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Mixed AR(1) Time Series Models with Marginals Having Approximated Beta Distribution

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Advances in Time Series Analysis and Forecasting (ITISE 2016)

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Abstract

Two different mixed first order AR(1) time series models are investigated when the marginal distribution is a two-parameter Beta \(\mathrm{B}_2(p,q)\). The asymptotics of Laplace transform for marginal distribution for large values of the argument shows a way to define novel mixed time-series models which marginals we call asymptotic Beta. The new model’s innovation sequences distributions are obtained using Laplace transform approximation techniques. Finally, the case of generalized functional Beta \(\mathrm{B}_2(G)\) distribution’s use is discussed as a new parent distribution. The chapter ends with an exhaustive references list.

Dedicated to Professor Jovan Mališić to his 80th birthday anniversary.

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Notes

  1. 1.

    The LT of a PDF actually coincides with the moment generating function \(\mathsf M_X\) of the input rv X with negative parameter \(\mathsf E\, \mathrm{e}^{-sX} \equiv \mathsf M_X(-s)\).

  2. 2.

    Updated extensions of Erdélyi’s theorem are obtained also in [24] and [39].

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Authors and Affiliations

  1. Applied Mathematics Institute, Óbuda University, Bécsi út 96/b, Budapest, 1034, Hungary

    Tibor K. Pogány

  2. Faculty of Maritime Studies, University of Rijeka, Studentska 2, 51000, Rijeka, Croatia

    Tibor K. Pogány

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  1. Tibor K. Pogány
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Correspondence to Tibor K. Pogány .

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Editors and Affiliations

  1. CITIC-UGR, University of Granada, Granada, Spain

    Ignacio Rojas

  2. CITIC-UGR, University of Granada, Granada, Spain

    Héctor Pomares

  3. CITIC-UGR, University of Granada, Granada, Spain

    Olga Valenzuela

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Pogány, T.K. (2017). Mixed AR(1) Time Series Models with Marginals Having Approximated Beta Distribution. In: Rojas, I., Pomares, H., Valenzuela, O. (eds) Advances in Time Series Analysis and Forecasting. ITISE 2016. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-55789-2_12

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