How to do Univariate Heteroscedasticity Test

Question

I just wanted to know how to do Heteroscedasticity Test on a Univariate Model?

• ex: an univariate autoregressive model
• ex: an univariate ARCH/GARCH model

If it is possible, how does one do that in R?

Answer 1

This question was answered in 1988 http://www.unc.edu/~jbhill/tsay.pdf by R.Tsay and implemented in AUTOBOX in 1990. As of this date (today) no other forecasting/time series package has implemented his elegant and creative solution. Simply adjust your series for time trend changes, level shift changes, seasonal pulses and pulses AND the correct ARIMA structure. Verify that the model parameters are constant over time and then search for change points in error variance as he recommends.

Edited to respond to Nick ..

As you may know ARCH/GARCH concerns itself with developing an ARIMA model for the squared residuals. The problem is if you have unusual (one-time) anomalies these are dealt with by incorporating pulse indicator series, yielding a zero residual for each identified point. Squaring these residuals leads to a distribution that has long tails and is not amenable to ARIMA. When I programmed and implemented ARCH/GARCH so that I could jump on the "next new thing" I found that it was fundamentally inconsistent with Intervention Detection schemes. Essentially ARCH/GARCH provides a possible solution for a "change in variance" that may well be more easily handled by Intervention Detection (violations in the expected value). Thus at this point in time my preferences (Occam's Razor) for the simplest solution/transformation/drug/remedy causes me to keep the solution as simple as possible but not too simple. The current release of AUTOBOX treats variance heterogeneity by identifying anomalies, parameter changes and deterministic variance changes and no need for power transformations via Box-Cox... If all this fails the user can square the residuals and build an arima model to construct his/her own ARCH/GARCH model. Here I stand, I can do no other!