Datestamping the Bitcoin and Ethereum Bubbles

TL;DR: The authors examined the existence and dates of pricing bubbles in Bitcoin and Ethereum, two popular cryptocurrencies using the Phillips et al. (2011) methodology and concluded that Bitcoin is almost certainly in a bubble phase.

Abstract: We examine the existence and dates of pricing bubbles in Bitcoin and Ethereum, two popular cryptocurrencies using the Phillips et al. (2011) methodology. In contrast to previous papers, we examine the fundamental drivers of the price. Having derived ratios that are economically and computationally sensible, we use these variables to detect and datestamp bubbles. Our conclusion is that there are periods of clear bubble behaviour, with Bitcoin now almost certainly in a bubble phase.

Summary

1. Introduction

• Or are the rises due to more fundamental characteristics of the assets construction.
• The aim of this paper is to test whether underlying fundamentals relating to both Bitcoin and Ethereum, denoted as the blockchain position, the hashrate and liquidity as measured by the volume of daily transactions, can be designated as drivers of price growth since the inception of both cryptocurrencies.
• The first measure relates to mining difficulty reflects how difficult it is to find a new block relative to the easiest that it could be in the past.
• As more miners join, the rate of block creation will increase, which causes the difficulty to increase in compensation to push the rate of block creation back down.
• This paper is structured as follows: Section 2 describes the selected methodology.

2.1. Testing for Bubbles

• Bitcoin is a peer-to-peer digital asset, which claims to be decentralised and independent of monetary authority influence (Nakamoto [2008]).
• Transactions take place directly between users, and are verified by network nodes.
• Alabi [2017] adopts a very different approach, using ideas from network theory to find periodically collapsing bubbles.
• The authors find evidence to suggest that Bitcoin prices are prone to substantial bubbles.
• Urquhart [2017] measures the efficiency of Bitcoin returns over a six-year period (between August 2010 and July 2016) using a number of tests for randomness (Ljung-Box, Runs, Bartels, Automatic variance test, BDS, R/S Hurst tests).

2.2. Data

• The authors source their data from historical API’s (application programming interfaces1) for the period between 9 January 2009 and 9 November 2017 resulting in 3,227 observations based on the fundamentals of Bitcoin.
• Bitcoin pricing data is used after the 18 July 2010 due to a significant number of missing observations in the dataset due to periods of reduced liquidity in the growth of the crytocurrency.
• The cryptocurrency market is a market that operates day round, year round, so the authors have no gaps.
• Figure 1 plots the time series trajectories of Bitcoin and Ethereum.
• It is important to note that the price of one Bitcoin did not increase above $1 until the 16 April 2011.

3. Datestamping Cryptocurrency Bubbles

• Shown in Figure 2 are indicators of normalized statistics for Bitcoin and in Figure 3 for Ethereum.
• These are normalized as being the ratio of the backwards SADF calculated statistic to the simulated critical value, all less one to centre at zero.
• In this context then a bubble would be indicated when the price series is identified as a bubble but the fundamental drivers are not so identified.
• The authors observe very few consistent periods of bubbles indicated.
• What is intriguing is that the recent explosive growth in Bitcoin prices has not been accompanied by sustained bubble signals.

4. Conclusions

• This paper provides insight into the relationship between the relationship of cryptocurrency pricing discovery and internal fundamental explanatory variables that can generate the conditions and environment in which a pricing bubble can thrive.
• Based on the above presented analysis, the authors conclude that there is no clear evidence of such a persistent bubble in the market for both Bitcoin or Ethereum.
• This does not imply that the price is "correct", merely a statistical indicator being absent.
• Considering the theoretical interlinkages between the price of both Bitcoin and Ethereum and their relationship with blockchain position, hashrate and liquidity respectively, the authors can state that there are distinct short-term time period in which each fundamental influences the price dynamics of both crytocurrency, however, these effects dissipate quickly.
• The authors do find evidence that supports the view that Bitcoin is currently in a bubble phase and has been since the price increased above $1,000.

