Introduction

Introduction of the Internet has completely changed 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 though the interconnection between 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 Second Life). Even though the digital currencies are almost isolated from the real economies, their prices (exchange rates) have experienced quite an erratic behavior in the recent months. Specifically, the BitCoin currency – the most popular of the digital currencies – started the year of 2013 at levels of $13 per a BitCoin and rocketed to $230 on 9 April 2013 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 9 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 model1, purchasing power parity2,3 and uncovered interest rate parity4,5 – in a satisfactory manner. In general, currencies can be seen as standard economic goods which are priced by interaction of supply and demand 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 fixed (if the currency amount is fixed) or it evolves according to some publicly known algorithm, which is the case of the BitCoin market. The demand 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 dominated by short-term investors, trend chasers, noise traders and speculators. The fundamentalist segment of the market is completely missing due to the fact that there are no fundamentals allowing 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. Quite 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 strategies6,7,8,9,10,11,12. 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 study the relationship between 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 between a price level of BitCoin and the searched terms as well as a dynamic relationship which is bidirectional. Moreover, we uncover an asymmetry between effects of search queries related to prices above and below a short-term trend.

Results

Dataset

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 1 minute. However, the market remained highly illiquid for approximately the 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 return during a specific day. Fig. 1 depicts the evolution of the BitCoin liquidity. As a benchmark, we also show a number of 1-minute ticks associated with an 8-hour trading day. Even though the BitCoin market is a 24/7 market, we use the 8-hour trading day as a simple 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 starting on 1 May 2011 with an ending date of 30 June 2013. For Google Trends, we are working with weekly data and as such, we obtain 113 observations in total; while for Wikipedia, daily data are available so that we have 788 observations.

Figure 1
figure 1

Evolution of ticks number.

Number of ticks with a non-zero return per day is shown. The red line represents a number of ticks for an 8-hour trading day and is shown just for illustration. It is visible that for the starting days of existence of the BitCoin market, there was practically no liquidity. Approximately since May 2011, liquidity has reached satisfactory levels.

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Evolution of both pairs – Google Trends (weekly) and Wikipedia (daily) with corresponding BitCoin prices – is illustrated in Fig. 2. 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) = 19.3850[<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. 3 where a strong linear correlation between logarithmic prices and logarithmic search frequencies is evident. The fact that such correlation is most apparent for the log-log specification is the first hint for an analysis of the logarithmic transforms rather than the original series. Moreover, the log-log specification also allows for an easy 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.

Figure 2
figure 2

BitCoin price and search queries evolution.

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 2013 is accompanied with rocketing search queries in both databases.

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Figure 3
figure 3

Relationship between BitCoin price and search queries.

Double logarithmic illustration of correlation between 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 whole range with correlation of 0.8786 and 0.8271 for Google Trends and Wikipedia, respectively.

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Stationarity & cointegration

To cover various combinations of relationships, we initially study all standard transformations of the original series, i.e. the logarithmic transformation, the first differences and the first logarithmic differences. For each of the series, we test their stationarity using the KPSS14 and ADF15 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 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.

Table 1 Stationarity and unit-root tests
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Turning now to the analysis of the dynamic properties and interconnections between 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 development16,17 over monetary economics18,19, international economics20,21,22 to energy economics23,24 as it enables to study a long-term relationship between 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 Johansen25 – the trace and the likelihood tests. In Tab. 2, we show 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 first pair, we need to turn to the vector autoregression (VAR) methodology applied on the first logarithmic differences (see the Methods section for more details) and for the second pair, we stick to the standard cointegration and vector error-correction model (VECM) framework.

Table 2 Cointegration tests between BitCoin prices and search queries
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General results

Starting with the Google Trends results, we are firstly interested in the dynamic relationship between 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 approach, i.e. VAR(1) is applied on the first logarithmic differences. To control for potential autocorrelation and heteroskedasticity inefficiencies, we opt for heteroskedasticity and autocorrelation robust (HAC) standard errors. The results are summarized in Fig. 4. The charts show 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 first and 1.2% in the second 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 increased interest in the BitCoin currency measured by the searched terms increases its price. As the interest in the currency increases, the demand 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 quite easy 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.

