Volatility estimation for Bitcoin: A comparison of GARCH models

TL;DR: In this article, the authors explore the optimal conditional heteroskedasticity model with regards to goodness-of-fit to Bitcoin price data and find that the best model is the AR-CGARCH model, highlighting the significance of including both a short run and a long run component of the conditional variance.

About: This article is published in Economics Letters.The article was published on 2017-09-01 and is currently open access. It has received 730 citations till now. The article focuses on the topics: Conditional variance & Autoregressive conditional heteroskedasticity.

Summary

1. Introduction

• The analysis of Bitcoin has recently received much attention.
• This can be attributed to its innovative features, simplicity, transparency and its increasing popularity (Urquhart 2016), while since its introduction it has posed great challenges and opportunities for policy makers, economists, entrepreneurs, and consumers (Dyhrberg 2016b).
• Bitcoin has therefore a place in the financial markets and in portfolio management (Dyhrberg 2016a), and examining its volatility is crucial.

2. Data and methodology

• The data used are the daily closing prices for the Bitcoin Coindesk Index from 18th July 2010 (as the earliest date available) to 1st October 2016, which corresponds to a total of 2267 observations.
• The data are publicly available online at http://www.coindesk.com/price.
• The returns are calculated by taking the natural logarithm of the ratio of two consecutive prices.
• The models used in this research consist of an Autoregressive model for the conditional mean and a first-order GARCH-type model for the conditional variance2, as follows 2.
• The optimal model is chosen according to three information criteria, namely Akaike (AIC), Bayesian (BIC) and Hannan-Quinn (HQ), all of which consider both how good the fitting of the model is and the number of parameters in the model, rewarding a better fitting and penalising an increased number of parameters for given data sets.

3. Empirical results

• Table 1 presents the summary statistics for the daily closing returns of the Bitcoin price index.
• It can be noticed that the log-likelihood value is maximised under the AR(1)-CGARCH(1,1) model.
• Finally, even though the residuals of the AR(1)-CGARCH(1,1) model still depart from normality, the value of the Jarque-Bera test has considerably decreased compared with the corresponding value for the returns.
• This finding seems to be consistent with the study of Bouoiyour and Selmi (2016) which showed that the optimal model for the period between December 2010 and December 2014 is the CMT-GARCH model, which also consists of both a transitory and a permanent component.

4. Conclusion

• Cryptocurrencies are a globally spreading phenomenon that is frequently and also prominently addressed by media, venture capitalists, financial and governmental institutions alike (Glaser et al. 2014).
• The Bitcoin market in particular has recently seen huge growth.
• As Bitcoin is mainly used for investment purposes, examining its volatility is of high importance.
• The authors found evidence that the optimal model in terms of goodness-of-fit to the data is the AR-CGARCH, a result which suggests the importance of having both a short-run and a long-run component of conditional variance.
• Hence, it can be a useful tool for portfolio and risk management, and their results can help investors make more informed decisions.

Figures

Table 1. Descriptive statistics and unit roots tests.

Table A.2 Estimation results of GARCH-type models for Bitcoin returns.

Fig. 1. Daily closing prices and price returns of the Coindesk Bitcoin Index (US Dollars).

Table A.1 GARCH-type models used.

Frequently asked questions

Q1. What are the contributions in "Volatility estimation for bitcoin: a comparison of garch models" ?

In this article, the authors explore the optimal conditional heteroskedasticity model with regards to goodness-of-fit to the data. 

Q2. What are the future works in "Volatility estimation for bitcoin: a comparison of garch models" ?

Bitcoin is different from any other asset on the financial market and thereby creates new possibilities for stakeholders with regards to risk management, portfolio analysis and consumer sentiment analysis ( Dyhrberg 2016b ). Hence, it can be a useful tool for portfolio and risk management, and their results can help investors make more informed decisions. 

Q3. What is the purpose of this article?

In this research their interest lies particularly in low-order models, since low orders of GARCH-type models can catch most of the nonlinearity of the conditional variance, and hence only the first order models are presented for simplicity. 

Q4. What are the two types of models used in this research?

The models used in this research consist of an Autoregressive model for the conditional mean and a first-order GARCH-type model for the conditional variance2, as follows2 

Q5. What is the current status of the Bitcoin market?

2014; Baek and Elbeck 2015; Dyhrberg 2016a), the Bitcoin market is currently highly speculative, and more volatile and susceptible to speculative bubbles than other currencies (Grinberg 2011; Cheah and Fry 2015). 

Q6. What criteria are used to choose the optimal model?

The optimal model is chosen according to three information criteria, namely Akaike (AIC), Bayesian (BIC) and Hannan-Quinn (HQ), all of which consider both how good the fitting of the model is and the number of parameters in the model, rewarding a better fitting and penalising an increased number of parameters for given data sets. 

Q7. What is the way to describe the volatility of the Bitcoin price?

The authors found evidence that the optimal model in terms of goodness-of-fit to the data is the AR-CGARCH, a result which suggests the importance of having both a short-run and a long-run component of conditional variance. 

Q8. What is the name of the author?

Paraskevi Katsiampa E-mail address: p.katsiampa@shu.ac.ukMoreover, the presence of long memory and persistent volatility (Bariviera et al. 2017) justifies the application of GARCH-type models. 

Q9. What is the way to estimate the volatility of the Bitcoin price?

In addition, according to the results of both the Augmented Dickey-Fuller (ADF) and Phillips-Perron (PP) unit-root tests the authors fail to accept the null hypothesis of a unit root for the returns, and, hence, stationarity is guaranteed. 

Q10. Why has Bitcoin received so much attention lately?

This can be attributed to its innovative features, simplicity, transparency and its increasing popularity (Urquhart 2016), while since its introduction it has posed great challenges and opportunities for policy makers, economists, entrepreneurs, and consumers (Dyhrberg 2016b). 

Q11. What is the significance of the Jarque-Bera test?

even though theresiduals of the AR(1)-CGARCH(1,1) model still depart from normality, the value of the Jarque-Bera test has considerably decreased compared with the corresponding value for the returns. 

Q12. How many observations are used in this research?

The data used are the daily closing prices for the Bitcoin Coindesk Index from 18th July 2010 (as the earliest date available) to 1st October 2016, which corresponds to a total of 2267 observations.