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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.

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

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ 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