6
$\begingroup$

I am using the function McLeod.Li.test in the TSA package. According to the help file in R, this function “Performs the McLeod-Li test for conditional heteroscedasticity (ARCH).”

However, it has been mentioned on page 50 of the book “Introduction to Time Series and Forecasting, Brockwell and Davis, 2nd edition” that the McLeod-Li test “can be used as a further test for the iid hypothesis”.

Question: Is it true to say that the McLeod-Li test can be used to check the “conditional heteroscedasticity” as well as the “iid assumption”? If not, which one is the correct null hypothesis?

Improve this question
$\endgroup$

1 Answer 1

Reset to default
2
$\begingroup$

The McLeod-Li test can be used as a test of independence and it can also be used to test the hypothesis of no ARCH. In fact, the McLeod-Li test can be used as a general misspecification test against nonlinearity. See Teräsvirta, Tjøstheim and Granger (2010), (pages 140-1 and 178-9).

You may find it useful to know that it is stated in Patterson, and Ashley (2000), (page 40), that the null hypothesis is that the series is i.i.d.

I hope this information helps you, and rather than go into the particulars, I refer you to the aforementioned sources.

As a side note, it's worth mentioning that some tests can be used for a variety of purposes. For example, the BDS test can be used to test the i.i.d hypothesis, but it can also be used to test for the presence of non-linearity. I think this is a similar situation to the usage of the McLeod-Li test.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

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