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I have a time series of a stock return over more than 2 years. It's stationary (Augmented Dickey-Fuller test is significant). The plot looks like this: enter image description here

The ACF and PACF look like this:

enter image description here

enter image description here

I think these properties suggest a specification of ARIMA(1,0,0) or ARIMA(1,0,1) although I think the former is likely more suitable. I divide the data into train and test sets by the ratio of 75/25 and estimate ARIMA(1.0.0) on the train data. However, the forecast results (on the train data, over the period of the test data) seem odd:

enter image description here

The forecast values have some variations for about the first week, but after that it's all homogeneous (values and confidence intervals).

What may be the cause of this problem? Is the ARIMA model likely improperly specified, e.g., a missing time trend or drift component? And will incorporating other independent variables be the next consideration?

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    $\begingroup$ What aspect(s) of the results "seem odd"? At first blush, your data are close to a form of white noise, for which the best forecast indeed is the mean. $\endgroup$ – whuber Nov 20 '19 at 18:37
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    $\begingroup$ Seems that it might be correct at least based on what you have showed us. $\endgroup$ – Harto Saarinen Nov 20 '19 at 19:26
  • $\begingroup$ By odd I mean I haven't seen such a forecast result, but that's more to say I haven't seen much. I read some references and find out that the ARIMA models are not suitable for this type of data (asset returns, which are most of the time stationary or even white noise). A volatility model is better. $\endgroup$ – NonSleeper Nov 21 '19 at 12:00

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