Is there an equivalent of ARMA for rank correlation?

I am looking at extremely non linear data for which the ARMA/ARIMA models do not work well. Though, I see some autocorrelation, and I suspect to have better results for non linear autocorrelation.

1/ is there an equivalent of the PACF for rank correlation? (in R?)

2/ is there an equivalent of ARMA model for non linear / rank correlation (in R?)

Answer

Answering with the comment by mpiktas, as it is IMHO a good answer.

The usual answer to non-linearity in context of ARMA models is ARCH/GARCH models. For your first question, it is probably possible to construct PACF using rank correlation concepts, it will boil down probably to independent component analysis. As for the second the answer is probably no, but for this Asymptotic normality of the quasi maximum likelihood estimator for multidimensional causal process by Bardet and Wintenberger might be of interest, since it involves non-linear specification and ARMA is a subclass of it.

Attribution
Source : Link , Question Author : RockScience , Answer Author : Martin Modrák

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