<p>Bitcoin is usually characterised by high volatility and the resulting high risk levels coupled with regulatory uncertainties commonly associated with the cryptocurrency market, may negatively impact risk-averse investors. As such, reliable volatility modelling and forecasting approaches are crucial in understanding the digitalised cash system’s risk characteristics. This study makes several key contributions. First, it introduces the sinusoidal-enhanced Fourier grey Markov model (FOGMS), designed to improve forecasting accuracy for highly volatile datasets like Bitcoin by capturing oscillatory patterns and random fluctuations more effectively. Second, the study conducts a comparative analysis of conventional time series methods, such as ARMA and GARCH models, against the enhanced FOGM model, demonstrating its superior performance in forecasting Bitcoin volatility across four test cases. Finally, through empirical testing, the proposed FOGMS model achieves a very good correlation, significantly lower RMSE and Log Cosh values in all test cases, outperforming traditional time series approaches in predictive accuracy thus offering valuable insights into advanced grey models for financial forecasting in volatile markets.</p>