BitCoin meets Google Trends and Wikipedia: Quantifying the relationship inbetween phenomena of the Internet era, Scientific Reports
BitCoin meets Google Trends and Wikipedia: Quantifying the relationship inbetween phenomena of the Internet era
Digital currencies have emerged as a fresh fascinating phenomenon in the financial markets. Latest events on the most popular of the digital currencies – BitCoin – have risen crucial questions about behavior of its exchange rates and they suggest a field to investigate dynamics of the market which consists practically only of speculative traders with no fundamentalists as there is no fundamental value to the currency. In the paper, we connect two phenomena of the latest years – digital currencies, namely BitCoin, and search queries on Google Trends and Wikipedia – and examine their relationship. We display that not only are the search queries and the prices connected but there also exists a pronounced asymmetry inbetween the effect of an enhanced interest in the currency while being above or below its trend value.
Introduction of the Internet has entirely switched the way real economy works. By enabling practically all Internet users to interact at once and to exchange and share information almost cost-free, more efficient decisions on the markets are possible. Even tho’ the interconnection inbetween digital and real economies has hit several bumps such as the DotCom Bubble of the break of the millennium, the benefits are believed to have overcome the costs.
One of the fascinating phenomena of the Internet era is an emergence of digital currencies such as BitCoin, LiteCoin, NameCoin, PPCoin, Ripple and Ven to name the most popular ones. A digital currency can be defined as an alternative currency which is exclusively electronic and thus has no physical form. It is also not issued by any specific central bank or government of a specific country and it is thus practically detached from the real economy. Note that a digital and a virtual currency are not synonymous since the virtual currencies are trading currencies in virtual worlds (most frequently in the massive multiplayer online games – MMOGs – such as World of Warcraft or 2nd Life). Even tho’ the digital currencies are almost isolated from the real economies, their prices (exchange rates) have experienced fairly an erratic behavior in the latest months. Specifically, the BitCoin currency – the most popular of the digital currencies – commenced the year of two thousand thirteen at levels of $13 per a BitCoin and rocketed to $230 on nine April two thousand thirteen potentially creating an absurd profit of almost 1700% in less than four months. Later the same year, the price soared even higher to $395 on nine November 2013, which accounts for a profit of approximately 2900% since the beginning of 2013.
Such behavior cannot be explained by standard economic and financial theories – e.g. future cash-flows model one , purchasing power parity Two,Trio and uncovered interest rate parity Four,Five – in a satisfactory manner. In general, currencies can be seen as standard economic goods which are priced by interaction of supply and request on the market. These are driven by macroeconomic variables of an issuing country or institution (or entity in general) such as GDP, interest rates, inflation, unemployment, and others. As there are no macroeconomic fundamentals for the digital currencies, the supply function is either immobile (if the currency amount is motionless) or it evolves according to some publicly known algorithm, which is the case of the BitCoin market. The request side of the market is not driven by an expected macroeconomic development of the underlying economy (as there is none) but it is driven only by expected profits of holding the currency and selling it later (as there are no profits from simply holding the currency due to no interest rates of the digital currencies). The market is thus predominated by short-term investors, trend chasers, noise traders and speculators. The fundamentalist segment of the market is totally missing due to the fact that there are no fundamentals permitting for setting of a “fair” price. The digital currency price is thus driven solely by the investors’ faith in the perpetual growth. Investors’ sentiment then becomes a crucial variable.
However, it is not a trivial task to find a good measure or proxy of investors’ sentiment in this matter. Fairly recently, search queries provided by Google Trends and Wikipedia have proved to be a useful source of information in financial applications ranging from the home bias and the traded volume explanations through the earnings announcements to the portfolio diversification and trading strategies 6,7,8,9,Ten,11,12 . The frequency of searches of terms related to the digital currency can be a good measure of interest in the currency and it can have a good explanatory power.
Here, we probe the relationship inbetween prices of the BitCoin currency (for a detailed description of a functioning of the currency, refer to Ref. 13) and related searched terms on Google Trends and Wikipedia. We find a striking positive correlation inbetween a price level of BitCoin and the searched terms as well as a dynamic relationship which is bidirectional. Moreover, we uncover an asymmetry inbetween effects of search queries related to prices above and below a short-term trend.
