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ARIMA (Box-Jenkins) and ARIMAX (Box-Tiao) Modeling and Forecasting

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

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