Testing for Multiple Bubbles in Bitcoin Markets: A

Accepted Manuscript Title: Testing for Multiple Bubbles in Bitcoin Markets: A Generalized Sup ADF Test Authors: Chi-Wei Su, Zheng-Zheng Li, Ran Tao, Deng-Kui Si PII: DOI: Reference:

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Please cite this article as: Su, Chi-Wei, Li, Zheng-Zheng, Tao, Ran, Si, Deng-Kui, Testing for Multiple Bubbles in Bitcoin Markets: A Generalized Sup ADF Test.Japan and the World Economy https://doi.org/10.1016/j.japwor.2018.03.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Testing for Multiple Bubbles in Bitcoin Markets: A Generalized Sup ADF Test Chi-Wei Su

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School of Economics, Qingdao University

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Zheng-Zheng Li*

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Department of Finance, Ocean University of China

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Ran Tao

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Technological Center, Shandong Entry-Exit Inspection and Quarantine Bureau

Deng-Kui Si

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School of Economics, Qingdao University 

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Corresponding author: Zheng-Zheng Li, PhD, Department of Finance, Ocean University of China, Qingdao, Shandong, China. TEL: 86-15698119237. Address: 238, Songling Rd., Qingdao, Shandong, China. E-Mail: [email protected].

Highlights

Whether bubbles exist in Bitcoin markets



Tracks when bubbles will occur and collapse

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Apply the generalized sup Augmented Dickey-Fuller test method

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Consistent with the bubble model improved by Gurkaynak (2008),

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Bitcoin bubbles collapse due to administrative intervention by economic authorities

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

Abstract This study investigates whether bubbles exist in Bitcoin markets and tracks when they will occur and collapse. We apply the generalized sup Augmented Dickey-Fuller test method proposed by Phillips et al. (2013). The results show that there have been four explosive bubbles in China and the U.S. market, primarily occurring during the

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periods of huge surges in Bitcoin prices. This is consistent with the bubble model improved by Gurkaynak (2008), in which asset price is decomposed into fundamental

and bubble components. In particular, exogenous shocks, including foreign or domestic

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economic events, lead to the origination of bubbles. A serious financial crisis may

trigger long-term and large-scale bubbles, whereas relatively short-term bubbles are caused by domestic components. It can be inferred that Bitcoin can be used as a hedge

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against market-specific risk. Finally, Bitcoin bubbles collapse due to administrative

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intervention by economic authorities. Therefore, the government should manage public

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expectations to maintain confidence in authority and reduce speculation behavior to

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stabilize the asset price and financial market.

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JEL: G01, G12, C01

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Keywords: Bitcoin; Price bubble; Speculation; GSADF

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1. Introduction

This study examines the existence of bubbles in the formation and evolution of

Bitcoin’s (BTC) price. BTC is a cryptocurrency that has recently emerged as a popular

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medium of exchange; it has rich and extensive areas of application (Nakamoto, 2008). Central to its operation is the blockchain, which records all transactions between BTC clients (Eyal and Sirer, 2014). Although BTC is being accepted as a form of payment, especially in online markets, it is typically defined as virtual currency because BTC performs poorly as a unit of account and a store of value. To our knowledge, it exhibits high time series volatility, which tends to undermine any usefulness of BTC as a unit 1

of account. Therefore, BTC’s value is almost completely untethered to that of other currencies, which makes its risk nearly impossible to hedge for businesses and customers and renders it nearly useless as a tool for risk management (Yermack, 2014). Furthermore, BTC’s decentralized financial network is prone to be attacked. It has already been attacked on numerous occasions and is in danger of experiencing additional attacks (Bradbury, 2013).

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BTC has had different functions from a macroeconomic perspective since its

invention. On the one hand, BTC is preferred to replace existing financial institutions

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(Kerner, 2014), an alternative to cash (Evans-Pughe, 2012) and a hedge against

economies with rampant inflation (Richardson, 2014). Specifically, BTC can be recognized as an instrument along with gold and other assets to minimize risks

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(Dyhrberg, 2016). On the other hand, BTCs can be used for money laundering because

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they offer an accessible facility for the transfer of value across international borders without reliance on the (heavily regulated) traditional financial and credit institutions

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(Stokes, 2012). Furthermore, BTC’s vast proliferation, high liquidity and lack of

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regulation (Grinberg, 2012) may encourage black market activities to flourish and

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individuals and organizations are prone to be attacked by cybersecurity issues. Even global economic stability is prone to be threatened (Plassaras, 2013). Specifically, there was the “Bitcoin WannaCry virus” worldwide on May 12, 2017, which viciously

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hacked users over the internet. Furthermore, BTC is related to other types of financial assets. For instance, coordination channeled through foreign exchange market