We analyze the dynamic properties of the BitCoin currency (as the most popular of the digital currencies) and the search queries on Google Trends and Wikipedia as proxies of investors’ interest and attention. Time series for the BitCoin currency at the most liquid market (Mt. Gox) are available since 17.7.2010 with the highest reported frequency (a tick) of one minute. However, the market remained very illiquid for approximately the very first year of its existence. To separate the period into the illiquid and the liquid one, we investigate a number of ticks with a non-zero comeback during a specific day. Fig. One depicts the evolution of the BitCoin liquidity. As a benchmark, we also demonstrate a number of 1-minute ticks associated with an 8-hour trading day. Even tho’ the BitCoin market is a 24/7 market, we use the 8-hour trading day as a ordinary benchmark of a liquid market. We observe that the number of ticks gets closer to the threshold value approximately in the middle of 2011. Closer inspection uncovers that since the beginning of May 2011, the number of ticks has fluctuated around the 8-hour benchmark. Therefore, we analyze the series beginning on one May two thousand eleven with an ending date of thirty June 2013. For Google Trends, we are working with weekly data and as such, we obtain one hundred thirteen observations in total; while for Wikipedia, daily data are available so that we have seven hundred eighty eight observations.
Number of ticks with a non-zero come back per day is shown. The crimson line represents a number of ticks for an 8-hour trading day and is shown just for illustration. It is visible that for the kicking off days of existence of the BitCoin market, there was practically no liquidity. Approximately since May 2011, liquidity has reached satisfactory levels.
Evolution of both pairs – Google Trends (weekly) and Wikipedia (daily) with corresponding BitCoin prices – is illustrated in Fig. Two. Obviously, the daily series of Wikipedia entries provides a more detailed picture of the behavior of the Internet users’ interest and attention together with a higher potential for a more precise statistical analysis. We observe that the prices of the digital currency are strongly correlated with the search queries of both engines. Specifically, the correlations reach the levels of 0.8786 (with t(111) = Nineteen.3850[<0.01], p-value is shown in the square brackets) and 0.8271 (with t(786) = 41.2587[<0.01]) for Google Trends and Wikipedia, respectively. The strength of these relationships is nicely illustrated in Fig. Three where a strong linear correlation inbetween logarithmic prices and logarithmic search frequencies is evident. The fact that such correlation is most apparent for the log-log specification is the very first hint for an analysis of the logarithmic converts rather than the original series. Moreover, the log-log specification also permits for an effortless interpretation of the relationship as the elasticity. Such notion is more stressed in the next section where the stationarity and cointegration of the series are discussed.
Weekly series for BitCoin and Google Trends are shown on the left and daily series for BitCoin and Wikipedia are shown on the right. Search terms are evidently positively correlated with the prices with correlation of 0.8786 and 0.8271 for Google Trends and Wikipedia, respectively (for a log-log scale). The BitCoin bubble of two thousand thirteen is accompanied with rocketing search queries in both databases.
Dual logarithmic illustration of correlation inbetween BitCoin prices and the searched term (Google Trend on the left and Wikipedia on the right) is shown. A positive dependence is evident and it holds for practically the entire range with correlation of 0.8786 and 0.8271 for Google Trends and Wikipedia, respectively.
Stationarity & cointegration
To cover various combinations of relationships, we primarily explore all standard transformations of the original series, i.e. the logarithmic transformation, the very first differences, and the very first logarithmic differences. For each of the series, we test their stationarity using the KPSS fourteen and ADF fifteen tests. As both tests have opposite null and alternative hypotheses, they form an ideal pair for the stationarity vs. unit-root testing. In Tab. 1, all these results are summarized. For the BitCoin prices (both daily and weekly), we find both the original and the logarithmic series to be non-stationary and to contain the unit-root. Correspondingly, their very first differences are stationary. The same results are found for the Wikipedia daily views but for the Google Trends queries, we find the unit-root only for the logarithmic transformation of the searched terms series. For this reason and also for more convenient interpretation, we opt for the logarithmic series.
