The predictability of cryptocurrencies
(Finance Focus Area)
Erwin Raap (S2961776)
Abstract
This paper examines the predictability of technical trading rules in the cryptocurrencies. A bivariate predictive regression is employed to test the predictability of the technical trading rules. The results indicate that the technical trading rules employed in this paper do indeed have predictable power for cryptocurrencies. The momentum trading rule and the
exponential moving average provide the most explanatory power. This paper also examines the predictability of cryptocurrencies amongst themselves by performing a Vector
Autoregression analysis. Both the substitute effect and the whole market effect are present in the results of the VAR model, i.e. positive and negative statistically significant coefficients. We found that cryptocurrencies are interconnected with each other at a statistically
significant level. Especially Tether shows to have casual effects with other cryptocurrencies. These results have implication for investments, hedging and diversification of risk
Supervisor: Ioannis Souropanis
1 1. Introduction
The relationship between technical trading rules and asset classes in the literature is plentiful. Different empirical methods and performance metrics are employed to examine the relationship between technical trading rules and different asset classes. A mix of positive and negative relationships were found. This indicates that the literature can be used for both hedging purposes and diversification of risk. The literature regarding technical trading rules and cryptocurrencies is divided into two different streams. The first stream of literature finds that technical trading rules produce positive statistically significant coefficient for different asset classes. The second stream of literature indicates no significant relationship between technical trading rules and asset classes. No significant relationship is usually established when the excess return are corrected by, for example, transaction costs.
In this paper, the aim is to examine the link between 67 technical trading rules and ten cryptocurrencies in order to establish a relationship between technical trading rules and the cryptocurrency market. Based on irrationalities in the market, one might expect that technical trading rules have explanatory power in the cryptocurrency market because
cryptocurrencies are said to have no fundamental value. Moreover, this paper also examines the relationships between cryptocurrencies themselves. This is examined to determine whether cryptocurrencies can be forecasted by its own values and the present and/or past values of other cryptocurrencies. Based on herding behavior, cryptocurrencies are expected to move in a tandem. The results of the Vector Autoregression comply with herding
behavior. The Vector Autoregression model in this paper, therefore, adds value to this literature. This paper adds value to the literature by examining 67 different technical trading rules on the top 10 most liquid cryptocurrencies in the market and combines this
information with the examination of relationships between cryptocurrencies themselves. Using up-to-date date, robust results for both the bivariate regression and the VAR model can be useful for investors.
2 cryptocurrencies.
The remaining parts of this paper are structured as follows: section 2 is the literature review, section 3 describes the data, section 4 documents the methodology, section 5 summarizes the results and section 6 presents the conclusion.
3 2 Literature review
2.1 Efficient market hypothesis
Technical analysis is to make predictions and forecasts based on past prices by means of charts and indicators. This implies that one can be profitable based on past prices. This contradicts the well-known efficient market hypothesis (Fama, 1970). This hypothesis states that prices always reflect the available information. The price of a security or another asset class is equal to its fundamental value.
According to the weak form efficiency, stocks and other assets reflect information and are not correlated on a day-to-day basis. In other words, the weak efficiency form implies that stock follow a random walk. Moreover, the weak form efficiency implies that trends cannot predict future prices which is important because technical analysis is based on following and forecasting trends. There is literature that shows contradicting evidence. Lo and Mackinlay (1988) They tracked weekly stock market data and tested the random walk model. They concluded that significant positive serial correlation of weekly returns was present in the data. Hence, the stock market does show signs of inefficiency.
2.2 Theoretical framework for technical analysis
Opponents of the efficient market hypothesis claim that markets and investors behave irrationally. Opponents claim that markets are inefficient because of several reasons. Firstly, they argue that investors exhibit irrationalities like heuristics (Barber & Odean, 2008), self-serving biases and the disposition effect (Odean, 1998).
Secondly, investors’ behaviour are systematically biased, where one is too optimistic/pessimistic, under/overreacts, and feels pride/regret. The former is very important for the research of technical trading rules (Baker & Wurgler, 2007). Investors behave irrationally but in the same way. A well-known behavioural concept is herding. Herding implies that behaviours of individuals in a group (herd) align. Herding is also found in cryptocurrency markets. Because of herding investors behave in the same way, which leads to cryptocurrencies to move in a tandem (Ballis & Drakos, 2020).
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often refuted by literature. Literature regarding market anomalies is plentiful. For example, Levis (1989) showed that the London Stock Exchange exhibited several market anomalies. Size effect was one of them. Zaremba and Szyska (2016) provide evidence that the moment effect is present in the Polish Stock exchange. Hence, the efficient market hypothesis does not hold according to the literature regarding market anomalies. Therefore, an equilibrium is not always restored.
The cost of information is creating irrationalities. Neely and Weller (2003) states that technical analysis, due to high transactions costs and time consuming learning experiences, is not very useful for individual investors. Once the returns are corrected for transactions costs and the amount of trading hours are considered, they find no evidence of excess returns.
Technical analysis
Hsu et al. (2016) provide a comprehensive examination of technical trading rules in the foreign exchange market. They subdivide the technical trading rules in 5 different classes: moving average trading rules; oscillator trading rules; filter trading rules; support-resistance trading rules; and channel breakout trading rules.
The literature on technical rules is plentiful in asset markets. Oberlechner (2001) indicated that foreign exchange traders relied on technical analysis on forecasting up to a period of 3 months. Lo, Mamaysky and Wang (2000) wrote an article of the foundations of technical analysis. They examined whether technical analysis added value. They concluded that particular indicators or technical patterns provide valuable information regarding investment decision-making, which strike with the efficient market hypothesis. The most important indicators according to them are head-and-shoulders, tops and bottoms, triangle tops and bottoms, rectangle tops and bottoms and double tops and bottoms.
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is more profitable compared to a buy-and-hold strategy. Zarrabi, Snaith and Coakly (2017) and Neely et al. (2014) show that technical trading rules still have predictable powers. Zarrabi et al. (2016) show that up to 75% of the rules examined in the paper have predictive abilities, even when the rules are controlled for transaction costs for most of the currencies. Neely et al. (2014) show that the combination of both technical trading rules and macroeconomic variables increases the explanatory power for equity risk premium.