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interventions may be effective because they attract fundamentals if the original BTC prices are efficient (Kurihara and Fukushima, 2017). However, BTC could provide new concepts in terms of volume, payment methods, anonymity, and so on. The sharing of

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various types of information will be dynamic and evolves significantly over time (Brandvold et al. 2015). Sound trading and economic growth via BTC are expected. BTC’s introduction in 2008 coincided with the bottom of the global financial crisis, and BTC has found adherents among people who lack confidence in the world financial system (Yermack, 2014). The price has experienced extreme fluctuations, but it shows 2

an overall upward trend. On 4 December 2013, the BTC price reached its peak and exceeded international gold prices. Then, the price of BTC plummeted sharply and maintained a low level until 2015, when the price of BTC sharply increased, and it reached a record level again in 2017. According to Williams (2014), the volatility of BTC price is seven times greater than that of gold, eight times greater than the S&P 500, and 18 times greater than the U.S. Dollar (USD). This, combined with BTC activities,

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motivates this study to investigate why the BTC price has extreme changes and whether multiple bubbles exist in BTC markets.

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The daily transaction flow of BTC trades suggests that the vast majority of

worldwide demand originates in two countries: the U.S. and China (Yermack, 2014). Ponsford (2015) indicates that China has become a large investment center for BTC

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since it was introduced in 2011 and exceeds the U.S. in trading volume. However, there

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is a difference in BTC price between the Chinese and U.S. trading markets1, which may

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be influenced by special components of these countries. Although one country’s significant events will influence other countries, these factors have effects on the

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domestic market immediately and shock the BTC trading price instantly. For example, regulations differ relative to technological, economic, social, financial, and political

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forces between China and the U.S., which contribute to the countries’ regulatory and legal frameworks (Ponsford, 2015). Specifically, BTC reached legal status in some

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states in the U.S. in 2014. Furthermore, the U.S. hopes to establish BTC as a worlddominated currency with a huge potential for online trading. Conversely, China’s

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central bank issued the “Notice on the Prevention of the Risk of Bitcoin” in December 2013, stating that BTC is not a real currency. Virtual currency exchanges in China are not licensed by the country's central bank to accept or pay Chinese Yuan (CNY) to their

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customers. Additionally, financial institutions are not allowed to use BTC in transactions. Meanwhile, domestic sites have announced that they do not accept BTC as a payment method. On 4 September 2017, the authorities banned initial coin offerings 1

The reason for the existence of price difference are recognized there is no central authority regulating the price. The arbitrary potentially exists, but it requires additional fees in setting up and verifying accounts at multiple exchanges and there is still the risk that the price differences will have normalized or even reversed by the time your transfer goes through. 3

(ICO) and declared that the exchange platform would be closed on 30 September, resulting in a sharp decline in BTC price. China has witnessed an explosion of digital currency trading, invoking fears concerning speculative investing and financial risks. As a result, the Chinese regulatory authority has imposed changes and control measures, which will inevitably have a significant impact on the international BTC market. The outline of this paper is as follows: Section 2 presents the literature review.

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data and reports our results. The final section provides the conclusion.

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Section 3 discusses the theoretical model and methodology. Section 4 introduces the

2. Literature Review

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van Wijk (2013), Ciaian et al. (2015), Bouoiyour and Selmi (2015) and Bouoiyour

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et al. (2016) believe that BTC price may be potentially determined by long-term

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fundamentals. Specifically, Buchholz et al. (2012) argue that one of the most important determinants of BTC price in the long-run is the interplay between its supply and

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demand. Additionally, van Wijk (2013) stresses the significant role of global financial

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development (in particular, stock markets, exchange rates, and oil price measures) on the long-term value of BTC. Kristoufek (2014) adds that an increase in the estimated output reflecting the volume of transactions leads to a decrease in BTC price in the long

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term. Moreover, Ciaian et al. (2015) and Bouoiyour and Selmi (2015) support that the

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trade and exchange transactions expand the utility of holding BTC, which result in an increase in its price in the long term. BTC, without commodity or institutional backing, has been verified to have a fundamental value of zero (Cheah and Fry, 2015). BTC has value as a unit of currency only through confidence; individuals and organizations grant

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it value and accept it as payment for goods or services (Stokes, 2012). Therefore, it can be inferred that the BTC prices are internally driven by buyers and sellers and are not affected by fundamental economic factors. Dowd (2014) illustrates that BTC prices appear to contain a considerable speculative component. This component is motivated by investors and may potentially signify bubbles (Dale et al., 2005). 4

