Estimating Bitcoin Volatility with GARCH Models and NIG Errors

Summary

The paper compares sGARCH, iGARCH, and tGARCH models for estimating volatility in Bitcoin returns. Each model is paired with Student t, generalized error, and normal inverse Gaussian (NIG) distributions to represent features such as volatility clustering, heavy tails, and skewness. The comparison focuses on how well these model and distribution combinations capture the return series’ behavior.

The reported results favor NIG for representing fat tails and skewness, and identify tGARCH with NIG as the strongest specification among those examined. The authors attribute tGARCH’s advantage to its ability to represent different volatility responses to positive and negative news. They suggest NIG may also suit other cryptocurrencies because their returns are often leptokurtic. The document provides no details on sample period, evaluation metrics, forecast performance, or trading results, so its conclusions are limited to the reported model comparison and may not generalize across assets or periods.

Key ideas

• GARCH-family models can represent volatility clustering in Bitcoin returns.
• The study compares Student t, generalized error, and normal inverse Gaussian return distributions.
• The normal inverse Gaussian distribution is reported to capture skewness and heavy tails well.
• tGARCH allows volatility responses to positive and negative shocks to differ.
• The reported preferred specification is tGARCH with normal inverse Gaussian errors.

Tags

# Estimating the volatility of Bitcoin using GARCH models


# Estimating the volatility of Bitcoin using GARCH models









In this paper, an application of three GARCH-type models (sGARCH, iGARCH, and tGARCH) with Student t-distribution, Generalized Error distribution (GED), and Normal Inverse Gaussian (NIG) distribution are examined. The new development allows for the modeling of volatility clustering effects, the leptokurtic and the skewed distributions in the return series of Bitcoin. Comparative to the two distributions, the normal inverse Gaussian distribution captured adequately the fat tails and skewness in all the GARCH type models. The tGARCH model was the best model as it described the asymmetric occurrence of shocks in the Bitcoin market. That is, the response of investors to the same amount of good and bad news are distinct. From the empirical results, it can be concluded that tGARCH-NIG was the best model to estimate the volatility in the return series of Bitcoin. Generally, it would be optimal to use the NIG distribution in GARCH type models since time series of most cryptocurrency are leptokurtic.

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