Open AccessAR(1) time series with approximated Beta marginal
Author(s) -
Božidar V. Popović
Publication year - 2010
Publication title -
publications de l'institut mathématique
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.