According to Blanchard and Watson (1982), a stochastic bubble occurs when speculators purchase a financial asset at a price above its fundamental value with the expectation of a subsequent capital gain. Given the assumption of rational behavior and expectations, the price of an asset must simply reflect market fundamentals. Additionally, the price depends on information concerning current and future returns from this asset. When the current market price depends partially on the expected rate of

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market price change, it is possible that the market will create a price bubble with price driven by arbitrary, self-fulfilling expectations. If such bubbles persist, investors are

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irrational in their failure to profit from the “overpriced” asset, which is referred as “irrational bubbles”. Deviations from this market fundamental value are taken as

preliminary evidence of irrationality (Flood and Garber, 1980). Kindleberger (2000)

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describes bubbles as a rapid increase in the price of an asset, with the initial increase

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generating expectations of further increases which attracts new buyers via a process

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generally called irrational exuberance (Shiller, 2005).

Recently, BTC has been touted as a bubble gathering market (Swartz, 2014; Cheah

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and Fry, 2015; Fry and Cheah, 2016). Grinberg (2011) explains that BTC is susceptible

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to irrational bubbles, which would collapse demand relative to supply. Confidence in BTC could collapse due to unexpected changes in investment returns imposed by the software developers, a government crackdown, the creation of superior competing

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alternative currencies, or a deflationary spiral. Furthermore, Dowd (2014) provides evidence that BTC prices contain speculative bubbles. This finding is confirmed by

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Cheah and Fry (2015), who indicate that the bubble component within BTC is substantial. Based on this, Fry and Cheah (2016) prove that the BTC market contains a

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substantial speculative component and is extremely volatile. It is widely accepted that collapse of asset bubbles and financial crises are closely

related (Ahamed, 2009; Reinhart and Rogoff, 2009). For instance, a decrease in oil prices facilitated a bubble’s burst and caused the most severe banking crisis and recession (Allen and Gale, 1999; Lammerding et al., 2012). The Great Recession in 2008 occurred because of the collapse of the housing market bubble in the U.S. 5

followed by a long period of rapid growth in real estate prices (Gaber et al., 2014). Similarly, the collapse of BTC bubbles may weaken the overall confidence of investors, which could lead to the “Butterfly Effect”2. Previous researchers have explored different types of methodologies to test potential bubbles. Diba and Grossman (1988) note that the volatility of the difference between the asset price and the fundamental price is sufficient for bubble detection, and

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the unit root and cointegration tests are used to identify the volatility. However, the

evidence of bubbles reported by these studies remains inconclusive, which causes doubt

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concerning the empirical validity of these techniques (Brenner and Kroner, 1995).

Evans (1991) argues that unit root tests have little ability to detect periodically collapsing bubbles because periodic processes behave as I(1) processes or even

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stationary linear autoregressive processes when the probability of collapse is significant.

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Although the procedure from Hall et al. (1999) offers certain appealing features such

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as regime probability estimation, the recent work by Shi (2011) reveals that the Markovswitching model is susceptible to false detection or spurious volatility.

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Furthermore, Grinberg (2011) posits that BTC tends to create irrational bubbles;

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however, he does not provide the quantitative empirical evidence to support this verdict. MacDonell (2014) analyzes the trend of BTC prices and confirms the existence of bubbles at the end of 2013; specifically, he suggests that speculation is the primary force

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motivating BTC values. However, in his view, a bubble occurs during a period of significant volatility, which is less convincing. Cheah and Fry (2015) estimate BTC’s

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fundamental value, but do not locate the specific points at which bubbles occur. Fry and Cheah (2016) focus on the counteraction between BTC and Ripple in the cryptocurrency markets and develop an econophysics model for bubbles. Regardless,

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they neglect the explosive behavior of speculative bubbles and cannot determine whether there are multiple bubbles. It is difficult to calculate the fundamental or intrinsic value of one BTC, which is different from its “fair” value (Garcia et al., 2014). Although previous studies explore BTC bubbles, they primarily concentrate on the BTC

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Based on weather related concepts, the flap of butterfly wings may eventually lead to tornadoes. 6

price relative to USD. They neglect specific components in China (i.e., management and intervention by the government) that impact the price and lead to different price change trends between the U.S. and Chinese markets. In addition, they are incapable of detecting the multiple bubbles during the entire period. The importance of our contribution to the existing literature is the use of generalized sup ADF (GSADF) (Phillips et al., 2011, 2012, 2013) to estimate possible

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multiple bubbles in both BTC Chinese and U.S. markets, and the comparison of the two

markets. Homm and Breitung (2012) suggest that compared with other full-sample

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procedures’ recursive formulas, the procedure created by Phillips et al. (2011) performs satisfactorily for structural breaks and is particularly effective as a real-time bubble detection algorithm. Furthermore, the approach by Phillips et al. (2013) is suitable for

