The high frequency multifractal properties of Bitcoin

Abstract

Following the new advances in encryption and network computing, Bitcoin emerged as a private sector system facilitating peer-to-peer exchange via distributed ledgers based on blockchains, driving a transformational change towards a global economy outside the core financial system. The main purpose of this paper is to examine the multifractal properties of the Bitcoin price using high frequency data. The methods used are the wavelet transform modulus maxima and the multifractal detrended fluctuation analysis. The results indicate that Bitcoin exhibits a large degree of multifractality in all examined time intervals, and the main source of multifractality is attributed to the high kurtosis and the fat distributional tails of the series returns.

Hybrid Forecasting Models Based on the Neural Networks for the Volatility of Bitcoin

“…In order to find the optimal GARCH model for the hybrid model, we provide AIC and BIC values in Table 2 and three measures to compare the performances of the models for forecasting volatilities in Table 3. According to the results in Table 2 and AIC and BIC criteria, EGARCH (3,3) model is the best model. On the other hand, according to the results in Table 3, we can see that the GJR-GARCH(1,1) model performs the best among the introduced GARCH family models.…”

“…We first forecast the volatility of Bitcoin price using the classic GARCH family models. Concretely, we use GARCH, EGARCH and GJR-GARCH model among the GARCH family models and the (p, q) parameters ranging from (1,1) to (3,3). In order to find the optimal GARCH model for the hybrid model, we provide AIC and BIC values in Table 2 and three measures to compare the performances of the models for forecasting volatilities in Table 3.…”

“…To examine well the proposed models based on the HONN, we present a summary of the input variables of each model in Table 10. In Table 10, 'LV t ' is in Equation (6), 'GT' means Google trends data, 'VIX' means VIX index data, 'GJR-GARCH(1,1)' means forecast by GJR-GARCH(1,1) and 'EGARCH(3,3)' means forecast by EGARCH (3,3). Tables 7 and 8 present the results of the HONN model without the outputs of GARCH models as shown in Table 10.…”

“…To find the inefficiency, Urquhart employed a battery of highly powerful tests for randomness and found evidence of inefficiency. The high-frequency multifractal properties of Bitcoin were examined in [3]. Gajardo et al [4] analyzed the asymmetric multifractal cross-correlations among stock market indices, commodities and Bitcoin.…”

Bitcoin Analysis and Forecasting Through Fuzzy Transform

“…In the case of Bitcoin prices using high frequency data, in [38] it is shown that it exists a large degree of multi-fractality in all examined time intervals which can be attributed to the high kurtosis and the fat distributional tails of the series returns; in [39] there is evidence about the leverage effect as the most powerful effect in volatility forecasting; volatility is also analysed in [40] in terms of the property of the long memory parameter to be significant and quite stable for both unconditional and conditional volatilities at different time scales. Extending the study to several high frequency cryptocurrencies data, in [41] the investigation on stylized facts is developed in terms of the Hurst exponent of dependence between four different cryptocurrencies.…”