Question about Autocorrelation

[Ynwe]

Hey,

In my output I have an obvious issue with autocorrelation. Durbin-Waston has a value of 1.1 and a Q-Statistic under Residual Diagnostics shows me pretty much that I have autocorrellation. So I add an AR (1) term. Now durbin watson goes up to 1.6, the Q-Statistic overall seems to be fine too now, but one of my key variables has a p value increase from .0347 to .21. The AR term itself is significant at a 5% level (0.0404). What does this mean? Does this mean I have to throw that variable out now, given that I add a AR 1 term?

[startz]

The fact that a variable is "insignificant" does not mean you should throw it out.

[Ynwe]

The fact that a variable is "insignificant" does not mean you should throw it out.

but why does the adding of an AR term suddenly render a variable insignificant?

[startz]

Generally because when serial correlation is ignored the reported standard errors are wrong. Adding AR(1) gives the correct standard errors. In addition, sometimes serial correlation indicates misspecification.

[Ynwe]

Generally because when serial correlation is ignored the reported standard errors are wrong. Adding AR(1) gives the correct standard errors. In addition, sometimes serial correlation indicates misspecification.

so this means, that in the original output, the standard errors were wrong due to a AR taking place that the model was ignoring. This led to GDP being given as a significant variable due to miscalculations. Adding an AR term yields it insignificant at a high level. so due to the addition of the AR term, we know that the past values are explaining present and future values to a certain extent and that the GDP variable does actually not add significant information to the regression that I originally thought it was doing. Is there anything else to say about AR and the Variable GDP?

Also, the SC, AIC and Hannan-Quinn Criteria haven't improved by much between these two modells. Wouldn't this mean that the addition of the A term overall only made the new model only very slightly better than the older one`?

[startz]

That seems right.