A MATH FUNCTION OF A KNOWN X IS NEEDED
A MATH FUNCTION OF A KNOWN X IS NEEDED
- Consider a case where the true but unknown model is:
Y(t) = v0*X(t) + v1*X(t)**2 + 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)**2 + A(t)
It is clear that if we correlate e(t) and X(t)**2
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 Sine(X), Cosine(X) , Sqrt(X) , Log(X) ....etc. compute
partial correlations which will measure the expected impact of
the trial candidate. Select that one which has maximum correlation.
These approaches to developing new variables from existing series have not had much
success with time series data and are usually not recommended.
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