**1. Introduction**

The cryptocurrency market is an emerging market comprised of thousands of digital assets including Bitcoin. A cryptocurrency is a digital asset that uses cryptography and decentralised governance to secure a ledger of transactions. Cryptocurrencies can also be used as a medium of exchange; for background, refer to the review article by Milutinovi´c (2018). Bitcoin, introduced in Nakamoto (2009), is an example of the world's first cryptocurrency; its core innovation established digital scarcity, regulated and audited via a novel decentralised governance mechanism. Financial analysts, chartists and the news media often report on Bitcoin's fractal features (Chambers 2019); however, academic research has shown mixed evidence for multifractal or monofractal scaling with Mensi et al. (2019); Lahmiri and Bekiros (2018); Stavroyiannis et al. (2019) presenting a case for multifractal scaling, while Nadarajah and Chu (2017); Bariviera (2017); Bariviera et al. (2017); Zhang et al. (2018) presenting a case for monofractal scaling. The inconclusive evidence of fractal scaling could be a result of the different detection methods along with varied assumptions. Salat et al. (2017) emphasise that implementation of existing multifractal detection methods can be a perilous undertaking. Moreover, Sly (2006) and Grahovac and Leonenko (2014) demonstrate that attempts to use the scaling function to detect multifractality may mistakenly give rise to false positive results, due to heavy-tailed effects. This calls into question the reliability of the above-mentioned results. Therefore, a detailed examination of scaling functions in the presence of heavy tails is required to bridge the gap between the theory and empirical realities. As an application of the new method we present here, we seek to understand Bitcoin's scaling properties to assist practitioners with model selection for the purpose of risk managemen<sup>t</sup> and volatility forecasting. Given the novel nature of digital assets, it is also of interest to observe similarities in scaling behaviour between Bitcoin and other asset classes. In this paper, we address the central research question: Do Bitcoin prices exhibit multifractal scaling? To answer this question, we investigate the effect of heavy-tails on the scaling function and study scenarios in which false positive<sup>1</sup> detection occurs. If multifractal scaling is plausible, it could indicate the need to incorporate more complex scaling behaviour into pricing models. In the case of Bitcoin, capturing complex scaling behaviour could result in better volatility forecasting. This paper develops an empirical method that tests for multifractal scaling in the presence of heavy tails. Its application is not limited to financial time series, however. This paper is structured as follows. In the rest of this section, we introduce multifractal stochastic processes and their simulation methods. We then explain how the multifractal scaling function is distorted by the presence of heavy tails. In Section 2, we propose a new empirical hypothesis test and construct the look-up table to form rejection and acceptance regions. Then, in Section 3, we apply our hypothesis test to detect multifractal scaling in Bitcoin prices and compare the scaling behaviour of Bitcoin to other financial assets, including the S&P500 index, the Nasdaq Composite Index, the USD/JPY exchange rate, and Gold Futures. Our method detects more complex scaling behaviour in emerging technology asset classes such as Bitcoin and the Nasdaq Composite Index.
