2
$\begingroup$

I'm working to develop a forecasting model for a quarterly seasonal variable (quarterly estimated individual income tax payments) using several candidates for non-seasonal independent variables (quarterly average value of S&P 500, dividend income, interest income, etc.).

I understand that I need to prewhiten the dependent and independent variables in order to generate a cross-correlation function to identify the appropriate rational transfer function for the independent variables, but the seasonal dependent variable and candidate non-seasonal independent variables require different differencing operations to be stationary. Using year-over-year differencing for the non-seasonal variables leads to over-differencing, often with AR and/or MA terms near 1.0.

Is the only solution to create a synthetic seasonally adjusted series for the dependent variable before prewhitening? Or is there another way to prewhiten variables that require different differencing opterations?

$\endgroup$
0
$\begingroup$

there is no need for the pre-whitening differencing operators to be the same for all variables in the tf model. If your software requires that then perhaps you need more generalized software. See https://autobox.com/pdfs/PREFERRED.pdf .

For example a panel from AUTOBOX ( a piece of software that I have helped to develop) shows the generality enter image description here

Step by Step:

1) deterimine order of differencing for both Y and candidate X

2) apply differencing operators

3) identify an arma filter for the suitably differenced candidate X

4) apply that arma filter to both the suitably differenced X and suitably differenced Y

5) compute cross-correlations using results from step 4 to identify TF model

$\endgroup$
  • $\begingroup$ Thank you. For clarification, I'm attempting to use the cross-correlation plots from SAS Proc ARIMA to identify an appropriate transfer function. Would the CCF plots produce valid results if I, for instance, first use a differencing operator of 1 for quarterly-average S&P 500 and an AR(1) model to produce white-noise residuals and then use the resulting filtered series for the seasonal dependent variable (estimated payments) using a differencing operator of 4 for both series? $\endgroup$ – Edwin McLenaghan Oct 18 at 14:27
  • $\begingroup$ I definitely don't think so as sequential approaches are usually inferior ..but only your data knows for sure. The SAS proc is deficient in many way including being blind-sided by anomalies in any series and also doesn't wholly treat the concern for homegeneity of the tf model's error process. $\endgroup$ – IrishStat Oct 18 at 14:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.