On an Absolute Autoregressive Model and Skew Symmetric Distributions
Keywords:Absolute autoregressive process, Estimation of skewness parameter, Singular distributions, Skew-normal distribution, Skew-Cauchy distribution
By exploiting the connection between a popular construction of a well-known skew-normal distribution and an absolute autoregressive process, we show how the stochastic process approach can lead to other skew symmetric distributions, including a skew-Cauchy distribution and some singular distributions. In so doing, we also correct an erroneous skew-Cauchy-distribution in the literature. We discuss the estimation, for dependent data, of the key parameter relating to the skewness.
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