engleski

On mixed AR(1) time series model with approximated beta marginal

We consider the mixed AR(1) time series model $X_t$, when $X_t$ has the two-parameter beta distribution $B_2(p, q), p\in (0, 1], q>1$. Special attention is given to the case $p=1$ when the marginal distribution is approximated by the power law distribution closely connected with the two parameter Kumaraswamy distribution . 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 distri-bution. We also consider estimation issues of the model.

Mixed AR(1) model; Power law distribution; Two parameter beta distribution; Kumaraswamy distribution; Kummer function of the first kind; Wright function

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