On the contrary, Neely and Weller (2003) state that technical analysis, due to high transactions costs and time consuming learning experiences, is not very useful for individual investors. Moreover, Hoffmann and Shefrin (2014) say that individual investors that utilize technical analysis make bad decisions regarding their portfolio performance, which leads to worse returns than investors who do not utilize technical analysis. Hence, there are both positive and negative results in the literature regarding the predictable power of technical trading rules
6 3. Data section
3.1 Cryptocurrency data
This section will elucidate the data that is used in this article. The data for cryptocurrencies is
retrieved from Yahoo Finance.1It provides up-to-date information since it incorporates the
very latest information on prices and volume. Yahoo Finance provides us with the adjusted closing prices of the cryptocurrencies together with the complementary market
capitalisation values. A volume weighted average of the market pair prices is used to calculate the cryptocurrency prices. The market pair prices are calculated by using the unconverted price from an exchange and CoinMarketCap’s reference prices to convert it to dollars. The reported volume is calculated by adding the reported volumes over all
cryptocurrency exchanges together in the last 24 hours (Liu & Tsyvinski, 2020).
Daily data of the top 10 cryptocurrencies by market capitalisation is retrieved from Yahoo Finance. The market capitalisation of this sample is approximately 85% of the total
market.2 Hence, the sample represents the total market of cryptocurrencies appropriately.
The data set spans from 1st of October 2017 to 9th of November 2020. The sample comprises
the following cryptocurrencies: Bitcoin (BTC), Ethereum (ETH), Tether (USDT), Ripple (XRP), Bitcoin Cash (BCH), Chainlink (Link), Binance (BNB), Litecoin (LTC), Cardano (ADA), EOS (EOS). Many cryptocurrencies have data that dates from 2014 or 2015 on Yahoo Finance. Bitcoin
and Ripple, for example, started on the 17th of September in 2014. However, Cardano is the
newest cryptocurrency in this sample with a total of 1136 daily observations. Hence, every cryptocurrency has 1136 daily observations to make each cryptocurrency equal, except for Tether. Tether is the only cryptocurrency that deviations from the selection criteria
described above. Tether, a stable coin, is backed by the US dollar on a one-for-one basis. This is meant to create stable prices and moreover stable investments in cryptocurrencies. In the beginning period of Tether’s release, this trait led to hardly any deviations in its price. If we
would start Tether’s timeframe on the 1st of October 2017, the technical trading rules would
lead to no results since collinearity problems would occur due to Tether’s characteristics. In
order to circumvent the errors that resulted from this , Tether starts at the 30th of January,
2017. The overview of timeframes for each cryptocurrency is documented in table I. They
1 The power behind Yahoo Finance’s cryptocurrency data section comes from Coinmarketcap.com.
Coinmarketcap.com is the most referenced price-tracking website. Recently, CoinMarketCap was acquired by Binance. This acquisition allows CoinMarketCap to obtain more in-depth cryptocurrency data.
2 There are roughly 7500 cryptocurrencies according to CoinMarketCap. The total market
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are ranked based on their market capitalisation, i.e. the most liquid cryptocurrencies is on top and the least liquid cryptocurrency in this sample is on the bottom of the table.
Table II reports the descriptive statistics for the log returns of the cryptocurrencies employed in this sample. The log returns are calculated according to equation (1).
𝐿𝑛 ( 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡
𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡−1
) (1) where AdjCloset is the adjusted closing price at time t; and AdjCloset-1 is the adjusted closing
price at time t-1. Noteworthy in Table II, is that the daily mean log returns over the sample
period do not exceed 0.295% for all cryptocurrencies. The mean log returns fluctuate between -0.039% and 0.295%. The standard deviation for Tether (0.006) is the lowest of all the cryptocurrencies being scrutinised, due to Tether’s characteristics as described above. The other log returns’ standard deviation values fluctuate between 4.2% for Bitcoin and 7.7% for Chainlink. Cardano recorded the largest 1-day log return increase with a value of 86.2%. Whereas Chainlink recorded the largest 1day log return decline with a value of -61.5% Interestingly, only the three cryptocurrencies show negative skewness values for the log returns. Negative skewness implies that the left tail of the distribution is longer or fatter.. The log returns only have leptokurtic distributions. The Sharpe ratios documented in Table II also provide useful insights. The Sharpe ratio is a measure of average returns corrected for the risk free investment rate (5 Year US treasury Yield of 0.36%) per unit of risk or volatility (in this case the standard deviation). It is a method to calculate risk-adjusted returns. Interestingly, 10 out of 10 cryptocurrencies do not provide a positive Sharpe ratio.
Nevertheless, this does not imply that investments in the particular cryptocurrencies cannot be beneficial. An investment can, for example, be used to diversify a portfolio. Bitcoin, for
Table I
Timeframes per cryptocurrency
This table displays the timespan for every individual cryptocurrency and their respective observations. No missing values were recorded
Cryptocurrency Starting date Ending Date Observations
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example, can be used for this purpose, as discussed in other studies (see, e.g., Bouri et al., 2017; Dyhrberg, 2016).
Figure 1 displays the price charts for our sample. As indicated above, each individual cryptocurrency has its own timespan which is also displayed in the price charts. Remarkable was the boom in prices in 2017/2018, which was due to several reasons. Firstly, there was a growing interest for cryptocurrencies. Secondly, there was a lot more media coverage which led to more attention. According to Barber & Odean (2008), retail investors are more likely to buy attention grabbing firms. They found that individual investors have a higher trading volume on high-attention trading days. Therefore, the higher exposure of cryptocurrency in the media, partly led to the increase in prices. Thirdly, the inflows for investing in
cryptocurrencies were attractive. Finally, one significant alteration in trading
cryptocurrencies was the announcement of Bitcoin futures. This legitimized Bitcoin as a financial instrument. Investors, now, had the opportunity to speculate on Bitcoin’s price without genuinely investing in bitcoins. In 2020 another development was reported by PayPal, who announced that Bitcoin alongside Ethereum, Litecoin, and Bitcoin Cash could soon be bought and sold via PayPal. The cryptocurrencies could then be used to buy
products from customers whom accept PayPal. Noteworthy is the steep increase in Bitcoin’s price in 2020. Dyhrberg (2016) argues that Bitcoin is considered virtual gold. The covid-19 crisis in 2020 persuaded investors to use the hedging abilities of Bitcoin, which partly led to its increase. Tether’s price chart deviates in flow from the other cryptocurrencies. It displays its characteristics accurately. The chart shows that Tether experiences little volatility over
Table II
Summary Statistics
This table displays the summary statistics of the cryptocurrencies employed in this sample. It reports the daily mean, standard deviation, maximum value, minimum value, skewness and excess kurtosis for the log returns. The Sharpe ratio is also provided. The 5 Year US-Treasury rate of 0.36% is used as the risk-free return.
