Test Day and Lactation Yield Predictions in Italian Simmental Cows by ARMA Methods

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Autoregressive Moving Average (ARMA) models, originally developed in the context of time series analysis, were used to predict Test Day (TD) yields of milk production traits in dairy cows. ARMA models are able 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 models are very simple and can be easily implemented in data recording software, even at the farm level.