Seasonal autoregressive integrated moving average (SARIMA) time-series model for milk production forecasting in pasture-based dairy cows in the Andean highlands

Abstract

Milk production in the Andean highlands is variable over space and time. This variability is related to fluctuating environmental factors such as rainfall season which directly influence the availability of livestock feeding resources. The main aim of this study was to develop a time-series model to forecast milk production in a mountainous geographical area by analysing the dynamics of milk records thorough the year. The study was carried out in the Andean highlands, using time–series models of monthly milk records collected routinely from dairy cows maintained in a controlled experimental farm over a 9-year period (2008–2016). Several statistical forecasting models were compared. The Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percent Error (MAPE) were used as selection criteria to compare models. A relation between monthly milk records and the season of the year was modelled using seasonal autoregressive integrated moving average (SARIMA) methods to explore temporal redundancy (trends and periodicity). According to white noise residual test (Q = 13.951 and p = 0.052), Akaike Information Criterion and MAE, MAPE, and RMSE values, the SARIMA (1, 0, 0) x (2, 0, 0)12 time-series model resulted slightly better forecasting model compared to others. In conclusion, time-series models were promising, simple and useful tools for producing reasonably reliable forecasts of milk production thorough the year in the Andean highlands. The forecasting potential of the different models were similar and they could be used indistinctly to forecast the milk production seasonal fluctuations. However, the SARIMA model performed the best good predictive capacity minimizing the prediction interval error. Thus, a useful effective strategy has been developed by using time-series models to monitor milk production and alleviate production drops due to seasonal factors in the Andean highlands.