[R] statistics - hypothesis testing question

[Leeds, Mark (IED)]

I estimate two competing simple regression models, A and B where the LHS
is the same in both cases but the predictor is different (
I handle the intercept issue based on other postings I have seen ). I
estimate the two models on a weekly basis over 24 weeks. 
So, I end up with 24 RSquaredAs and 24 RsquaredBs, so essentally 2 time
series of Rsquareds. This doesn't have to be necessarily thought of as a
time series problem but, is there a usual way, given the Rsquared data,
to test 

H0 : Rsquared B = Rsquared A versus H1 : Rsquared B > Rsquared A 

so that I can map the 24 R squared numbers into 1 statistic. Maybe
that's somehow equivalent to just running 2 big regressions over the
whole 24 weeks and then calculating a statistic from those based on
those regressions ?

I broke things up into 24 weeks because I was thinking that the
stability of the performance difference of the two models could be 
examined over time. Essentially these are simple time series regressions
X_t = B*X_t-1 + epsilon so I always need to consider
whether any type of behavior is stable.  But now I am thinking that,  if
I just want one overall number,  then maybe I should be considering all
the data simultaneously ? 

In a nutshell,  I am looking for any suggestions on the best way to test
whether Model B is better than Model A where

Model A :  X_t = Beta*X_t-1 + epsilon

Model B :  X_t = Betastar*Xstar_t-1 + epsilonstar


Thanks fo your help.
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