Making Sense of Differences Between Durbin-Watson Test, ACF, and auto.arima Trying to make sense of my results. I'm trying to assess if an intervention had an effect on infection rates using an interrupted time series design. I have monthly data on infection rates for approximately 4 years.
I developed a simple segmented regression design, and following advice from articles I've read like this one. I ran a Durbin-Watson test on the residuals from my model (with infection as the dependent and time as independent), and, lo and behold, the test statistic = 1.24 and p = 0.001.
I went ahead with trying to select an ARIMA model. When mapping the ACF, I see the following:

I took a look at the output from auto.arima from the forecast package, which suggested a regression with ARIMA(0,0,0) errors, which I understand would be the same thing as my initial linear regression. The AIC of the (0,0,0) and the (1,0,0) are extremely similar (within .01 of each other) but I'm not sure that the difference is meaningful.
My question is, what do I make of the suggestion of AR(1) from the DW test in light of no other evidence of autocorrelation? Am I missing / violating some assumption of the DW test that renders it unusable in this situation? I'd like to use the simpler model for the benefit of my audience if possible, but I'd like my conclusions to be as strong as possible.
I'm a final year student in a medicine program, please forgive me if I've missed some introductory concept here.
I also included a plot of the residuals from the linear model. I see what looks like a strong negative correlation from index 20 - 25. That's not related temporally to my intervention, I was wondering if this is what's driving the positive DW test.


Durbin Watson is a very old test and there are much better ones now, if more complex. It only test for AR 1 although in this case it probably did not matter since at most you have AR1. You might want to try some of the the newer test to confirm what the DW is saying, however. One thing that is strange to me is that you are testing segmented regression/interrupted time series so you assume the pattern changed over time, after the intervention. Yet the ARIMA model you generated shows stationarity. Which suggests nothing changed. Did your raw data suggest a change at all after the intervention? If the pattern of data remained essentially unchanged over time I am not certain why you ran segmented regression or interrupted time series.
It is possible I don't understand what you were testing. :) I assume it is some type of data over time which you think changed its pattern at some point. The (0,0,0) model does not suggest that to me.
