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On the existence of some skew normal stationary processes

Author

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  • Marco Minozzo

    (Department of Economics (University of Verona))

Abstract

Recently some authors have introduced in the literature stationary stochastic processes, in the time and in the spatial domains, whose finite-dimensional marginal distributions are multivariate skew-normal. Here we show with a counter-example that the characterizations of these processes are not valid and so that these processes do not exist. Moreover, more generally, we also show that it is very unlikely that there might exist stationarity stochastic processes having all their finite-dimensional marginal distributions to be multivariate skew-normal. Besides, we point our attention to some valid constructions of stationary stochastic processes which can be used to model skewed data.

Suggested Citation

  • Marco Minozzo, 2011. "On the existence of some skew normal stationary processes," Working Papers 20/2011, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:20/2011
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    References listed on IDEAS

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    1. Reinaldo B. Arellano‐Valle & Adelchi Azzalini, 2006. "On the Unification of Families of Skew‐normal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 561-574, September.
    2. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    3. Hosseini, Fatemeh & Eidsvik, Jo & Mohammadzadeh, Mohsen, 2011. "Approximate Bayesian inference in spatial GLMM with skew normal latent variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1791-1806, April.
    4. Arjun Gupta & John Chen, 2004. "A class of multivariate skew-normal models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 305-315, June.
    5. T. R. A. Corns & S. E. Satchell, 2007. "Skew Brownian Motion and Pricing European Options," The European Journal of Finance, Taylor & Francis Journals, vol. 13(6), pages 523-544.
    6. Adelchi Azzalini, 2005. "The Skew‐normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(2), pages 159-188, June.
    7. Arellano-Valle, R. B. & del Pino, G. & San Martín, E., 2002. "Definition and probabilistic properties of skew-distributions," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 111-121, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Marco Minozzo & Luca Bagnato, 2021. "A unified skew‐normal geostatistical factor model," Environmetrics, John Wiley & Sons, Ltd., vol. 32(4), June.
    2. M. Alodat & M. AL-Rawwash, 2014. "The extended skew Gaussian process for regression," METRON, Springer;Sapienza Università di Roma, vol. 72(3), pages 317-330, October.
    3. Stéphane Lhuissier, 2019. "Bayesian Inference for Markov-switching Skewed Autoregressive Models," Working papers 726, Banque de France.
    4. Chunsheng Ma, 2013. "Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 941-958, October.
    5. Marco Minozzo & Clarissa Ferrari, 2012. "Monte Carlo likelihood inference in multivariate model-based geostatistics," Working Papers 33/2012, University of Verona, Department of Economics.
    6. Jiangyan Wang & Miao Yang & Anandamayee Majumdar, 2018. "Comparative study and sensitivity analysis of skewed spatial processes," Computational Statistics, Springer, vol. 33(1), pages 75-98, March.

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    More about this item

    Keywords

    multivariate skew-normal distribution; autocorrelation function; spatial process; stationary process; geostatistics; generalized linear mixed model;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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