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Statistical analysis of bitcoin during explosive behavior periods.

José Antonio Núñez1, Mario I Contreras-Valdez1, Carlos A Franco-Ruiz1

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The normal inverse Gaussian (NIG) distribution effectively models bitcoin (BTC) returns, even during volatile bubble periods. This finding aids in developing hedging strategies against cryptocurrency market fluctuations.

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Area of Science:

  • Quantitative Finance
  • Computational Statistics
  • Cryptocurrency Analysis

Background:

  • Bitcoin (BTC) exhibits extreme volatility and bubble-like price behavior, posing challenges for traditional financial modeling.
  • Existing theories struggle to classify and predict the dynamics of cryptocurrencies due to their unique characteristics.

Purpose of the Study:

  • To assess the suitability of the normal inverse Gaussian (NIG) distribution for modeling Bitcoin returns.
  • To investigate the NIG distribution's performance in capturing volatility and bubble episodes in cryptocurrency data.
  • To explore the potential of NIG for developing risk management strategies in cryptocurrency markets.

Main Methods:

  • Applying the normal inverse Gaussian (NIG) distribution to historical Bitcoin price data against major global currencies.
  • Analyzing time segments exhibiting bubble behavior (price surges and collapses).
  • Conducting out-of-sample tests to compare NIG performance against generalized hyperbolic (GH) distributions.

Main Results:

  • The NIG distribution demonstrated a robust ability to fit Bitcoin returns across all observed time segments, including periods of high volatility and market bubbles.
  • NIG's heavy-tailed property and closure under convolution make it suitable for capturing extreme price movements and measuring multivariate risk.
  • Out-of-sample validation showed NIG's fitting performance comparable to that of generalized hyperbolic (GH) distributions.

Conclusions:

  • The normal inverse Gaussian (NIG) distribution is a viable statistical tool for modeling the complex return dynamics of Bitcoin.
  • Findings support the use of NIG for enhanced risk assessment and the development of hedging strategies against cryptocurrency volatility.
  • This research provides a foundation for future statistical analyses of cryptocurrencies and their multivariate distributions.