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The title pretty much explains it already:

If I have enough data points that I can plot my entire forecast density and it ends up looking like this, does it mean that it is heteroscedastic and I should be using GARCH and volatility modeling and not just straight up ARIMA or Holt-Winters?

enter image description here

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  • $\begingroup$ Are the data on which the graph is based a time series? If they are, you could look at the development of volatility over time, and there are more informative diagnostics for that than kernel density (which ignores the time structure), e.g. ACF and PACF of the squared series. Otherwise I doubt you need to consider GARCH or volatility at all. $\endgroup$ – Richard Hardy Sep 13 '19 at 15:07
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This might be just a difference in the expected value for at least two subsets suggesting a possible level or trend change. Only your data knows for sure . Post your original data and "I will ask it" to disclose the truth.

Be like a doctor .. try and not do damage to your data by applying unwanted and unneeded procedures.. When investigating issues like you have , look for possible non-constancy in the expected value ... thus Intervention Detection might be useful to properly segment/classify your data.

If that is of little help .. consider evaluating change points in model parameters over time to deal with non-constancy in either the expected value or the estimated variance . The estimated error variance can change over tine suggesting either a power transform or Weighted Least Squares.

Finally if none of the above remedies/analyses help then you might want to apply more potentially complex procedures such as ARCH or GARCH which expressly deal with the idea that the error variance is best handled with an arima model as it is a stochastic sequence.

The KISS strategy should be adhered to by applying minimally invasive procedures/medecines.

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