Does daily Twitter sentiment affect the price movements of Bitcoin?

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Does daily Twitter sentiment affect the price movements

of Bitcoin?

Abstract

This research attempts to contribute to the discussion by exploring sentiment as an important determinant of Bitcoin’s price movements. It examines the effect of Twitter sentiment on Bitcoin’s price movements. Additionally, a Granger causality is tested between Bitcoin’s return and intraday spread with Twitter sentiment. Within a 79-days timeframe (December 9th, 2017 – February 25th, 2018), 11203 Twitter post, from the top 19 Bitcoin accounts

recommended to follow by Fortune magazine, were collected. The Tweets were analysed and sorted per sentiment by a sentiment analysis. The ordinary least square regression results show a significant negative relation between daily sentiment score and return. Further, a significant positive influence was observed between daily sentiment score and Bitcoin’s intraday spread. Additionally, a significant negative effect between the volume of positive Tweets and intraday spread was noticed. Also, an unidirectional Granger causality from sentiment score to return was found. Finally, the conclusion of this research is that Twitter sentiment influences Bitcoin’s price movements.

Keywords: Bitcoin, Twitter, Investor Sentiment, Sentiment Analysis, Prediction, Return,

Volatility

Name:

Olivier Garos

Student number: 10624090

Program:

Economics and Business (BSc ECB)

Specialization:

Finance and Organisation

Supervisor:

dr. Jeroen E. Ligterink

Date:

26-06-2018

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STATEMENT OF ORIGINALITY

This document is written by Student Olivier Garos who declares to

take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is

original and that no sources other than those mentioned in the text and

its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the

supervision of completion of the work, not for the contents.

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1. Introduction

2. Literature Review

2.1 What is Bitcoin

2.2 The purpose of Bitcoin

2.3 The effect of emotions on the investors’ decision-making process

2.4 Sentiment and Bitcoin value

2.5 Hypotheses

3. Methodology

3.1 Data

3.2 Variables

3.3 Model

3.4 Granger causality test

4. Results and Analysis

4.1 Descriptive Statistics

4.2 Correlations

4.3 OLS Regression Results

4.4 Granger Causality Test Results

4.5 Robustness of Results

5. Conclusion

5.1 Summary and Discussion

5.2 Limitations and Further Research

References

Appendix

Appendix A – the supply of Bitcoins following Coindesk

Appendix B – Multicollinearity test results by VIF tests

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1. Introduction

During 2017, the value of the Bitcoin experienced exponential growth, and increased more than 1300%. On December 17th, 2017 it reached the $20.000 threshold, its historical highest exchange price.1 As a result of these extreme price jumps, an increase of bubble theories linked to the Bitcoin appeared.2 Bitcoin’s current exchange price dropped dramatically below $7000, apparently confirming these theories.3 Bubble theories often state that public

sentiment plays a significant role in asset prices during periods of extreme price volatility (Pollock et al., 2008). In today’s world, exchanging knowledge and information is an

essential element of learning and improving skills. By using social media platforms, investors can obtain more detailed information about the experiences and thoughts of their peers. The data collected from these online platforms serve as a collective indicator of sentiment (Dessai & Kamat, 2012).

This Bachelor thesis in Finance and Organisation attempts to contribute to this discussion by exploring sentiment as an important determinant of Bitcoin’s price movements. Traditionally, the effect of public sentiment is measured by media attention and behavior of high-status actors (Pollock et al., 2008). However, this study uses Twitter activity as an indicator of public sentiment. Twitter4 , an online social networking platform and microblogging service, serves as an important instrument for businesses and individuals to interact and share

information. Additionally, Twitter has become a popular platform to exchange ideas and opinions about investment decisions. The aim of this study is to determine whether daily Twitter sentiment affects Bitcoin’s price movements, especially during a period with excessive volatility.

Recently, Bitcoin’s extreme price volatility has been the subject of many studies (Dyhrberg, 2015; Gavotti, 2016; Kasper, 2017). A related study has analyzed the causalities between Bitcoin price and business transactions on the one hand and Bitcoin and investors’

attractiveness on the other hand (Bouoiyour et al., 2014). Likewise, several studies have been conducted that analyze the causality between the Bitcoin and Tweets containing signals regarding Bitcoin (Kaminski, 2014; Matta et al., 2015). Nonetheless, public attention for the cryptocurrency has grown exponentially since these studies (Lee, 2016).

This study contains five chapters and is organized in the following order. The next chapter presents the literature review, covering recent literature on Bitcoin, the purpose of Bitcoin, the effect of emotions on investors’ decision-making process, sentiment, and Bitcoin’s value. Then, the hypotheses, based on the existing research, are stated. The third chapter discusses, the research methodology, including the model and data used in the study. The fourth chapter presents the study’s results and analysis, followed by a discussion. Finally, the fifth chapter discusses the study’s conclusion.

1

Coinmarketcap.com, visited on June 19th, 2018

2

The Economist, https://www.economist.com/blogs/buttonwood/2017/11/greater-fool-theory-0 3

Coinmarketcap.com, visited on June 19th, 2018

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2. Literature Review

2.1 What is Bitcoin

In 2009, Satoshi Nakamoto created Bitcoin, a purely peer-to-peer version of electronic cash that provides online payments to be sent directly between individuals and do not involve a financial institution (Nakamoto, 2008). Until 2009, commerce on the internet was based on financial institutions that acted like trustworthy third parties (2008). In 1998, Dai Wei published a paper called b-money, which described the concept of cryptocurrency, he suggested the idea of a new form of money that uses cryptographic control, rather than a central authority (Dai, 1998). Because of the inherent weakness of the trust based model and inspired by the Dai Wei’s paper, Nakamoto designed an electronic payment system built on cryptographic proof instead of trust. This allows any two willing parties to transact directly with each other without the need for a “trusted” third party (2008).

Beyond the absence of a central authority, Nakamoto stated that the cryptographic-based model should eliminate the double-spending problem, one of the main issues related to previous forms of digital currency. The double-spending problem stems from the possibility that the same digital coin may be spent twice. In Nakamoto’s cryptographic model the transactions are impossible to reverse. Still, the only way to control the duplicaton of a payment is to be aware of all payments made. Therefore, Nakamoto designed a public ledger within the Bitcoin network, called “block chain”. This ledger saves every transaction ever processed, and makes it possible for user’s computers to verify the payment’s validity. The authenticity of every payment is secured by digital signatures corresponding to the receiving addresses, enabling all users to remain in full control over transferring Bitcoins from their Bitcoin “wallet”.5 The validation process is done by computers, which verify the transactions in the Bitcoin network by solving complex mathematical algorithms. This protects sellers from fraud; and routine escrow mechanisms can be easily implemented to protect buyers (Nakamoto, 2008). The validation activity is called “mining”. As a reward the “miners” receive new Bitcoins every time their computer has found a solution for the validation algorithms; this is the only way to obtain new created Bitcoins. According to Bitcoin’s algorithms, the pace of coin supply is regulated in such a way that an average of 6 Bitcoins is created per hour. This pace of supply diminishes over time. 6 The maximum future supply of

5

https://bitcoin.org/en/faq#how-does-bitcoin-work

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coins is 21 million, which is projected to be reached in 2033.7 Bitcoin’s supply has been thus regulated since its initiation (Yermack, 2013).

