A LEAD OF A KNOWN X VARIABLE IS NEEDED

Consider a case where the true but unknown model is: Y(t) = v0*X(t) + v1*X(t+1) + A(t) where A is an i.i.d. ( gaussian ) error distribution and where the current tentative, albeit incorrect model is Y(t) = v0*X(t) + e(t) thus we have a case where e(t) = v1*X(t+1) + A(t)

It is clear that if we correlate e(t) and X(t+1), we will identify a statistically significant relationship which will then lead to the required augmentation strategy.


The strategy is then clear, for all possible or candidate "new variables" such as the X(t+1), X(t+2),....X(t+k)....etc. compute partial correlations which will measure the expected impact of the trial candidate. Select the one which has maximum correlation.

These approaches to developing new variables from existing series have had outstanding success with time-series data.

A known or anticipated change in the future value of an X variable may have a "ripple effect" for a number of previous time points.

This phenomena is quite natural with the purchase of consumer products a week or two ahead of major holidays. The reason being is that the distributor who is the purchaser from the manufacturer acquires inventory for subsequent resale to the outlet who then sells it to the ultimate consumer. Thus significant sales arise weeks before the actual holiday.

Another example is when customers know ahead of time about future price actions on the part of the seller. Such knowledge can lead to either reduced or increased sales in anticipation of future known events.