Objective: To evaluate whether detrended fluctuation analysis (DFA) provides information that improves the diagnostic ability of the oximetry signal in the diagnosis of paediatric sleep apnoea–hypopnoea syndrome (SAHS). Approach: A database composed of 981 blood oxygen saturation (SpO2) recordings in children was used to extract DFA-derived features in order to quantify the scaling behaviour and the fluctuations of the SpO2 signal. The 3% oxygen desaturation index (ODI3) was also computed for each subject. Fast correlation-based filter (FCBF) was then applied to select an optimum subset of relevant and non-redundant features. This subset fed a multi-layer perceptron (MLP) neural network to estimate the apnoea–hypopnoea index (AHI). Main results: ODI3 and four features from the DFA reached significant differences associated with the severity of SAHS. An optimum subset composed of the slope in the first scaling region of the DFA profile and the ODI3 was selected using FCBF applied to the training set (60% of samples). The MLP model trained with this feature subset showed good agreement with the actual AHI, reaching an intra-class correlation coefficient of 0.891 in the test set (40% of samples). Furthermore, the estimated AHI showed high diagnostic ability, reaching an accuracy of 82.7%, 81.9%, and 91.1% using three common AHI cut-offs of 1, 5, and 10 events per hour (e h−1), respectively. These results outperformed the overall performance of ODI3. Significance: DFA may serve as a reliable tool to improve the diagnostic performance of oximetry recordings in the evaluation of paediatric patients with symptoms suggestive of SAHS.