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.