Abstract
We consider the mixed AR(1) time series model
for −1 < β p ≤ 0 ≤ α p < 1 and α p − β p > 0 when X t has the two-parameter beta distribution B2(p, q) with parameters q > 1 and \({p \in \mathcal P(u,v)}\), where
Special attention is given to the case p = 1. Using Laplace transform and suitable approximation procedures, we prove that the distribution of innovation sequence for p = 1 can be approximated by the uniform discrete distribution and that for \({p \in \mathcal P(u,v)}\) can be approximated by a continuous distribution. We also consider estimation issues of the model.
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Popović, B.V., Nadarajah, S. & Ristić, M.M. A new non-linear AR(1) time series model having approximate beta marginals. Metrika 76, 71–92 (2013). https://doi.org/10.1007/s00184-011-0376-2
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DOI: https://doi.org/10.1007/s00184-011-0376-2