Chaos, Solitons and Fractals 139 (2020) 109994 Contents lists available at ScienceDirect Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos Multifractal behavior in return and volatility series of Bitcoin and gold in comparison ¸ Sahin Telli ∗ , Hongzhuan Chen College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, China a r t i c l e i n f o Article history: Received 26 December 2019 Revised 17 April 2020 Accepted 6 June 2020 Keywords: Bitcoin Gold Multifractal detrended fluctuation analysis Returns Volatility Structural change, a b s t r a c t In this study, we investigate multifractal nature of return and volatility (proxied by absolute and squared returns) series of Bitcoin and gold throughout full sample periods and sub-sample periods which are de- cided accordingly the results of the structural breaks in the full sample periods. Applying the Multifractal Detrended Fluctuation Analysis (MFDFA), it is found that Bitcoin return series have distinctly different multifractal properties than of gold. Our evidence shows that all return and volatility series of Bitcoin have a persistent behavior, and have higher degree of multifractality than of gold. Using rolling windows approach, we confirm the persistence and the higher degree of multifractality of Bitcoin time series. Re- turn series of gold have uncorrelated behavior while volatility series of gold have persistent behavior. Moreover, applying structural break test for the series of complexity parameters retrieved from the mul- tifractal analysis of the return and volatility series of gold and Bitcoin, our results indicate that time series of gold have different regimes with different characteristics of multifractality. Furthermore, impact of temporal correlations and fat-tails is also examined and both are found to be the source of multifrac- tality in the return series of Bitcoin and gold. In volatility series of Bitcoin, multifractality arises mostly due to long-range correlations and fat-tails. However, presence of long-range correlations and fat-tails in the original volatility series of gold mostly yields to less degree of multifractality. © 2020 Elsevier Ltd. All rights reserved. 1. Introduction Bitcoin is a currency of a blockchain network which handles all the transactions using an inspirational approach distributed time- stamped server between peers as its shortly described by its cre- ator [1]. Its creator, pseudonymous Satoshi Nakamoto, does not owns the network, but holds bitcoins 1 that is mined in the net- work. Bitcoin, which is a living proof of that digital money gener- ation initiatives have resulted in success, has earned great reputa- tion and potential use in 10 years, and meanwhile many new cryp- tocurrencies (altcoins) have been created. The technology behind cryptocurrencies is being adopted more and more every day con- sidering the potential to transform many sectors by creating busi- ness models that do not require reliable third-party institutions for security or audition purposes. Bitcoin attraction is tracked via Google trend [2], and interest in Bitcoin is measured by statistics regarding to internet activi- ties such as Google search queries, Wikipedia page visits, Twit- ter and Facebook posts [3,4]. Additionally, motives such as Liber- ∗ Corresponding author. E-mail address: sahintelli@yahoo.com ( ¸ S. Telli). 1 https://blog.bitmex.com/satoshis- 1- million- bitcoin/. tarian ideology or investment expectations are found to have no role in Bitcoin use mostly, and illegal activities and computer pro- gramming found to be motives leading interest behind adoption of Bitcoin [5]. However, since the network is not an asset owned by any central authority similar to gold just being an asset of earth and considering the developments associated with global risks and uncertainty as Greek and European sovereign debt crisis [6], the Cypriot banking crisis, 2 and the developments with the US, China, Russia and Brexit, 3, 4, 5 growing attraction gives Bitcoin a role to be a new asset of safe haven assets class. Ref. [7,8] compare similari- ties/dissimilarities between gold and Bitcoin regarding to the reac- tion to macroeconomic news surprises. Ref. [9] found that Bitcoin was robust to Brexit. In the literature studies, hedging capabilities of Bitcoin is also discussed. Bitcoin is found to be a useful hedging tool in between gold and US dollar [7] and it has the similar hedg- 2 https://www.cnbc.com/id/100597242. 3 https://www.forbes.com/sites/billybambrough/2019/06/21/ bitcoin- brexit- and- boris- johnson/#661584197c07. 4 https://www.home.saxo/- /media/documents/campaigns/outrageous- predictions/ outrageouspredictions2017.pdf. 5 https://www.cnbc.com/2016/12/07/bitcoin- price- could- rise- to- 2000- in- 2017 - driven- by- trump- policies- us- dollar- inflation- rocketing.html. https://doi.org/10.1016/j.chaos.2020.109994 0960-0779/© 2020 Elsevier Ltd. All rights reserved.