# white noise problem of ARIMA model

I 've used ARMA model for forecasting stock price, but the raw input data(original stock price) is not stationary, so I use the first order difference of raw data, but the acf and pacf figure shows the first order differential data is the white noise.Doses that mean I should not use ARIMA model to predict the stock price?

• Why doesn't that indicate that the first difference model is acceptable? – Michael Chernick May 11 '18 at 13:20

"Doses that mean I should not use ARIMA model to predict the stock [returns]?"

No, it means if you do, then you should pick an ARIMA(0,1,0) (for the log price). Assuming that model is true, your predictions will depend heavily on the mean or intercept parameter.

On the other hand, if you do believe that stock returns are "more predictable" then you might look to models that are not in the ARIMA family.

• I could be missing something, but I don't understand why a model with no parameters would be useful...or why you introduced the idea of logging. – rolando2 May 11 '18 at 17:31
• An ARMA(0,0) has $2>0$ parameters. And you take the log because the change in the log price is the same as the continuously compounded return. – Taylor May 11 '18 at 18:01

Stock returns will generally behave like white noise (think about why...) However, volatilities usually do not. Thats why we put so much effort into modeling volatilities.

Consider doing an acf plot of the squared returns or of the absolute value of returns - I expect there you will find evidence of what we call volatility clustering i i.e returns of large magnitude tend to be followed by returns with large magnitude...

To answer your question: you probably should not try to use ARIMA models to forecast stock returns - but that does not mean you should give up on ARIMA or modeling altogether.