The noise (or residual) series for an ARMA model must be stationary, which means that both the expected values of the series and its autocovariance function are independent of time.

The standard way to check for nonstationarity is to plot the series and its autocorrelation function. You can visually examine a graph of the series over time to see if it has a visible trend or if its variability changes noticeably over time. If the series is nonstationary, its autocorrelation function will usually decay slowly.

Another way of checking for stationarity is to use the stationarity tests described in the section Stationarity Tests.

Most time series are nonstationary and must be transformed to a stationary series before the ARIMA modeling process can proceed. If the series has a nonstationary variance, taking the log of the series can help. You can compute the log values in a DATA step and then analyze the log values with PROC ARIMA.

If the series has a trend over time, seasonality, or some other nonstationary pattern, the usual solution is to take the difference of the series from one period to the next and then analyze this differenced series. Sometimes a series might need to be differenced more than once or differenced at lags greater than one period. (If the trend or seasonal effects are very regular, the introduction of explanatory variables can be an appropriate alternative to differencing.)