Cryptocurrency Price Bubble Detection Using Log-Periodic Power Law Model and Wavelet Analysis

In this article, we establish a method to detect and formulate price bubbles in the cryptocurrency markets. This method identifies abnormal crashes through violations of the exponential decaying property. Confirmations of bubble bursts within these anomalies are obtained through wavelet analysis. By decomposing the cryptocurrency price into the high-frequency and low-frequency factors, we distinguish the price regimes versus the periods with bubbles and crashes in both time and frequency domains. In addition, we apply the log-periodic power law model to fit the bubble formation. In the analysis of eight cryptocurrencies—Bitcoin, Ethereum, Litecoin, Antshares, Ethereum Classic, Dash, Monero, and OmiseGO—from 15 May 2018 to 28 November 2022, we identify 24 bubbles. Some of them exhibit a significant and strong exponential growth pattern.