This research assesses the prediction of Bitcoin prices using the autoregressive integrated moving average (ARIMA) and long-short-term memory (LSTM) models. We forecast the price of Bitcoin for the following day using the static forecast method, with and without re-estimating the forecast model at each step. We take two different training and test samples into consideration for the cross-validation of forecast findings. In the first training sample, ARIMA outperforms LSTM, but in the second training sample, LSTM exceeds ARIMA. Additionally, in the two test-sample forecast periods, LSTM with model re-estimation at each step surpasses ARIMA. Comparing LSTM to ARIMA, the forecasts were much closer to the actual historical prices. As opposed to ARIMA, which could only track the trend of Bitcoin prices, the LSTM model was able to predict both the direction and the value during the specified time period. This research exhibits LSTM's persistent capacity for fluctuating Bitcoin price prediction despite the sophistication of ARIMA.