IBM® SPSS® Amos™ 28

The autocorrelation plot displays the estimated correlation between the sampled value at any iteration and the sampled value k iterations later for k = 1, 2, 3, ….

Lag, along the horizontal axis, refers to the spacing at which the correlation is estimated. In ordinary situations, we expect the autocorrelation coefficients to die down and become close to zero, and remain near zero, beyond a certain lag. In the autocorrelation plot shown above, the lag-10 correlation—the correlation between any sampled value and the value drawn 10 iterations later—is approximately .4. The lag-35 correlation lies below .10, and at lag 40 and beyond the correlation is effectively zero. This indicates that by 40 iterations, the MCMC procedure has essentially forgotten its starting position, at least as far as this estimand is concerned. Forgetting the starting position is equivalent to convergence in distribution.