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Non‐Gaussian autoregressive processes with Tukey g‐and‐h transformations

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  • Yuan Yan
  • Marc G. Genton

Abstract

When performing a time series analysis of continuous data, for example, from climate or environmental problems, the assumption that the process is Gaussian is often violated. Therefore, we introduce two non‐Gaussian autoregressive time series models that are able to fit skewed and heavy‐tailed time series data. Our two models are based on the Tukey g‐and‐h transformation. We discuss parameter estimation, order selection, and forecasting procedures for our models and examine their performances in a simulation study. We demonstrate the usefulness of our models by applying them to two sets of wind speed data.

Suggested Citation

  • Yuan Yan & Marc G. Genton, 2019. "Non‐Gaussian autoregressive processes with Tukey g‐and‐h transformations," Environmetrics, John Wiley & Sons, Ltd., vol. 30(2), March.
    • Handle: RePEc:wly:envmet:v:30:y:2019:i:2:n:e2503
    DOI: 10.1002/env.2503
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    Cited by:

    1. Douissi, Soukaina & Es-Sebaiy, Khalifa & Alshahrani, Fatimah & Viens, Frederi G., 2022. "AR(1) processes driven by second-chaos white noise: Berry–Esséen bounds for quadratic variation and parameter estimation," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 886-918.
    2. Felipe Tagle & Marc G. Genton & Andrew Yip & Suleiman Mostamandi & Georgiy Stenchikov & Stefano Castruccio, 2020. "A high‐resolution bilevel skew‐t stochastic generator for assessing Saudi Arabia's wind energy resources," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.

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