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Autoregressive Moving Average (ARMA) models, originally developed in the contest of time series analysis, were used to predict Test Day (TD) yields of milk production traits in dairy cows. ARMA models areable to take into account both the average lactation curve of homogeneous groups of animals and the residual individual variability that may be explained in terms of probability models, such as Autoregressive (AR) and Moving Average (MA) processes. Milk, fat, and protein yields of 6000 Italian Simmental cows with 8 TD records per lactation were analyzed. Data were grouped according to parity (1st, 2nd, and 3rd calving) and fitted to a Box-Jenkins ARMA model in order to predict TD yields in five situations of incomplete lactations. Reasonable accuracies have been obtained for a limited horizon of prediction: average correlations among actual and predicted data were 0.85, 0.72, and 0.80 for milk, fat and protein yields when the first predicted TD was one step ahead (on average 42d) of the last actual record available. Cumulative 305-d yields were calculated using all actual (actual yields) or actual plus forecasted (estimated yields) daily yields. Accuracy of lactation predictions was remarkable even when only a few actual TD records were available, with values of 0.88 for milk and protein and 0.84 for fat for the correlations between actual and estimated yields when 6 out of 8 TD records were predicted. Accuracy rapidly increases with the number of actual TD available: correlations were about 0.96 for milk and protein and 0.93 for fat when 4 out of 8 TD records were predicted. In comparison with other prediction methods, ARMA modelsare very simple and can be easily implemented in data recording software, even at the farm level.

Test day (TD) records of milk production traits (milk yield, fat, and protein percentages) of 534 Italian buffalo cows were analyzed with a mixed linear model in order to estimate lactation curves pertaining to different ages at calving and different seasons of calving. Milk yield lactation curves of younger animals were lower than those of older animals until 20 wk from parturition. No effect of age at calving could be observed for fat and protein percentages. Season of calving affected milk yield only in the first phase of lactation, with the lowest production levels for summer calvings; no effect could be observed on fat and protein contents. Average correlations among TD measures within lactation were 0.59, 0.31, and 0.36 for milk yield, fat, and protein percentages, respectively. Five standard linear functions of time were able to reconstruct the average lactation curves. Goodness of fit was satisfactory for all models considered, although only the five-parameter model was flexible enough to fit all the three traits considered with excellent results.