With all such questions the issue is:
"what is the question you are attempting to answer?".
ARIMA regresses on to the trend and variation in the past.
this means that it is making (internally) calls on the amount of "non stationary"...ie trend
and variation (volatility) all built into your setting of the ARIMA rules.
This can provide some very useful information.
However so do other methods.
including simple curve fitting.
To look at volatile data with only one method risks only getting the insight that method offers.
I would recommend using at least too methods, each with different foundations to allow you to say something useful about the trend and the variation.
However what they would be would depend on your objective.
It is easy to be mislead by the method and its character so you are asking the right question it just requires more information to be answered well..
I am sure there are more experienced heads on here that can guide you when you explain your objective.
Dear Murray,
I need to forecast financial data under the irregular patterns...
For high volatility data the data are heteroscedastic i.e. the variance is non-constant. For such data the variance is modelled to give a member of the ARCH family. ARIMA modelling is not the best in this circumstance because it models the mean rather than the variance. Therefore ARCH modelling is preferable with highly volatile data.
So Ette describes the situations that ARIMA can work within.
However, there are some issues on which I would take a different position.
High volatility is a subjective term, that if applied pre analysis might make you feel the non trend components are random. You can have volatility and it be repeating over time.
or you can have random noise, they can look the same before analysis.
Moreover, with regard to trend versus non tending signals in the data, ARIMA is very useful if your objective is to uncover the mean/trending elements, as are many other methods. Beware that sophisticated methods bring both better fit and more complex limitations (in terms of explainability)
However if this is typical information as seen in econometric modelling then often a random walk will predict the future as well as sophisticated econometric models.
ARCH is not a modelling method I use so cannot comment on its suitability or not, however my comments still apply ie what are your objective here?
Dear Ette and Murray, thank you very much for your information....
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