Figures

Figure 1: Bitcoin and Ethereum Prices (US$)

Table 1: Descriptive Statistics for Bitcoin and Ethereum

Figure 3: Datestamping the Ethereum Bubbles

Figure 2: Datestamping the Bitcoin Bubbles

Full text

Electronic copy available at: https://ssrn.com/abstract=3079712
Datestamping the Bitcoin and Ethereum Bubbles
Shaen Corbet
a
, Brian Lucey
b∗
, Larisa Yarovaya
c
a
DCU Business School, Dublin City University, Dublin 9
b
Trinity Business School, Trinity College Dublin, Dublin 2
c
Anglia Ruskin University - Lord Ashcroft International Business School
∗
Corresponding Author: Blucey@tcd.ie
Abstract
We examine the existence and dates of pricing bubbles in Bitcoin and Ethereum, two popular
cryptocurrencies using the Phillips et al. [2011] methodology. In contrast to previous papers, we
examine the fundamental drivers of the price. Having derived ratios that are economically and
computationally sensible, we use these variables to detect and datestamp bubbles. Our conclusion
is that there are periods of clear bubble behaviour, with Bitcoin now almost certainly in a bubble
phase.
Keywords: Cryptocurrencies; Digital Assets; Bitcoin; Ethereum; bubbles
JEL Codes: C58, G10, G14,
Preprint submitted to SSRN December 1, 2017

Electronic copy available at: https://ssrn.com/abstract=3079712
1. Introduction
Are there bubbles in cryptocurrencies? If so, when do they manifest? Or are the rises due
to more fundamental characteristics of the assets construction. We examine two of the largest,
Bitcoin and Ethereum. The European Central Bank [2012] found that cryptocurrencies do not
jeopardise financial stability, due to their limited connection to the real economy, the low volumes
traded and the lack of wide user acceptance. This ECB conclusion in 2012 was associated with
the caveat that the growth of cryptocurrency markets and their integration to the global economy
must be monitored, since cryptocurrencies remain the potential source of financial instability. In
the five years since the release of this report, the market for crytocurrencies has evolved signifi-
cantly. Figure 1 portrays the substantial price appreciation that has been observed in Bitcoin since
2013. To provide assurances and clarity with regards to broad financial stability, it is important to
clarify as to whether this substantial increase in price has been predominantly driven by underlying
fundamentals, or whether it can be denoted as a speculative bubble.
The aim of this paper is to test whether underlying fundamentals relating to both Bitcoin
and Ethereum, denoted as the blockchain position, the hashrate and liquidity as measured by the
volume of daily transactions, can be designated as drivers of price growth since the inception of both
cryptocurrencies. Having derived ratios that are economically and computationally sensible we then
use these measures to detect and datestamp bubbles. The three measures were selected to best
represent the key theoretical components of cyrptocurrency pricing structures. The first measure
relates to mining difficulty reflects how difficult it is to find a new block relative to the easiest that
it could be in the past. As more miners join, the rate of block creation will increase, which causes
the difficulty to increase in compensation to push the rate of block creation back down. The second
measure relates to hashrate which is the speed at which a computer is completing an operation in
the Bitcoin code. A higher hashrate when mining increases your opportunity of finding the next
block and receiving payments. Finally, the relationship between cryptocurrency returns, volatility
and liquidity has been established by Donier and Bouchaud [2015] and Balcilar et al. [2017].
This paper is structured as follows: Section 2 describes the selected methodology. Section
3 describes the datestamping procedures and analyses the results of our test for bubbles in the
Bitcoin and Ethereum markets. Finally, Section 4 present our conclusions.
2

2. Methodology
2.1. Testing for Bubbles
Bitcoin is a peer-to-peer digital asset, which claims to be decentralised and independent of
monetary authority influence (Nakamoto [2008]). Transactions take place directly between users,
and are verified by network nodes. Kroll et al. [2013], provides a detailed description of the mining
process. Miners add verified transactions to a publicly distributed ledger, or blockchain, and are
incentivised to do so by the reward of transaction fees and new bitcoins. Böhme et al. [2015] provide
a detailed description of the technology behind Bitcoin, including: the blockchain, mining, mining
pools, transaction fees and wallets. The authors also detail the early use cases of Bitcoin, areas of
risk involved, and examine the potential for future regulation.
Despite the very large volume of commentary, scholarly research is surprisingly scant on the
existence of bubbles in cryptocurrencies. Garcia et al. [2014] examines feedback loops in social
media to Bitcoin price, but presupposes the existence of bubbles. Similarly, Kristoufek [2015] also
pre-supposes a bubble. Both of these take their inspiration from Shiller et al. [1984]. More formal
testing based on economic fundamentals does exist. Alabi [2017] adopts a very different approach,
using ideas from network theory to find periodically collapsing bubbles. The idea motivating this
paper is that as a network the number of users is a key determinant of value to the users. Formally
speaking a bubble is where the value of an economic asset deviates, persistently, from fundamental
values (Diba and Grossman [1988]). Thus to have any hope of assessing the presence or otherwise
of a bubble some evaluation must take place of the fundamentals.
Cheah and Fry [2015] test for evidence of speculative bubbles in Bitcoin returns, using two
assumptions for intrinsic rate of return and intrinsic level of risk. The authors find evidence to
suggest that Bitcoin prices are prone to substantial bubbles. In addition, they empirically estimate
the value of Bitcoin to be zero. In a more recent study, Fry and Cheah [2016] the authors uncover
evidence of a spillover from Ripple to Bitcoin, which exacerbates price-falls in Bitcoin. Such an effect
raises concerns about the long-term sustainability of Bitcoin, with regard to increased competition
from rival cryptocurrencies. The authors also examine the effect of a number of external events
on the Bitcoin market (a technical software glitch in 2013; the closure of the Silk Road website in
2013) and find that they brought about an end in the speculative bubble, a scenario which was
repeatedly observed during the dot-com bubble. More recently, Corbet et al. [2017a] analyse in
3

