Crypto-currency bubbles: an application of the Phillips–Shi–Yu (2013) methodology on Mt. Gox bitcoin prices

TLDR: In this paper, the authors conduct an econometric investigation of the existence of bubbles in the bitcoin market based on a recently developed technique that is robust in detecting bubbles, that of Phillips et al. (2013a).

Abstract: The creation of bitcoin heralded the arrival of digital or crypto-currency and has been regarded as a phenomenon. Since its introduction, it has experienced a meteoric rise in price and rapid growth accompanied by huge volatility swings, and also attracted plenty of controversies which even involved law enforcement agencies. Hence, claims abound that bitcoin has been characterized by bubbles ready to burst any time (e.g. the recent collapse of bitcoin’s biggest exchange, Mt Gox). This has earned plenty of coverage in the media but surprisingly not in the academic literature. We therefore fill this knowledge gap. We conduct an econometric investigation of the existence of bubbles in the bitcoin market based on a recently developed technique that is robust in detecting bubbles – that of Phillips et al. (2013a). Over the period 2010–2014, we detected a number of short-lived bubbles; most importantly, we found three huge bubbles in the latter part of the period 2011–2013 lasting from 66 to 106 days, with the ...

Figures

Table 1 reports the summary statistics of the variable. Panel A of Table 1 shows the overall summary statistics while Panel B depicts the autocorrelation plot. The mean is 2.1598 and the standard deviation is 2.4711, suggesting that the bitcoin price variable is somewhat overdispersed. However, no significant departure from normality is found as both skewness and kurtosis are -0.1526 and 2.6203, respectively. Figure 3 seems to suggest that there is an upward trend with ups and downs with bitcoin prices in log scale. As shown in Panel B, the time series of the bitcoin price is highly persistent because its autocorrelation is close to one (i.e., 0.9971) and statistically significantly different from zero at lags 1 to 20. Thus, it is important to determine whether this trend is deterministic or stochastic. To this end, we use the augmented Dickey-Full test. The results on the augmented Dickey-Fuller test basically show that the time series are non-stationary in most cases (see Table 2). For example, if we allow for a trend in the underlying data-generating process, the ADF test clearly indicates that the variable is non-stationary so is the case where there is no drift term specified in the datagenerating process. In the case where a drift is allowed, the null hypothesis that there is a unit root cannot be rejected with lag =1 and 2. The null is only rejected if the lag is either zero or three. However, as argued in PSY (2013a), the possibility that a bubble that bursts off in the sample period will render the variable pseudo-stationary if the period after the burst is also included in the ADF test. That is why we need to employ some tests like GSADF test that do not suffer from this limitation and the results are reported in the next section.

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Crypto-currency bubbles: an application of the Phillips–Shi–
Yu (2013) methodology on Mt. Gox bitcoin prices
Author
Cheung, AK, Roca, E, Su, JJ
Published
2015
Journal Title
Applied Economics
Version
Accepted Manuscript (AM)
DOI
https://doi.org/10.1080/00036846.2015.1005827
Copyright Statement
© 2015Taylor & Francis (Routledge). This is an Accepted Manuscript of an article published
by Taylor & Francis in Applied Economics on 04 Feb 2015, available online: https://
www.tandfonline.com/doi/10.1080/00036846.2015.1005827
Downloaded from
http://hdl.handle.net/10072/154740
Griffith Research Online
https://research-repository.griffith.edu.au

1

Crypto-Currency Bubbles:An application of the Phillips-Shi–Yu (2013) methodology on
Mt. Gox bitcoin prices
Adrian (Wai-Kong) Cheung
*
, Eduardo Roca

and Jen-Je Su

*
Department of Finance and Banking, School of Economics and Finance,
Curtin University, Perth, WA6102, Australia

Department of Accounting, Finance and Economics,
Griffith University, Brisbane, QLD4111, Australia
Abstract
The creation of Bitcoin heralded the arrival of digital or crypto-currency and has been
regarded as a phenomenon. Since its introduction, it has experienced a meteoric rise in price
and rapid growth accompanied by huge volatility swings, and also attracted plenty of
controversies which even involved law enforcement agencies. Hence, claims abound that
bitcoin has been characterised by bubbles ready to burst any time (e.g. the recent collapse of
Bitcoin’s biggest exchange, Mt Gox). This has earned plenty of coverage in the media but
surprisingly not in the academic literature. We therefore fill this knowledge gap. We conduct
an econometric investigation of the existence of bubbles in the bitcoin market based on a
recently developed technique that is robust in detecting bubbles - that of Phillips, Shi and Yu
(2013a). Over the period 2010-2014, we detected a number of short-lived bubbles; most
importantly, we found three huge bubbles in the latter part of the period 2011-2013 lasting
from 66 days to 106 days, with the last and biggest one being the one that ‘broke the camel’s
back” - the demise of the Mt Gox exchange.
Keywords: bitcoin, bubbles, crypto-currency
JEL codes: G01, G12, C01
------------------------------------------------------------------------------------------------------------

Corresponding author. Adrian (Wai-kong) Cheung, Department of Finance and Banking, School of
Economics and Finance, Curtin University, Perth, WA6102, Australia; Tel.: +61 8 9266 9977; Fax: +618 9266
3026; E-mail: adrian.cheung@curtin.edu.au.

