diagnostic tests with robust cov Wald instead of LM

[josef-pkt]

Stata regress postestimation mentions Wald tests instead of LM test that don't require homoscedasticity assumption.

For example Breush Godfrey acorr test already has a F-test option
http://statsmodels.sourceforge.net/devel/generated/statsmodels.stats.diagnostic.acorr_breush_godfrey.html
but I never seen the connection with robust standard errors before, and I don't know if that version is actually correct with unspecified heteroscedasticity.

closely related #1168

[josef-pkt]

related just reading a paper that compares heteroscedasticity tests and uses time series data in the example.
Koenker, breush-pagan looks the best overall (under correctly specified alternative in power in Monte Carlo)
Lyon Tsai 1996: "A comparison of tests for heteroscedasticity"

I think none of the tests is robust to serial correlation, and might not be valid in the time series example.

Wooldridge and others:
use heteroscedasticity tests that are robust to serial correlation
use serial correlation tests that are robust to heteroscedasticity

not seen yet:
test serial correlation and heteroscedasticity at the same time

[josef-pkt]

Note: This might not be so clear. I'm still mixing up which extra assumptions we use in the various tests, like mean tests need variance assumption, and variance tests need assumptions on 4th moments.

[josef-pkt]

Very nice overview over assumptions required for acorr tests, plus examples using new Stata user command actest that includes other tests as special cases under restrictive assumptions

http://ideas.repec.org/p/boc/norl13/6.html

Christopher F Baum & Mark E Schaffer, 2013.
"A general approach to testing for autocorrelation,"
2013 Stata Conference 6, Stata Users Group.

Doesn't include a description of the Cumby-Huizinga test, but sound just like a Wald test with (HC, AC, HAC, or cluster) robust covariance.