QUESTION:

By the way, we are mightily impressed by the performance of Autobox over Regression (not that we would

have used regression on the whole series). If we only use the last 18 months data, we get around 85% R

-squared.

ANSWER:

NOT TO DAMPEN YOUR ENTHUSIASM ......BUT By its very nature outlier detection, dummy variables

representing either one time only events, permanent events ( level shift ), seasonally repetitive events

( seasonal dummy ) and local time trends BY DEFINITION increase the R-SQUARED. The improvement

in R-SQUARED does not necessarily transfer to improved forecasting accuracy on a one-to- one basis.

What I am trying to point out is that the elimination of background, read omitted variables, allows one to

more closely ( correctly ) estimate the form and nature of the relationship between the dependent and

proposed causal variables. It should not be assumed that if the variance of the model's errors reduces by

300% that the resultant model accuracy will be improved by 300%. I believe that correct lag structures

are difficult to ascertain and to quantitatively assess when variables are omitted. This is because the

omitted variables increase the background noise and consequently increase the standard errors of

currently estimated parameters. This enlargement of the standard errors of the estimated coefficients

causes one to exclude potentially important variables because of the downward bias in the t test.

Furthermore, model augmentation strategies are impeded because of the bloated or inflated model errors

preempting cross-correlation checks which are important in identifying omitted lags for the currently

selected set of input or cause variables. These omitted variables may be either stochastic or

deterministic. AUTOBOX uses the ARIMA structure for the errors as a proxy for the omitted, perhaps

unknown, stochastic series and INTERVENTION VARIABLES for the omitted, perhaps unknown,

deterministic series. Prof. Ord at Georgetown University in the US refers to this as THE ALICE IN

WONDERLAND TEST, insofar as the perception of everything being OK is generated by the obfuscation

caused by the incorrect model specification.