This paper aims at detecting sleep apnoea-hypopnoea syndrome (SAHS) from single-channel airflow (AF) recordings. The study involves 148 subjects. Our proposal is based on estimating the apnoea-hypopnoea index (AHI) after global analysis of AF, including the investigation of respiratory rate variability (RRV). We exhaustively characterize both AF and RRV by extracting spectral, nonlinear, and statistical features. Then, the fast correlation-based filter is used to select those relevant and non-redundant. Multiple linear regression, multi-layer perceptron (MLP), and radial basis functions are fed with the features to estimate AHI. A conventional approach, based on scoring apnoeas and hypopnoeas, is also assessed for comparison purposes. An MLP model trained with AF and RRV selected features achieved the highest agreement with the true AHI (intra-class correlation coefficient = 0.849). It also showed the highest diagnostic ability, reaching 92.5 % sensitivity, 89.5 % specificity and 91.5 % accuracy. This suggests that AF and RRV can complement each other to estimate AHI and help in SAHS diagnosis.