This study proposes a data-driven methodology to complement existing time-series measurement tools for turbulent flows. Specifically, a cluster-based transition network model is employed for the estimation of velocity time traces and their corresponding statistics. The method is tested on a laboratory-modelled turbulent boundary layer over a step change in surface roughness, where velocity time series are recorded for training and validation purposes via Laser Doppler Anemometry. Results show that our approach can estimate velocity and momentum flux statistics within experimental uncertainty over a rough surface through an unsupervised approach, and across the step change in roughness through a semi-supervised variant. The friction velocity across the domain is also estimated with 10% relative error compared to the measured value. The proposed methodology is interpretable robust against the main methodological parameters. A reliable data-driven framework is hence provided that can be integrated within existing laboratory setups to supplement or partially replace measurement systems, as well as to reduce wind tunnel running times.