Figure 4
figure 4

Response dynamics for Google Trends.

Impulse-response functions for the first logarithmic differences of BitCoin prices and Google Trends search queries. Positive relationship is evident in both directions. Responses are also partly asymmetric.

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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. 5, 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 immediate shifts in Fig. 4. In the first 7 days (a trading week), an increase in prices causes an increasing positive reaction of the daily views. After the first week, the effect stabilizes but the interest in BitCoin measured by the daily views does not return back to the initial level. The complete transmission is around 0.05, i.e. a 10% change 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 between 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 between 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 increasing interest coming in hand with the increasing prices (possibly a bubble forming) has a same effect as an increasing interest connected to the decreasing prices (possibly a bubble burst).

Figure 5
figure 5

Response dynamics for Wikipedia.

Impulse-response functions for the logarithmic transformations of BitCoin prices and Wikipedia daily views. There is a positive effect of price changes 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.

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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 between interest due to the positive or negative events. Specifically for the BitCoin, there is a big difference between searching for the information during an increasing 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 4 for Google Trends and of 7 for Wikipedia due to different sampling frequency) and zero otherwise. This way, we try to distinguish between a positive feedback defined as a reaction to an increasing 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. 4. Here, we can see that practically the whole 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. 5, we find that the positive and negative feedback are practically symmetric around the zero reaction. That is – the reaction of prices to changes in the Wikipedia interest is similar for the prices being both above and below the trend but for the sign of the reaction. The complete transmission is around 0.05 and −0.05 for the positive and negative feedback, respectively. This is a crucial result because without the separation between 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 continue soaring up. But if the prices decline, the increased interest pushes them even lower.

Discussion

Digital currencies are new economic instruments with special attributes. Probably the most important 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 between 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 between price level of the digital currency and both the Internet engines, we also find a strong causal relationships between 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 hand with the expectations about a financial asset with no underlying fundamentals. Speculation and trend chasing evidently dominate the BitCoin price dynamics.

Specifically, we find that while the prices are high (above trend), the increasing interest pushes the prices further atop. From the opposite side, if the prices are below their trend, the growing interest pushes the prices even deeper. This forms an environment suitable for a quite frequent emergence of a bubble behavior which indeed has been observed for the BitCoin currency. We believe that the paper will serve as a starting 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.

Methods

Data

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 focus 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 between 1.5.2011 and 30.6.2013 due to illiquidity of the market in the period before (see Fig. 1 and the main text).

For the purposes of distinguishing between 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 1 if the condition in • is met and 0 otherwise and N is a number of periods taken into consideration for the moving average. For the Google Trends series, we use N = 4, i.e. 4 weeks (a trending month) and for the Wikipedia series, we utilize N = 7, i.e. 7 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.

Stationarity tests

For testing stationarity, we utilize the Augmented Dickey-Fuller test (ADF)15 and the KPSS test14. 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.

Cointegration

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 short memory26,27.

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 simple OLS estimator28. 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 tests25 – 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 first differences of the originally used series.

Vector autoregression

Vector autoregression is a standard procedure for analyzing (ideally causal) relationship between multiple series29,30. 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 first differences {Δxt} and {Δyt} are I(0) and thus stationary so that the system can be easily estimated using either the ordinary least squares or maximum likelihood procedures. Parameters β1, β2, γ1 and γ2 are themselves not as important 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 allows 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 immediate responses whereas in the VECM framework, the permanent shifts in the studied variables are examined26,27,32.

Additional information

Data retrieval: Search volume data were retrieved by accessing the Google Trends website (http://www.google.com/trends) on 5 July 2013 and the Wikipedia article traffic statistics site (http://stats.grok.se) on 21 August 2013. BitCoin series were obtained from http://www.bitcoincharts.com between 5.–8.7.2013.