties of the process, discuss point estimation of the parameters and find the asymptotic distribution of the proposed estimators. We also propose a test based on our model for checking if the count time series considered is deflated or inflated of zeros. Two empirical illustrations are presented in order to show the potential for practice of our zero-modified geometric INAR(1) process. This article contains a Supporting Information.

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  • Wagner Barreto-Souza, 2015. "Zero-Modified Geometric INAR(1) Process for Modelling Count Time Series with Deflation or Inflation of Zeros," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(6), pages 839-852, November.
    • Handle: RePEc:bla:jtsera:v:36:y:2015:i:6:p:839-852
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    File URL: http://hdl.handle.net/10.1111/jtsa.12131
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    References listed on IDEAS

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    1. 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.
    2. Simos Meintanis & Dimitris Karlis, 2014. "Validation tests for the innovation distribution in INAR time series models," Computational Statistics, Springer, vol. 29(5), pages 1221-1241, October.
    3. Mátyás Barczy & Márton Ispány & Gyula Pap & Manuel Scotto & Maria Silva, 2012. "Additive outliers in INAR(1) models," Statistical Papers, Springer, vol. 53(4), pages 935-949, November.
    4. Mansour Aghababaei Jazi & Geoff Jones & Chin-Diew Lai, 2012. "First-order integer valued AR processes with zero inflated poisson innovations," Journal of Time Series Analysis, Wiley Blackwell, vol. 33(6), pages 954-963, November.
    5. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
    6. R. K. Freeland & B. P. M. McCabe, 2004. "Analysis of low count time series data by poisson autoregression," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 701-722, September.
    7. Miroslav M. Ristić & Aleksandar S. Nastić & Ana V. Miletić Ilić, 2013. "A geometric time series model with dependent Bernoulli counting series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 466-476, July.
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    Cited by:

    1. Christian H. Weiß & Annika Homburg & Pedro Puig, 2019. "Testing for zero inflation and overdispersion in INAR(1) models," Statistical Papers, Springer, vol. 60(3), pages 823-848, June.
    2. Wagner Barreto-Souza & Sokol Ndreca & Rodrigo B. Silva & Roger W. C. Silva, 2023. "Non-linear INAR(1) processes under an alternative geometric thinning operator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 695-725, June.
    3. Raju Maiti & Atanu Biswas & Bibhas Chakraborty, 2018. "Modelling of low count heavy tailed time series data consisting large number of zeros and ones," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 407-435, August.
    4. Tobias A. Möller & Christian H. Weiß & Hee-Young Kim & Andrei Sirchenko, 2018. "Modeling Zero Inflation in Count Data Time Series with Bounded Support," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 589-609, June.
    5. Wagner Barreto-Souza, 2019. "Mixed Poisson INAR(1) processes," Statistical Papers, Springer, vol. 60(6), pages 2119-2139, December.

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