Autocorrelation problem (Breusch-Godfrey versus residuals plots)

[RJ Bremer]

Dear Statalist,

I have found somewhat contradictory results regarding autocorrelation and I would like to have your expertise on this topic.

To give you some background information.
I started out with the following model: r_t = beta₀ + beta₁*tax + beta₂*monday +beta₃*cc_d + error term
Previous studies suggest that I should include a single lag of the dependent variable r_t, namely r_t-1.
Hence, the second model is: r_t = beta₀ + beta₁*tax + beta₂*monday +beta₃*cc_d + beta₄*r_t-1 + error term
Furthermore, it is a time-series dataset with daily data ranging from 1973 to 2014 with several gaps.

Because I wanted to know if there still was any autocorrelation in the residuals I used the Breusch Godfrey test, because it has no problem with lagged dependent variables (In contrary to DW).

Below you find the results of a Breusch-Godfrey test with 4 lags.
As you can see, in any case the H₀ is rejected in any case. This suggests that there is still autocorrelation. Furthermore, the p-value only gets smaller when I test for more than 4 lags.


However, when I checked the residuals of the second model using:

predict resid, residuals

ac resid

I found something rather interesting.



This graph does not suggest that there is autocorrelation after adding the lagged dependent variable (LDV). For comparison, you can find the ac graph of the residuals from the first model (i.e. without LDV) below.



What could explain these contradictory results?
Furthermore, should I 'thrust' the Breusch-Godfrey test statistic or the autocorrelation graphs?

Thank you in advance!

Best regards,

RJ

[Joao Santos Silva]

Dear RJ,

I cannot see the pictures you posted. Anyway, the -ac- is not a valid way to check for serial correlation of the residuals.

All the best,

Joao