Abstract
This study establishes a GARCH model for the logarithmic return series of Bitcoin prices to analyze volatility within the experimental timeframe. Findings indicate that Bitcoin exhibits significant price volatility and heightened sensitivity to external shocks. The analysis suggests that Bitcoin predominantly functions as a speculative financial instrument, with severe price bubble phenomena.
Data Selection and Processing
1.1 Data Selection
1.1.1 Data Object and Timeframe
Daily closing prices of Bitcoin—market-consensus values—were selected as the primary data. The study period spans January 4, 2016, to October 25, 2019, comprising 1,406 daily closing prices.
1.1.2 Data Source
Sourced from Feixiaohao, a Chinese blockchain data analytics platform renowned for its real-time行情, trends, and asset tracking.
1.1.3 Data Preprocessing
Non-stationary Bitcoin prices were transformed via logarithmic returns to stabilize trends:
[ r_t = \ln(P_t) - \ln(P_{t-1}) ]
This yielded 1,405 logarithmic return data points (Figure 2).
1.2 Graphical Analysis of Preprocessing
- Figure 1: Bitcoin price index (2016–2019) shows extreme fluctuations, particularly during regulatory shifts (e.g., Japan’s 2017 recognition, U.S. ETF rumors).
- Figure 2: Logarithmic returns exhibit "clustering" volatility—calm periods (pre-2017) versus high volatility (2017–2018).
Empirical Analysis
2.1 Descriptive Statistics
- Skewness: Left-tailed asymmetry.
- Kurtosis > 3: Leptokurtic distribution (fat tails).
- Jarque-Bera test: Rejects normality ((p < 0.01)).
2.2 Model Construction
2.2.1 Stationarity Check
ADF test:
| Variable | ADF Statistic | p-value |
|------------|---------------|---------|
| ( r_t ) | -46.9636 | 0.000 |
→ Confirms stationarity.
2.2.2 Autocorrelation Analysis
- ACF/PACF: Inconclusive tails → Tested AR(1), MA(1), ARMA(1,1).
- Model Selection: AR(1) chosen via minimized AIC/SC scores.
2.2.3 ARCH Effect Testing
LM test (( p = 0.0000 )) → Significant ARCH effects.
2.2.4 GARCH Model
Finalized GARCH(1,1) equation:
[ \sigma_t^2 = 6.04 \times 10^{-6} + 0.2595 \epsilon_{t-1}^2 + 0.7818 \sigma_{t-1}^2 ]
Post-test: Residuals show no ARCH effects (( p > 0.05 )), validating the model.
Key Findings
3.1 Data Insights
- External Shocks: Regulatory announcements (e.g., country-level bans/endorsements) drastically impact prices.
- Price Volatility: Rapid fluctuations, especially post-shocks, underscore instability.
3.2 Empirical Conclusions
- Speculative Nature: Bitcoin’s lack of intrinsic value and regulatory gaps foster投机行为.
- Bubble Severity: Prices detach sharply from fundamentals, indicating泡沫化.
FAQ Section
❓ Why is Bitcoin so volatile?
Bitcoin’s limited supply, speculative demand, and sensitivity to regulatory news amplify price swings.
❓ How reliable is the GARCH model for Bitcoin?
GARCH(1,1) effectively captures Bitcoin’s volatility clustering, though extreme events may require tail-risk extensions.
❓ Does Bitcoin have long-term investment value?
Given its泡沫化, Bitcoin suits high-risk portfolios but lacks stability for conservative investors.
👉 Explore Bitcoin trading strategies
References
- Li Yuan (2019). Bitcoin Price Volatility and Risk Prevention. Market Weekly.
- Sun Fangjiang (2016). Regulatory Reflections on Bitcoin’s Price Swings. Financial Accounting.
- Liu Xin (2018). Literature Review on Bitcoin Research. Economic Perspectives.