spollard777 wrote:In using TsayNL, the m and l values are the same. Does l refer to the length of the delay? It is not clear why l and m are the same. In the multivariate case they seem to be allowed to be different as you have presented it.
There's no real sense of a "delay" in the Tsay test. Instead, it's a test between a linear AR and a non-linear version of the same set of regressors, hence it includes just the interaction terms between the original regressors. If you're looking for a test against STAR with a specific delay, use STARTEST
instead; the LST variant in TSAYNLTEST
is much less focused on such a specific alternative.