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Parameter estimation and diagnostic tests for INMA(1) processes

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  • Boris Aleksandrov

    (Helmut Schmidt University)

  • Christian H. Weiß

    (Helmut Schmidt University)

Abstract

The INMA(1) model, an integer-valued counterpart to the usual moving-average model of order 1, gained recently importance for insurance applications. After a comprehensive discussion of stochastic properties of the INMA(1) model, we develop diagnostic tests regarding the marginal distribution (overdispersion, zero inflation) and the autocorrelation structure. We also derive formulae for correcting the bias of point estimators and for constructing joint confidence regions. These inferential approaches rely on asymptotic properties, the finite-sample performance of which is investigated with simulations. A real-data example illustrates the application of the novel diagnostic tools.

Suggested Citation

  • Boris Aleksandrov & Christian H. Weiß, 2020. "Parameter estimation and diagnostic tests for INMA(1) processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 196-232, March.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:1:d:10.1007_s11749-019-00653-7
    DOI: 10.1007/s11749-019-00653-7
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    References listed on IDEAS

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    1. Brännäs, Kurt & Quoreshi, Shahiduzzaman, 2004. "Integer-Valued Moving Average Modelling of the Number of Transactions in Stocks," Umeå Economic Studies 637, Umeå University, Department of Economics.
    2. 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.
    3. Cossette, Hélène & Marceau, Étienne & Toureille, Florent, 2011. "Risk models based on time series for count random variables," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 19-28, January.
    4. Andreia Hall & Manuel Scotto & João Cruz, 2010. "Extremes of integer-valued moving average sequences," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 359-374, August.
    5. Cossette, Hélène & Marceau, Etienne & Maume-Deschamps, Véronique, 2010. "Discrete-Time Risk Models Based on Time Series for Count Random Variables," ASTIN Bulletin, Cambridge University Press, vol. 40(1), pages 123-150, May.
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    Cited by:

    1. Boris Aleksandrov & Christian H. Weiß & Carsten Jentsch, 2022. "Goodness‐of‐fit tests for Poisson count time series based on the Stein–Chen identity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 35-64, February.

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