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I'm fitting a stock price time series data to ARIMA model and I have a question about the assumption.

Is it that ARIMA only applies to stationary data? The ACF and PACF of the data (and the logged return too)both show it's non-stationary. So can I still fit ARIMA to it?

The residuals of the fitted model actually shows it works quite and well. But I worry about the assumption.

Thanks!!

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  • $\begingroup$ By the way, I use the command auto.arima, does it mean that I don't have to care about the stationarity because it will automatically compute the best differencing lag? $\endgroup$ – Shijie Wang Dec 9 '14 at 5:21
  • $\begingroup$ From the documentation (cran.r-project.org/web/packages/forecast/forecast.pdf), if the parameter of the differencing is missing then auto.arima will choose the optimal one based on the statistical test KPSS. $\endgroup$ – Arrigo Dec 9 '14 at 7:52
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What you should do:

  • read a general introduction to time series analysis before you apply these methods otherwise you will misinterpret the results.
  • time series are assumed to be covariance stationary. This is in short that their mean is the same for all points in time and that the covariance between two observations only depends on the lag.
  • the "I" in ARIMA means that time series could be integrated. This means that you have to difference them in order to get something stationary.

You can start to read in this excellent online text book by Rob Hyndman and George Athana­sopou­los.

In the case of stock prices you should look at log-returns, which can usually be assumed to be a stationary time series.

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