<![CDATA[This paper presents a comprehensive statistical analysis of Bitcoin's daily returns, focusing on their unique characteristics and implications for financial modeling and market behavior. The descriptive statistics reveal a mean daily return of 0.001912 and a standard deviation of 0.044069, highlighting high volatility. The skewness of -1.297892 and kurtosis of 22.099740 indicate a left-skewed, leptokurtic distribution with frequent extreme price movements. The Jarque-Bera test statistic of 95428.68, with a p-value of 0.0, strongly rejects the null hypothesis of normality, suggesting that traditional financial models assuming normally distributed returns may be inappropriate for Bitcoin. The ADF test statistic of -12.303, with a p-value of 7.36e-23, confirms the stationarity of Bitcoin's daily returns, validating their suitability for time series analysis techniques such as ARIMA and GARCH models. Autocorrelation analysis uncovers significant short-term predictability in Bitcoin returns, challenging the weak form of market efficiency, though this predictability diminishes over time. The Runs Test, with a z-score of 2.56 and a p-value of 0.01, further supports the presence of short-term non-random behavior. Additional visualizations, including the daily closing price plot, histogram, and boxplot of daily returns, illustrate the high volatility and substantial variability in Bitcoin's market behavior. The findings underscore the need for specialized risk management strategies and financial models tailored to the cryptocurrency market's unique dynamics. While Bitcoin offers opportunities for high returns, it also poses significant risks due to its volatile nature and frequent extreme price movements. Future research should explore advanced models accounting for heavy tails and volatility clustering and examine the impact of external factors such as regulatory changes and macroeconomic events on Bitcoin's statistical properties. Understanding these characteristics is crucial for informed investment decisions and effective trading strategies in the evolving cryptocurrency market.]]>
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