Milk Production and Climate Variability in a High-Andean Dairy System: A Longitudinal Case Study

Climatic variability can modify milk production through direct and indirect pathways, yet monthly farm time series also exhibit temporal dependence. A longitudinal, observational, single-case study was conducted in the San Francisco dairy system, Carchi, Ecuador, from March 2019 to December 2024. Of 70 calendar months, 64 had complete analytical information, and 58 were eligible for two-lag models. Ten model specifications were compared based on model fit, information criteria, residual diagnostics, seasonality assessment, and temporal validation. Mean daily milk production was 233.49 ± 47.90 L day^-1. The selected model was a second-order autoregressive model with a calendar trend and mean temperature at t - 2 (adjusted R2 = 0.827; Akaike information criterion = 519.52; Bayesian information criterion = 529.83; root mean squared error = 19.56 L day^-1). The temperature coefficient was 10.844 L day^-1 °C^-1 (p < 0.001 with robust standard errors). Annual harmonic terms did not improve model fit, and precipitation at t - 1 yielded only marginal improvement. The number of cows in production varied across 54 months (26.02 ± 4.11; range: 18-37). The observed temperature association should be interpreted at the system level; it does not demonstrate direct causality or individual cow productivity and requires external validation.