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any frequency of data and is considered a formal statistical estimation of bubble

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existence, whereas other methods depend on the subjective judgment of the deviations

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from the intrinsic values. Therefore, this test is more objective for real-time bubble detection. A further contribution of this study is the development of a new strategy for

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determining the dates of bubbles. Specifically, it uses the recursive procedure against

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critical values for the standard right-tailed ADF statistic and uses a first crossing time occurrence for date origination and collapse (Phillips et al., 2011, 2012, 2013). Standard unit root tests are used for the alternative stationary hypothesis located on the left-side

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of the probability distribution. However, the GSADF test proposes hypotheses based on the right-side of the probability distributions where the location of the test statistic

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for an explosive root is confirmed. In addition, the GSADF tests allow a periodic test for possible non-stationary behavior of a time series against mildly explosive alternatives. Mildly explosive behavior is modeled by an autoregressive process with a

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root that exceeds but remains near unity. Thus, if an explosive root exists, i.e., if the alternative hypothesis of mildly explosive behavior is not rejected, then the GSADF test provides a tool for recognizing a bubble process and for consistently locating its occurrence and bursting (Phillips and Yu, 2009; Phillips et al., 2011). The GSADF test also has the advantage of detecting bubbles even under a condition of potential 7

misspecification of the market fundamental process. Instead of establishing the beginning point of the sample, the GSADF test extends the sequence by changing both the beginning and the ending points over a feasible range of flexible windows. We use the GSADF test to evaluate multiple explosive bubbles in the Chinese and U.S. BTC markets. The GSADF test presented in this paper is not simply an ex post detection technique, but an anticipative dating algorithm than can assist regulators in

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their market monitoring behavior by means of early warning diagnostic tests. These

types of warning systems ideally must have a low false detection rate to avoid

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unnecessary policy measures and a high positive detection rate to ensure early and

effective policy implementation (Phillips et al., 2011). The results show that there were four bubbles in China and the U.S. Our findings are in agreement with the theoretical

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model that speculation has a major effect on the bubble evolution process. Specifically,

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certain domestic components cause shocks within their country. However, significant

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international events including a serious financial crisis may trigger bubbles and spread to other countries rapidly. The government intervention in the BTC market leads to a

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decrease in price and the bursting of bubbles.

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3. Theoretical Model and Methodology

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The literature concerning the identification of the speculative bubble from market fundamentals derive from the Lucas (1978) asset pricing model. Then, Blanchard and

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Watson (1982), Shiller (1984), Tirole (1982, 1985), Evans (1989), Diba and Grossman (1988), Froot and Obstfeld (1991), and Gurkaynak (2008) improve the econometric methods that are applied to test the financial price bubbles. The most common model

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for testing the intrinsic bubble begins with the following equation (Gurkaynak, 2008):

Pt  (1  rf ) 1 Et ( t 1  U t 1 )

(1)

where Pt is the BTC price during period t , rf

is the free-risk rate, Et is the

expectation,  t 1 represents the return during period t  1 and U t 1 is the invisible 8

component in the market. 

i

1 Pt   ( ) Et ( t i  U t i ) i 0 1  rf f

for i  0,1, 2,...

(2)

where Pt f is the fundamental BTC price and  t i is the dividend during period t  i . It describes the determinants in the fundamental price without a bubble.

Bt  (1  rf ) 1 Et ( Bt 1 )

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(3)

is any sequence of random variables that satisfies the homogeneous expectation

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equation. Pt  Pt f  Bt

(4)

Equation (4) denotes the general solution to Equation (1) as the sum of a market 𝑓

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fundamentals component, 𝑃𝑡 , and another component commonly referred to as the

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bubble component, 𝐵𝑡 . If a bubble exists in the BTC price, Equation (3) requires that

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any rational investor who is willing to buy BTC must expect the bubble to expand at

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rate 𝑟𝑓 . If 𝐵𝑡 is strictly positive, it encourages speculative investor behavior. A rational investor is willing to buy an “overpriced” BTC since he believes that there will be

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sufficient compensation for the extra payment 𝐵𝑡 through price increases. If investors expect prices to increase at rate 𝑟𝑓 and therefore purchase additional BTC, the BTC

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price will indeed increase and complete the self-fulfilling process. Diba and Grossman (1988) recommend the strategy of employing a stationarity

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test for the logarithmic asset price and observable market fundamentals considering the explosive attribute of bubbles. The conventional stationarity test is based on the standard ADF test or the Phillips-Perron test (Phillips and Perron, 1988), which has an

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explosive alternative hypothesis. Consider the following model: ∆𝑝𝑡 = 𝛼 + 𝛽𝑝𝑡−1 + ∑𝑘𝑖=1 𝛾𝑖 ∆𝑝𝑡−𝑖 + 𝜀𝑖 , 𝜀𝑖 ~𝑁𝐼𝐷(0，𝜎 2 )

