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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
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.
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Apr 2, 2013 at 2:37