2.2 The purpose of Bitcoin

According to Bitcoin’s founder, Nakamoto, Bitcoin was designed as an alternative to the existing trust-based payment systems. From this perspective, Bitcoin can be perceived as an alternative currency. It operates at a global level and can be used as a currency for all kinds of transactions (for both virtual and tangible goods and services), thereby competing with fiat currencies like the euro or the US dollar (European Central Bank, 2015).

According to Ali et al. (2014), money has three functions. Economic theory identifies money by the role it plays in society and the extent to which it serves the following functions: • A store of value to transfer purchasing power from today to some future date. • A medium of exchange which has the function to make payments.

• A unit of account as a standard to measure the value of any item that is for sale.

An asset’s usefulness as a store of value depends on the user’s expectation regarding its future supply and demand. Bitcoins are not fixed to any real-world currency. The exchange rate depends on the supply and demand (European Central Bank, 2012). As discussed above, the supply of Bitcoin does not depend on a central authority or on a monetary policy.

Although the supply is constrained, the prospects of future demand are far less predictable, not only because of the absence of intrinsic demand (for use in production or for

consumption) but also because of the absence of a central authority behind digital currencies. Due to the underlying cryptographic underlying technology, the digital currency is attractive for those engaged in criminal activities (Trautman, 2014). At the same time, taxing

authorities are facing problems of verifying the profits made by Bitcoin users. As a result, international governments are debating the regulatory needs that result from the disruptive changes due to the cryptocurrency.8 Central authorities are seeking to capture the benefits of the technological innovations, but they are simultaneously attempting to protect individual privacy and political stability (Trautman, 2016). The uncertainty of future laws around

7 Bitcoin.org, https://bitcoin.org/en/faq#how-are-bitcoins-created 8 Reuters.com, https://www.reuters.com/article/us-g20-argentina-bitcoin/g20-leaders-to-hold-fire-on-cryptocurrencies-amid-discord-sources-idUSKBN1GV2QR

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Bitcoin has affected the currency’s demand. This has led to speculation about the Bitcoin’s price movements which is based on a belief about its future use as media of exchange and a belief that it will continue to remain in demand even further into the future (Ali et al., 2014).

Bitcoin does not have an intrinsic value, however, one measure of its value as a medium of exchange is the number of retailers that are willing to accept the cryptocurrency as payment (Yermack, 2014). As noted earlier, the number of retailers prepared to accept payment in Bitcoin has increased substantially.9 However, Fred Ersham, co-founder of Coinbase, the leading digital wallet service, estimated in a March 2014 interview that 80% of activity on his site was related to speculation (Goldman Sachs, 2014). That is, Bitcoin users hold their tokens as speculative asset rather than using them for day-to-day transactions. Another handicap of Bitcoin is the difficulty in acquiring new Bitcoins, whose supply is predictable tied to “mining activity”, a complex process done by computers (European Central Bank, 2012). Even when a consumer is successful in mining Bitcoins or sourcing them from an online exchange, payments cannot be made with a credit card and the consumer must find a way to store them securely (Yermack, 2014). In order to keep the Bitcoins, users must store the coins in a digital wallet on their computer. This implies a risk of losing Bitcoins due to hackers or viruses. Consumers must thus find suitable antivirus and back-up measures (European Central Bank, 2012).

There is little evidence of any digital currency being used as a unit of account. There are only a small number of transactions between Bitcoin users involving two individuals negotiating and agreeing upon a price in Bitcoins, and these are believed to be isolated and largely unconnected (Ali et al., 2014). Retailers, who accept payment in digital currencies, usually update their prices with high frequency to compensate Bitcoin’s extreme volatility and to remain a relatively stable price. This implies that the Bitcoin is not an instrument to measure the value of any particular item that is for sale.

In 2015, Kristoufek attempted to define whether Bitcoin can be seen as a safe haven, a speculative bubble, or a form of business income. The research analysed Bitcoin’s price

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fluctuations and investigated the potential drivers of its price, such as supply-demand fundamentals and, technical and speculative causes. The results show that in lower

frequencies, drivers like exchange-trade ratio have a significant role. In the same research, Kristoufek noticed that businesses’ speculative behaviors are a powerful driver of Bitcoin’s fluctuations. Generally, explosive price periods are the result of a sharp rise in investors’ attractiveness, while a rapid decline period is caused by a lack of attractiveness. Bouoiyour et al. (2015) analysed whether Bitcoin can be seen as a payment system or a speculative asset by examining two causal relationships, between Bitcoin price and the exchange-trade ratio and between price and investors’ attractiveness. As a measure of investor’ interest, the study used the frequency of the search query “Bitcoin” in Google’s search engine. Their findings show that Bitcoin price is Granger-caused by investor’ attractiveness. This supports the idea that Bitcoin is used mainly as a speculative asset and is affected by speculative beliefs.

2.3 The effect of emotions on the investors’ decision-making process

Many economists have attempted to determine asset price by using the classical rational method: calculating the price of any asset depending on the present value of all future expected cash flows and discount rates. All “rational” expectations in economic models assume that ‘all information is in the price’, which states that prices immediately react to any news and therefore “no money is left on the table” (Kindleberger, 2005). Accordingly, Siegel states that an asset’s price is not rational when it does not equal the price based on its market fundamentals for a period, disregarding random shocks (Siegel, 2003). A fundamental is usually understood to be a long-run equilibrium consistent with a general equilibrium (Rosser, 2000). Contrary to the rational expectation assumption, the adaptive expectation assumption states that the future valuation of certain variables depends on the recent values of these variables. The idea “the trend is your friend”, implies that if prices have been increasing, they will continue to increase. This view uses a backward-looking method in which future prices are based on prices of the recent past (Kindleberger, 2005).

