Does bitcoin hedge against the economic policy uncertainty: Based on the continuous wavelet analysis

Cai, Yuxin; Zhu, Zeqi; Xue, Qi; Song, Xinyu Article Does bitcoin hedge against the economic policy uncertainty: Based on the continuous wavelet analysis Journal of Applied Economics Provided in Cooperation with: University of CEMA, Buenos Aires Suggested Citation: Cai, Yuxin; Zhu, Zeqi; Xue, Qi; Song, Xinyu (2022) : Does bitcoin hedge against the economic policy uncertainty: Based on the continuous wavelet analysis, Journal of Applied Economics, ISSN 1667-6726, Taylor & Francis, Abingdon, Vol. 25, Iss. 1, pp. 983-996, https://doi.org/10.1080/15140326.2022.2072674 This Version is available at: https://hdl.handle.net/10419/314195 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Journal of Applied Economics ISSN: (Print) (Online) Journal homepage: www.tandfonline.com/journals/recs20 Does bitcoin hedge against the economic policy uncertainty: based on the continuous wavelet analysis Yuxin Cai, Zeqi Zhu, Qi Xue & Xinyu Song To cite this article: Yuxin Cai, Zeqi Zhu, Qi Xue & Xinyu Song (2022) Does bitcoin hedge against the economic policy uncertainty: based on the continuous wavelet analysis, Journal of Applied Economics, 25:1, 983-996, DOI: 10.1080/15140326.2022.2072674 To link to this article: https://doi.org/10.1080/15140326.2022.2072674 © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. Published online: 21 Jul 2022. Submit your article to this journal Article views: 1267 View related articles View Crossmark data Citing articles: 7 View citing articles Full Terms & Conditions of access and use can be found at https://www.tandfonline.com/action/journalInformation?journalCode=recs20 Does bitcoin hedge against the economic policy uncertainty: based on the continuous wavelet analysis Yuxin Cai a , Zeqi Zhu b , Qi Xue a and Xinyu Song a a School of Management, Shanghai University, Baoshan, Shanghai, China; b Fu Foundation School of Engineering and Applied Science, Columbia University, New York, NY, USA ABSTRACT This article aims to test a causal nexus between bitcoin market and economic policy uncertainty. We use the continuous wavelet analysis to investigate lead-lag relationship between bitcoin market and economic policy uncertainty in different time-frequency domains. Our findings show the negative relationship between bitcoin returns and economic policy uncertainty around the period of bitcoin’s currency recognition and COVIC-19 pandemic crisis both daily and monthly time series test. Furthermore, we find that the causality relationship between bitcoin and economic policy uncertainty is relatively indistinct around the period of bitcoin’s currency recognition, while bitcoin returns are leading economic policy uncertainty changes during COVID-19 pandemic crisis, indicating the economic policy uncertainty fluctuation trend can refer to the fluctuation of bitcoin, bitcoin can be viewed as a leading indicator, but it could not be employed as a safe-haven asset hedge against uncertainty during the period of COVID-19 pandemic. ARTICLE HISTORY Received 25 October 2021 Accepted 28 April 2022 KEYWORDS Bitcoin; economic policy uncertainty; lead-lag relationship; continuous wavelet analysis 1. Introduction After the global financial crisis, a new digital currency named bitcoin created by Satoshi Nakamoto quickly gathered international interest and momentum because of online payments without utilizing the central ledgers of financial institutions. In 2016, bitcoin captured more than 80% of all cryptocurrency capitalization (Ethereum, Litecoin, Ripple, etc.), then attracted a lot of researchers focus on bitcoin market’s efficiency, features, predictability, security, comparison of stock, currency and commodity markets, etc. (AlYahyaee, Mensi, & Yoon, 2018; Bariviera, 2017; Ciaian, Kancs, & Rajcaniova, 2021; Gyamerah, 2020). Bitcoin market displays long-memory and multifractality features (Al-Yahyaee et al., 2018), therefore, Bitcoin is an inefficient market (Bariviera, 2017). Compared with gold market, stock market and currency markets, bitcoin market is the most inefficient market (Al-Yahyaee et al., 2018). As the high-frequency bitcoin price series, Gyamerah (2020) forecasted one-minute time interval of the price series of bitcoin. With increasing uncertainty due to the COVID-19 pandemic, economic policy uncertainty (EPU) has been paid more and more attention, some studies argue that which financial products can CONTACT Yuxin Cai [email protected] School of Management, Shanghai