The ARIMA procedure provides the identification, parameter estimation, and forecasting of autoregressive integrated moving-average (Box-Jenkins) models, seasonal ARIMA models, transfer function models, and intervention models. The ARIMA procedure includes the following features:

• complete ARIMA (Box-Jenkins) modeling with no limits on the order of autoregressive or moving-average processes

• model identification diagnostics including the following:

  • autocorrelation function

  • partial autocorrelation function

  • inverse autocorrelation function

  • cross-correlation function

  • extended sample autocorrelation function

  • minimum information criterion for model identification

  • squared canonical correlations

• stationarity tests

• outlier detection

• intervention analysis

• regression with ARMA errors

• transfer function modeling with fully general rational transfer functions

• seasonal ARIMA models

• ARIMA model-based interpolation of missing values

• several parameter estimation methods including the following:

  • exact maximum likelihood

  • conditional least squares

  • exact nonlinear unconditional least squares (ELS or ULS)

• prewhitening transformations

• forecasts and confidence limits for all models

• forecasting tied to parameter estimation methods: finite memory forecasts for models estimated by maximum likelihood or exact nonlinear least squares methods and infinite memory forecasts for models estimated by conditional least squares

• diagnostic statistics to help judge the adequacy of the model including the following:

  • Akaike’s information criterion (AIC)

  • Schwarz’s Bayesian criterion (SBC or BIC)

  • Box-Ljung chi-square test statistics for white-noise residuals

  • autocorrelation function of residuals

  • partial autocorrelation function of residuals

  • inverse autocorrelation function of residuals

  • automatic outlier detection