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A NOTE ON THE DISTRIBUTIONS OF NON‐LINEAR AUTOREGRESSIVE STOCHASTIC MODELS
Author(s) -
Pemberton J.,
Tong H.
Publication year - 1981
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.1981.tb00310.x
Subject(s) - autoregressive model , mathematics , star model , white noise , skew , ergodic theory , stable process , stationary ergodic process , stationary distribution , stationary process , stochastic process , statistical physics , mathematical analysis , econometrics , statistics , autoregressive integrated moving average , time series , markov chain , physics , invariant measure , astronomy
. 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.