In behavioral economics, the rational assumptions used in the economic models were replaced with consistent assumptions based on psychological research (Valliere & Peterson, 2004). According to Baker and Ricciardi, emotional processes, mental errors, and individual character affect the investor’s behavior (2014). Correspondingly, they state that the investor’s decision-making process considers the quantitative (objective) and qualitative (subjective)

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aspects of the investment asset. These qualitative features are sensible for emotional biases and leads to decision-making based on feelings rather than facts (2014). Accordingly, Pollock et al.(2008)assertthat during stable economic times, investors prefer to avoid risk before making profit. Nonetheless, a speculative boom changes this preference. New assumptions respecting risk seem to spread across investment communities. Pollock et al. state that

investors start to ignore their private information or preference and start to follow the public’s belief by mimicking recent actions of those who actualized successes. This process is called a follow-the-leader movement. At that moment, the decision to invest is often not based on rational expectations but mostly based on the positive feedback of family or friends, or based on media coverage (Kindleberger, 2005). Positive media coverage, which reports the success stories of companies, has a particularly substantial impact on the mania. Due to the media attention, the demand for the assets increases (Rodrigue et al., 2008). As a result, the groupthink phenome will emerges. According to Morgan (1986), “Human beings have a tendency to get trapped in conceptual frameworks of their own creation”. In what Morgan calls “psychic prisons”, people try to fit all their data to reinforce the created logic even where there are negative payoffs. This enlarges the euphoria and accelerates the economic expansion (1986). Another biases related to positive sentiment is called the “hold” bias proposed by Zhang and Swanson (2010).They state that investors, during periods with positive sentiment, prefer not to trade their assets due to the fear of missing future profits (2010).

Behavioral biases based-on negative or doubtful emotions often have more impact on an investor’s decision-making process (Ameriks et al., 2009). Levin et al. (1986) and, Reyna and Brainerd (1991) describe the degree of uncertainty related to the investment affects the level of rationalization. This deviation from rationalism is due to the loss-aversion bias, which refers to the desire to avoid the feeling of regret after a choice whose results are revealed to be either bad or inferior (2014). Another negative emotional bias is due to worry. The act of worrying evokes memories or visions that change an investor’s judgment about the

speculative asset (2014). In agreement with this idea, Ricciardi finds in his research that investments associated with more anxiety result in a lower level of investor risk tolerance (2011). This supports the idea that the decision-making process is affected by negative or doubtful emotions (2011).

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2.4 Sentiment and Bitcoin value

Recently, the amount of research related to Bitcoin has increased substantially, mostly related to its price formation, its main price drivers and its volatility. Ciaian et al (2014) investigated Bitcoin’s price formation and the effect of public sentiment by analysing the relationship between its demand and supply fundamentals. Common financial indicators were used, such as like crude oil price and the Dow Jones index. Besides the effect of each factor, the authors studied the interactions of all variables on Bitcoin’s price. They found that Bitcoin’s price is determined by the market forces of supply and demand according to the standard economic models of currency price formation developed by Barro (1979). In particular, demand-side drivers, like the size of Bitcoin’s market, have a large impact on Bitcoin’s price formation. Additionally, they investigated the relationship between investment attractiveness and

Bitcoin’s price formation. Investors ‘attractiveness was measured by Bitcoin-related searches on Wikipedia and new posts on Bitcointalk.org. However, the researchers could not reject the null hypothesis, which implied that investor’s attractiveness and speculation have no

significant impact on Bitcoin’s price formation.

Bourie et al (2016) analysed Bitcoin’s return and volatility. The particular goal of their research was to study the usefulness of Bitcoin as an opportunity to hedge against the US equity market. Therefore, they included the US implied volatility index (VIX) in their study. This index is created by the Chicago Board Options Exchange can be seen as an uncertainty indicator for the US market. The measure excludes option prices, and correspondingly, it does not solely reflect information of historical volatility, but also the expectations of investors on future market conditions. In this way Bourie et al were able to test for causality between Bitcoin’s volatility and the US stock market. Their findings show that Bitcoin’s volatility and the VIX are negatively related.

According to Kristoufek (2015), Bitcoin’s long-term price formation depends on fundamental elements such as transaction volume, supply and popularity. Additionally, as an index for overall economic sentiment, the author included the Financial Stress Index (FSI) created by the Federal Reserve Bank of Cleveland. He found a positive relationship between increasing FSI and an increase in the price of Bitcoin. Furthermore, Bitcoin’s popularity was studied by queries in Google and Wikipedia. Kristoufek concluded that in addition to a strong

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bidirectional causal relation between queries and prices (2015). Davies (2014) conducted a similar study and, showed a relationship between Bitcoin’s volatility and its popularity, determined by online searches in Google that contained the word “Bitcoin”. In the same study, he also analysed Bitcoin’s popularity as measured by Tweets. However, the author could not conclude a relationship between Bitcoin’s volatility and Tweets related to Bitcoin.

2.5 Hypotheses

The central question of this thesis is: Does Twitter sentiment affect the Bitcoin’s price movements. The main research question is divided into the three sub-hypotheses described below:

𝐇𝐚𝟏𝐚: The volume of daily Tweets related to Bitcoin influences Bitcoin’s daily realized

return of Bitcoin

According to Baker and Ricciardi (2014) and Kindleberger (2005), investment decisions are affected by both positive and negative emotions. The following hypotheses were, therefore, formulated:

𝐇_𝐚𝟏𝐛: The volume of daily positive Tweets related to Bitcoin influences Bitcoin’s daily realized return of Bitcoin

𝐇_𝐚𝟏𝐜: The volume of daily negative Tweets related to Bitcoin influences Bitcoin’s daily realized return of Bitcoin

Further, to test the findings of Brown (1999), Antweiler and Frank (2004), and Davies

(2014), this research seeks to address the relationship between Bitcoin’s volatility and Twitter sentiment. Hence, the following hypotheses were tested:

𝐇_𝐛𝟏𝐚: The volume of daily Tweets related to Bitcoin influences Bitcoin’s volatility

𝐇𝐛𝟏𝐛: The volume of daily positive Tweets related to Bitcoin influences Bitcoin’s volatility

𝐇𝐛𝟏𝐜: The volume of daily negative Tweets related to Bitcoin influences Bitcoin’s volatility

Finally, it was tested if Twitter sentiment is useful in predicting Bitcoin’s price movements. As a result, the following hypotheses were tested:

𝐇_𝐜𝟏𝐚: The volume of daily Tweets related to Bitcoin is useful in predicting Bitcoin’s price movements

𝐇_𝐜𝟏𝐛: The volume of daily positive Tweets related to Bitcoin is useful in predicting Bitcoin’s price movements

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𝐇𝐜𝟏𝐜: The volume of daily negative Tweets related to Bitcoin is useful in predicting Bitcoin’s

price movements

3. Methodology

3.1 Data

The aim of this research is to test for causality between Bitcoin’s daily exchange price and the Twitter sentiment related to Bitcoin.

