On Bartlett's test for correlation between time series

Let (X\) Yi)',... ,(-Xn, Yny be a sample from a bivariate regular normal distribution with independent components. If r' is the sample correlation coefficient then it is known that Er = 0, varr' = + 0 ( n ~ f ) (1.1) n (see Cramer [4], § 27.8 and § 29.7). If {Xt} and {Yt} are independent time series then the variance of the sample correlation coefficient does not obey the formula (1.1). Let {et} and {rjt} be two independent strict white noises such that et ~ -V(0,<7i) and r}t ~ N(0,<T2). Consider AR(1) processes