## IntroductionEdit

This procedure estimates nonseasonal and seasonal univariate ARIMA
(**A**uto**r**egressive **I**ntegrated **M**oving **A**verage) 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.

## IllustrationEdit

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.

## DataEdit

The dependent variable and any independent variables should be numeric.

## AssumptionEdit

The series should have a constant mean over time.