Twitter is an online social networking platform where users communicate by posting short messages. Twitter users post messages called Tweets, which are limited to 280 characters. Tweets often contain an opinion. It is, therefore, interesting to evaluate the opinion of Twitter users about Bitcoin. In order to collect the Tweets containing the word “Bitcoin”, a Twitter Application Programming Interface is used in Python. In this study, the Application

Programming Interface was programmed to capture all Tweets from the top 19 Bitcoin accounts that were recommended by Fortune magazine as accounts to follow.10 In total, 17292 English-language Tweets that mentioned the subject were collected. The dataset contained Tweets posted during a 79-day period from December 9th, 2017 to February 25th, 2018. Hence, a total of 79 days is analyzed. This period is interesting since the Bitcoin daily exchange price reached his highest historical value on December 17th, 2017.11 Accordingly, the mined Tweets are from the period before and after the price peak. Afterwards, all Tweets without the term “Bitcoin” and retweets were removed. Finally, the special characters, due to abbreviations in the gathered Tweets, were replaced using regular expressions. This resulted in a dataset of 11203 with Tweets consisting solely alphabetical and numerical characters. In order to investigate whether daily Twitter sentiment has an effect on Bitcoin’s price movements, the collected Tweets must be ordered by sentiment after performing a sentiment analysis on the Tweets. This process, also known as opinion mining, is common method in R, which can identify and extract subjective information from Tweets (Pang and Lee, 2008).A sentiment score was assigned to each Tweet, on a scale from -5 to 5, in which -5 indicates a

10

http://fortune.com/2017/12/27/bitcoin-twitter/

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very negative sentiment and 5 a very positive sentiment. Liu (2012) developed the applied sentiment analysis.

3.2 Variables

In order to test the effect of overall sentiment on Bitcoin’s price movements, the average daily sentiment score was calculated (Pak and Paroubek, 2010). Additionally, to test the positive and negative specific effect, the amount of daily positive and negative Tweets was determined. Finally, to test the effect of the total volume of Tweets related to Bitcoin, the daily volume of Tweets was calculated. The selected variables and its description can be found in Table 1.

Table 1. Sentiment variables and its description

Variable Description

Sentiment score Daily sum of sentiment score of Tweets, a one day lagged value is used in de analyses

Sum positive Number of positive Tweets per day, a one day lagged value is used in de analyses

Sum negative Number of negative Tweets per day, a one day lagged value is used in de analyses

Overall activity _{Total Tweets per day a one day lagged value is used in de analyses} Further, relevant market data from Bitcoin was captured from Coinmarketcap.com, which selects the 400 highest-volume traded markets of the past 24 hours. The value of the market movements of the cryptocurrency is calculated by taking the volume weighted average of the Bitcoin variables reported in each market.12 The Bitcoin variables, used in this research, can be found in Table 2. Following the methodology of Kaminski (2016), this study uses intraday spread as a proxy of daily volatility.

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Table 2. Bitcoin variables and its description

Price Closing price in dollars, captured from Coinmarketcap.com

Return (Closing pricet - Closing pricet-1) / Closing pricet-1

Intraday spread Daily Highest - Lowest price

Brown (1999) identifies that investors’ sentiment can affect asset price and cause additional volatility. In addition to intraday spread, the volatility of the return and intraday spread were determined on a weekly basis. A total of 11 weeks is observed. The following variables were used in the research:

Table 3. Bitcoin’s volatility variables and its description

Volatility return Weekly standard deviation of return * √7

Volatility intraday spread Weekly standard deviation of intraday spread * √7

Finally, control variables were added to the regression models. Since the VIX is perceived as a proxy for the volatility of the US stock market, it is useful to control for investors’

sentiment (Bourie et al., 2016). Additionally, following the study by Van Wijk (2013), three global financial indicators (S&P 500, gold and crude oil prices) were added to control for overall economic activity. Finally, the volume traded in Bitcoins is added to control for market activity (Brailsford, 1996; Baker and Wurgler, 2006; Ciaian et al., 2014). The control variables and its description can be found in Table 4:

Table 4. Mean Values of Sample Control variable data

VIX _{Daily closing value of the VIX, natural logarithmic value used in analyses} S&P 500 _{Daily closing price of the S&P 500, natural logarithmic value used in analyses} Gold _{Daily closing price of gold (per ounce), natural logarithmic value used in analyses} Oil _{Daily closing price of crude oil (per gallon), natural logarithmic value used in analyses}

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3.3 Model

In order to test and qualify the effect of Twitter sentiment on Bitcoin’s price movements, several ordinary least squares regressions were done. Since there are three hypotheses to test, each hypothesis had its own model.

(a)To test if the volume of daily Tweets related to Bitcoin influences Bitcoin’s daily realized return, the following to regressions were done:

𝐑𝐞𝐭𝐮𝐫𝐧 = α + βSentimentscore_t−1+ βOverall_Activity_t−1 + βVolumBTC_t + βVIX_t + βSP500t+ βOilt+ βGoldt+ ε

Furthermore, in order to test the sentiment specific effect of daily Tweets related to Bitcoin on Bitcoin’s daily realized return, the following regression was done:

𝐑𝐞𝐭𝐮𝐫𝐧 = α + βSum_Positivet−1 + βSum_Negativet−1+ βVolumBTCt + βVIXt +

βSP500_t+ βOil_t+ βGold_t+ ε

Additionally, in order to test for robustness, the same regressions were done but on a weekly basis:

𝐖𝐞𝐞𝐤𝐥𝐲_𝐫𝐞𝐭𝐮𝐫𝐧 = α + βWeekly_sentiment_score + βWeekly_overall_activity + βWeekly_volume_BTC + βWeekly_VIX + βWeekly_SP500 + βWeekly_oil + βWeekly_gold + ε

(b)To test the relationship between Twitter sentiment and Bitcoin’s volatility, the following regressions were done:

𝐈𝐧𝐭𝐫𝐚𝐝𝐚𝐲 𝐬𝐩𝐫𝐞𝐚𝐝 = α + βSentimentscore_t−1+ βOverall_Activity_t−1 + βVolumBTC_t + βVIXt + βSP500t+ βOilt+ βGoldt+ ε

𝐈𝐧𝐭𝐫𝐚𝐝𝐚𝐲 𝐬𝐩𝐫𝐞𝐚𝐝 = α + βSum_Positive_t−1 + βSum_Negative_t−1+ βVolumBTCt + βVIX_t + βSP500_t+ βOil_t+ βGold_t+ ε

Additionally, in order to test for robustness, the same regressions were done but on a weekly basis:

𝐖𝐞𝐞𝐤𝐥𝐲 𝐢𝐧𝐭𝐫𝐚𝐝𝐚𝐲 𝐬𝐩𝐫𝐞𝐚𝐝 =

α + βWeekly_sentiment_score + βWeekly_overall_activity + βWeekly_volume + βWeekly_VIX + βWeekly_SP500 + βWeekly_oil + βWeekly_gold + ε

Finally, in addition to the volatility measured by intraday spread, the effect of the weekly Twitter sentiment on volatility of return and intraday spread was tested:

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𝐕𝐨𝐥𝐚𝐭𝐢𝐥𝐢𝐭𝐲 𝐫𝐞𝐭𝐮𝐫𝐧 = α + βWeekly_sentiment_score + βWeekly_overall_activity + βWeekly_volume + βWeekly_VIX + βWeekly_SP500 + ε

