<![CDATA[Bitcoin is the largest cryptocurrency by market capitalization and one of the most volatile financial assets, which makes forecasting its price both important and difficult. This study evaluates the ability of the Autoregressive Integrated Moving Average (ARIMA) model and the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) family to predict the price and volatility of Bitcoin. Using daily data from 1 January 2018 to 30 June 2026, the models are estimated on a training sample of 2,737 observations and evaluated on a test sample of 365 days through rolling one step ahead forecasts. The Box and Jenkins procedure selects ARIMA(2,1,0) for the mean, and diagnostic tests reveal strong ARCH effects in its residuals. Among GARCH(1,1), GJR GARCH, and EGARCH specifications, the GARCH(1,1) t model provides the best fit. Out of sample, ARIMA reduces the price forecast error by only 0.28% relative to a random walk, the difference is not significant in the Diebold and Mariano test, and directional accuracy is 51.0%, no better than chance. In contrast, GARCH models forecast volatility significantly better than rolling and EWMA benchmarks, and combining ARIMA with GARCH(1,1) t produces 95% prediction intervals with correct coverage (94.2%), whereas ARIMA with constant variance does not. The results indicate that the Bitcoin price level is close to unpredictable, consistent with weak form efficiency, but that its risk is predictable, so ARIMA and GARCH are more useful for quantifying uncertainty than for forecasting the price itself.]]>
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