Summary Statistics of cryptocurrency returns
Cryptocurrency Mean SD Max Min Skewness Excess Kurtosis Sharpe Ratio
9 time.
Figure 2 documents the log returns over time. The charts display little change over time. The values remain the same as time progresses. This implies that the probability of a daily return falling within a certain interval is the same over time. Interestingly, is the significant decline for each cryptocurrency in March 2020. Figure 2 displays a steep decline for every individual cryptocurrency in March. This decline is due to the start of the pandemic of the covid-19 crisis. However, even a deviation as large as the ones displayed in the charts, the log returns do eventually return back to its mean value.
Figure 1
10 Figure 2
Log return charts over time
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3.2 Technical trading rules
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are employed in this paper that are well-known in literature (see Hsu et al., 2016; Neely et al., 2014; Zarrabi et al., 2017).
3.2.1 Moving average trading rules
Moving average (MA) trading rules try to find patterns and recognize breaks from patterns. It is one of the trend-following technical trading rules that is analysed in the academic literature by, for example Sullivan et al. (2016). MA’s can indicate an instantaneous buy signal whenever a short-term moving average crosses a long-term moving average from below. A change in trends is detected by the MA trading rules as the short-term moving average reacts quicker to recent shifts in prices compared to the long-term moving average. Moving averages can range from simple mathematical calculations to relatively more
complex calculations. The most plain form of moving averages is the simple moving average, calculated accordingly to formula (2) (Souropanis et al., 2019).
𝑥𝑖,𝑡 = { 1 𝑖𝑓 𝑀𝐴𝑠,𝑡 ≥ 𝑀𝐴𝑙,𝑡 0 𝑖𝑓 𝑀𝐴𝑠,𝑡 < 𝑀𝐴𝑙,𝑡 } , 𝑀𝐴𝑗,𝑡 = ( 1 𝑗) ∑ 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡−1 𝑓𝑜𝑟 𝑗 = 𝑠, 𝑙 𝑗−1 𝑖=0 (2)
where MAs,t is the short-term moving average at time t; MAl,t is the long-term moving average
at time t; and AdjCloset is the adjusted closing price at time t. Based on Hsu et al. (2016) the
specification for s =[1,2,5,10] and for l =[25,50,100], shown as MA(s,l). However, simply moving averages by construction create a lag. The simple moving averages assign the same weights to every datapoint, which creates a lag between the simple moving average and the price.
To reduce the lag, a different MA is used: exponential moving average (EMA). The EMA is a relatively more complex moving average as is displayed in formula (3). The EMA assigns higher weights to more recent data points. The weight assigned to the data points decreases exponentially as the data points become older. Hence, the EMA has a quicker response to recent movements in prices.
𝑥𝑖,𝑡= {
1 𝑖𝑓 𝐸𝑀𝐴𝑠,𝑡 ≥ 𝐸𝑀𝐴𝑙,𝑡
0 𝑖𝑓 𝐸𝑀𝐴𝑠,𝑡 < 𝐸𝑀𝐴𝑙,𝑡
} , 𝐸𝑀𝐴𝑗,𝑡 = (𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡− 𝐸𝑀𝐴𝑗,𝑡−1) ∗ 𝑚 + 𝐸𝑀𝐴𝑡−1 (3)
where EMAs,t is the short-term exponential moving average at time t; EMAl,t is the long-term
exponential moving average at time t; AdjCloset is the adjusted closing price at time t;
EMAj,t-1 is the exponential moving average at time t-1 for j=s,l; and m is the weighting
multiplier given by 𝑚 = 2
𝑗+1 (Zarrabi et al.,2017). The specifications that are employed for
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3.2.2. Oscillator trading rules
Oscillators are commonly known as the overbought or oversold indicators. Oscillators try to find signs of overbought and/or oversold assets. They indicate that prices move upwards (downwards) too quickly and that the market will correct the prices downwards (upwards). A popular momentum oscillator is the Relative Strength Index which is described by equation (4).
𝑅𝑆𝐼𝑡 (ℎ) = 100 ∗ (
𝑈𝑡(ℎ)
𝑈𝑡(ℎ) + 𝐷𝑡(ℎ)
) (4)
where Ut (h) denotes the cumulated ‘up movement’ over the previous h days and Dt (h)
denotes the cumulated ‘down movement’ over the previous h days. The ‘up/down movement’ are explicitly explained in formula (5).
𝑈𝑡(ℎ) = {
1 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 > 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡−1
0 𝑖𝑓 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 } , 𝑎𝑛𝑑 𝐷𝑡(ℎ) = {
1 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 < 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡−1
0 𝑖𝑓 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 } (5)
where AdjCloset is the adjusted closing price at time t; AdjCloset-1 is the adjusted closing
price at time t-1. The two specifications used for h =[7,14], based on Hsu et al. (2016). The overbought (oversold) threshold 50 + v (50- v) is prespecified and triggers a sell (buy) signal. Several thresholds can be examined in order to test the RSI, as is shown by Hsu et al. (2016).
The specifications for v=[20,25,30] are employed, shown as (RSI(h) with v=…). The RSI
indicator generates a sell or buy signal as is explained in formula (6) and (7), respectively. 𝑥𝑖,𝑡= { 1 𝑖𝑓 𝑅𝑆𝐼𝑖,𝑡 ≥ 50 + 𝑣 0 𝑖𝑓 𝑅𝑆𝐼𝑠,𝑡 < 50 + 𝑣} (6) 𝑥𝑖,𝑡 = { −1 𝑖𝑓 𝑅𝑆𝐼𝑖,𝑡 ≤ 50 − 𝑣 0 𝑖𝑓 𝑅𝑆𝐼𝑠,𝑡 > 50 − 𝑣 } (7)
3.2.3 Filter trading rules
Filter trading rules are, in contrast to oscillator rules, following trends. These rules indicate a buy (sell) signal whenever the price of an asset has increased (decreased) by a prespecified percentage x above (below) its most recent low (high) value over the previous d days. The filter trading rules generate a buy or sell signal as is elaborated in formulas (8) and (9), respectively.