University, Baoshan, Shanghai, China JOURNAL OF APPLIED ECONOMICS 2022, VOL. 25, NO. 1, 983–996 https://doi.org/10.1080/15140326.2022.2072674 © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/ licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. FINANCE AND BANKING ECONOMICS hedge against EPU (Balcilar, Gupta, & Pierdzioch, 2016; Bams, Blanchard, Honarvar, & Lehnert, 2017; Beckmann, Berger, & Czudaj, 2019; Bouri, Roubaud, Jammazi, & Assaf, 2017; Cai, Tao, Y, & Yan, 2020; Shehzad, Bilgili, Zaman, Kocak, & Kuskaya, 2021). However, no conclusive results have been reached about the form and the causal direction of the volatility linkage between cryptocurrency markets and EPU. So, it is important to explore the dynamic relationship between the bitcoin markets and EPU, and whether bitcoin can hedge against the economic policy uncertainty. Many literatures discussed whether bitcoin can be used as a hedging asset applying different analysis (Bouri, Shahzad, Roubaud, Kristoufek, & Lucey, 2020; Mokni, Ajmi, Bouri, & Vinh, 2020; Nguyen, Nguyen, Nguyen, & Pham, 2019; Smales, 2019; Wang, Xie, Wen, & Zhao, 2019). Wang et al. (2019) examine the risk spillover effect from economic policy uncertainty to bitcoin at different risk levels using multivariate quantile model and Granger causality risk test. Mokni et al. (2020)show that an increase in the economic policy uncertainty level is associated with an increase in the optimal weight of bitcoin in the portfolio before the bitcoin crash of December, and after the bitcoin crash, there is a negative effect of economic policy uncertainty on the dynamic conditional correlations between bitcoin and the USA stock markets. Bouri et al. (2020) find the least dependent between bitcoin and the stock markets among bitcoin/gold/commodities and stock markets using the wavelet coherency approach. Aslanidis, Bariviera, and López (2022) indicate that there is a bidirectional flow of information between Google Trends attention and cryptocurrency returns up to 6 days, so cryptocurrencies are linked to a Google Trends attention. Other discussions about bitcoin price volatility, price discovery, information efficiency, etc., are reviewed by Bariviera and Merediz-Solà (2021) for detail. As the inconsistencies in the time series of bitcoin price (Alexander & Dakos, 2019), different with Dyhrberg (2016), Baur, Dimpfl, and Kuck (2018) and Cheikh, Zaied, and Chevallier (2020) used GARCH models to test bitcoin market’ volatility, we use the continuous wavelet analysis to extend the time-frequency test between bitcoin price and economic policy uncertainty. This method does not require the two series to be stationary of cointegrated which exhibits a major advantage of widely accommodating financial series, regardless of stationary properties. Therefore, the continuous wavelet analysis can describe how the volatility linkage between two series develops over time and varies across different frequency bands in a highly intuitive way. The main advantage of continuous wavelet analysis is decomposing series by different time scale and provides information about the lead-lag relationship between two time series. It has been widely used to identify the leading indicator between two interactive factors or estimate the comovement and causality between two time series (Aloui et al., 2016; Cai et al., 2020; Chen, Chen, & Tseng, 2017; Matar, 2020; Zaremba, Umar, & Mikutowski, 2019). So, we can test whether bitcoin can be viewed as a leading indicator hedge against the economic policy uncertainty across different times and frequencies using continuous wavelet analysis. Aloui et al. (2016) find a strong positive association in the short term and a negative linkage for longer time-scales between Islamic stock and bond markets among the Gulf Cooperation Council countries using wavelet approach. Zaremba et al. (2019) discussed the inflation hedging properties of commodities in UK using wavelet analysis, showing that the co-movement is strong at the aggregate level and for energy, industrials or agriculturals from 13 th to the 19 th centuries, but it visibly weakened in the 20 th century. 