I have 9500 closing prices of s&p500. I took daily return of the prices dailyreturn and then log return of the prices logreturn=log(1+dailyreturn). Now I checked the data using augmented Dickey-Fuller test and it shows unit root.

Even Phillip-peron test shows the same. Normally asset log returns should not have a unit root. So what am I doing wrong? If all is correct can we use this series for an arma-garch or arma-gjrGarch model.


closed as unclear what you're asking by Sycorax, mkt, kjetil b halvorsen, COOLSerdash, Carl Dec 6 '18 at 5:14

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  • $\begingroup$ What would you do if you found a unit root on any other data set? $\endgroup$ – Sycorax Nov 12 '18 at 17:27
  • $\begingroup$ hi sycorax. for removing unit root normally i would take again a difference or use an arima model. i differenced the series. still the adf test showed unit root. i took another difference making it I(2) but still adf test shows unit root. i did seasonal differencing... i de-trended the data but no change in the test result. i'am testing adf test with AR and AR with drift and lags 1 to 40 lags (lags chosen as per shchwert criterion of maximum lag.) i don't know what do i have to do to remove the unit root. in tsay's book most models use log returns without any modification. help in this matter. $\endgroup$ – azim sikandar Nov 13 '18 at 4:29
  • $\begingroup$ Could you add a reproducible example ? $\endgroup$ – Juho Kokkala Dec 1 '18 at 10:34
  • $\begingroup$ From this, "The daily return measures the dollar change in a stock’s price as a percentage of the previous day’s closing price." However, when this is calculated on the same site, rather than a percentage change, the dollar difference of a stock is shown. Which definition is being used will modify any answer to the question. Thus, to clarify, how this is calculated should be given in the question. $\endgroup$ – Carl Dec 6 '18 at 5:14