𝐕𝐨𝐥𝐚𝐭𝐢𝐥𝐢𝐭𝐲 𝐢𝐧𝐭𝐫𝐚𝐝𝐚𝐲 𝐬𝐩𝐫𝐞𝐚𝐝 =

α + βWeekly_sentiment_score + βWeekly_overall_activity + βWeekly_volume + βWeekly_VIX + βWeekly_SP500 + ε

3.4 Granger Causality test

A Granger (Granger, 1968) causality test was used to check if a daily time series of Twitter sentiment would be useful for predicting the market movements of the return on Bitcoin. However, the concept is explained by the example of the return of Bitcoin and the daily sentiment score. This statistical concept of causality tests how much of the return can be described by its own historical values as well as lagged values of the sentiment score. If the return is better predicted when the lagged values of sentiment score are added, compared with relying solely on the historical values of return, Granger states that sentiment score Granger-causes the return of Bitcoin (1968). If this causality is irreversible, it is said to be an

unidirectional causality from sentiment score to return. It is said that return and sentiment score are statistically independent when there is no significant causality between both scalars. The two-variable models can be formulated as follows, where 𝛽_𝑖 is the regression coefficient:

𝑅𝑒𝑡𝑢𝑟𝑛𝑡 = 𝛼𝑡+ ∑ 𝛽𝑖𝑅𝑒𝑡𝑢𝑟𝑛𝑡−1+ 𝜀𝑡 𝑛 𝑖=0 𝑅𝑒𝑡𝑢𝑟𝑛_𝑡 = 𝛼_𝑡+ ∑ 𝑐_𝑖𝑅𝑒𝑡𝑢𝑟𝑛_𝑡−1 𝑛 𝑖=0 + ∑ 𝛽_𝑖𝑆𝑒𝑛𝑡𝑖𝑚𝑒𝑛𝑡 𝑆𝑐𝑜𝑟𝑒_𝑡−1+ 𝑢_𝑡 𝑛 𝑖=0 𝑤𝑖𝑡ℎ 𝐻0: 𝛽1 = 𝛽2 = ⋯ = 𝛽𝑛 = 0

The error terms are 𝜀_𝑡 and 𝑢_𝑡, and p is the optimal lags of Y and X. As shown above, the null hypothesis states that sentiment score does not Granger cause return. The first model includes only n-lagged values of the Return to forecast 𝑅𝑒𝑡𝑢𝑟𝑛_𝑡. In the second equation, lagged values of sentiment score are added; these are expressed by 𝑆𝑒𝑛𝑡𝑖𝑚𝑒𝑛𝑡 𝑆𝑐𝑜𝑟𝑒𝑡−1. The test

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statistic for the Granger causality test is f, which has the following definition:

RSS0 and RSS1 are the sum of squares residuals of both equations, T is the number of observations. If the f is greater than the critical value for an f distribution, the null hypothesis can be rejected. This implies that sentiment score has a Granger causal relationship with return.

However, to implement Granger causality on the Bitcoin variables and daily Twitter sentiment, the time series must have a stationary covariance (1968). Thus, an augmented Dickey-Fuller test must been done to check for stationarity (Dickey and Fuller, 1979). The equation of the Augmented Dick-Fuller test is defined by the equation below, where n is lag order and εt is a white noise term.:

∆𝑅𝑒𝑡𝑢𝑟𝑛_𝑡 = 𝛼 + 𝛽_𝑡+ 𝛾𝑅𝑒𝑡𝑢𝑟𝑛_𝑡−1+ 𝛿₁∆𝑅𝑒𝑡𝑢𝑟𝑛_𝑡−1+ ⋯ + 𝛿_𝑛−1∆𝑅𝑒𝑡𝑢𝑟𝑛_{𝑡−𝑛+1}+ 𝜀_𝑡 The null hypothesis states that there is non-stationarity in the covariance, H0: γ = 1. Therefore, the H0 hypothesis must be rejected.

4. Results

This chapter discusses the results of the analysis. Based on the stated hypotheses, the

statistical significance of each variable in the regressions is discussed and conclusions drawn. In this research, each variable is tested against three levels of statistical significance: a 99%, a 95% and a 90% confidence level.

4.1 Descriptive statistics

Table 5. Total number of Tweets and its sentiment

Total Tweets Positive Tweets Negative Tweets Neutral Tweets Average Sentiment Score

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Table 6. Mean Values of Sample Sentiment data

Variable Obs Mean Median Std. Dev. Min Max

Sentiment score ₇₉ _0.1390 _0.1064 _0.1385 _-0.0685 _0.6486 Sum positive 79 38.5696 21 36.2338 0 165 Sum negative ₇₉ _27.7848 ₁₆ _29.5417 ₀ ₁₃₁ Overall activity ₇₉ _141.8101 ₈₈ _137.5986 ₁ ₅₃₂

Table 7. Mean Values of Sample Bitcoin data

Variable Obs Mean Median Std. Dev. Min Max

Price 79 12756.87 11786.3 3166.659 6955.27 19497.4

Return 78 -0.0034 0.0010 0.0689 -0.1685 0.1478049

Intraday spread 79 1.3827 1.1864 0.7100722 0.4993 4.1104

Table 8. Mean Values of Sample Volatility of Sentiment data

Variable

Obs Mean Median Std. Dev. Min Max

Volatility Return

11 0.1748484 0.1574525 0.042653 0.129997 0.262339

Volatility Intraday spread

11 1.442138 1.459911 0.758011 0.418601 2.719405

Table 9. Mean Values of Sample Control variable data

Variable Obs Mean Std. Dev. Min Max

VIX ₇₉ _2.607187 _0.37812 _2.213754 _3.619529 S&P 500 79 7.911219 0.023429 7.855932 7.963067 Gold 79 7.179027 0.02674 7.12447 7.212442 Oil 79 4.120513 0.046346 4.035832 4.193738 Volume ₇₉ _197542.9 _96489.34 _88770.22 ₆₂₀₉₈₆

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Figure 1: The behavior of the daily sum of Tweets

Figure 2: The evolution of Bitcoin’s closing price and intraday spread

0.00 100.00 200.00 300.00 400.00 500.00 600.00 09/12/2017 09/01/2018 09/02/2018 Overall activity Sum of Positive Sum of Negative Sum of neutral $5,000.00 $10,000.00 $15,000.00 $20,000.00 $25,000.00 Dat e 14 /12/2 017 20 /12/2 017 26 /12/2 017 01 /01/2 018 07 /01/2 018 13 /01/2 018 19 /01/2 018 25 /01/2 018 31 /01/2 018 06 /02/2 018 12 /02/2 018 18 /02/2 018 24 /02/2 018 Close Intraday Spread

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Figure 3. The evolution of Bitcoin’s trade volume (in BTC)

