autoregressive regression for test scores

[Zozo_star]

I am regressing score(t)=b0 + b1score(t-1) + b2score(t-1)^2 + b3score(t-1)^3 where score(t-1) is previous score and score(t) is current score. I control for ethnicity, gender and year levels. I was expecting that b1 is positive to show that prior score predicts a positive relationship with current score. But my b1 is negative and b2 is positive and b3 is negative although the coeffcients are very small. How do I interepret b1 b2 and b3? 

[SteveDenham]

Make sure that your values for score(t-1) have been re-centered on zero.  I think the signs are the result of squaring and cubing values so that there are very large values driving your fit. If you consider that the autoregression is actually a characteristic of the errors around the scores, which are assumed to be normal(0, sigma^2) this will make more sense.  

SteveDenham