Testing for Self-exciting Jumps in Bitcoin Returns

Abstract

Cryptocurrencies, especially Bitcoin (BTC), have drawn extraordinary worldwide attention. The characteristics of BTC include a high level of speculation, extreme volatility, and price discontinuity. This paper investigates the self-exciting jumps in Bitcoin prices using a new nonparametric test proposed by Boswijk et al. (2018). We have the following discoveries. First, we document evidence of self-exciting jumps in Bitcoin returns, the strength of self-excitation does not increase monotonically with jump size, and the most self-excitation events occur with mild-sized jumps. Second, we find strong asymmetry in the self-excitation, which is triggered, on average, more by bad (negative) jumps than good (positive) jumps. Third, in bear markets, the self-excitation is triggered, on average, more by bad jumps than good jumps; in bull markets, however, the self-excitation triggered by good jumps is not more evident than bad jumps. Fourth, we find significant intraday aftershock effect of self-excitation, and the aftershocks triggered by bad jumps are more evident than the aftershocks triggered by good jumps. Finally, if we detect jumps by using a formal test, previous conclusions still hold and we document more evidence of self-exciting jumps.

Keywords: Bitcoin; self-excitation; good jumps; bad jumps; high frequency data; FinTech