Does applying ARMA-GARCH require stationarity?

I am going to use the ARMA-GARCH model for financial time series and was wondering whether the series should be stationary before applying the said model.
I know to apply ARMA model the series should be stationary, however I’m not sure for ARMA-GARCH since I’m including GARCH errors which imply volatility clustering and non-constant variance and hence non-stationary series no matter what transformation I do.

Are financial time series usually stationary or non-stationary?
I tried applying ADF test to a few volatile series and got p-value<0.01 which seems to indicate stationarity but the principle of volatile series itself tells us that the series isn’t stationary.

Can somebody clear that up for me?I’m getting really confused

Answer

Copying from the abstract of Engle’s original paper:
“These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance”.

Continuing with the references, as the author who introduced GARCH shows (Bollerslev, Tim (1986). “Generalized Autoregressive Conditional Heteroskedasticity“, Journal of Econometrics, 31:307-327)
for the GARCH(1,1) process, it suffices that $\alpha_1 + \beta_1 <1$ for 2nd-order stationarity.

Stationarity (the one needed for estimation procedures), is defined relative to the unconditional distribution and moments.

ADDENDUM
To summarize here discussion in the comments, the GARCH modeling approach is an ingenious way to model suspected heteroskedasticity over time, i.e. of some form of heterogeneity of the process (which would render the process non-stationary) as an observed feature that comes from the existence of memory of the process, in essence inducing stationarity at the unconditional level.

In other words, we took our two “great opponents” in stochastic process analysis (heterogeneity and memory), and used the one to neutralize the other -and this is indeed an inspired strategy.

Attribution
Source : Link , Question Author : ankc , Answer Author : Alecos Papadopoulos

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