I am working on modeling what amounts to a time series, the DV is measured 40 times a day on 40 different days— the actual timing of measurements on a given day varies, and the number of days between these sessions also varies.
I am told that with such data (this is a single participant case study) autocorrelation is expected to be a problem, and so we should 'worry' about it and try to account for it. However, in my regression model I see no signs of autocorrelation in the residuals– either when looking at an ACF plot or when using the Durbin-Watson test. I thought— how can this be, if apparently its 'always' a problem? Then I saw that if I remove a certain independent variable, namely the session # itself, then I do see serious autocorrelation. Compare the models and ACF plots below:
You can see that in the first ACF plot, lag-1 is significant, and there is a clear decreasing trend, whereas in the second the lag-1 is tiny and there is no obvious trend. The different between these models of course, as you can see at the heading, is that the latter includes session # as an independent variable.
Is it WRONG for any reason to include that variable (session)?? It is of interest– we want to know if the dv is changing with session, so a priori this is the model I designed. And if that is okay, which I can't see why it wouldn't be, then I don't understand why everyone doesn't just "solve" autocorrelation issues in regression by including an independent variable that 'captures' the non-independent nature of the trial structure. Any thoughts/comments on this are VERY welcome, I have to wrap my head around all of this before I can start writing a paper about our results!
and 
and 
. Since anomalies are present the appropriate regression needs to take into account these effects. Following are the three models ( including any necessary lag structures in the two inputs ) and the appropriate ARIMA structure obtained from an automatic transfer function run using AUTOBOX ( a piece of software I have been developing for the last 42 years )
and 
and 
. We now take the three cleansed series returned from the modelling process and estimate a minimally sufficient common model which in this case would be a comtemporary and 1 lag PDL on tweets and a contemporary PDL on wiki with an ARIMA of (1,0,0)(0,0,0). Estimating this model locally and globally provides insight as to the commonality of coefficients .
with coefficients 
. The test for commonality is easily rejected with an F value of 79 with 3,291 df. Note that the DW statistic is 2.63 from the composite analysis. The summary of coefffici
ents is presented here. The OP poster reflected that the only software he has access to is insufficient to be able to answer this thorny research question.
Best Answer
Yes, you can sometimes solve an autocorrelation problem in a regression model by adding a variable, if it's the right variable.
Or, as you've demonstrated, you can create autocorrelation problems by dropping a variable.
Most forecasting books are likely to have an example. If you want a specific reference, Hanke and Wichern, Business Forecasting, 9th edition, page 347.