（5）

where 𝑝𝑡−1 is the logarithmic BTC price and 𝑘 is the number of lags determined by significance tests in the empirical application. NID denotes independent and normal distribution. The null hypothesis is = 1, meaning that 𝑝𝑡−1 is a unit root process, i.e., ∆𝑝𝑡 is stationary. The alternative hypothesis is 𝛽 > 1, which implies that 𝑝𝑡−1 is 9

explosive (∆𝑝𝑡 is non-stationary). However, Phillips and Yu (2011) argue that their tests have discriminatory power in that they are sensitive to changes when a process changes from a unit root to a mildly explosive root or vice versa. This sensitivity is much greater than in left-tailed unit root tests against stationary alternatives. Therefore, when detecting periodically collapsing bubbles, conventional unit root tests have limited capability (Evans, 1991). To overcome this weakness, Phillips and Yu (2011)

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propose the supreme of recursively determined ADF t-statistics.

The sup ADF (SADF) test relies on repeated estimation of the ADF model on a

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forward expanding sample sequence, and the test is obtained as the sup value of the

corresponding ADF statistic sequence. The window size 𝑟𝑤 expands from 𝑟0 to 1, where 𝑟0 is the smallest window width and 1 is the largest sample window width (i.e.,

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the total sample size). The starting point 𝑟1 of the sequence is fixed at 0; therefore, at

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the ending point of each sample, 𝑟2 equals 𝑟𝑖 , changing from 𝑟0 to 𝑟1 . The ADF 𝑟

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statistic for a sample that ranges from 0 to 𝑟2 is denoted by 𝐴𝐷𝐹0 2 . The SADF statistic

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is defined as follows: SADF(𝑟0 ) = 𝑠𝑢𝑝𝑟2 ∈(𝑟0 ,1) {𝐴𝐷𝐹𝑟2 }

(6)

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SADF has proven to be effective when there is a single bubble episode in the sample period. However, there may be multiple bubbles in the BTC price. Phillips et al.

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(2012, 2013) demonstrate that when the sample period contains multiple bubble episodes, the SADF test may suffer. This is particularly evident in a long sample period

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or in rapidly changing markets where more than one episode of exuberance is suspected. To overcome this weakness and address multiple periods of exuberance and collapse, the GSADF test introduces flexible window widths in its implementation (Phillips et

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al., 2012, 2013). The GSADF test repeatedly executes a series sample sequence based on the ADF test. In addition to varying the end point of the regression of 𝑟2 from 𝑟0 to 1, the GSADF test extends the sample coverage by changing the beginning and the ending point of the recursion over a feasible range of flexible windows. Specifically, it allows starting point 𝑟1 to change from 0 to 𝑟2 − 𝑟0 . Because the GSADF test evaluates additional sub-samples of the data and has greater window flexibility, the 10

accuracy in detecting explosive behavior in multiple episodes has improved. Thus, it is more efficient than the SADF test in detecting explosive behavior when multiple bubbles occur in the time series. The superior performance of the GSADF test is demonstrated in simulations comparing the two tests in terms of their size and ability to detect bubbles. Phillips et al. (2012, 2013) define the GSADF statistic to be the largest ADF statistic over the feasible ranges of 𝑟1 and 𝑟2 ; they denote this statistic as

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GSADF(𝑟0 ), as follows: 𝑟

GSADF(𝑟0 ) = 𝑠𝑢𝑝𝑟2 ∈(𝑟0 ,1),𝑟1 ∈(0,𝑟2 −𝑟0 ) {𝐴𝐷𝐹𝑟12 }

(7)

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When the regression model includes an intercept and the null hypothesis is a random walk with an asymptotically negligible drift, we present the limit distribution of the GSADF test statistic as follows: 𝑟 1

1⁄

𝑟 1

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𝑟𝑤 [𝑤(𝑟2 )2 −𝑤(𝑟1 )2 −𝑟𝑤 ]−∫𝑟 2 𝑤(𝑟)𝑑𝑟 [𝑤(𝑟2 )−𝑤(𝑟1 )] 𝑟 1

1⁄ 2

𝑟𝑤 2 {𝑟𝑤 ∫𝑟 2 𝑤(𝑟)2 𝑑𝑟 −[∫𝑟 2 𝑤(𝑟)𝑑𝑟 ]2 }

}

(8)

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1

𝑠𝑢𝑝𝑟2 ∈(𝑟0 ,1),𝑟1 ∈(0,𝑟2 −𝑟0 ) {2

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where 𝑟𝑤 = 𝑟2 − 𝑟1 is a standard Wiener process. Phillips et al. (2012, 2013) infer that

