*3.1. Application to Bitcoin*

In this section, we apply our proposed hypothesis test to Bitcoin prices in order to address our research question: Do Bitcoin prices exhibit multifractal scaling? Both the global simplex statistic and the localised concavity measures are employed and reported. Two Bitcoin data sets are used in this paper:


Let {*P*(*t*), *t* = 0, 1, ..., *T*} denote the open prices of Bitcoin. We define *X*(*t*) to be the mean-centered log-prices

$$X(t) = \ln P(t) - \ln P(0) - \mu t\_\prime$$

where *μ* = 1*T* ∑*Ti*=<sup>1</sup> ln *P*(*i*) *<sup>P</sup>*(*<sup>i</sup>*−<sup>1</sup>). The mean-centered log-returns are then defined as

$$r(t) = X(t) - X(t-1).$$