4.2 Correlations

Table 10. Correlations of Closing Price with its control variables

Closing Price Volume S&P 500 Gold Oil

Closing Price ₁ Volume _0.6696 ₁ S&P500 _-0.0901 _-0.001 ₁ Gold _0.7157 _0.6724 _0.1858 ₁ Oil _-0.5757 _-0.2885 _0.6023 _-0.1611 ₁

Table 11. Correlations of Return and Intraday spread with the Overall Sentiment-related Variables

Return Intraday Spread Sentiment Score Overall Activity VIX

Return ₁ Intraday Spread _-0.2284 ₁ Sentiment Score _-0.0301 _-0.1343 ₁ Overall Activity _0.035 _-0.4167 _0.2513 ₁ VIX _-0.0639 _-0.325 _0.075 _0.5221 ₁ 0.00 100000.00 200000.00 300000.00 400000.00 500000.00 600000.00 700000.00 Dat e 13 /12/2 017 18 /12/2 017 23 /12/2 017 28 /12/2 017 02 /01/2 018 07 /01/2 018 12 /01/2 018 17 /01/2 018 22 /01/2 018 27 /01/2 018 01 /02/2 018 06 /02/2 018 11 /02/2 018 16 /02/2 018 21 /02/2 018

Volume traded (BTC)

volume btc

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Table 12. Correlations of Return and Intraday spread with the Positive and Negative Sentiment-related Variables

Return Intraday Spread Sum Positive Sum negative VIX

Return ₁ Intraday Spread _-0.2284 ₁ Sum Positive _0.0567 _-0.411 ₁ Sum Negative _0.0437 _-0.362 _0.9406 ₁ VIX _-0.0639 _-0.325 _0.5386 _0.5119 ₁

From Table 12 it can be seen that the sum positive and sum negative values have a high level of correlation. To ensure that no problematic level of multicollinearity is present, variance inflation factor (VIF) tests were done for each regression model. The results of the VIF test can be found in the appendix.

4.3 OLS regressions

Table 13. Variable Regression Results of Daily Realized Return

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VARIABLES Return Return

Sentiment score -0.0978* (0.0561) Overall activity -0.00416 (0.00938) VIX 0.00978 0.0250 (0.0490) (0.0476) S&P500 0.0764 0.269 (0.831) (0.716) Volume -0.0517** -0.0509* (0.0250) (0.0273) Oil -0.235 -0.502 (0.437) (0.394) Gold -0.504 0.321 (0.412) (0.918) Sum positive 0.0146 (0.0298) Sum negative 0.00472 (0.0190) Constant 4.611 -1.881 (6.291) (8.060) Observations 78 78 R-squared 0.130 0.107

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It was tested whether the volume of daily Twitter sentiment related to Bitcoin influences Bitcoin’s daily realized return.

Robust standard errors are in parentheses

Subscripts indicate the level of significance of the coefficients different from zero *** (p<.01), ** (p<.05) and *( p<.1).

As can be seen from Table 13, the sentiment variable (1) is a significant negative coefficient to estimate the daily realized return with a 10% level of significance. It shows that if the lagged sentiment score increases 1%, the daily realized return will decrease 0.0978%. As a result, it can be stated that sentiment score has an effect on the return of Bitcoin and 𝐇𝐚𝟎𝐚

can be rejected. It is interesting that the effect is opposite from that was found by Kristoufek (2013,2015) and Bouoiyour et al. (2015). However, Table 5 shows that during the observed period, Bitcoin’s return on average decreased with 0.0034%. According to Morgan’s study (1986), investors are habitually captured in psychic prisons during periods with negative pay-offs, which implies that they try to fit all the data into their created logic. This behavioral bias could be the explanation of the surprising effect of the sentiment variable on the daily

realized return. Inconsistent with the findings of Glaser and Bouoiyour et al. (2015), Table 13 shows that neither the volume of positive nor the volume of negative Tweets has a significant effect on Bitcoin’s daily realized return (2). Therefore, it cannot be said that the volume of positive or negative Tweets affects the return of Bitcoin, implying that 𝐇𝐚𝟎𝐛 and 𝐇𝐚𝟎𝐜 was

not rejected. Nonetheless, these results are consistent with the findings of Kaminski (2016) and Davies (2016).

Furthermore, the volume variable shows a significant negative coefficient to estimate the daily realized return with a 5% (1) and 10% (2) level of significance . It indicates that if the volume increases by 1%, the daily realized return will decrease by 0.0517% (1) and 0.0509% (2). This is consistent with the findings of Baker and Wurgler (2006).They state that during period with high sentiment, returns are relatively low.

Table 14. Variable Regression Results of Daily Intraday spread

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VARIABLES Intraday spread Intraday spread

Sentiment score 0.654** (0.284) Overall activity 0.101 (0.0660) VIX -1.028*** -1.089*** (0.239) (0.232) S&P500 -3.314 -4.557

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(3.535) (3.365) Volume 1.299*** 1.281*** (0.204) (0.204) Oil 1.382 2.872 (1.690) (1.686) Gold 2.211 -3.144 (2.818) (5.195) Sum positive -0.325** (0.147) Sum negative 0.0375 (0.0902) Constant -6.668 36.44 (35.71) (41.85) Observations 78 78 R-squared 0.715 0.703

It is tested whether the volume of daily Twitter sentiment related to Bitcoin influences Bitcoin’s intraday spread. Robust standard errors are in parentheses

Subscripts indicate the level of significance of the coefficients different from zero *** (p<.01), ** (p<.05) and *(p<.1).

From Table 14 it can be seen that the sentiment variable (1) has a positive coefficient to estimate the intraday spread with a 5% level of significance. It shows that if the sentiment score increases by 1%, the daily realized return will increase by 0.654%. Since intraday spread is used as a measure of daily price volatility (Kaminski, 2016), the results suggest that sentiment score affects the volatility of Bitcoin. Therefore, 𝐇𝐛𝟎𝐚 was rejected. This is

consistent with the findings of Kaminski (2016). In his study, he proves that this relationship confirms the idea of “nowcasting”, which refers to the idea of investors predicting the present (Giannone et al., 2008; Choi and Varian, 2012). From this table, we can see that the volume of positive Tweets has a significant negative coefficient at a level of significance of 5%. Hence, the volume of positive Tweets per day has a significant influence on the volatility of Bitcoin, and 𝐇𝐛𝟎𝐛 was rejected. The negative effect on the intraday spread can be explained

by the study of Zhang and Swanson (2010). The authors suggest that optimistic sentiment results in a “hold” bias. This implies that investors prefer not to trade their assets during periods of positive sentiment. As a result, volatility decreases (2010).