𝑥𝑖,𝑡 = {
1 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 ≥ 𝑀𝑜𝑠𝑡 𝑟𝑒𝑐𝑒𝑛𝑡 𝑙𝑜𝑤 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒[𝑡,𝑡−𝑑)∗ (1 + 𝑥)
0 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡< 𝑀𝑜𝑠𝑡 𝑟𝑒𝑐𝑒𝑛𝑡 𝑙𝑜𝑤 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒[𝑡,𝑡−𝑑)∗ (1 + 𝑥)
14 𝑥𝑖,𝑡= {
−1 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 ≤ 𝑀𝑜𝑠𝑡 𝑟𝑒𝑐𝑒𝑛𝑡 ℎ𝑖𝑔ℎ 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒[𝑡,𝑡−𝑑)∗ (1 − 𝑥)
0 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 > 𝑀𝑜𝑠𝑡 𝑟𝑒𝑐𝑒𝑛𝑡 ℎ𝑖𝑔ℎ 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒[𝑡,𝑡−𝑑)∗ (1 − 𝑥) } (9)
where AdjCloset is the adjusted closing price at time t; AdjCloset,t-d is the adjusted closing
price over the evaluation period [t,t-d]; and x is the required percentage above (below) the most recent low (high) that generates a signal. To generate one signal, both equations are combined into one signal, i.e. a +1 and -1 for the same data point would then generate neither a buy nor a sell signal because it has the value of zero. Based on the paper of Hsu et al. (2016) the following specifications are employed for x = [0.5, 1.0, 5.0, 10.0] in % and d = [1,2,5,10], shown as Filter(x,d).
The second filter strategy is a momentum trading rule. A simple momentum indicator indicates ‘positive’ (negative) momentum when the current price is higher (lower) than its level d days ago. This positive (negative) momentum indicator generates a buy or sell signal accordingly. The momentum rule is elaborated in formulas (10) and (11) for a buy or sell signal, respectively. 𝑥𝑖,𝑡= { 1 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑖𝑛𝑔𝑡 ≥ 𝐴𝑑𝑗𝑐𝑙𝑜𝑠𝑖𝑛𝑔𝑡−𝑑 0 𝑖𝑓 𝐴𝑑𝑗𝑐𝑙𝑜𝑠𝑖𝑛𝑔𝑡 < 𝐴𝑑𝑗𝑐𝑙𝑜𝑠𝑖𝑛𝑔𝑡−𝑑 } (10) 𝑥𝑖,𝑡 = { 1 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑖𝑛𝑔𝑡 ≥ 𝐴𝑑𝑗𝑐𝑙𝑜𝑠𝑖𝑛𝑔𝑡−𝑑 0 𝑖𝑓 𝐴𝑑𝑗𝑐𝑙𝑜𝑠𝑖𝑛𝑔𝑡 < 𝐴𝑑𝑗𝑐𝑙𝑜𝑠𝑖𝑛𝑔𝑡−𝑑 } (11)
where AdjCloset is the adjusted closing price at time t; AdjCloset-d is the adjusted closing
price over the evaluation period where d, is the number of days for the momentum delay. To generate one signal, both equations are combined into one signal, i.e. a +1 and -1 for the same data point would then generate neither a buy nor a sell signal because it has the value of zero. Daily signals are computed for d=9,12 based on Neely et al. (2014), shown as
Momentum(d).
3.2.4. Support-resistance trading rules
Support-resistance trading rules indicate a buy (sell) signal whenever an asset surpasses its highest/resistance (lowest/support) price level over the previous n days by a prespecified percentage x. Resistance (support) can be defined as the price level an asset has difficulty
rising past (falling below). Hence, the support-resistance trading rules indicate a buy (sell) signal whenever the resistance (support) level is breached. The signals are generated accordingly to formulas (12) and (13).
𝑥𝑖,𝑡= {
1 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 > 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑙𝑒𝑣𝑒𝑙 [𝑡,𝑡−𝑛]∗ (1 + 𝑥)
0 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 ≤ 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑙𝑒𝑣𝑒𝑙 [𝑡,𝑡−𝑛]∗ (1 + 𝑥)
15 𝑥𝑖,𝑡= {
−1 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 < 𝑠𝑢𝑝𝑝𝑜𝑟𝑡 𝑙𝑒𝑣𝑒𝑙 [𝑡,𝑡−𝑛]∗ (1 − 𝑥)
0 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 ≥ 𝑠𝑢𝑝𝑝𝑜𝑟𝑡 𝑙𝑒𝑣𝑒𝑙 [𝑡,𝑡−𝑛]∗ (1 − 𝑥) } (13)
where AdjCloset is the adjusted closing price at time t; resistance level[t,t-n] is the resistance
level over the evaluation period n; support level[t,t-n] is the support level over the evaluation
period n; and x is the required percentage above(below) the resistance (support) level that generates a signal. To generate one signal, both equations are combined into one signal, i.e. a +1 and -1 for the same data point would then generate neither a buy nor a sell signal because it has the value of zero. There are 4 versions employed of the index for
x=[1.0,5.0,10.0] in % and d=[1,5,10,20] based on Hsu et al. (2016), shown as
Support-resistance(x,d)
3.2.5. Channel breakout trading rules
Channel breakout trading rules can be performed by drawing lines on a price chart.
However, there are also quantitative rules. Hence, an imaginary channel between the high and low price is constructed. A channel is constructed when the high price over a particular time period d is within a certain boundary c. If the price breaks out to the upside
(downside) by a certain percentage x, a buy (sell) signal is generated. This is explicitly documented in formulas (14) and (15).
𝑥𝑖,𝑡= { 1 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 > 𝑢𝑝𝑝𝑒𝑟 𝑏𝑜𝑢𝑛𝑑 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 [𝑡,𝑡−𝑑]∗ (1 + 𝑥) 0 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 ≤ 𝑢𝑝𝑝𝑒𝑟 𝑏𝑜𝑢𝑛𝑑 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 [𝑡,𝑡−𝑑]∗ (1 + 𝑥) } (14) 𝑥𝑖,𝑡 = { −1 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 < 𝑙𝑜𝑤𝑒𝑟 𝑏𝑜𝑢𝑛𝑑 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 [𝑡,𝑡−𝑑]∗ (1 − 𝑥) 0 𝑖𝑓 𝐴𝑑𝑗𝐶𝑙𝑜𝑠𝑒𝑡 ≤ 𝑙𝑜𝑤𝑒𝑟 𝑏𝑜𝑢𝑛𝑑 𝑐ℎ𝑎𝑛𝑛𝑒𝑙 [𝑡,𝑡−𝑑]∗ (1 − 𝑥) } (15)
where AdjCloset is the adjusted closing price at time t; upper bound channel[t,t-n] is the upper
bound level of the fictional channel over the evaluation period between time t and d; lower
bound channel[t,t-n] is the lower bound level of the fictional channel over the evaluation period between time t and d; and x is the required percentage above(below) the upper (lower) bound channel that generates a signal. To generate one signal, both equations are combined into one signal, i.e. a +1 and -1 for the same data point would then generate neither a buy nor a sell signal because it has the value of zero. The specifications for
d=[5,20], c%=[1.0, 5.0, 10.0], and x=[0.5, 1.0, 5.0] based on Hsu et al. (2016), shown as
Channel breakout(d,c,x).
