On an Absolute Autoregressive Model and Skew Symmetric Distributions


  • Dong Li Tsinghua University
  • Howell Tong University of Electronic Science and Technology of China




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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How to Cite

Li, D., & Tong, H. (2020). On an Absolute Autoregressive Model and Skew Symmetric Distributions. Statistica, 80(2), 177–198. https://doi.org/10.6092/issn.1973-2201/10420