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the GSADF test nests the SADF test. These two statistics converge to the standard normal distribution if the true process is a random walk. Phillips et al. (2012, 2013)

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apply a simulation to obtain the asymptotic critical values of the ADF statistic distributions under the null hypothesis that the true process is a random walk. The first

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step is to simulate the standard Wiener process. Because the Wiener process is continuous and stochastic, only a path sampled with a finite number of points can be

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generated. Suppose that 𝑛1 , 𝑛1 … 𝑛𝑁 are equally spaced with a finite interval. At each point, a Gaussian random variable with a mean of zero and a variance of 1/N is generated. The right-tail critical values of the GSADF statistic are larger than those of

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the SADF statistic. We implement numerical simulations to obtain the asymptotic critical values, and employ a bootstrap method to compute the finite sample distributions. Pavlidis et al. (2012) suggest that this method does not require that the fundamental process be specified. Additionally, it is not affected by a possible explosive root of the determinants of the BTC price because it contains a date-stamping strategy.

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4. Data and Empirical Results We use the BTC weekly average prices in both CNY and USD collected from the Wind database. The sample period is between June 16, 2011, and September 30, 2017. Figure 1 shows the price has experienced huge fluctuations since 2011, when BTC was

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initially used in China. It is obvious that BTC price was low and stable prior to 2013, basically less than 100 yuan. However, the market price increased rapidly, peaked at

nearly 1000 yuan in April 2013 and gradually recovered. This spike may have been

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initiated by a financial crisis in Cyprus, which saw the small nation’s credit rating plummet to junk status. BTC price increased again, peaking at nearly 7000 yuan in November 2013, and then declined sharply. After dropping to nearly 2000 yuan, it

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rebounded to 4000 yuan briefly in June 2014. Then, it fell gradually to less than 2000

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yuan. However, the price rallied again and increased rapidly to approximately 8000

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yuan in early 2017. It was unexpected that the price reached a peak of nearly 25000 yuan. In general, the BTC price has surged and fluctuated dramatically since the market

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began. The increase in price from 14 yuan to over 25000 yuan occurred within six years.

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Given such a return, there is no doubt that the price for BTC might contain a considerable speculative component. From Figure 2, we can see the basically similar

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trend but little difference within the Chinese market.

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4.1.The Empirical Result on Chinese BTC Market We then employ the SADF and GSADF tests to date the bubble periods of the BTC

price. The empirical results were obtained after 10000 replications. Several conclusions

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could be drawn from the results presented in Tables 1. Based on the results, we can infer that there are bubbles in the price (CNY) of BTC. In Table 1, we reject the null hypothesis of H 0 : r  1 at the 1% significance critical values (i.e., 18.344>1.336, 20.644>2.603), where 18.344 and 20.644 are the SADF and GSADF statistics for the full data series, respectively. The results provide evidence that the price of BTC contains explosive sub-periods. Therefore, we conclude that there is significant 12

evidence of exuberance in the BTC price based on SADF and GSADF tests; specifically, we can assert the possible presence of bubbles. As we illustrate above, the GSADF test outperforms the SADF test in detecting explosive behavior because the GSADF test evaluates additional sub-samples of the data and has greater window flexibility (Phillips et al. 2012, 2013). We graph the

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estimated results according to the GSADF test, with 95% confidence intervals, in

Figures 1 and 2. The start date of a bubble denotes the first observation where the

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GSADF statistic is greater than the critical value, while the end date of a bubble is

defined as the first observation after that start date at which the GSADF statistic descends below the critical value. Based on the figure, we observe that there are four

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BTC bubbles during the sample period in China. Phillips et al. (2013) confirm that the

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moving sample GSADF method outperforms the SADF test based on an expanding

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sample size in detecting explosive behavior, especially in multiple bubble episodes, and it seldom yields false alarms because the GSADF test evaluates additional subsamples

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of the series. Therefore, we can infer that there is evidence of multiple bubbles in the

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BTC markets.

