Geodesic
A new uniform Ar(1) time series model (nuar(1))
Publications de l'Institut Mathématique, _N_S_68 (2000) no. 82, p. 145

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We present a new first-order autoregressive time series model (so-called NUAR(1) model) for continuous uniform $(0,1)$ variables, given by $ X_n=\begin{cases} \alpha X_{n-1}, \text{ w.p. } \alpha,\\ \beta X_{n-1}+\varepsilon_n, \text{ w.p. } 1-\alpha, \end{cases} $ where $0\alpha,\beta1$, $(1-\alpha)/\beta\in\{1,2,\dots\}$ and $\{\varepsilon_n\}$ is the innovation sequence of independent and identically distributed random variables, such that each $X_n$ has continuous uniform $(0,1)$ distribution. The distribution of the innovation sequence and autoregressive structure of NUAR(1) model are discussed. It is shown that this model is partially time-reversible if the parameters are equal. We give also the estimates of the parameters of the model.
Classification : 62M10
Keywords: Autoregressive process, continous uniform (0,1) distribution, time series, estimation, random coefficients, residuals 
@article{PIM_2000_N_S_68_82_a15,
     author = {Miroslav M. Risti\'c and Biljana \v{C}. Popovi\'c},
     title = {A new uniform {Ar(1)} time series model (nuar(1))},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {145 },
     publisher = {mathdoc},
     volume = {_N_S_68},
     number = {82},
     year = {2000},
     zbl = {1087.62102},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_2000_N_S_68_82_a15/}
}
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Miroslav M. Ristić; Biljana Č. Popović. A new uniform Ar(1) time series model (nuar(1)). Publications de l'Institut Mathématique, _N_S_68 (2000) no. 82, p. 145 . http://geodesic.mathdoc.fr/item/PIM_2000_N_S_68_82_a15/