984 Y. CAI ET AL. Bahramian and Saliminezhad (2020) tested a causal nexus between capacity utilization and inflation in the US using wavelet coherency and phase differences, showing that capacity utilization and inflation can be related to each other in the short term significantly and primarily, and mostly capacity utilization contains forecasting ability for inflation in the short-term frequency, whereas in the medium and long term, the causal link changes often. This paper focus on a causal nexus between bitcoin market and economic policy uncertainty to confirm whether bitcoin can hedge against EPU. We use the EPU index to quantify global economic policy uncertainty from Economic Policy Uncertainty website (www.policyuncertainty.com). EPU index explored by Davis (2016) is a GDPweighted average of national EPU indices for 16 countries that account for two-thirds of global output. Each national EPU index reflects the relative frequency of owncountry newspaper articles that contain a trio of terms pertaining to the economy, uncertainty and policy-related matters. For the bitcoin price, we choose bitcoin close and weighted price from the Bitstamp exchange. In September 2013, the USA Senate discussed the impact and opportunities brought by bitcoin. The seminar weakened the negative role of bitcoin and encouraged the direction of scientific and technological innovation of bitcoin. Federal Reserve Chairman Ben Bernanke also expressed cautious optimism and wishes for the bitcoin, 1 and this marked the recognition of bitcoin in real sense. Through the continuous wavelet analysis, we found that bitcoin returns and economic policy uncertainty are negatively correlated around the period of bitcoin’s currency recognition and COVIC-19 pandemic crisis both daily and monthly time series test. The causality relationship between bitcoin and EPU is relatively indistinct around the period of bitcoin’s currency recognition in 2013 by daily time series test. By monthly time series test around 2013 and both daily and monthly time series test during COVID-19 pandemic crisis, the results show that bitcoin returns are leading economic policy uncertainty changes, indicating EPU fluctuation trend can refer to the fluctuation of bitcoin, bitcoin can be viewed as a leading indicator, but it could not be employed as a safe-haven asset hedge against uncertainty during the period of COVID19 pandemic. 2. Methodology Wavelet analysis breaks empirical analysis into time-frequency components, which both time and frequency changing information of the time series can be well visualized. Wavelet analysis’ advantage is not only handling irregular data series, but also decomposing series by time scale (Daubechies, 1992), so that economic variables can be accommodate on different time scales simultaneously (Ramsey, 2002). There are two kinds of wavelet transforms: discrete wavelet and continuous wavelet transforms which 1 See SEC (Securities and Exchange Commission) Testimony before the Senate Committee on Homeland Security and Governmental Affairs. 30 August (https://www.documentcloud.org/documents/835843-virtual-currency-hearings. html). The document of virtual-currency-hearings in page 10 (also can search in Board of Governors of the Federal Reserve System website). “These types of innovations [such as Bitcoin] may pose risks related to law enforcement and supervisory matters, there are also areas in which they may hold long-term promise, particularly if the innovations promote a faster, more secure and more efficient payment system.” JOURNAL OF APPLIED ECONOMICS 985 can extract the local amplitudes of a time series in time and frequency domains. The continuous wavelet analysis mainly involves wavelet coherency and phase-difference. Based on a mother wavelet φ, a family φτ;s of “wavelet daughter” is defined as: φτ;stð Þ :¼1 ffiffiffiffiffi sj j pφtτ s � �:τ;s2R;s�0 (1) where τ is a translation parameter depicting where the mother wavelet φ is centred, and s is a scaling factor determining the wavelet compressed or stretched. If sj j<1, then the mother wavelet φ tð Þ is compressed, if sj j>1, shows that the mother wavelet is stretched across frequencies. We choose Morlet wavelet 2 as the mother wavelet, which is given as: φ tð Þ ¼ π1 4exp i� ω0tð Þexp 1 2t2 � � (2) where ò þ1  1 φ tð Þj j2dt <þ1, and ò þ1  1 φ tð Þj jdt ¼0. Based on the mother wavelet, the continuous wavelet transform is defined as Wx;φτ;sð Þ ¼ ò þ1  1x tð Þ 1 ffiffiffiffiffi sj j pφ�tτ s � �dt (3) where * denotes the complex conjugation of the Morlet wavelet. The time series is expanded into a time-frequency space depending on τ and s. Then, the wavelet power spectrum is given as: WPSxτ;sð Þ ¼ Wxτ;sð Þj j2(4) Further, the cross-wavelet transform of two different time series, x tð Þ and y tð Þ is defined as: Wxy τ;sð Þ ¼ Wxτ;sð ÞW� yτ;sð Þ (5) where Wxτ;sð Þand Wyτ;sð Þare the continuous wavelet transforms of x tð Þand y tð Þ. And the dynamic correlation in