## Negative LM statistic in testing for autocorrelation

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elmst616
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Joined: Fri Apr 29, 2016 2:36 pm

### Negative LM statistic in testing for autocorrelation

I am attempting some testing of adequacy in the post estimation of a STAR model. Specifically I'm attempting to test for the presence of no autocorrelation using the methods of Eitrheim and Terasvirta (1996). This is a Serial Correlation LM test which is Chi-squared distributed.

Summary of methods from Eitrheim and Terasvirta:

The test can be performed in three stages as follows.
(i) Estimate the STAR model by NLS under the assumption of uncorrelated errors and compute the residual sum of squares SSRo.
(ii) Estimate the auxiliary equation and compute the residual sum of squares, SSR.
(iii) Compute the test statistic LM = {(SSRo- SSR)/q}/{SSR/(T- n- q)}, where n is the dimension of the gradient vector z.

However, I'm obtaining a negative LM test statistic. I'm thinking this simply means that the auxiliary regression is clearly a worse fit. But I'm unsure because Chi-squared distributions are non-negative.