both the time and frequency domain the relationships between three popular cryptocurrencies and
a variety of other financial assets, finding evidence that support the view that cryptocurrencies
may offer diversification benefits for investors with short investment horizons. Time variation in
the linkages reflects external economic and financial shocks. Blau [2017] argued that high volatility
of Bitcoin is not related to the high speculative activity in this period. The ambiguity of the results
exemplifies the debates about whether the cryptocurrencies are a speculative investment asset or a
currency. To be considered as a currency (i.e. money), cryptocurrencies should serve as a medium
of exchange, be used as a unit of account, and allow to store value; however, cryptocurrencies are
barely managing to fulfil all those properties (Bariviera et al. [2017]). Urquhart [2017] measures
the efficiency of Bitcoin returns over a six-year period (between August 2010 and July 2016) using
a number of tests for randomness (Ljung-Box, Runs, Bartels, Automatic variance test, BDS, R/S
Hurst tests). Randomness test are utilised due to the fact that, in efficient markets, prices follow
a random walk. The authors find returns to be significantly inefficient over the entire sample.
When divided into two equal sub-samples, two tests indicate efficiency of returns in the latter
sample, suggesting that Bitcoin may be moving towards becoming more efficient. Corbet et al.
[2017b] examined the reaction of a broad set of digital assets to US Federal Fund interest rate and
quantitative easing announcements providing evidence of differing volatility reactions, indicating
a diverse market in which not all cryptocurrencies are comparable to Bitcoin. Baek and Elbeck
[2015] find evidence to suggest that Bitcoin returns are driven by buyers and sellers internally,
and not by fundamental economic factors. Using de-trended ratios, the authors determine Bitcoin
returns to be 26 times more volatile than those of the S&P 500 index, suggesting that Bitcoin is a
speculative investment vehicle. The authors however, determine that this classification may change
as usage grows, volatility decreases and Bitcoin attracts market and economic influence. In doing
so, Bitcoin may become a more balanced investment vehicle, driven both internally and externally.
Cheung et al. [2015] perform an econometric investigation of bubbles in the Bitcoin market, using
the Phillips et al. [2015] methodology (a technique which has proven to be robust in detecting
bubbles). Using this method, the authors detect a number of short-lived bubbles, and three large
bubbles (2011-2013) lasting from 66 to 106 days. The bursting of these bubbles is found to coincide
with a number of major events that occurred in the Bitcoin market as the most significant of these
leading to the demise of the Mt. Gox exchange.
4

2.2. Data
We source our data from historical API’s (application programming interfaces
1
) for the period
between 9 January 2009 and 9 November 2017 resulting in 3,227 observations based on the funda-
mentals of Bitcoin. Bitcoin pricing data is used after the 18 July 2010 due to a significant number
of missing observations in the dataset due to periods of reduced liquidity in the growth of the cry-
tocurrency. Ethereum was initially released on the 30 July 2015 and we have analysed a complete
dataset between 7 August 2015 and 9 November 2017 representing 826 observations.
The cryptocurrency market is a market that operates day round, year round, so we have no
gaps. Figure 1 plots the time series trajectories of Bitcoin and Ethereum. The evolution of the
recent price increases in both cryptocurrencies has been significant. It is important to note that
the price of one Bitcoin did not increase above $1 until the 16 April 2011. On the 3 June 2011, it
increased above a value of $10 and traded below that level for the following year. In early 2013,
there was substantial momentum evident and the price of Bitcoin first closed above $100 on 2 April
2013. Between 30 October 2013 and 29 November 2013, the explosive nature of cryptocurrency
prices were first evident as within 31 days the price of Bitcoin grew from closing at $201.50 to that
of $1,049.35 per Bitcoin. Although the price reversed and fell to levels below $300 in the following
three years, on 3 January 2017, the price once again breached $1,000 and a month later was closing
daily above this substantial threshold. By 21 May 2017, Bitcoin closed above $2,000. By the 14
August 2017, it was valued at $4,000 and by 4 November 2017 it cost $7,000 per Bitcoin. Table 1
presents descriptive statistics of the volatility and price levels of both Bitcoin and Ethereum.
2.3. The Phillips et al. Methodology
Phillips et al. [2011] proposed a recursive ex ante method that is found to be capable of detecting
exuberance in asset price series during inflationary periods that is capable of acting as an early
warning system. Our selected research methodology is based upon the work of Phillips and Yu
[2011] who developed a methodology that analysed the house price bubble of the 2000’s in the
United States and Phillips et al. [2015] who developed on previous work when allowing for flexible
window widths in the recursive regressions on which the testing procedures are based using a
sup ADF (SADF) to test for the presence of a bubble through the inclusion of a sequence of
1
An API is a set of functions and procedures that allow the creation of applications which access the features or
data of an operating system, application or other service.
5

