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Transfer Functions and prewhitening - Need help

Hi Team,

Its related to Transfer functions and specifically Prewhitening. The documentation guide says that there is a table in Box et al. (1994) that illustrates what transfer functions look like based on different specifications.

appreciate your inputs on this table. (Not sure where to find)

Thanks

Murali

 

Re: Transfer Functions and prewhitening - Need help

Here is an old powerpoint slide deck that at the end describes the transfer function time series model.  If I remember correctly, the modeling process is to 

1. Pre-Whiten the input series:  find an ARIMA model for the X that essentially transforms the input X series to random noise
2. Look at the correlations of lags of the pre-whitened X series with the output series and pick a lag for the X series to use 
3. Do a regression of Y on the lagged prewhitened X series
4. Fit an ARIMA model the residuals of that model.  

I also attached an example data set with a couple of fitted transfer function models.  Happy to look at this together with you if you want to dive deeper.  

 

Re: Transfer Functions and prewhitening - Need help

Thanks for this Sam.  I've worked in single variable Time Series ARMA models dating back to graduate school (a LONG time ago), then got away from it for a while.  While I'm still comfortable with AR(I)MA models, I struggle with Transfer Functions.  If you and @Muralidhara decide to get together to discuss, I'd be interested in listening in!

Re: Transfer Functions and prewhitening - Need help

I found myself rarely follow the conventional wisdom because it is laborious to compare with what are in the book side by side. I usually just end up with trying different orders. The practice is not unreasonable, because none of the patterns in the book has big orders. And computer is faster these days, it is faster to just try a bunch.