From Figure 1, we identify two bubbles in 2013. The first originates on February 7 and bursts on April 18, which is a duration of nearly three months. The second begins

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on November 7 and collapses on December 12. The spike in price can be attributed to the economic crises in Spain and Cyprus; specifically, the two nations’ credit ratings

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plummeted to junk status. With increasing uncertainty concerning the future of Cyprus’ banks, investors attempting to avoid taxes and locating other havens for their assets exchanged their government-backed currencies for BTCs, pushing trading volumes and

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values to historically high levels (Cohan, 2013). As European countries struggle to recover from financial crises, an increasing number people appear to lose confidence in traditional currencies and turn to BTC as an alternative form of currency, as demonstrated by the explosion in BTC’s value (Plassaras, 2013). BTC demand in portions of Europe has become too high, thereby increasing the price worldwide. 13

Additionally, BTC has been regarded as a legal currency so that the specific policy risk is reduced. Specifically, the U.S. government regulated BTC exchanges to prevent money laundering by shutting down Silk Road3 (Tsukerman 2015). The Treasury’s Financial Crimes Enforcement Network (FinCEN) has announced actions to increase monitoring of money laundering activities to include companies that trade in BTCs (Satter, 2013). Additionally, the German Ministry of Finance recognizes BTC as an

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accounting unit, which means that BTC in Germany is considered a legal currency (Wu and Pandey, 2014). These actions are the result of a growing consensus that the

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government would ultimately accept BTC (MacDonell, 2014). Therefore, investors have increased confidence and their enthusiasm in the BTC market. Furthermore, another factor that leads to an increase in price can be attributed directly to BTC;

U

specifically, that the total amount of BTC is fixed. Thus, BTC has a characteristic that

N

the value is reduced by half every four years. 2013 is the beginning of decay and a sensitive time window for investing in BTC. Investors purchase BTC fanatically using

A

their excess liquidity. Finally, the People’s Bank of China (PBC) announced a regulation

M

called the “Notice on the Prevention of the Risk of Bitcoin”, which prohibits financial

ED

institutions from using BTC because it is not an actual currency in China. The regulation shocked the BTC market and prices briefly plummeted, contributing to the bubble’s burst (Cheah and Fry, 2015).

PT

The next bubble occurs at the beginning of 2017. The price of BTC continued to increase in 2016 due to the development of blockchain 4 technology, leading to the

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expected appreciation of BTC. However, the U.S. Federal Reserve is expected to increase interest rates, while the CNY is anticipated to depreciate. Specifically, investors hedge BTC because of their inflation expectations and lower exchange rates

A

in China. This bubble bursts because PBC emphasizes that BTC is a particular virtual commodity that cannot be used as a circulated currency. As a response, BTC prices

3

Silk Road is a black-market shopping site using covert services. This website trades in Bitcoin, and the exchange rate is linked to the dollar. 4 The blockchain is a growing historical “book of records” containing all of the information concerning all network transactions. Every BTC client maintains a complete copy of the blockchain, stored locally in the form of raw binary data (Garcia et al., 2014). 14

plummeted more than 10%. We determine that the final bubble begins on May 18, 2017, and collapses on September 14. This increase in price is because of the “WannaCry” hacker attack. Furthermore, an increasing number of people concentrate on the development of blockchain, stimulating the BTC price. BTC (represented by the blockchain) is considered a subversion of the underlying financial industry technology and will be able to be applied to the securities, banking, insurance and other financial

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industries (Crosby et al., 2016); this is widely accepted as the fundamental reason for the long-term increase in BTC prices. Thus, investors are attracted to BTC with great

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enthusiasm because of its continually increasing price. Meanwhile, more than 80% of

China's BTC investors are in pursuit of short-term profits; less than 14% of users intend to be long-term holders. BTC has become a means for speculators to pursue short-term

U

interests. Thus, the price is easily manipulated by speculators, contributing to high

N

speculative risk. On September 4, 2017, the PBC issued a notice concerning the

A

prevention of financial risks due to token issuance and eliminated all BTC exchange. China's ICO ban and fears of additional regulations have prompted a sell-off that has

M

eliminated billions of dollars of cryptocurrencies’ value since they reached record highs

ED

at the beginning of the month. The price of BTC decreased sharply and the bubble burst following this announcement.

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4.2.The Empirical Result on the U.S. BTC Market

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Similarly, we reject the null hypothesis (21.321>1.336, 22.329>2.603) in Table 2, which price is represented in USD. Specifically, we can identify four bubbles from Figure 2. The first occurs and quickly ends in August 2012, when Priateat40 (a trading

A

website in the U.S.) declared that they were no longer accepting bitcoin payment, thus repressing the increasing price. The timing of the next three bubbles basically corresponds to the bubbles in the Chinese market. Perhaps the global events affected all of the BTC markets. It is noteworthy that the PBC’s ban of BTC trading triggered enormous panic in speculators and even influenced the U.S. market in 2017. Thus, it can be predicted that this bubble is going to burst. However, we can see the difference 15

between these figures is that the bubbles burst in 2012 in the U.S. market and in 2017 in the Chinese market. As mentioned above, the bubbles’ originations are attributed to domestic components. For instance, Priateat40’s ban of BTC trading in 2012 in the U.S. and the depreciation of CNY implemented artificially by China's central bank increased the BTC price in 2017. These events do not have a profound impact or affect other countries.