16
They state that it could cause biases in statistical inferences. This paper studies a total of 67 technical trading rules. A combination of the parameters used in Hsu et al. (2015),
Souropanis et al. (2019), Zarrabi et al. (2017), and Neely et al. (2014). Appropriate
parameters are selected that lie within the ranges used in these papers. Table III documents an overview of the technical trading rules parameters that are used in this paper. The abbreviations that are used to describe them are in the first column. The particular
parameter for each indicator is reported in the second column. The description is reported in the third column. Lastly, the fourth column displays the specific valuations that are used for each indicator in this paper.
Table III
Parameters for technical trading rules
This table documents the following trading rules: moving average (MA), exponential moving average (EMA), Relative Strength Index (RSI), Filter Rules (FR), Support and resistance (SR), Channel breakouts (CB), and moment rule (MR)
Parameters Description Value
MA j Term period of the moving average s, l
s short-term moving average 1,2,5,10
l long-term moving average 25,50,100
EMA j
term period of the exponential moving
average s,l
m weighting multiplier 2/(j+1)
s short-term exponential moving average 5
l long-term moving exponential average 12
RSI h evaluation period 7,14
50 + v overbought threshold 20,25,30
50 - v oversold threshold 20,25,30
FR d number of days for the time delay filter 1,2,5,10
x band for buy signal 0.005, 0.01, 0.05, 0.10
SR d
number of days for the
resistance/support level 1,5,10,20
x band for buy signal 0.01,0.05,0.10
CB d Channel period 5,20
c channel boundary 0.01,0.05,0.10
x band for buy signal 0.005,0.01,0.05
17 4. Methodology
4.1 Bivariate predictive regression
Neely et al. (2014) point out that the conventional framework for the analysis of equity risk premia is the bivariate predictive regression. The bivariate regression model is applied when one variable is employed to predict or explain the variation in the dependent variable. The bivariate regression model is documented in equation (16).
𝑟𝑡+1 = 𝑎𝑖+ 𝐵𝑖∗ 𝑋𝑖,𝑡+ 𝑒𝑖,𝑡+1 (16)
where the equity risk premium, rt+1, is the return of an asset class corrected for the risk-free
investment rate over the time period starting from t to t+1; ai is the constant term which is
the expected value of the equity risk premium if the predictor is equal to a value of zero; xi,t
is a variable that is set to predict the equity risk premium at time t; ei,t+1 is the error term
which is assumed to have a zero mean. The true parameters of the equation are unknown as is the error term. The parameters are predicted by the coefficients and the error terms are estimated by the residuals. By preference, the error term has a zero mean and the error term does not show signs of positive/negative correlation, i.e. the errors are independent of each other. The former condition is met if the constant term is included in the equation. The error term is also assumed to have a constant variance, i.e. homoskedasticity.
4.2 Technical trading rules
The bivariate regression model of section 3.1 is slightly altered to regress the technical
trading rules that are employed in this paper. The Xi,t is replaced with xi,t to transform the
regression from a regular bivariate regression for equity risk premiums to a regression that scrutinizes the technical trading rules. This is displayed in equation (17).
𝛥𝑟𝑡+1 = 𝑎𝑖+ 𝑏𝑖∗ 𝑥𝑖,𝑡+ 𝑢𝑖,𝑡+1 (17)
where Δrt+1, is the 1-day log return of the cryptocurrency over the time period starting from t
to t+1; ai is the constant term which is the expected value of 1-day log return of the
18
go long (short) in the cryptocurrency; ui,t+1 is the error term which is assumed to have a zero
mean. The parameters are predicted by the coefficients and the error terms are estimated by the residuals. By preference, the error term has a zero mean and the error term does not show signs of positive/negative correlation, i.e. the errors are independent of each other. The former condition is met if the constant term is included in the equation. The error term is also assumed to have a constant variance, i.e. homoskedasticity.
4.3 White test and Breusch-Pagan test
There are two methods applied in this paper to test whether error terms display differences in variances, i.e. heteroskedasticity: the White test and the Breusch-Pagan test. Both tests examine the residuals of a regression. This is an informal method for detecting
heteroskedasticity. The White test and the Breusch-Pagan test can both be classified as tests known as Lagrange multiplier tests. These tests are based on the estimated variance form displayed in equation (18).
ê𝑖2 = α1 + α2∗ 𝑧𝑗2+ α3∗ 𝑧𝑗3+ ⋯ + α𝑠∗ 𝑧𝑠+ 𝑣 (18)
where ê2 are the squared least-squares residuals and z2,z3,…,zs are the variance equation
regressors. The Breusch-Pagan test regresses the squared residuals on the original
predictors. It assumes linearity in the auxiliary regressions as is documented in equation 18. .
The Breusch-Pagan test results in a chi-square statistic: χ2 = N * R2. The White test regresses the
squared residuals on the original predictors, the corresponding squared terms of the original predictors and the cross products of the original predictors. Hence, the White test is a
special case of the Breusch-Pagan test. The auxiliary regression for the White test is specified in equation (19).
ê𝑖2= α0 + α1∗ 𝑧𝑖1+ ⋯ + α𝑠∗ 𝑧𝑖𝑠+ 𝑎𝑠+1∗ 𝑧𝑖𝑠2 + ⋯ 𝑎2𝑠∗ 𝑧𝑖𝑠2 + 𝑎2𝑠+1∗ (𝑧𝑖1∗ 𝑧𝑖2)+ ⋯ + 𝑣 (19)
where ê2 are the squared least-squares residuals; z2,z3,…,zs are the variance equation
regressors; 𝑧𝑖𝑠2 are the squared terms of the original regressors; and 𝑧𝑖1∗ 𝑧𝑖2 are the cross
19
the chi-square statistic of the Breusch-Pagan test: χ2 =N * R2 . The specifics regarding the
hypotheses of the Breusch-Pagan test and White test are documented in formulas (20)-(23).
