In an AR(1) covariance structure, what is assumed about the correlation between scores over time?

• A. The correlation stays constant
• B. The correlation decreases over time
• C. The correlation increases over time
• D. The correlation is unpredictable

Answer: (B)

AR(1) covariance structure captures the idea that measurements that are closer in time are more alike, and the influence of one score on a score further in time fades. In a stationary AR(1) process, the correlation between scores separated by k time units is rho^k, where rho is the autoregressive parameter with |rho| < 1. As k increases, rho^k gets smaller, so the correlation decreases with time lag. This means nearby scores are more strongly related than distant ones, which is exactly the behavior described by the option that the correlation decreases over time. If rho is positive, the correlation remains positive but weakens as the gap grows (and if rho is negative, the sign can flip, though the magnitude still fades).