**1. Introduction**

Bitcoin is a celebrated yet controversial digital currency that continues to attract much attention from users, investors, and regulators across the globe. It is a completely decentralised digital currency without a regulator, with transactions recorded in a publicly distributed ledger called a blockchain [1,2]. New transactions are bucketed into 'blocks' and written onto the end of a 'chain' of pre-existing blocks representing old transactions, hence the name 'blockchain'. Despite wide price fluctuations and periods of booms and busts, Bitcoin holds a major volume in the cryptocurrency domain. Notably, new Bitcoin is introduced into circulation via a process called 'mining', through which transactions are validated for a blockchain. Successful miners are rewarded newly minted Bitcoin for synchronising Bitcoin transactions after solving a complex hashing puzzle. In the process of such proof-of-work mining, new Bitcoins are issued at intervals of almost 10 min, and finding a single block of Bitcoin involves approximately 10 hash computations. While less energy-intensive mechanisms of mining, such as proof-of-space or proof-of-stake, have recently emerged to secure transactions on blockchain by enabling computer networks to collaborate, their application cannot guarantee security and raises significant technological issues. This is why proof-of-work remains the most popular mechanism of mining.

Bitcoin miners operate specialised mining devices with increasingly advanced hardware, such as application-specific integrated circuits (ASICs). They generally use multiple

**Citation:** Ghosh, B.; Bouri, E. Is Bitcoin's Carbon Footprint Persistent? Multifractal Evidence and Policy Implications. *Entropy* **2022**, *24*, 647. https://doi.org/10.3390/ e24050647

Academic Editors: Stanisław Drozd˙ z,˙ Jarosław Kwapie ´n and Marcin W ˛atorek

Received: 18 March 2022 Accepted: 1 May 2022 Published: 5 May 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

machines to synchronise Bitcoin transactions and optimise their odds of getting the mining reward, which requires repeatedly running and cooling multiple mining machines. Notably, enormous energy resources are wasted in the Bitcoin mining process. In fact, the mining process consumes huge amounts of electricity [3], and the resulting electricity consumption has been measured at 110.53 TWh per year, exceeding the energy consumption of the Netherlands, inducing a carbon footprint of 36.95 megatons of CO2 per year, comparable to that of New Zealand. Rising Bitcoin prices make mining very lucrative and attractive, which leads to more electricity consumption [1,4] and greater carbon footprints.

Previous studies show that electricity consumption has a direct and positive relationship with CO2 emissions [5], and a study of Chinese and Russian electricity markets finds that Bitcoin price volatility is positively correlated with the utility market pricing volatility [6]. The public transaction record (blockchain) is also very energy intensive. However, proof-of-work consumes significantly more energy than proof-of-stake. The number of miners may decline over time or move to more energy-efficient machines [7].

In this paper, we contribute to the above debate on the carbon footprint of Bitcoin mining by examining the long memory process in Bitcoin electricity consumption that reflects the CO2 emissions of the mining process. Specifically, we use daily data on the Bitcoin Energy Consumption Index (BECI) over the period 25 February 2017 to 25 January 2022 and apply fractionally integrated GARCH (FIGARCH) models and multifractal detrended fluctuation analysis (MFDFA).

Accordingly, we extend the above literature, which remains silent on whether Bitcoin's carbon footprint, measured by energy consumption, exhibits a long memory process. Interestingly, the true long memory process has many facets, which make its application to Bitcoin electricity consumption very informative. Its implications matter to the choice of the most suitable policies that should be applied to address the carbon footprint of Bitcoin mining. For linking stationary long memory and the types of policy (transitory versus permanent), Belbute & Pereira [6,8] argue that if emissions are stationary, then transitory policies (i.e., promotion of energy efficiency, switching from fossil fuel to green energy etc.) will have only transitory effects and fade away in the long-term. Conversely, if emissions are non-stationary, then transitory policies will have a lasting permanent effect [6,8]. Concerns over the energy consumption of Bitcoin mining are indicated by McCook [9], who includes mining-rig procurement and cooling calculations, and argues that Bitcoin is less harmful to the environment than gold mining. Bitcoin's carbon footprint is comparable to that of Ireland [10], and Mora et al. [11] confirm that the estimated CO2 emissions from Bitcoin could make the globe warmer by 2 ◦C. Howson [12] expresses concern about the carbon footprint of Bitcoin, while Krause and Tolaymat [10] show that the mining of 4 cryptocurrencies (Bitcoin, Ethereum, Litecoin, and Monero) generated 3–15 million tonnes of CO2 emissions over the period 1 January 2016 to 30 June 2018. Sedlmeir [13] points to the huge energy consumption of blockchains, especially on the basis of the number of transactions they operate.

In fact, a strong statistical dependence of a mean-reverting time series indicates long memory, long-range dependence or simply persistence [14–16]. Generally, the dependence becomes weaker with time but not in the presence of long memory. Non-stationary time series also show evidence of persistence, sometimes even more strongly than stationary series. Thus, mean reversion holds the key to true long memory. Past and present values are connected by a fractionally integrating parameter, d, which must be empirically calibrated. A partially long memory exists when d = 0, since a significant mean reversion happens at first difference. For such cases, permanent policy changes are recommended to address the carbon footprint of Bitcoin mining. However, for pure long memory (d = 0), the effects generated by transitory policy shocks persist for a long time, and thereby the type of long memory indicates the preferred type of policy that should be adopted by regulators and policymakers to address the carbon footprint of Bitcoin mining.

Following this introduction, Section 2 describes the data and methodology. Section 3 presents and discusses the results. Section 4 concludes and offers policy implications.
