I just read the paper of Engle & Ng (1993) in which they introduced the sign bias test (positive sign bias t., negative sign bias t., joint test). I have a problem understanding what the test statistic is.
Is it $\chi^2$ with 3 DF for the joint and 1 DF for the other tests?



1 Answer 1


P. 1759-1760 of the paper give answers to your questions.

P. 1759:

The LM test statistic is asymptotically distributed as chi-square with $m$ degrees of freedom when the null hypothesis is true, where $m$ is the number of parameter restrictions.

See equations (9a)-(9c) to find that the number of parameter restrictions is 1 for sign bias, negative sign bias and positive sign bias test.

Also, p. 1760 reads explicitly about the joint test:

In particular, the LM statistic follows a chi-square distribution with 3 degrees of freedom.

(See equation 10.)


Your Answer

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

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