Suppose one is attempting to run regression on the following two economic indicators:
Employment and Business Cycle
(please see graphic below)
Linear Regression won't work here because level of Business Cycle (say, from 0 to 100) includes both 'coming down' and 'going up.'
The regression coefficient for Business Cycle will always be not significant because Business Cycle values will include offsetting 'going up' and 'coming down' values.
Yet one knows that Business Cycle level is indeed important.
One would additionally need to include a second variable -- whether the cycle is 'going up' or 'coming down.' Change from Previous Period sounds appropriate.
Thus, Multiple Regression might be usable.
I'm curious on your take. How can one best go about working with this oscillator dilemma?
I'm using this as a general example of handling oscillators
(sinusoidal-shaped independent variables over time).
In the above case we have only one such variable, Business Cycle.
Suppose we have 1000 such variables.
Proc GLMSELECT permits us to check to see which of the variables appear most
significant - variable selection techniques.
But, as shown, 'oscillators' present special challenges. Not sure how to
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