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While I am new to forecasting, I have spent a significant amount of time looking into the stationarity requirement of forecasting models such as linear regression, linear regression with ARIMA errors, and the various model families encapsulated with ARIMA.

What's not clear to me is why it appears the more common theme (from my research at least) is to apply the forecasting model of choice to timeseries of (log) returns. There doesn't seem to be much support for forecasting differenced timeseries.

And I haven't found any resource that specifically talks about the advantages of using returns over differenced levels.

My questions:

If the differenced timeseries is stationary, why is it less correct to use it?

What are the possible reasons a forecaster must use the returns timeseries (assume stationary) when the differenced timeseries is stationary too?

My question is on univariate timeseries. But I suppose this applies to multivariate timeseries as well.

Any insight/comments appreciated.

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  • $\begingroup$ Logging and differencing deal with different types of non-stationarity. Logging, sometimes, deals with change of variance over time. Its often recommended you log the data to deal with this issue before you difference. As far as I know differencing does not eliminate this problem. Some economic analysis log for theoretical reasons - but that is a different issue. $\endgroup$ – user54285 Aug 11 '20 at 21:21

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