Geodesic
$AR(1)$ Time Series with Approximated Beta Marginal
Publications de l'Institut Mathématique, _N_S_88 (2010) no. 102, p. 87

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We consider the $AR(1)$ time series model $X_t-\beta X_{t-1}=\xi_t$, $\beta^{-p}n\mathbb{N}mallsetminus\{1\}$, when $X_t$ has Beta distribution $\mathrm{B}(p,q)$, $p\in(0,1]$, $q>1$. 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 $\operatorname{Kum}(p,q)$, $p\in(0,1]$, $q>1$. Using the Laplace transform technique, we prove that for $p=1$ the distribution of the innovation process is uniform discrete. For $p\in(0,1)$, the innovation process has a continuous distribution. We also consider estimation issues of the model.
Classification : 62M10 33C15 66F10 60E10
Keywords: Beta distribution, Kumaraswamy distribution, approximated Beta distribution, Kummer function of the first kind, first order autoregressive model 
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     author = {Bo\v{z}idar V. Popovi\'c},
     title = {$AR(1)$ {Time} {Series} with {Approximated} {Beta} {Marginal}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {87 },
     publisher = {mathdoc},
     volume = {_N_S_88},
     number = {102},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2010_N_S_88_102_a5/}
}
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Božidar V. Popović. $AR(1)$ Time Series with Approximated Beta Marginal. Publications de l'Institut Mathématique, _N_S_88 (2010) no. 102, p. 87 . http://geodesic.mathdoc.fr/item/PIM_2010_N_S_88_102_a5/