Oscillator Dilemma

[NKormanik]

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?

Thanks!

Nicholas Kormanik

[art297]

One way would be to include time, time**2, and time**3 as predictor variables.

Art, CEO, AnalystFinder.com

[NKormanik]

Are those (time**2 and time**3) 'interaction variables'?

[NKormanik]

My hunch is that an additional variable must be introduced. Employment and
Business Cycle are insufficient by themselves.

For instance, add in Change in Business Cycle.

Thus:

Y = Employment
X1 = Level of Business Cycle, 1-to-100
X2 = Change in Business Cycle from previous period

Regression Model:
Y = f(X1, X2)

This might solve the problem of, Is X1 heading up or down??

[NKormanik]

"Interaction Effect" - One variable depends on the level of another
variable.

Clearly that's the case at hand.

That raises the SAS question, should the "Interaction Effect" be explicitly
included?

Y = f(X1, X2, X1*X2)

[art297]

My guess would be no, they shouldn't be included. However, I'll leave that for the forum's statisticians to chime in.

Art, CEO, AnalystFinder.com

[Reeza]

Two common approaches are to add in variables for seasonality or or smoothing it out using moving averages. 

[Ksharp]

two ways:

1) try other model like PROC LOESS, PROC TRANREG .

2) time series analysis SAS/ETS, like PROC ARIMIA, PROC UCM .

Calling @Rick_SAS

[NKormanik]

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
handle it.

[Reeza]

This is time series and econometric modeling. Searching within those spaces will give you options. I work parallel to an econometrics team. I’ve never heard the term 'oscillator' it’s usually referenced as the business cycle or boom bust cycle.

[Ksharp]

PROC GLMSELECT only can handle LINEAR relation, not non-linear .

I suggest you post it at SAS/ETS forum, there is someone could answer your question.

or try PROC PLS .