𝐵𝑟𝑒𝑢𝑠𝑐ℎ 𝑃𝑎𝑔𝑎𝑛 ∶ 𝑁𝑢𝑙𝑙 𝐻𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠 (𝐻0 ): 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑖𝑛 ɛ 𝑖𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 𝜎2 (20)
𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑣𝑒 𝐻𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠 (𝐻1): 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑖𝑛 ɛ 𝑖𝑠 𝑛𝑜𝑡 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ≠ 𝜎2 (21)
𝑊ℎ𝑖𝑡𝑒 𝑇𝑒𝑠𝑡 ∶ 𝑁𝑢𝑙𝑙 𝐻𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠 (𝐻0): 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑖𝑛 ɛ 𝑖𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = 𝜎2 (22)
𝐴𝑙𝑡𝑒𝑟𝑛𝑎𝑡𝑖𝑣𝑒 𝐻𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑠 (𝐻1): 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑖𝑛 ɛ 𝑖𝑠 𝑛𝑜𝑡 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 ≠ 𝜎2 (23)
If one would reject the null hypothesis of either the Breusch-Pagan test or the White test, the variance statistic is significantly different from being constant. This implies that the error terms experience fluctuations over time and do not remain constant. Hence, heteroskedasticity is present in the error terms. 4.4 Stationarity tests Stationarity implies that the mean, variance and autocorrelation of the data do not alter over time. If one uses nonstationary data, statistically significant results can be obtained from irrelevant data, i.e. a spurious regression. A graph of the data over time, a correlogram, and the Augmented Dicky-Fuller test are conducted to check whether the data is stationary or nonstationary. A graph visually documents insights in the processes that are analysed. A correlogram provides statistics of correlation at different time lags, for example autocorrelation coefficients. The value of the autocorrelation coefficient is between zero and one. An autocorrelation coefficient of one would describe a nonstationary process. It implies that unexpected events or shocks, are highly persistent. The Augmented Dicky-Fuller (ADF) test is regularly used to verify non-stationarity in time series data. The test determines whether differencing is necessary to transform nonstationary data to stationary data. The test is explicitly described in formula (25). 𝑥𝑡 = 𝜑 ∗ 𝑥𝑡−1+ ∑ 𝑎𝑖∗ ∆ 𝑥𝑡−1 𝑝 𝑖=1 + 𝑢𝑡 (25)
where xt is the dependent variable at time t; xt-1 is the first difference of the dependent
20
error term; and φ is equal to 1 if there is a unit root. The null hypothesis of the ADF states that a unit root (φ=1) is present. The alternative hypothesis implies that the data does not contain a unit root (φ < 1). The optimal amount of lags for p are determined by information criteria, i.e. AIC and BIC. The equations for AIC and BIC are documented in formulas (26) and (27).
𝐴𝐼𝐶 = ln(σ̂2) +2𝑘
𝑇 (26) 𝐵𝐼𝐶 = ln(σ̂2) +2𝑘
𝑇 ∗ ln(𝑇) (27)
where σ̂2 is the residual variance; k is the total numbers of parameters estimated and T is the
sample size. As is displayed in the formulas (26) and (27), BIC punishes the complexity of a model harder.
4.5 Vector Autoregression
Griffin and Shames (2020) show that Tether has significant explanatory powers for the prices of Bitcoin and 6 other cryptocurrencies. They examined the prices of the cryptocurrencies during the 2017 boom. By the use of algorithms they found that the patterns in the price of Bitcoin and 6 other cryptocurrencies can be explained by the net flow of Tether. Hence, the prices for the cryptocurrencies do not only reflect simple supply/demand. 58.8% of bitcoin’s compounded return can be attributed to lagged net flows of Tether. The other six
cryptocurrencies (Dash, Ethereum Classic, Ethereum, Litecoin, Monero, and Zcash) compounded returns are for 64.5% attributable to net flows of Tether. Hence, price manipulation does have substantial effect in this market for cryptocurrencies.
The VAR model in this paper tests whether more cryptocurrencies have explanatory power in the prices of Bitcoin and whether other cryptocurrencies can be predicted by cryptocurrencies as well. Vector autoregressive models (VARs) are a generalisation of univariate autoregressive models. A VAR model is a systems regressions model, i.e. the model regresses more than one dependent variable. The VAR model is flexible and it is easy to generalise. The VAR(p) model can be expressed according to formula (28).
21
where Yt is a vector of endogenous dependent variables with Yt =( Y1t ,…, YKt ) (for this
research it includes the 10 cryptocurrencies); v is a (K x 1) vector of all intercepts; Yt-1 is the
first lag of the vector of endogenous variables of the dependent variables at time t-1 with Y
t-1 =( Y1t-1 ,…, YKt-1 ); Yt-p is the Pth lag of the vector of endogenous variables of the dependent
variables at time t-p; Φp is the matrix of estimated coefficients at lag order p; and ut is the
vector (KT x 1) of error terms which is a white noise (WN) disturbance term with E(uKt)=0
with i=1,2…K, and non-singular variance covariance matrix Ω.
The optimal amount of lags p is determined based on information criteria. The advantage of information criterion is that it does not assume normality. Financial data is usually not normally distributed. Hence, the information criterion fits appropriately. The use of multivariate versions of the information criteria is described in formulas (29) and (30).
𝑀𝐴𝐼𝐶 = ln (|𝜮̂| +2𝑘 ′ 𝑇 (29) 𝑀𝐵𝐼𝐶 = ln (|𝜮̂| +2𝑘 ′ 𝑇 ∗ ln(𝑙𝑛(𝑇)) (30)
where Σ̂ is the variance-covariance matrix of residuals; T is the sample size; and k’ is the total
number of parameters in all the equations. The total number of parameters are equal to
p2*k + p for p equations in the VAR system, each with p lags of the k variables.
4.6 Stability test for VAR model
Even though the optimal lag order is determined by information criteria as described above, it does not guarantee that the results from the regressions are effective. Strict stability conditions are necessary for VAR models to produce effective results. In order to test the stability of a VAR model, one can perform a stability test. To elucidate the stability test, a VAR(1) model is displayed in equation (31).
