Ar(1) Time Series with Approximated Beta Marginal
نویسنده
چکیده
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.
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