Creating an ARIMA Model | Teradata Vantage - Creating an ARIMA Model - Teradata Vantage

An ARIMA (Autoregressive Integrated Moving Average) model is based on the seasonal portion, the non-seasonal portion, and number of periods per season. The values are the following:

• p: The order of the auto-regressive component.
• d: The degree of non-seasonal order differencing.
• q: The order of the moving-average component.
• s: The period.
• P: The degree of seasonal auto-regressive component.
• D: The seasonal differencing.
• Q: The degree of seasonal moving-average component.
• S: The number of periods per season.

The following procedure is an example of how to create an ARIMA model:

1. Determine if a series is stationary by creating a composite plot using TD_PLOT with the following:
   • Time series
   • Auto-correlation results (TD_ACF)
   • Partial auto-correlation results (TD_PACF)
   • Spectrum analysis (line spectrum (TD_LINESPEC) or power spectrum (TD_POWERSPEC)) results
2. [Series series is non-stationary] Use the following tasks to make the series stationary:
   • Remove unit roots, such as TD_SEASONALNORMALIZE or TD_DIFF.
   • Remove trends, such as TD_DIFF or TD_LINEAR_REGR with TD_BINARYSERIESOP.
   • Remove periodicities, such as TD_GENSERIES4SINUSOIDS with TD_BINARYSERIESOP.
   • Remove heteroscedastic variance with TD_POWERTRANSFORM.
3. Use TD_ACF and TD_PACF results to perform model identification and determine the best model candidates using the Box and Jenkins ARIMA modeling approach.
4. Use TD_ARIMAESTIMATE with each model candidate, and store the associated goodness-of-fit metrics in a table.
5. Perform statistical tests on the ARIMA estimate residuals for each candidate, and look for signs of serial correlation, periodicities, and heteroscedastic variance. Store the results in a table.
6. Examine the candidates, and eliminate ones which are worth pursuing past the estimate phase.
7. Use TD_ARIMAVALIDATE on each remaining candidate, and store the goodness-of-fit and model selection metrics in a table.
8. Perform statistical tests on the ARIMA estimate residuals for each candidate, and determine if the residuals can be classified as being white noise (residual series with zero mean, no periodicities, no serial correlation, and homoscedastic variance). Store the results in a table.
9. Examine the goodness-of-fit metrics, model selection metrics, and statistical results, and select the best models for forecasting.
10. Forecast using the selected models.