𝒀𝑡 = 𝑣 + 𝜱1∗ 𝒀𝑡−1+ 𝒖𝑡
= (𝐼𝑘+ 𝜱1+ ⋯ + 𝜱1 𝑗
) ∗ 𝑣 + 𝜱1𝑗+1∗ 𝒀𝑡−𝑗−1+ ∑𝑗𝑖=0𝜱1𝑖 ∗ 𝒖𝑡−1 (31)
Lütkepohl (1991) and Hamilton (1994) argue that if all the eigenvalues of 𝜱1 have a modulus
less than one, the VAR(1) model is stable. They also generalize this for p lags: if all the
22
than one, the VAR(p) model is stable. However, if all the roots of the companion matrix are inside the unit circle, the VAR(p) model is stable. The unit circle functions as a stability indicator.
4.7 Granger causality test
The Granger causality test is a concept that examines the causality of two signals, purely based on predictions. It investigate the flow of information between time series. In plain, if a signal x causes another signal y it is said there is Granger causality. The intuition behind Granger causality is: if lags of x in combination with the past values of y are able to increase the predictable power of the regression compared to only y’s previous values x ‘Granger-causes’ y. Hence, if x and the lags of x improve the statistical significance, x is said to ‘Granger-cause’ y. If this is not the case, equation (32) holds.
𝑀𝑆𝐸 [𝑃𝑟𝑜𝑗(𝒀𝑡+ℎ|𝒀𝒕, ⋯ , 𝒀𝑡−𝑝, 𝑿𝑡, ⋯ , 𝑿𝑡−𝑝)]= 𝑀𝑆𝐸 [𝑃𝑟𝑜𝑗(𝒀𝑡+ℎ|𝒀𝒕, ⋯ , 𝒀𝑡−𝑝)] (32)
Equation (32) implies that there is no significant improvement in the mean squared error of the projection of Y conditional on the information of X. Hence, x is not able to explain any significant variation in y, i.e. y is exogenous in the time series sense with respect to x (Hamilton, 1994).
To test for Granger causality an F-test is performed based on a multivariate autoregression for lags of x and lags of y, as is described in equation (33).
𝑦𝑡 = 𝑐 + 𝛼1∗ 𝑦𝑡−1+ 𝛼2∗ 𝑦𝑡−2+ ⋯ + 𝛼𝑝∗ 𝑦𝑡−𝑝+ 𝛽1∗ 𝑥𝑡−1
+𝛽2∗ 𝑥𝑡−2+ ⋯ + 𝛽𝑝∗ 𝑥𝑡−𝑝+ 𝑢𝑡 (33)
where yt-1 is the first lag of the y; yt-2 is the second lag of y; yt-p is the pth lag of y; xt-1 is the
first lag of x; xt-2 is the second lag of x; xt-p is the pth lag of x; and ut is the error term. The null
hypothesis of the Granger causality is documented in equation (34).
23
An F-test is conducted to test this hypothesis. The residual sum of squares (RSS) of equation (32) is compared with the RSS of a univariate autoregression for only y and the lags of y as is indicated by equation (35)
𝑆 =𝑇 ∗ (𝑅𝑆𝑆𝑦,𝑥− 𝑅𝑆𝑆𝑦
𝑅𝑆𝑆𝑦
(35)
where RSSy,x is the sum of squared residuals of a multivariate autoregression for both lags of
x and lags of y; and RSSy is the sum of squared residuals of a univariate autoregression of only y and the lags of y. One would reject the null hypothesis described in equation (34), if the test static S is greater than the 5 percent critical values for a χ2 (p) variable.
5. Results
5.1 Empirical results of the technical trading rules
There are a few individual rules for each cryptocurrency that do not produce a coefficient and corresponding test results. The reasons for this is that collinearity problems occur when there are zero buy/sell signals for a technical trading rule. All the individual regressions and their corresponding test statistics are provided in appendix II. Table IV documents the number of rules that produce a statistically significant positive coefficient at a 10%
significance level. The results imply that the technical trading rules that are examined in this paper, do have predictable power for cryptocurrencies. Based on the results, 10 out of 10 cryptocurrencies can be forecasted using technical indicators at a 10 percent significance level, i.e. there is at least one technical trading rule that produces a statistically significant positive coefficient at a 10 percent significance level.
24
Tether is an outlier compared to the other cryptocurrencies. A reasons for this is the price behaviour of Tether. Tether almost only showed increasing returns over the
timeframe. For many data points, this resulted in a buying signal (x=1). This in combination with the constant increasing returns resulted in a high percentage (79%) of technical trading rules being statistically significant at a 10 percent significance level.
Table IV also documents the performances of the technical trading rules over the entire sample. The best-performing trading rules are the momentum rule(MR) and the exponential moving average(EMA). Both the MR and the EMA produced statistically
significant positive coefficients for 70% of the regressions. Filter rules (FR) are the third best technical trading rules with 44% of the coefficients produced, being statistically significant at a 10 percent significance level. The support and resistance trading rules are performing the worst with only 17% of the rules resulting in statistically significant positive coefficients. In total 33% of the technical trading rules produce a statistically significant positive coefficient.
Table V documents the results for the best-performing individual technical trading rules that are employed in this paper. The best-performing individual technical trading rules (at a 10% significance level or lower) result in statistically significant positive coefficients ranging from 1.04% for EOS to 40.5% for Tether. For 8 out of the 10 (i.e. 80%)
cryptocurrencies, a version of a channel breakout rule(CB) is the best performing rule. The Table IV
Predictive ability of technical trading rules
This table summarizes the technical trading rules employed in this paper. The number of rules that produce a statistically significant positive coefficients are documented
(at a 10% significance level)
Cryptocurrency RSI MA EMA FR SR CB MR Total
25
best-performing trading rule is only different for both Bitcoin Cash and EOS, the RSI(14, with v=30) and the support-resistance (1,20) rule respectively.
5.2 Heteroskedasticity tests results
Table VI summarizes the results of both the White test and the Breusch-Pagan test for all the technical trading rules employed. We report the individual results for the 67 predictors and 10 cryptocurrencies in appendix III in order to save space. Most cryptocurrencies display heteroskedastic error terms for at least 10% of all the technical trading rules. Tether, for example, shows that almost 80 percent of the technical trading rules have a p-value below the 5 percent rejection threshold. Hence, in 80% the null hypothesis of the Breusch-Pagan test is rejected, i.e. the error terms are heteroskedastic. To be conservative, all regressions are performed with robust standard errors.
