# Interpretation of McLeod-Li test for ARCH effect

I want to know if I need to use ARCH/GARCH model for my time series. How can I use McLeod.Li.test in R to do that and how should I interpret the result? the description in R help was not clear for me because in the example of the R help they used difference of the log of the time series and I do not know why? Also, how should I interpret the resulted plot? R help example is like this:

data(CREF)
r.cref=diff(log(CREF))*100
McLeod.Li.test(y=r.cref)


Thanks

You really just need a test for ARCH effects in your data set.

The steps:

Run an $\mbox{AR}(q)$ model on the data. Estimate the least squares regression model

$\hat{\epsilon}_{t}^{2}=\beta_{0}+\sum_{i=1}^{q}\beta_{i}\hat{\epsilon}_{t-i}^{2}$,

where $\hat{\epsilon}_{t}$ are the residuals from an $\mbox{AR}\left(q\right)$ model. If any of the coefficients are significantly different from zero, there are ARCH effects in the data.

I'm not sure of the difference between this test and the McLeod-Li test, but they should be very similar. You can find several sources by doing a Google search for "Engle 1982 test for arch effects", also found this: http://faculty.washington.edu/ezivot/econ589/ch4.pdf

• Is q for AR(q) the same order that we find through model identification techniques like ACF and PACF plots? Also, if the model identification showed ARMA or MA models are better fit, Do we still find the residuals of an AR(q) model?
– Fred
Apr 2, 2013 at 2:27
• Good question. You could identify q using AIC, R does it automatically. I don't think you need an ARMA model - if you look at the pdf by Zivot, you only need to test for ARCH effects to justify the use of a GARCH model. He (and other authors) only present the test involving an AR model. Apr 2, 2013 at 2:37