Turning now to the analysis of the dynamic properties and interconnections inbetween the series, we are firstly interested in a potential cointegration relationship. Cointegration methodology has proved very useful in various economic and financial studies ranging from economic development 16,17 over monetary economics Legitimate,Nineteen , international economics 20,21,22 to energy economics 23,24 as it enables to examine a long-term relationship inbetween series as well as their short-term dependence via the error-correction models (see the Methods section for more details). To test for the cointegration relationships, we utilize two tests of Johansen twenty five – the trace and the likelihood tests. In Tab. Two, we demonstrate the results for both pairs and we find that the BitCoin series are not cointegrated with the Google Trends series but the connection to the Wikipedia series can be described as the cointegration. Therefore, for the very first pair, we need to turn to the vector autoregression (VAR) methodology applied on the very first logarithmic differences (see the Methods section for more details), and for the 2nd pair, we stick to the standard cointegration and vector error-correction model (VECM) framework.
Commencing with the Google Trends results, we are firstly interested in the dynamic relationship inbetween the search queries on Google – namely “BitCoin” (note that the search query frequency is not case sensitive so that the various versions of the word, such as “BitCoin”, “Bitcoin” and “bitcoin”, are included) – and price of the currency. Based on the Akaike, Hannan-Quinn and Schwarz-Bayesian information criteria, we use a single lag in the VAR treatment, i.e. VAR(1) is applied on the very first logarithmic differences. To control for potential autocorrelation and heteroskedasticity inefficiencies, we opt for heteroskedasticity and autocorrelation sturdy (HAC) standard errors. The results are summarized in Fig. Four. The charts demonstrate the response of a corresponding variable to a shock in the impulse variable. As we are working with logarithmic differences, we can interpret these shocks as a proportional reaction to a 1% shock. A 10% shock in the search queries yields a reaction of approximately 0.8% in the very first and 1.2% in the 2nd period, i.e. a total 2% reaction, and the effect vanishes for the latter periods. However, the influence also works from the opposite side and it again lasts (remains statistically significant) for two periods. The reaction to a 10% shock in search queries is followed by a total reaction of 0.8% (0.55% and 0.25% for the periods, respectively) of the prices. Putting these two together, we find that the enlargened interest in the BitCoin currency measured by the searched terms increases its price. As the interest in the currency increases, the request increases as well causing the prices to increase. However, as the price of BitCoin increases so does also the interest of not only investors but also a general public. Note that it is fairly effortless to invest into BitCoin as the currency does not need to be traded in large bundles. This evidently forms a potential for a bubble development.
Impulse-response functions for the very first logarithmic differences of BitCoin prices and Google Trends search queries. Positive relationship is evident in both directions. Responses are also partly asymmetric.
Turning now to the results of the Wikipedia daily views, we are interested in the same relationship as in the previous case but now based on the vector error-correction model (VECM) with seven lags (VECM(7)) based on the information criteria. In Fig. Five, we present the response functions which are, however, different from the previous ones as these represent permanent shifts in the response variable compared to the instantaneous shifts in Fig. Four. In the very first seven days (a trading week), an increase in prices causes an enhancing positive reaction of the daily views. After the very first week, the effect stabilizes but the interest in BitCoin measured by the daily views does not come back back to the initial level. The finish transmission is around 0.05, i.e. a 10% switch in prices is connected to a 0.5% permanent shift in the Wikipedia views. From the opposite side, we do not observe any statistically significant effect coming from the daily views to prices. The difference inbetween Wikipedia and Google Trends might be caused by the fact that of course the two engines are different and individuals using these two can have different motives and can be interested in different specifics. Nonetheless, we believe that both engines provide interesting insights into the functioning and relationship inbetween the digital currency and a general interest in the currency. Apart from the standard effects, we are also interested whether the reaction of prices to the searched terms is symmetric, i.e. whether an enhancing interest coming in mitt with the enhancing prices (possibly a bubble forming) has a same effect as an enlargening interest connected to the decreasing prices (possibly a bubble burst).
Impulse-response functions for the logarithmic transformations of BitCoin prices and Wikipedia daily views. There is a positive effect of price switches on daily views on Wikipedia site. The opposite effect is not statistically significant. However, when the effects are separated into a positive and a negative feedback, the effect becomes statistically significant.
