## Članak

 članak: 1 od 1
Publications de l'Institut Mathematique
2010, vol. 88, br. 102, str. 87-98
neklasifikovan
doi:10.2298/PIM1002087P

AR(1) time series with approximated Beta marginal
(naslov ne postoji na srpskom)
Statistical Office of the Republic of Serbia, Belgrade

### Sažetak

(ne postoji na srpskom)
We consider the AR(1) time series model Xt - βXt-1 = ξt, β-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.

### Ključne reči

Beta distribution; Kumaraswamy distribution; approximated Beta distribution; Kummer function of the first kind; first order autoregressive model

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