A hybrid model is proposed for the short-term online prediction of tidal currents. The harmonic residual analysis (HRA) model is designed to augment the numerical schemes employed by tidal energy installations by forecasting the residual error of existing methods. Using a combination of techniques from Information and Fractal Theory, a novel component selection criterion for singular spectrum analysis (SSA) is used to remove true noise from the residual time series and to decompose the signal into components that are appropriate for linear-recurrent forecasting (LRF) and high order fuzzy time series (HOFTS) respectively. The performance of the HRA method is evaluated using a combination of simulated and real data from sites in the United Kingdom and the United States. Results demonstrate the model’s viability for 6-minute and 1-hour forecast horizons across sites exhibiting variable degrees of non-linearity. Empirical analysis of the resultant tidal energy forecast verifies the superior accuracy and reliability of the HRA method when compared with existing numerical schemes. Simulated data from three sites at the Pentland Firth, UK is also provided to facilitate further study of the site’s power generation characteristics and to allow for direct model performance comparisons.