Multi-fidelity Kriging (MFK) surrogate modeling combines data of varying accuracy, such as experimental tests and numerical simulations, to improve predictive performance. Autoregressive models are commonly used to capture correlations across fidelity levels, offering interpretability compared to purely data-driven approaches. However, existing MFK frameworks based on autoregressive models often suffer from high computational costs. In this work, we revisit the MFK approach, extending it to account for sparsity in the multi-fidelity setting, maintaining the efficiency of classical sparse approximations while keeping accuracy. We illustrate our framework in a 1D toy example, and assess it on a large-scale multi-fidelity aerodynamic dataset that combines wind tunnel experiments with CFD simulations. In both cases, our framework is capable of handling heteroscedastic noise. Training performance is reduced by approximately 88\% while maintaining accuracy compared to standard MFK, highlighting the benefit of incorporating sparse approximations in complex engineering applications.