 # Positive and negative serial correlations

Hi, I have a question about positive and negative serial correlation, it’s a detail but I was curiously wondering if any of you could explain why positive serial correlation leads to a smaller Standard error (then leading to too many Type I errors) while negative leads to higher standard error (and thus too many Type II errors). Did I miss something? Thanks in advance! Nick

Take it to the extremes and see if you see it then. What if the serial correlation among the residuals is -.99, what do the residuals look like and what would happen if you modeled that? Then do the same for 0.99.

so do you mean if the serial correlation was +.99 and we plotted it the line would look like a much better fit. standard error lower… and if we plotte the -.99 the serial correlation would have a negative relationship thus the line would not be as good of a fit. thus the standard eror would be higher… ahhhh… i think i got it… thanks… plotting it helped me out… joey thanks alot Hi again, I must be too stupid to take the Level II exam, but I don’t see it… Why would it be different in terms of S.E. between correl = + or - .99? Because at the end when you take the absolute value (I always see a S.E. as a distance, which is an abolsute value), it is the same. Sorry to insist, especially on this detail, but I hate learning a thing when I don’t get it S.E. isn’t a distance although Sqrt(SSE) is (all this stuff with regression analysis is the Pythagorean theorem in disguise) A blackboard is good for this, but think of a model where the residuals were really highly positively correlated. At the extreme, we have the first half of our data with positive residuals and the second half with negative residuals. When we fit an OLS line through that our assumption that there is no structure to the residuals causes us to tilt the line through the center of the cloud and the line fits much better than it should (draw it). Of course it is just as likely to be negative residuals in the first half and positive in the second half, so the OLS estimators are unbiased. The negative correlation is the opposite kind of effect - the residuals go +,-,+,-,+ etc. and that oscillation of the residuals due to serial correlation looks like error variance.

I see it better now…actually that was this “oscillation” part that I needed to understand better. Thanks Joey for the clear and detailed answer, that helped a lot (as usual)!