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I. Introduction
Bitcoin heralded the coming of digital or crypto-currency. Its creation is attributed to a
Japanese computer programmer using the pseudonym Satoshi Nakamoto. It is supposed to be
a currency that overcomes the problems that beset existing currencies. Its supply is not at the
whims of regulators; rather it is protected by an “uncrackable” computer algorithm that
controls its supply which is set at a maximum of 21 million units. Mining of new bitcoins is
done through computer algorithms. Its transactions are open to the public and supposed to be
without transactions fees as these do not involve intermediaries (Lo and Wang, 2014). Given
all these qualities of bitcoin, it has been hailed as the future of money. Since its introduction
in 2009, its price has seen meteoric rise (see Figure 1). In December 2013, its price peaked at
USD1,200 per unit after it climbed by about 700% in that year. The volume of bitcoin in
circulation now stands at 12.7 million units and trading volume reached 85 million units in
2013 (see Figure 2) and actively traded against around 30 currencies (Biere et al., 2013).
This success of bitcoin has in fact spawned the introduction of other digital currencies such as
litecoin, namecoin, quackcoin, peercoin, anoncoin, zero coin, which operate on the same
concept as bitcoin but with minor modifications. Thus, bitcoin, in this sense, has truly
signalled the coming of the age of digital or crypto-currency.
In spite of its rapid growth, bitcoin has been mired in several controversies relating to
accusations of its use in illegal business activities
1
. There has been also reluctance by
regulatory authorities in a number of countries to endorse it as a currency and in fact, lately,
the Chinese government has explicitly banned financial institutions and businesses from

1
 For example, there has been allegations of bitcoin being  used in drug‐related activities facilitated by the e‐commerce
website,SilkRoad,whichhasattractedaninvestigationbytheFBI(TheEconomist,February1,2014)

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
using it.
2
Since its introduction, bitcoin has experienced a meteoric rise in its price.
However, this has also been accompanied by huge volatility swings, as can be seen in Figure
1. This has therefore led to constant claims in the investment industry and the media of the
bitcoin market being characterised by bubbles which could burst anytime. The recent
collapse of the Mt Gox Exchange, the biggest bitcoin exchange, is now taken as evidence that
there were indeed bubbles in the market and this has finally burst.
It is argued by some that by its very nature, bitcoin is destined to be characterised by bubbles
(Grinberg, 2011). It is supposed to be a currency but it does not essentially perform the
functions of a currency. Yes, it is a medium of exchange as it used by a number of
businesses; however, it fails as a store of value and as a unit of account because of its
volatility. It does not have any intrinsic value – it is simply anchored on a computer program.
Thus, it simply derives its value from being a speculative commodity, and because of this, it
is therefore bound to be characterised by bubbles.
In spite of these claims in the media and in the investment community of bitcoin being
characterised by bubbles, surprisingly, no systematic study yet that has been conducted on
this issue. There are a very few academic studies on bitcoin and most of these deal with legal
and institutional issues (Biere et al., 2013). To our knowledge, there is only one academic
study relating to the financial economics of bitcoin – the one by Biere et al. (2013). We
therefore address this knowledge gap. In this paper, we investigate the existence of bubbles
(e.g. explosive behaviours) in the bitcoin market based on recently developed econometric

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 For most of the  time, since its inception, at best,a number of governmental regulatory authorities have just turned a
blindeyeonbitcoin.However,some governmentshavestartedto “crackthe whip’onbitcoin.For instance,the French
government has explicitly warned against the use of bitcoin (http://m.theglobeandmail.com/report‐on‐
business/economy/economy‐lab/bursting‐the‐bitcoin‐bubble/article16327155/?service=mobile). Starting in December
2013,the Chineseregulatoryauthoritieshave alsoexplicitlybanned financialinstitutions andbusinessfrom using bitcoin
(April 14, 2014). India has also done the same as China although probably to a lesser extent
(http://www.businessspectator.com.au/article/2013/12/31/currency/bursting‐bitcoins‐bubble)

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
techniques, particularly that of Phillips, Shi and Yu (2013a; hereafter, PSY).
3
Our results
confirm claims of the existence and burst of bubbles in the bitcoin market. Over the period
2010-2014, we detected a number of short-lived bubbles but most importantly, we found
three huge bubbles in the latter part of the period (2011-2013) lasting from 66 days to 106
days, with the last one and also the biggest one occurring during the period November 2013
– February 2014. Our results confirm that the last bubble, indeed, burst, and thus, may have
been the fatal one that ‘broke the camel’s back” - the collapse of the Mt Gox exchange.
II. Bubbles: Definition, Detection and Existence in Asset Markets
Definition and Detection
There is no agreement as regards the definition of bubbles.
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One may take the asset-pricing
approach which defines bubbles as the part of the market price which exceeds or undershoots
an asset´s fundamental value (Diba and Grossman, 1988a; West, 1987; Van Norden, 1996;
and Wu, 1997). Detecting the existence of bubbles therefore entails determining first the
fundamental value of an asset. In its most generic form, the fundamental value of an asset is
the present value of the payoffs taking into account all available relevant information
(Taipalu, 2012). There exist a number of financial economics theories that provide
explanations as to what determine the fundamental value of an asset (see Taipalu, 2012).
However, bitcoin is hard to value as it does not have any clearly identifiable cash flows. It is
not even clear what its nature is. There is no agreement as to whether it is a currency or
commodity or both (Lo and Wang, 2014). It has no intrinsic value and its value simply
depends mostly on its speculative value. It has been argued that bitcoins are simply claims

