Cryptocurrency, particularly Bitcoin, is a significant financial asset for investors, but predicting its price is challenging due to its volatile and erratic nature. In this study, we suggest a novel ternary-frequency (TF) prediction scheme for Bitcoin prices, which combines complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), a time series clustering method, and the reconstruction of intrinsic mode functions (IMFs). In the proposed scheme, CEEMDAN was utilized to decompose Bitcoin’s daily price into IMFs, then prototypes of time series clustering were used to construct robust ensemble clusters. The IMFs in the ensemble clusters were reconstructed into ensemble time series and then identified as three different frequencies, which were respectively used in a prediction model to generate different predicted values, and then aggregated to produce the final prediction results. To generate three different TF Bitcoin price prediction schemes, this study employed three prominent prediction algorithms: autoregressive integrated moving average with exogenous variables (ARIMAX), multivariate adaptive regression splines (MARS), and extreme gradient boosting (XGB); these resulted in three distinct models, named TF-ARIMAX, TF-MARS, and TF-XGB. Empirical results from the two daily Bitcoin and one daily Ethereum closing price datasets showed that the proposed TF prediction scheme outperformed other benchmark approaches. Moreover, among the three TF models, TF-MARS produced superior prediction accuracy compared to both TF-ARIMAX and TF-XGB models, and proved to be an effective alternative for cryptocurrency price prediction.