Further, a negative coefficient of the VIX variable is observed in both regression models with a significance level of 1%. It means that a 1% increase of the VIX will result in a decrease in the intraday spread of 1.028% (1) and 1.089% (2). Hence, the results support the findings of Bourie et al. (2016). They suggest a possible safe-haven effect, in which investors try to hedge their risk during periods with excessive volatility. Additionally, the volume variable shows a significant positive coefficient, in both regressions, to estimate the intraday spread

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with a 1% level of significance. It indicates that if the volume increases by 1%, the intraday will increase with 1.229% (1) and 1.281% (2). This is consistent with the findings of

Brailsford (1996). He describes a positive relationship between volume traded and volatility.

Table 15. Variable Regression Results of the Volatility of Return and Intraday spread

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VARIABLES Volatility return Volatility spread

Weekly sentiment -0.0886 3.022

(0.256) (1.684)

Weekly overall activity -6.53e-05 0.00297**

(0.000131) (0.00105)

Weekly volume 0.0656 2.553**

(0.0939) (0.714)

Weekly VIX 0.00174 -0.0958***

(0.00374) (0.0194)

Weekly S&P 500 -3.36e-05 0.00278

(0.000325) (0.00173)

Constant -0.535 -35.80**

(1.669) (11.15)

Observations 11 11

R-squared 0.410 0.904

It is tested whether the weekly volume of Twitter sentiment related to Bitcoin influences Bitcoin’s weekly realized volatility of return and intraday spread.

Subscripts indicate the level of significance of the coefficients different from zero *** (p<.01), ** (p<.05) and *(p< .1).

No significant coefficient of the variables on the weekly volatility of return was observed in Table 15. Further elaboration about possible reasons can be found in Chapter 5 in the

discussion and limitations of the research sections. Also, Table 15 shows that the weekly total volume of Bitcoin-related Tweets has a negative effect with a significance level of 5%. This implies that a 1% change in overall activity results in an increase of 0.00297% of the weekly volatility of Bitcoin’s intraday spread. Therefore, 𝐇𝐛𝟎𝐚 was rejected. This effect is consistent

with the findings of Antweiler and Frank (2004). In their research, they find a relationship between communication activity and volatility. The authors even state that communication activity might induce market volatility. Further, in Table 15 can be seen that the coefficients of weekly volume traded and the weekly value of VIX are significant. This relationship has been explained above by the theories of Brailsford (1996) and Bourie et al. (2016).

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4.4 Granger causality tests

In this study, Granger causality tests were applied to test for causality between the sentiment-related variables and Bitcoin’s return and intraday spread.

Table 16. Variables tested on Granger causality

Dependent Variable Independent Variable

Return Sentiment Score

Return Sum Positive

Return Sum Negative

Intraday Spread Sentiment Score

Intraday Spread Sum Positive

Intraday Spread Sum Negative

However, the only significant result observed was the effect of Sentiment score on the return of Bitcoin, as shown in Table 17.

Table 17. Granger causality Wald test between Return and Sentiment score

It is tested whether the daily sentiment score Granger causes Bitcoin’s daily realized. Standard errors are in parentheses

From the results of the Granger causality test, it can be concluded that the daily sentiment scores, with a lagged value of two days, Granger causes Bitcoin’s daily returns at a significance level of 10%. Therefore, it can be said that the return of Bitcoin is better

predicted with the two-days lagged variable of sentiment score and 𝐇_𝐜𝟎𝐚 was rejected. This corresponds with the findings by Kristoufek (2015) and is consistent with Baker and

Ricciardi’s (2014) behavioral investor bias theory. The authors state that many investment decisions are affected by behavioral biases, such as the emotion of worrying and the trend-chasing bias.

H0: Sentiment score does not Granger cause Bitcoin's return

Test statistic p-value df

5.0314 0.081* 2

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4.5 Robustness of Results

In this study, ordinary least square regressions were used to test for the effect of Twitter sentiment on Bitcoin’s price movements. In these tests, the daily data from a period of 79 days was used. To test the robustness of the obtained results, the same tests were done on a weekly basis. Afterwards an augmented Dick-Fuller test was applied on return and sentiment score variables.

Table 18. Variable Regression Results of Weekly Realized Return (1)

VARIABLES Weekly return

Weekly sentiment -0.230

(0.149)

Weekly overall activity 7.89e-05

(6.66e-05) Weekly volume -0.104 (0.0709) Weekly VIX 0.000655 (0.00189) Weekly S&P500 -0.000215 (0.000223) Constant 1.866 (1.263) Observations 11 R-squared 0.434

It is tested whether the volume of weekly Twitter sentiment related to Bitcoin influences Bitcoin’s weekly realized return.

As Table 18 shows, none of the coefficients is significant. Therefore, it cannot be stated in this study that daily Twitter sentiment has a robust effect on return. Further, multicollinearity was observed between the weekly volume of positive and negative Tweets. Therefore, a robustness test on a weekly basis could not be performed. This will be further elaborated in the following chapter in the discussion and limitations sections.

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Table 19. Variable Regression Results of Weekly Intraday spread (1)

VARIABLES Weekly intraday spread

Weekly sentiment -0.0480

(0.141)

Weekly overall activity 0.000124

(6.57e-05) Weekly volume 0.0943* (0.0395) Weekly VIX -0.00688** (0.00222) Weekly S&P 500 -0.000308* (0.000136) Constant -0.0361 (0.625) Observations 12 R-squared 0.845

It is tested whether the volume of weekly Twitter sentiment related to Bitcoin influences Bitcoin’s weekly intraday spread.

As Table 11 shows, none of the coefficients related to sentiment are significant. Therefore, it cannot be stated in this study that daily Twitter sentiment has an robust effect on return. Also, multicollinearity was observed between the weekly volume of positive and negative Tweets. Therefore, a robustness test on a weekly basis could not be performed. This will be further highlighted in the following chapter.

Table 20. Augmented Dick-Fuller test applied on Return

Augmented Dick-Fuller test Obs = 77

Test Statistic 1% Critical Value Z (t) -9.076 -3.542 p-value for Z (t) = 0.0000

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Table 21. Augmented Dick-Fuller test applied on Sentiment score

Augmented Dick-Fuller test Obs = 78

Test Statistic 1% Critical Value

Z (t) -6.929 -3.541

p-value for Z (t) = 0.0000

As the results from Table 20 and Table 21 tell, the covariance of both variables is stationary. This implies that the variables can be used in a Granger causality test.

5. Conclusion

5.1 Summary and Discussion

This thesis has attempted to establish the relationship between Twitter sentiment and Bitcoin’s return, intraday spread and volatility. Additionally, Granger causality was tested between Bitcoin’s price movements and Twitter sentiment. The main hypothesis was that Twitter sentiment would affect Bitcoin’s price movements. The observed sample consisted of 11203 Tweets spread over a 79-days period between December 9th, 2017 and February 25th, 2018. The effect of daily overall sentiment score on daily return was studied. A negative coefficient of 0.0978% was found with a 10% level of significance. This is contrary to the findings of Kristoufek (2013, 2015) and Bouoiyour et al. (2015). Nonetheless, this effect is supported by Morgan’s psychic prison theory (1986). Afterwards, the observed effect of sentiment score was tested on a weekly basis to check for robustness. This test did not show any significance. Further, no significant effect was found for the volume of positive or negative Tweets on return. This corresponds with the findings of Kaminski (2016) and Davies (2016).