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Plentyoftheoriesalsoexistastowhybubblesexist(see,forexample,Griffinetal,2011,andTaipalus,2012).However,
this paper does not intend to test these theories.Our goal is mainly to detect whether bubbles existed in the bitcoin
market.
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Infact,theycanvarybydiscipline.SeeWaitesandVonMaravic(2010)foradiscussionofthisissue.

Frequently asked questions

Q1. What are the contributions in this paper?

The authors conduct an econometric investigation of the existence of bubbles in the bitcoin market based on a recently developed technique that is robust in detecting bubbles that of Phillips, Shi and Yu ( 2013a ). 

Q2. What are the future works in this paper?

Bitcoin heralded the introduction of digital currency and was therefore touted as the future of money. This is something that, perhaps, future researchers might want to take up. It was created for the purpose of overcoming the shortcomings of the existing currencies, particularly on the promise that its creation and supply will not be at the whim of regulators, and one that is based on transparency. 

Q3. Why does the bitcoin market appear to be characterized by bubbles?

it appears that bubbles in regulated markets come about due to such reasons as laxity in regulations, overtrading and overestimated growth prospects. 

Q4. What is the history of bubbles in the US?

In the 1920s, the US experienced a stock market boom particularly during the period 1927-29 which was followed by the great stock market crash of 1929 and the ensuing Great Depression. 

Q5. how is the drift compared to the stochastic trend?

In particular, if > 0, the drift is smallrelative to a linear trend; if > 0.5, the drift is small compared to the stochastic trend; if =0.5 and T , then the (standardized) behaves very much like a Brownian motion with drift. 

Q6. What has led to the bursting of the third bubble?

its meteoric price rise has been accompanied by huge volatilities which have led to claims by investors and in the media that bitcoin is a commodity that has been experiencing bubbles which could therefore burst anytime. 

Q7. What is the purpose of this study?

In this study, the authors conduct an econometric investigation of the existence of bubbles in the bitcoin market based on a recently developed technique of Phillips, Shi and Yu (2013a) that15   has been shown to robustly detect bubbles. 

Q8. What are the reasons why the bitcoin bubbles appear in the literature?

It should be pointed out that those studies that document the existence of bubbles argue that bubbles are caused by such factors as lax regulations or a breakdown in regulations (Sornette, 2003, and Herrera and 2003; Shiller, 2000; Vogel, 2010); growth prospects (Shiller 2000; Pastor and Veronesi 2004; Vogel 2010), inadequate market infrastructure that hinders the efficient flow of information (Taipalus, 2012), and overtrading (Vogel, 2010; Kindleberger, 2000; Heaton and Lucas, 2000). 

Q9. What is the purpose of the technique?

This technique is designed to detect stochastic explosive behaviour of a given time series since such explosive feature is commonly shared by all bubbles. 

Q10. What are the three approaches that are available in the literature?

They include the sigmoid curve approach (Foster and Wild, 1999), the Markovswitching process approach (Hall, Psaradakis and Sola, 1999) and the mildly explosive process approach (PSY, 2013a, 2013b, 2014). 

Q11. What are the three approaches that are available in the literature?

They include the sigmoid curve approach (Foster and Wild, 1999), the Markovswitching process approach (Hall, Psaradakis and Sola, 1999) and the mildly explosive process approach (PSY, 2013a, 2013b, 2014). 

Q12. what is the t-test statistic for the window size n?

The ADF t-test statistic for the window size n is:, , , (3)11   The standard ADF test is a special case with n = T. Given a fixed window size n and a fixed window end point r2, the authors can vary the starting point r1 and generate [r2 – n + 1] ADF statistics. 

Q13. What is the simplest way to determine the asymptotic distribution of the GSA?

PSY (2013b) derives the asymptotic distribution of GSADF statistic and shows that it is identical to the case where the regression model includes an intercept term and the null hypothesis is a unit root processes without drift. 

Q14. What is the purpose of the bubble test?

They develop a new bubble test to distinguish sub-martingale (exuberant or mildly explosive) behaviour from martingale behaviour soon after the change in behaviour occurs. 

Q15. What is the way to capture the evolution of Yt?

Psaradakis, and Sola (1999) propose to use a Markov-switching process (i.e., Markov chain) to capture the change from a non-bubble regime to a bubble regime. 

Q16. What is the history of the Tulipmania bubble?

there are three famous bubbles which occurred in the first half of the 1600s and 1700s - the Tulipmania, Mississippi Bubble and South Sea Bubble which are considered as classic cases (Taipalus, 2012 and Kindleberger, 2000).