Positive and negative feedback
A crucial disadvantage of measuring interest using the search queries on Google Trends or daily views on Wikipedia is the fact that it is hard to distinguish inbetween interest due to the positive or negative events. Specifically for the BitCoin, there is a big difference inbetween searching for the information during an enhancing trend or after the bubble burst. To separate these effects, we introduce a dummy variable equal to one if the price of BitCoin is above its trend level (measured by a moving average of four for Google Trends and of seven for Wikipedia due to different sampling frequency) and zero otherwise. This way, we attempt to distinguish inbetween a positive feedback defined as a reaction to an enlargening interest (measured by search queries) while the price is above its trend value and a negative feedback defined reversely.
For the Google Trends pair, the results are again illustrated in Fig. Four. Here, we can see that practically the entire reaction comes from the positive feedback as there is practically no statistically significant reaction to the negative movements of the prices in a sense of the search queries. Much more interesting results are found for the Wikipedia daily views. In Fig. Five, we find that the positive and negative feedback are practically symmetric around the zero reaction. That is – the reaction of prices to switches in the Wikipedia interest is similar for the prices being both above and below the trend but for the sign of the reaction. The finish transmission is around 0.05 and −0.05 for the positive and negative feedback, respectively. This is a crucial result because without the separation inbetween the positive and negative feedback, we do not find any reaction of the BitCoin prices to the Wikipedia views. However, if the effect is separated, the reaction is statistically significant and of an expected sign. If the prices are going up and the public interest in the matter is growing, the prices will likely proceed soaring up. But if the prices decline, the enlargened interest shoves them even lower.
Digital currencies are fresh economic instruments with special attributes. Very likely the most significant one of them is the fact that they have no underlying asset, they are not issued by any government or central bank and they bring no interest or dividends. Despite these facts, these currencies, and namely the BitCoin currency, have attracted the public attention due to the unprecedented price surges with possible profits of hundreds percent in just several weeks or months. In this paper, we analyzed the dynamic relationship inbetween the BitCoin price and the interest in the currency measured by search queries on Google Trends and frequency of visits on the Wikipedia page on BitCoin. Apart from a very strong correlation inbetween price level of the digital currency and both the Internet engines, we also find a strong causal relationships inbetween the prices and searched terms. Importantly, we find that this relationship is bidirectional, i.e. not only do the search queries influence the prices but also the prices influence the search queries. This is well in arm with the expectations about a financial asset with no underlying fundamentals. Speculation and trend pursuing evidently predominate the BitCoin price dynamics.
Specifically, we find that while the prices are high (above trend), the enlargening interest shoves the prices further atop. From the opposite side, if the prices are below their trend, the growing interest shoves the prices even deeper. This forms an environment suitable for a fairly frequent emergence of a bubble behavior which indeed has been observed for the BitCoin currency. We believe that the paper will serve as a commencing point of the research line dealing with statistical properties, dynamics and bubble-burst behavior of the digital currencies as these provide a unique environment for studying a purely speculative financial market.
Time series have been obtained from http://www.google.com/trends for Google Trends, http://stats.grok.se for Wikipedia and http://www.bitcoincharts.com for BitCoin. Note that the Google Trends series are normalized (so that the maximum value of the series is equal to 100) and rounded whereas the Wikipedia series provide the actual number of visits for the given day. For the BitCoin prices, we concentrate on the exchange rate with the USD at Mt. Gox platform as this provides the most liquid market. For the fact that Google Trends series are available only at the weekly frequency, we had to reconstruct the weekly series (with a same definition of the week) for the BitCoin prices. The weekly BitCoin prices are taken as an average of the daily closing prices of the specific weeks. The analyzed period ranges inbetween 1.Five.2011 and 30.6.2013 due to illiquidity of the market in the period before (see Fig. One and the main text).
For the purposes of distinguishing inbetween the positive and negative feedbacks for BitCoin prices, we create a pair of series – and – defined as and where Qt is the search frequency at time t and is an indicator function equal to one if the condition in • is met and zero otherwise, and N is a number of periods taken into consideration for the moving average. For the Google Trends series, we use N = Four, i.e. Four weeks (a trending month), and for the Wikipedia series, we utilize N = 7, i.e. Seven days (a trading week), due to the different frequency sampling. These two variables serve as a proxy for the search-term activity connected with the positive ( ) and the negative ( ) feedback.