To establish the relationship between Twitter sentiment and Bitcoin’s volatility, intraday spread was used as a short-term volatility proxy (Kaminski, 2016). A positive effect of sentiment score on intraday spread was observed with a 5% level of significance. This corresponds with the findings of Kaminski (2016). This finding is consistent with the idea of “nowcasting” suggested by Giannone et al. (2008) and Choi and Varian (2012). In addition, the volume of positive Tweets negatively affects the intraday-spread at a level of significance

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of 5%. According to this effect, Zhang and Swanson explain the observed influence is a result of the “hold” bias (2010). However, after testing for robustness, on a weekly base, none of the coefficients appeared to be significant. Additionally, the relationship between Twitter sentiment and the volatility of return and intraday spread has been tested on a weekly basis. The results show that none of the variables of interest had a significant influence on Bitcoin’s return. Nevertheless, a positive effect of overall activity was noted with a significance level of 5%. This supports the theorie of Antweiler and Frank (2004) suggesting that

communication activity might induce market volatility

Finally, to check if daily time series of Twitter sentiment would be useful to predict Bitcoin’s market movements. A Granger test was applied to test for causality between Twitter

sentiment and Bitcoin’s return and intraday spread. An unidirectional Granger causality from sentiment score to return was determined with a lagged value of two days. The observed causality was affirmed by the investor bias theory of Baker and Ricciardi (2014).

5.2 Limitations and further research

This study is not without limitations. Due to practical constraints, the observed sample contains the data from only 79 days, which is a relatively short period to test for causalities, specially, if testing the observed results for robustness. In future research, a sample data set from a period longer than 6 months is recommended. Also, because of the short period of data observation, it was not possible to distinguish the short, medium and long term effects of Twitter sentiment. In further research, it would be interesting to test the effect over different time frames.

Second, the sentiment analysis filtered Twitter sentiment for positive and negative emotions and assigned a score on a scale between 5 and -5. Future research may benefit from

distinguishing broader range of emotions, beyond only positive and negative feelings; for example, extraversion, agreeableness, conscientiousness, and negative affectivity. In this way, a more detailed relationship between Twitter sentiment and the price movements of Bitcoin can be determined.

Finally, a problem for accurately studying the effects of sentiment-related variables is finding relevant control variables. Most sentiment indices are determined on a weekly or monthly basis. Therefore, it is recommended for future research to test sentiment on the same interval.

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Appendices

Appendix A – The supply of Bitcoins following Coindesk.com

Appendix B – Results of VIF tests

Table 1. Results of VIF test applied on Return Regression Model (1)

Variable VIF 1/VIF

VIX _6.3 _0.158747 Oil _5.43 _0.183994 S&P500 _4.35 _0.229683 Gold _4.27 _0.234259 Overall activity _3.91 _0.255972 Sentiment score _1.3 _0.767044 Volume _1.3 _0.770647 Mean VIF _3.84 0 2000000 4000000 6000000 8000000 10000000 12000000 14000000 16000000 18000000 10 /01/2 009 10 /01/2 010 10 /01/2 011 10 /01/2 012 10 /01/2 013 10 /0 1/ 2 01 4 10 /01/2 015 10 /01/2 016 10 /01/2 017 10 /01/2 018

Supply of Bitcoins

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Table 2. Results of VIF test applied on Return Regression Model (2)

Gold 9.28 0.107807 Sum Positive _{7.73 0.129313} Sum Negative 6.48 0.154418 VIX _5.82 _0.17184 Oil 4.68 0.213644 S&P500 _3.92 _0.25514 Volume 1.4 0.713346 Mean VIF 5.62

Table 3. Results of VIF test applied on Intraday Spread Regression Model (1)

VIX 6.3 0.158747 Oil 5.43 0.183994 S&P500 4.35 0.229683 Gold 4.27 0.234259 Overall activity 3.91 0.255972 Sentiment score 1.3 0.767044 Volume 1.3 0.770647 Mean VIF 3.84

Table 4. Results of VIF test applied on Intraday Spread Regression Model (2)

Gold 9.28 0.107807 Sum Positive 7.73 0.129313 Sum Negative 6.48 0.154418 VIX 5.82 0.17184 Oil 4.68 0.213644 S&P500 3.92 0.25514 Volume 1.4 0.713346 Mean VIF 5.62

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Table 5. Results of VIF test applied on Volatility Return Regression Model

Volume 2.51 0.398982 Overall activity 2.35 0.425969 Sentiment score 2.32 0.431274 VIX 2.32 0.431703 S&P 500 1.21 0.828291 Mean VIF 2.14

Table 6. Results of VIF test applied on Volatility Intraday Spread Regression Model

Volume 2.51 0.398982 Overall activity 2.35 0.425969 Sentiment score 2.32 0.431274 VIX 2.32 0.431703 S&P 500 1.21 0.828291 Mean VIF 2.14

Table 7. Results of VIF test applied on Return Robust Regression Model (1)

Volume 2.51 0.398982 Overall activity 2.35 0.425969 Sentiment score 2.32 0.431274 VIX 2.32 0.431703 S&P500 1.21 0.828291 Mean VIF 2.14

Note that multicollinearity was observed, therefore the weekly Gold and Oil price was omitted.

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Table 8. Results of VIF test applied on Return Robust Regression Model (2)

Variable _VIF _1/VIF

Sum negative 162.77 0.006144 Sum positive 115.58 0.008652 Gold 27.23 0.036727 Oil 12.27 0.08153 VIX 9.64 0.103693 S&P 500 8.6 0.116232 Volume 3.59 0.278373 Mean VIF 48.53

Note that multicollinearity was observed, a robustness control on weekly basis was not valid.

Table 9. Results of VIF test applied on Intraday Spread Robust Regression Model (1)

Sentiment score 2.78 0.359246 Volume 2.63 0.380479 Overall activity 2.57 0.388437 VIX 2.39 0.418583 S&P 500 1.27 0.784952 Mean VIF 2.33

Note that multicollinearity was observed, therefore the weekly Gold and Oil price was omitted.

Table 10. Results of VIF test applied on Intraday Spread Robust Regression Model (2)

Sum negative 124.45 0.008036 Sum positive 101.14 0.009887 Gold 36.42 0.027456 Oil 23.17 0.043159 VIX 19.29 0.051837 S&P 500 12.89 0.077603 Volume 1.93 0.519236 Mean VIF 45.61

Does daily Twitter sentiment affect the price movements of Bitcoin?