Top panel: time series showing the estimated pseudo open-loop in black, compared with the VLT/SPHERE residual in blue for a random SAXO telemetry data set. Other plots (all with the same y-scale): various predictor residual phase variances (various green and purple lines) compared to the VLT/SPHERE residuals for the same data. The averaged phase variance, in μm², for the last 5 s is indicated in the top right corner of each plot. The forgetting s1t10 (abbrev. for) does not perform significantly better than the recursive s1t10 (abbrev. rec). Secondly, the s3t3 does not perform better than the s1t10.