For testing stationarity, we utilize the Augmented Dickey-Fuller test (ADF) fifteen and the KPSS test fourteen . ADF has a null hypothesis of a unit root (d = 1) against the alternative of no unit root (d < 1) whereas KPPS has a null of stationarity (d = 0) against an alternative of a unit root (d = 1). Using the pair of tests, we are able to identify whether the tested series is stationary or not.
If both analyzed series contain a unit root, we can test them for the cointegration. If both series are stationary, we can utilize the vector autoregression (VAR) framework.
We say that two series <xt> and <yt> are cointegrated CI(d, b) if they are both integrated of the same order d and there exists a linear combination of the two series which is integrated of order d − b. The standard cointegration is based on CI(1, 1) relationship, i.e. series <xt> and <yt> contain a unit root (they are both I(1)) and there exists ut = yt − α − βxt which is I(0), i.e. stationary with brief memory 26,27 .
If the series are cointegrated, the long-term equilibrium relationship is characterized by As long as the series are cointegrated, the parameters can be super-consistently estimated using the ordinary OLS estimator twenty eight . The lagged residual series is called the error-correction term and is interpreted as a deviation from the long-term equilibrium.
To test for the cointegration relationship, we use two Johansen tests twenty five – the trace test and the maximum likelihood test. If the series are found to be cointegrated CI(1, 1), the error-correction model (ECM) or the vector error-correction model (VECM) is standardly applied. If the analyzed series are not cointegrated, we need to proceed with the vector autoregression applied on the very first differences of the originally used series.
Vector autoregression is a standard procedure for analyzing (ideally causal) relationship inbetween numerous series 29,30 . In a case of the pair of series <xt> and <yt>, the vector autoregression of order p (VAR(p)) is written as with possibly correlated disturbances <ε1t> and <ε2t> and lag p selected according to some measure, usually an information criterion, such as the Akaike Information Criterion (AIC), Hannan-Quinn Information Criterion (HQIC) and Schwarz Information Criterion (SIC). Assuming that series <xt> and <yt> are I(1), their very first differences <Δxt> and <Δyt> are I(0) and thus stationary so that the system can be lightly estimated using either the ordinary least squares or maximum likelihood procedures. Parameters β1, βTwo, γ1 and γTwo are themselves not as significant as the statistical inference based on them, for our purposes mainly the Impulse-Response analysis. Impulse-Response analysis is based on a vector moving average representation of VAR and it shows what is the reaction of one variable to a unit shock in some other variable and how the effect vanishes in time. For details, see Refs. 29,30,31,32.
Vector error-correction model
Vector error-correction model (VECM) is a generalization of the vector autoregression which incorporates the long-term corrections so that both short-term and long-term dynamics can be studied. For cointegrated CI(1, 1) series, we have (VECM(q)) with q lags written as where parameters θi and κi control for the short-term dynamics and λi represent the error-corrections to the long-term cointegration relationship from Eq. 1. VECM(q) framework permits for a similar Impulse-Response analysis as the VAR framework. The main difference lays in the fact that the Impulse-Response in the VAR framework illustrates instantaneous responses whereas in the VECM framework, the permanent shifts in the studied variables are examined 26,27,32 .
Data retrieval: Search volume data were retrieved by accessing the Google Trends website (http://www.google.com/trends) on five July two thousand thirteen and the Wikipedia article traffic statistics site (http://stats.grok.se) on twenty one August 2013. BitCoin series were obtained from http://www.bitcoincharts.com inbetween Five.–8.7.2013.
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The support from the Grant Agency of the Czech Republic (GACR) under projects P402/11/0948 and 402/09/0965 is gratefully acknowledged.
Institute of Economic Studies, Faculty of Social Sciences, Charles University in Prague, Opletalova 26, one hundred ten 00, Prague, Czech Republic, EU
- Ladislav Kristoufek
Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod Vodarenskou Vezi Four, one hundred eighty two 08, Prague, Czech Republic, EU
- Ladislav Kristoufek
Search for Ladislav Kristoufek in:
L.K. solely wrote the main manuscript text, ready the figures and reviewed the manuscript.
The author announces no rivaling financial interests.
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