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Datestamping the bitcoin and ethereum bubbles" ?

The authors examine the existence and dates of pricing bubbles in Bitcoin and Ethereum, two popular cryptocurrencies using the Phillips et al. [ 2011 ] methodology. In contrast to previous papers, the authors examine the fundamental drivers of the price. 

Q2. What is the purpose of the GSADF test?

When multiple episodes of exuberance and collapse are included in the investigated sample which is common during rapidly changing market conditions, the generalised sup ADF (GSAFD) methodology is selected to test for the presence of bubbles as well as a recursive backward regression technique to time-stamp the bubble within the data. 

Q3. How do the authors determine that Bitcoin is a speculative investment vehicle?

Using de-trended ratios, the authors determine Bitcoin returns to be 26 times more volatile than those of the S&P 500 index, suggesting that Bitcoin is a speculative investment vehicle. 

Q4. What is the definition of a bubble?

For a bubble to be defined it is assumed that its duration should exceed a minimal period represented by δlog(T ), where δ is a frequency-dependent parameter. 

Q5. What is the purpose of this paper?

The aim of this paper is to test whether underlying fundamentals relating to both Bitcoin and Ethereum, denoted as the blockchain position, the hashrate and liquidity as measured by the volume of daily transactions, can be designated as drivers of price growth since the inception of both cryptocurrencies. 

Q6. What is the value of the quantity PtBt?

The quantity P f t = Pt−Bt represents the market fundamental and Bt satisfies the submartingale propertyEt(Bt+1) = (1 + rf )Bt (2)When Bt = 0 there is no bubble present and the degree of nonstationarity of the asset price is controlled by unobservable fundamentals, where asset prices will be explosive in the presence of bubbles. 

Q7. What is the sup statistic for a sample that runs from 0 to 1?

The starting point r1 of the sample sequence is fixed at 0, so the endpoint of each sample (r2) equals rw and changes from r0 to 1. 

Q8. What is the definition of the backward SADF test?

The backward SADF test performs a sup ADF test on a backward expanding sample sequence where the end point of each sample is fixed by r2 and the start point varies from 0 to r2− r0. 

Q9. What is the recursive ex ante method?

Phillips et al. [2011] proposed a recursive ex ante method that is found to be capable of detecting exuberance in asset price series during inflationary periods that is capable of acting as an early warning system. 

Q10. What is the main reason for the bubbles?

Phillips and Magdalinos [2007] stated that no matter what unobservable fundamentals were fuelling the origins of such observed bubbles, explosive or mildly explosive behaviour in asset price can be considered a primary indicator of market exuberance during the inflationary phase of a bubble3. 

Q11. What is the definition of a currency?

To be considered as a currency (i.e. money), cryptocurrencies should serve as a medium of exchange, be used as a unit of account, and allow to store value; however, cryptocurrencies are barely managing to fulfil all those properties (Bariviera et al. [2017]). 

Q12. What is the main reason why the authors found the bubbles to be so large?

The bursting of these bubbles is found to coincide with a number of major events that occurred in the Bitcoin market as the most significant of these leading to the demise of the Mt. Gox exchange. 

Q13. What is the definition of the backward sup ADF statistic?

The GSADF test implements the backward sup ADF test repeatedly for each r2 [r0, 1] and makes inferences based on the sup value of the backward sup ADF sequence BSADFr2(r0). 

Q14. What is the ECB's conclusion in 2012?

This ECB conclusion in 2012 was associated with the caveat that the growth of cryptocurrency markets and their integration to the global economy must be monitored, since cryptocurrencies remain the potential source of financial instability.