This study analyzes daily BTC/USD and ETH/USD prices over a 1419-day period from February 1, 2021, to November 20, 2024. Statistical methods, including Partial Autocorrelation Function (PACF), Autocorrelation Function (ACF), Unit Root Test, and optimal ARIMA models, are employed to investigate the stationarity and prediction of the cryptocurrency prices. The results suggest that BTC/USD series is stationary after first differencing, while the stationarity of ETH/USD series remains uncertain due to observed characteristics in the PACF and ACF plots. The Augmented Dickey–Fuller (ADF) test supports the stationarity of both series. Predictions for the subsequent 360 days indicate a consistent upward trend in BTC/USD and ETH/USD prices from December 2024 to November 2025. These findings offer valuable insights for investors and stakeholders in the cryptocurrency market to anticipate potential trends and make informed decisions based on the projected price movements of BTC/USD and ETH/USD.