Temporal trends related to recent climatic fluctuations are extracted from the longest glacier-wide winter and summer mass-balance series recorded in the Alps, at Glacier de Sarennes, France. For this, all point balances measured at the glacier surface are used, and different statistical models are developed and tested. First, Lliboutry's linear variance analysis model is extended to the two seasonal components of the balance. The explicit modelling of variability sources and correlations is proved useful for appropriately quantifying uncertainties in the different components of the balance and estimating missing data. Next, a non-exchangeable structure is added to model the winter and summer balance time series. Two change points separating different underlying trends are thus detected. The first change was in 1976, with a shift of +23% in the winter balance. The second was in 1982 for the summer balance series. These systematic changes explain 20-30% of the variability of the different components of the balance, the rest being made up of random interannual fluctuations. Simplified and/or less physically based models are less efficient in capturing data variability. As a result, the cumulative glacier-wide balance shows systematic parabolic trends, which result in an accelerated mass loss for Glacier de Sarennes over the last 25 years.