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A Note On The Distributions Of Non‐Linear Autoregressive Stochastic Models

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  • J. Pemberton
  • H. Tong

Abstract

. It is shown that an ergodic stationary non‐linear autoregressive stochastic process, perturbed by a white noise process with symmetric distributions, has symmetric stationary distributions if and only if the regression function is skew‐symmetric. The implications of this observation are discussed.

Suggested Citation

  • J. Pemberton & H. Tong, 1981. "A Note On The Distributions Of Non‐Linear Autoregressive Stochastic Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 2(1), pages 49-52, January.
    • Handle: RePEc:bla:jtsera:v:2:y:1981:i:1:p:49-52
    DOI: 10.1111/j.1467-9892.1981.tb00310.x
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    Cited by:

    1. Zacharias Psaradakis & Marián Vávra, 2022. "Using Triples to Assess Symmetry Under Weak Dependence," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1538-1551, October.
    2. Karapanagiotidis, Paul, 2013. "Empirical evidence for nonlinearity and irreversibility of commodity futures prices," MPRA Paper 56801, University Library of Munich, Germany.

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