different time-frequency domain can be investigated by the wavelet coherency. The wavelet coherency is defined as follows: Rxy ¼S Wxy  � ���� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi S Wx j j2  �S Wy ����2 � � r(6) which s is a scaling factor. And the phase-difference is applied to reveal the positive or negative correlation and lead-lag interaction between two different financial time series. The angle ϕxy of the complex coherency is the phase-difference, which is defined as: ϕxy ¼tan1=S Wxy  � � <S Wxy  � � ! (7) 2 There are different types of mother wavelets: Daubechies, Haar, Mexican hat, Morlet and so on. We choose Morlet wavelet because it provides the possibility of calculating the amplitudes and phases of continuous wavelet transforms, which can be used of the estimations of the wavelet power spectrum, wavelet coherency and the phase difference, it is the most applicable mother wavelet among the different types. 986 Y. CAI ET AL. where =ðÞand <ðÞare the imaginary part and real part, respectively. Because of the time, frequencies and the strength of the correlation between different time series are considered at the same time, wavelet coherency can provide a better measure of comovement that exists between different variables, but it does not determine the direction (the arrow point) of the co-movement. And the phase-difference which can detect information on the phase delay between oscillation in different time series as a function of frequency (Bloomfield, 2004) could be used to find the direction and causal relationship between different series. Different arrows (range of angles) indicate different lead-lag relationship between two series. 3. Data We use daily and monthly data on the bitcoin price and economic policy uncertainty variables covering January 2012 to June 2021. Alexander and Dakos (2019) underlined that the choice of data is relevant in cryptocurrency studies, and according to VidalTomás (2021), we choose close and weighted 3 data of bitcoin market which are the most active cryptocurrency markets. For economic policy uncertainty variables, we choose global EPU explored by Davis (2016) which is based on Baker, Bloom, and Davis (2016). We use this sample period due to the data availability of all the data sources. The original data were derived from the Economic Policy Uncertainty website and bitcoincharts website. The daily and monthly returns of bitcoin close price CBRt or weighted price WBRt are defined as the logarithmic difference of the monthly close price cpt or weighted price wpt, the formulas are as follows CBRt¼log cpt ð Þ log cpt1 ð Þ (8) WBRt¼log wpt ð Þ log wpt ð Þ (9) We set daily and monthly changes in EPU as follows: ΔEPUt¼EPUtEPUt1(10) CBRt,WBRt, ΔEPUt observations are illustrated in Table 1. Table 1. Descriptive statistic for BRt, ΔEPUt observations. Variable Mean(%) Max Min S.D. Skewness Kurtosis ADF No. Daily CBR .1111 .1466 −.2883 .0202 −1.3743 25.5550 −61.51*** 3469 WBR .1115 .1263 −.2155 .0173 −1.0004 17.9189 −47.92*** 3469 Δ EPU −1.6613 525.36 −381.67 62.29 .1837 9.4336 −91.95*** 3469 Monthly CBR 3.4008 .7404 −.2007 .1237 1.8314 11.7521 −8.41*** 114 WBR 3.4169 .7521 −.1920 .1244 1.8816 12.0339 −8.61*** 114 Δ EPU −45.82 122.63 −119.20 33.55 −.0205 5.7626 −14.97*** 114 *** Denotes the rejection of the null hypothesis at the 1% significance level. 3 Weighted data is calculated with the average of the prices across the 24-hour period. JOURNAL OF APPLIED ECONOMICS 987 Table 1 shows the descriptive statistics for daily and monthly bitcoin return, EPU change. Each bitcoin return of the mean value is close to zero, and its standard deviation is nearly zero except monthly EPU change. Each skewness is nearly zero and kurtosis are all smaller than 3, indicating no strong deviations from normality. The ADF test shows the stationarity of daily and monthly bitcoin return, EPU change at the 1% significance level. 