Enroute to its tour de force Autobox will evaluate numerous possible models/parameters that have been suggested by the data itself. In practice, a realistic limit is set on the maximum number of model form iterations. The exact specifics of each tentative model is not pre-set thus the power of Autobox emerges. The kind and form of the tentative models may never before have been tried. Each dataset speaks for itself and suggests the iterative process.

The Final Model could be as simple as:

1. A simple trend model or a simple ordinary least squares model.
2. An exponential smoothing model.
3. A simple weighted average where the weights are either equal or unequal.
4. A Cochrane-Orcutt or ordinary least squares with a first order fixup.
5. A simple ordinary least squares model in differences containing some needed lags.
6. A spline-like set of local trends superimposed with an arbitrary ARIMA model and perhaps a pulse or two.
   

The number of possible final models that Autobox could find is infinite and only discoverable via a true expert system like Autobox. A final model may require one or more of the following

Seasonal Structures:

1. Seasonal ARIMA structure where the prediction depends on some previous
   reading S periods ago.
2. Seasonal structure via a complete set of seasonal dummies reflecting a fixed response based upon the particular period.
3. Seasonal structure via a partial set of seasonal dummies reflecting a fixed response based upon the particular period.
   

The Final Model will satisfy both:

1. Necessity tests that guarantee the estimated coefficient is statistically significant.
2. Sufficiency tests that guarantee that the error process is:
   
• unpredictable on itself.
  
• not predictable from the set of causals.
• has a constant mean of zero.

The Final model will contain one or more of the following structures:

1. CAUSAL with correct lead/lag specification.
2. MEMORY with correct "autoregressive memory".
3. DUMMY with correct pulses, level shifts or spline time trends

Typical Forecasts

1. Daily Demand For Cash at an ATM Machine view graph
2. Monthly New Prescriptions for Diabetes view graph
3. Monthly Outbreak of Dengue Disease view graph
4. Weekly Sales of General Mills Frozen Biscuits view graph
5. Detecting a Lead Effect view graph
6. Daily Beer Sales for one Store-SKU view graph
7. Changing Times view graph
8. More Changing Times view graph
9. No Trend or Seasonality view graph
10. No Memory ..Just a Level Shift view graph
11. Czech GDP reflects democratization view graph