This procedure estimates nonseasonal and seasonal univariate ARIMA (Autoregressive Integrated Moving Average) models (also known as “Box-Jenkins” models) with or without fixed regressor variables. The procedure produces maximum-likelihood estimates and can process time series with missing observations.

An exampleEdit

You are in charge of quality control at a manufacturing plant and need to know if and when random fluctuations in product quality exceed their usual acceptable levels. You’ve tried modeling product quality scores with an exponential smoothing model but found—presumably because of the highly erratic nature of the data—that the model does little more than predict the overall mean and hence is of little use. ARIMA models are well suited for describing complex time series. After building an appropriate ARIMA model, you can plot the product quality scores along with the upper and lower confidence intervals produced by the model. Scores that fall outside of the confidence intervals may indicate a true decline in product quality.


For each iteration: seasonal and nonseasonal lags (autoregressive and moving average), regression coefficients, adjusted sum of squares, and Marquardt constant. For the final maximum-likelihood parameter estimates: residual sum of squares, adjusted residual sum of squares, residual variance, model standard error, log-likelihood, Akaike’s information criterion, Schwartz’s Bayesian criterion, regression statistics, correlation matrix, and covariance matrix.


The dependent variable and any independent variables should be numeric.


The series should have a constant mean over time.