Technical Abstract: Three models were compared: Model 1 had a first order autoregressive covariance structure among test day environmental components, Model 2 was a repeatability animal model using test day records, and Model 3 was an animal model using 305-day records. Data on 12,071 first lactations of Holstein cows with a total of 106,472 TD records were available on milk, fat, and protein yields and somatic cell scores (SCS). Estimates of genetic and environmental components of variance and autocorrelation coefficients were obtained with the ASReml program using average information algorithm. Likelihood ratio tests indicated that Model 1 was significantly better than Model 2 for all four traits. Model 1 had slightly lower estimates of heritability than Model 2 ranging from 0.08 to 0.10 for yield traits and 0.06 for SCS. Model 3 resulted in estimates of heritability ranging from 0.13 to 0.36. Similarly, estimates of repeatabilities and variance components associated with permanent environmental effects were always less for Model 1 than for Model 2. Removing permanent environmental effects from Model 1 resulted in inflated estimates of genetic variance and thereby biased estimates of heritability. The lowest rank correlations of predicted breeding values (PBV) of sires and cows were between those for Model 3 and Models 1 and 2 (0.71 to 0.87) for all traits. Correlations between PBV with Model 1 and Model 2 were always greater than 0.99 for both sires and cows for all traits. Of the top ten elite sires for milk yield, nine were common between Models 1 and 2, six between Models 1 and 3 and five between model 2 and 3 with similar patterns for the other traits. Both Model 1 and Model 2 resulted in similar accuracies of PBV for all traits with accuracies for sires almost twice those for cows. The autoregression covariance structure helped prevent overestimation of heritability and repeatability for all four traits.