# Is an ARIMA(0,0,0) with non-zero mean equivalent to white noise?

Is an ARIMA with a non-zero mean equivalent to white noise? If not, how should the mean be interpreted?

• Hi: Suppose in a fictitious world there was some guarantee that the interest rate on a stock, $X_t$, per day was 10 basis points continuosly compounded. Then, a model for the log price of that stock could be $log(P_t) = log(P_{t-1}) + .0010 + \epsilon_t$. The error term $\epsilon_t$ can still be thought of as an approximation to white noise. Arima-wise, the price difference could be thought of as ARIMA(0,0,0) with non-zero mean. – mlofton Feb 5 at 13:56
• ok! But is the price difference not an Arima(0,1,0) then? And it still does not answer if an Arima(0,0,0) with non-zero mean is white noise. Or am I missing something in your answer? – endorphinus Feb 6 at 8:25
• Isn't part of your definition of white noise that its mean be zero? If not, then you're using an unusual definition that you need to disclose if we're to be of much help. – whuber Feb 6 at 16:17
• @endorphinus: the link that whuber points to say that white noise requires a zero mean so, technically speaking, it can't be true. thanks to whuber for that knowledge. but, no, in the model I described, the log price difference is arima(0,0,0). the log price is arima(0,1,0). – mlofton Feb 7 at 11:01
• The mean is the expected value of each observation and all observations are uncorrelated. The best forecast of any future value is the mean. – whuber Feb 7 at 14:32