Cryptocurrency price bubble detection using log-periodic power law model and wavelet analysis

We establish a relatively more complete mechanism for detecting the price bubbles in the cryptocurrency markets, which excludes the external factors as far as possible to focus on the study of the characteristics of the price bubbles. This mechanism detects the abnormal rupture of the cryptocurrency price bubbles through the exponential distribution of the continuous descent distribution. The wavelet analysis is applied to decompose the cryptocurrency price and the high-frequency wavelet factor is devoted to determine the relatively stable interval of price time series in the time and frequency domains. In addition, the log-periodic power law (LPPL) model is used to fit the bubble intervals after finding 40 bubble intervals ranging approximately from July 1, 2017 to November 20, 2020 in the eight cryptocurrencies, which are Bitcoin (BTC), Ethereum (ETH), Litecoin (LTC), NEO, Ethereum Classic (EHC), Dash (DASH), Monero (XMR), OMG. and the price data is collected hourly. The result shows that Bitcoin has a significant benchmarking effect in the market and every correlation coefficient between the eight cryptocurrencies is more significant than 0.5. We propose a new range of periodic parameters of the LPPL model when using the hourly frequency of cryptocurrency price. The new interval reflects that the growth of some cryptocurrency bubbles is stronger in exponential growth, which is an essential supplement to the LPPL model in the cryptocurrency market