I am reading a book on time series. To make a non-stationary series stationary, sometimes we need to difference the series. When it comes to finance, prices are non-stationary. Many authors fit ARMA models to return time series but returns are either log-return or % return which is different to simple differencing. I had a look at the ACF of % return and a simple diff and they are different.

My question is, is it valid to use percent or log return rather then diff to make a price series stationary?

  • $\begingroup$ When plotting the ACF you're investigating the temporal behaviour of the return-process, and then it is recommended to use log-returns, as opposed to % returns. In general, questioning whether to use arithmetic/% returns or log-returns have been addressed here. Also, be aware that simply differencing the price process makes the differenced process non-comparable across asset dimension, which is one of the reasons we downscale the process with the previous price, as done with % returns. $\endgroup$
    – Pleb
    Apr 4, 2021 at 15:29
  • $\begingroup$ With stocks diff of prices is not a good idea because when price is 10 a diff of 1 has very different meaning than when price is 50. (Stock prices change a lot over the long run). That is why people prefer to use % or log returns. $\endgroup$
    – nbbo2
    Apr 4, 2021 at 15:29
  • $\begingroup$ You can apply fractional differentiation to convert an input series to a stationary form: quant.stackexchange.com/questions/58298/… $\endgroup$ Apr 4, 2021 at 18:23


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