AR(1) time series with approximated Beta marginal | Zendy

Božidar V. Popović | Zendy

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AR(1) time series with approximated Beta marginal

Author(s) -

Božidar V. Popović

Publication year - 2010

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1002087p

Subject(s) - mathematics , laplace transform , distribution (mathematics) , series (stratigraphy) , beta distribution , generalized beta distribution , beta (programming language) , marginal distribution , laplace distribution , combinatorics , mathematical analysis , statistics , probability distribution , distribution fitting , random variable , computer science , paleontology , biology , programming language

We consider the AR(1) time series model Xt ? ?Xt?1 = ?t, ??p ? N \ {1}, when Xt has Beta distribution B(p, q), p ? (0, 1], q > 1. Special attention is given to the case p = 1 when the marginal distribution is approximated by the power law distribution closely connected with the Kumaraswamy distribution Kum(p, q), p ? (0, 1], q > 1. Using the Laplace transform technique, we prove that for p = 1 the distribution of the innovation process is uniform discrete. For p ? (0, 1), the innovation process has a continuous distribution. We also consider estimation issues of the model.

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