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< Table 2 and Figure 2 are inserted about here>

Currently, the Chinese BTC market occupies the largest share of the global

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transaction market; it is reported that 70% of the world’s BTC are produced in China.

As a consequence, a price fluctuation in the Chinese BTC market affects the investment behavior of global investors. Based on the empirical results, generally, the occurrences

U

of BTC bubbles are in accordance with the asset price model; once bubble components

N

exist, the BTC price increases accordingly. Major international events may exert influence on global BTC markets and sustain the occurrence of a bubble for an extended

A

period of time. For instance, Cyprus’ economic crisis triggered a public panic of

M

government-backed currencies. To avoid potential risk, investors seek BTCs as a

ED

substitute for currencies. The surge in demand relative to the limited supply leads to the relatively long-term bubbles. The periods during which these bubbles occur in the BTC market in China are basically consistent with the periods during which the bubbles

PT

occur in the U.S. BTC market (Garcia et al., 2014; MacDonell, 2014; Cheung et al., 2015). However, certain domestic components would cause bubbles that could not be

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transmitted to other countries and quickly burst. Investors retain BTC because they believe that the value of BTC will increase while the CNY is expected to depreciate. BTC is recognized as a perfect speculative vehicle because there is no guarantee of

A

repayment at any time (Kristoufek, 2013; Yermack, 2014; Bouoiyour et al., 2015). In general, it can be seen that a bubble is usually accompanied by a sharp increase in BTC prices; conversely, decreasing prices cause the bubble to burst. Furthermore, we can infer that the extreme fluctuation in prices is created by speculation and hedging. Thus, government authorities should provide reasonable guidance to investors so they can 16

avoid huge fluctuations in financial markets.

5. Conclusion This study explores the multiple bubbles in the BTC markets in China and the U.S.,

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using the GSADF test method proposed by Phillips et al. (2013). The empirical results show that there have been four explosive bubbles, respectively. Generally, BTCs bubbles have been accompanied by volatile international events. That is, the occurrence

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of bubbles corresponds to the periods with an increase in price; conversely, decreasing

prices cause the bubbles to burst, which is consistent with the bubble model (Gurkaynak, 2008). Specifically, the beginning of the bubbles is derived from exogenous shocks,

U

including foreign or domestic economic events. Serious financial crises may trigger

N

global bubbles because crises cause investors have a negative reaction to government-

A

backed currencies; therefore, they will choose to pursue other assets, causing the BTC price to increase. Conversely, domestic components, such as the expected depreciation

M

of the CNY or currency regime changes, cause bubbles that are not inclined to transmit

ED

to other countries. In short, investors seek BTC as a safe haven to hedge against potential risks or as a speculative vehicle with which to earn profits. Eventually, the bubbles would collapse due to administrative intervention by economic authorities.

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Given the influence of speculation components on BTC price bubbles, government

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authorities should manage public anticipation and assist members of the public in recognizing the essence of virtual money and avoiding irrational investment to stabilize the financial market. Moreover, this should be the focus to guard against the spillover

A

of foreign financial risks.

17

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paper, No. 19747.

23

30,000

20,000

10,000 25 0

20

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15 10 5

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0 -5 I

II III IV I

II III IV I

II III IV I

II III IV

2012

2013

2014

2015 GSADF

II III IV I 2016

BTC

II III

2017

U

CV

I

Figure 1. GSADF test of the price (CNY) of BTC. Note: The upper curve represents

N

the price of BTC. The middle curve is the 95% critical value. The bottom curve represents

A

the GSADF statistic. The shadow are sub-periods with bubbles.

M

5,000 4,000

ED

3,000

1,000 0

PT

25

2,000

20

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15 10 5 0

A

I

II III IV I

II III IV I

II III IV I

II III IV

2012

2013

2014

2015

CV

GSADF

I

II III IV I 2016

II III 2017

BTC

Figure 2. GSADF test of the price (USD) of BTC. Note: The upper curve represents the price of BTC. The middle curve is the 95% critical value. The bottom curve represents the GSADF statistic. The shadow are sub-periods with bubbles.

24

Table 1. The SADF and GSADF tests results in CNY BTC price

SADF

GSADF

18.344***

20.644***

90%

0.969

1.817

95%

1.170

2.166

99%

1.336

2.603

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Critical value

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Note: * * * indicates significance at the 1% level. These tests are used by GAUSS 10 software.

Table 2. The SADF and GSADF tests results in USD SADF

GSADF

U

BTC price

22.329***

N

21.321***

0.969

95%

1.170

M

90%

A

Critical value

1.336

ED

99%

A

CC E

PT

Note: * * * indicates significance at the 1% level.

25

1.817 2.166 2.603