4. Empirical results 4.1. The wavelet power spectrum analysis Figure 1 displays the wavelet power spectrum of bitcoin return and ΔEPU. The color represents the strength of power, ranging from blue (low power) to yellow (high power). The cone of influence (COI) is given by a white line, which defines the regions affected by the edge effects. We mainly focus on the regions inside the COI. As shown in Figure 1 (a.2-c.2), the horizontal axis denotes the time component while the vertical axis denotes the frequency bands, from period 0.01 year (3.6 days) up to period 1 year. Figure 1 (a.1),(b.1) show the bitcoin return seems to present a stable pattern. We focus on the variation as shown in Figure 1 (a.2),(b.2), the volatilities of close and weighted bitcoin return are significant (at 5% significance level) in the 0– 0.01 year frequency band during 2013–2014. This implies the significant volatilities of bitcoin return when bitcoin was regarded as a recognitory form of currency in the very short term. Due to the stimulus economic policies after the global financial crisis and various countries’ governments express their position on bitcoin, a relatively high level of bitcoin volatilities as shown in the figures during that time in the very short term. Figure 1 (c.2) shows significant (at 5% significance level) volatilities of daily EPU changes in the 0–0.01 year frequency band starting in 2020. This means the high level of EPU changes from 2020 in the very short term. The results indicate that the impact caused by the COVID-19 is much significant than any other times. With the continuous control of the COVID-19 infection, the fluctuation of EPU began to alleviate. In Figure 1 (d.2-e.2), the volatilities of monthly close and weighted bitcoin return are significant (at 5% significance level) in the 0–1 year frequency band during 2013–2014, 0–0.05 year frequency band around 2014. This also implies the significant volatilities of bitcoin return when bitcoin was regarded as a recognitory form of currency in the very short term. The volatilities of close and weighted bitcoin return are significant in the 0– 0.05 year frequency band around 2018 and 2020 with the impact of supervision of bitcoin from 2018 and COVID-19 infection from 2020, but the impact is weaker than when it was regarded as a recognitory form of currency in 2013. Figure 1 (f.2) shows significant (at 5% significance level) volatilities of monthly EPU changes in the 0– 0.5 year frequency band starting in 2020. This also means the high level of EPU changes from 2020 in the very short term. The results also indicate that the impact caused by the COVID-19 is much significant than any other times. With the continuous control of the COVID-19 infection, the fluctuation of EPU changes began to reduce. The results of daily and monthly data are consistent, indicating the reliability of our conclusion. 988 Y. CAI ET AL. (a.1) (a.2) (b.1) (b.2) (c.1) (c.2) (d.1) (d.2) (e.1) (e.2) (f.1) (f.2) Figure 1. (a.1-c.1) The volatility of daily bitcoin return (daily CBRnWBR) and ΔEPU, (d.1-f.1) The volatility of monthly CBRnWBR and ΔEPU, respectively. (a.2-f.2) The wavelet power spectrum of daily and monthly CBRnWBR, ΔEPU respectively. The white line refers to the COI. The color code of power varies from blue (low power) to yellow (high power). JOURNAL OF APPLIED ECONOMICS 989 Dyhrberg, A. H. (2016). Bitcoin, gold and the dollar: A GARCH volatility analysis. Finance Research Letters, 16, 85–92. Gyamerah, S. A. (2020). On forecasting the intraday bitcoin price using ensemble of variational mode decomposition and generalized additive model. Journal of King Saud UniversityComputer and Information Sciences. doi:10.1016/j.jksuci.2020.01.006 Matar, A. (2020). Does electricity consumption impacting financial development? Wavelet analysis. Future Business Journal, 6(1), 18. Mokni, K., Ajmi, A. N., Bouri, E., & Vinh, V. (2020). Economic policy uncertainty and the bitcoin-US stock nexus. Journal of Multinational Financial Management, 57-58, 100656. Nguyen, T. V. H., Nguyen, B. T., Nguyen, K. S., & Pham, H. (2019). Asymmetric monetary policy effects on cryptocurrency markets. Research in International Business and Finance, 48, 335–339. Ramsey, J. B. (2002). Wavelets in economics and finance: Past and future. Studies in Nonlinear Dynamics and Econometrics, 6(3), 1–27. Shehzad, K., Bilgili, F., Zaman, U., Kocak, E., & Kuskaya, S. (2021). Is gold favourable than bitcoin during the COVID-19 outbreak? Comparative analysis through wavelet approach. Resources Policy, 72, 102163. Smales, L. (2019). Bitcoin as a safe haven: Is it even worth considering? Finance Research Letters, 30, 385–393. Vidal-Tomás, D. (2021). An investigation of cryptocurrency data: The market that never sleeps. Quantitative Finance, 21(12), 2007–2024. Wang, G. J., Xie, C., Wen, D. Y., & Zhao, L. F. (2019). When bitcoin meets economic policy uncertainty: Measuring risk spillover effect from EPU to bitcoin. Finance Research Letters, 31, 489–497. Zaremba, A., Umar, Z., & Mikutowski, M. (2019). Inflation hedging with commodities: A wavelet analysis of seven centuries worth of data. Economics Letters, 181, 90–94. 996 Y. CAI ET AL.