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A skew INAR(1) process on $${\mathbb {Z}}$$ Z

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  • Wagner Barreto-Souza
  • Marcelo Bourguignon

Abstract

Integer-valued time series models have been a recurrent theme considered in many papers in the last three decades, but only a few of them have dealt with models on $${\mathbb {Z}}$$ Z (that is, including both negative and positive integers). Our aim in this paper is to introduce a first-order, integer-valued autoregressive process on $${\mathbb {Z}}$$ Z with skew discrete Laplace marginals (Kozubowski and Inusah, Ann Inst Stat Math 58:555–571, 2006 ). For this, we define a new operator that acts on two independent latent processes, similarly as made by Freeland (Adv Stat Anal 94:217–229, 2010 ). We derive some joint and conditional basic properties of the proposed process such as characteristic function, moments, higher-order moments and jumps. Estimators for the parameters of our model are proposed and their asymptotic normality is established. We run a Monte Carlo simulation to evaluate the finite-sample performance of these estimators. In order to illustrate the potential for practice of our process we apply it to a real data set about stock market. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Wagner Barreto-Souza & Marcelo Bourguignon, 2015. "A skew INAR(1) process on $${\mathbb {Z}}$$ Z," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(2), pages 189-208, April.
    • Handle: RePEc:spr:alstar:v:99:y:2015:i:2:p:189-208
    DOI: 10.1007/s10182-014-0236-2
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    References listed on IDEAS

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    1. Hee-Young Kim & Yousung Park, 2008. "A non-stationary integer-valued autoregressive model," Statistical Papers, Springer, vol. 49(3), pages 485-502, July.
    2. Christian Weiß, 2008. "Thinning operations for modeling time series of counts—a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(3), pages 319-341, August.
    3. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    4. Tomasz Kozubowski & Seidu Inusah, 2006. "A Skew Laplace Distribution on Integers," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 555-571, September.
    5. Tjøstheim, Dag, 1986. "Estimation in nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 251-273, February.
    6. R. Freeland, 2010. "True integer value time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(3), pages 217-229, September.
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    Cited by:

    1. Wagner Barreto-Souza, 2019. "Mixed Poisson INAR(1) processes," Statistical Papers, Springer, vol. 60(6), pages 2119-2139, December.

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