5.3 Stationarity tests results
Figure 2 displays the log returns over time for each individual cryptocurrency. The charts display little change over time. The values remain within a certain boundary as time progresses. The log returns return to its mean value over time. Hence, the graphs indicate that all cryptocurrencies have a stationary process.
Table V
Predictive ability of the best-performing technical trading rules
This table documents the predictive ability of the technical trading rules. It shows the number of positive significant results, the best-performing individual trading rule and its corresponding return per cryptocurrency
Cryptocurrency # predictive rules Best Rule (BR) Return BR (%) t-stat BR
Bitcoin 22 Channel breakout (20,10,1) 2.23% 2.63***
Ethereum 24 Channel breakout (20,10,5) 4.73% 2.41**
Tether 53 Channel breakout (5,5,5) 40.55% 619.47***
Ripple 17 Channel breakout (20,5,5) 9.61% 54.38***
Bitcoin Cash 21 RSI (14) v=30 4.97% 2.28**
Chainlink 16 Channel breakout (20,10,0.5) 1.12% 4.95***
Binance 24 Channel breakout (20,5,0.5) 9.83% 54.93***
Litecoin 16 Channel breakout (5,1,0.5) 2.76% 16.87***
Cardano 23 Channel breakout (5,10,5) 1.79% 1.82*
EOS 5 Support-resistance (1,20) 1.04% 1.80*
26
The correlograms are report in appendix IV to save space. All the cryptocurrencies have a low autocorrelation coefficient, except for Tether. However, the autocorrelation coefficient for Tether does decrease as well over the 30 lags. The shock dies away relatively quick. Hence, the correlograms indicate that all cryptocurrencies have a stationary process. The Augmented Dicky-Fuller test is used to verify whether the data is stationary or nonstationary. The ADF is, as described by formula (25), dependent on the amount of p lags. The optimal amount of p lags are established based on information criteria, as is described in section 4.2. Table VII summarizes the selection of the optimal amount of lags and the
corresponding test statistics for the ADF. For most cryptocurrencies, both AIC and BIC result in the same selection for the optimal lag value. Both information criteria are reported to showcase any possible differences. The rejection or acceptation of the null hypothesis does not dependent on the information criterion that is chosen. The null hypothesis is rejected for every cryptocurrency based on both information criterion at a 1 percent significance level. Hence, the alternative hypothesis is accepted. Therefore, the Augmented Dicky-Fuller test indicates that all the returns are stationary.
Table VI
Heteroskedasticity tests
This table summarizes the results for both the white test and the Breusch-Pagan test for all technical trading rules employed
Currency % of rules P-value < 0.05 % of rules P-value < 0.05
Breusch-Pagan test White test
27
5.4 Vector Autoregression model results
The selection for the optimal amount of lags is provided in appendix V. The VAR model results displayed in Table III show both statistically significant positive and negative coefficients. This can be explained by two different effects that are present in the
cryptocurrency market. Firstly, the substitute effect implies that every cryptocurrency has a substitute. Many cryptocurrencies have features that are the same and therefore might be
substituted for one another. The second effect, that contradicts the substitute effect, is the
whole market effect. This effect states that the increase in interest and attention leads to more capital inflow and more investors.
Bitcoin shows to be highly predictable by other cryptocurrencies. The results indicate that at least one lag for 6 out of the 10 (i.e. 67%) cryptocurrencies have predictable power in Bitcoin. Moreover, Tether and EOS show that both the first and the second lag have
explanatory power for Bitcoin, i.e. both lags of Tether and lags EOS produce statistically significant coefficient at a 10 percent significant level or lower. The significant relationship between Tether and Bitcoin corresponds with the literature by, for example, Griffin and Shames (2020). Bitcoin’s own lags are only statistically significant for the 4 (Ethereum, Tether, Ripple, Bitcoin Cash) most liquid cryptocurrencies. Binance’s first lag produces statistically significant coefficient for 6 (Tether, Ripple, Chainlink, Binance, Litecoin, EOS) out of the 10 cryptocurrencies. Tether has even more predictable power. The VAR model
indicates that Tether’s first and second lags both produce statistically significant coefficients for 6 out of the 10 (i.e. 60%).
Table VII
Augmented Dicky-Fuller test
This table documents the test statistics for the Augmented Dicky-Fuller test.
Cryptocurrency AIC optimal lag Test-statistic BIC optimal lag Test-statistic
28
Table VIII
Vector Autoregression model
This table documents the results of the VAR model for log returns (p=2).
Variables Bitcoin Ethereum Tether Ripple Bitcoin Cash
29
Table VIII (continued)
Vector Autoregression model
This table documents the results of the VAR model for log returns (p=2)
Variables Chainlink Binance Litecoin Cardano EOS
30
Tether often serves as part of a trading pair for cryptocurrencies, which might be an explanation for its high predictable power. A trading pair can be described as exchanging one cryptocurrency for another cryptocurrency. If one believes that cryptocurrencies increase, they have to opportunity to invest in Tether. Tether’s characteristics as a stable coin and part of many trading pairs, provide investors with stability and later on the option to exchange Tether for other cryptocurrencies. If the expected cryptocurrencies actually increase later on, one might exchange Tether for other cryptocurrencies. The lags of Tether, therefore, might have explanatory power for other cryptocurrencies.
Another possible explanation for the statistically significant lags of cryptocurrencies, is described by Ballis and Drakos (2020). They studied 6 major cryptocurrencies. They
concluded that herding is present in the cryptocurrency market. Investors behave irrationally and copy the decisions of other investors. This results in cryptocurrencies behaving in a tandem. This can be confirmed by the results of the VAR, as lags of cryptocurrency have explanatory power for other cryptocurrency.
5.4 Stability Test results
A stability test that is performed in order to test whether all the roots of the companion matrix are inside the unit circle is shown below. The unit root diagram of the model is shown in Figure 3. The unit circle functions as a stability indicator. Figure 3 shows that two values are almost out of the unit circle, but the hard values indicate that all the values are less than one, i.e. all the roots are inside the unit circle. The hard values are provided in Appendix VI. This implies that the VAR model for two lags is stable. Hence, the results from the VAR (2) model are reliable.
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5.5 Granger causality results
The full results for the Granger causality test are provided in appendix VII in order to save space. Table VIII documents the results for the Granger causality test only for Bitcoin. It reports the excluded variable and the corresponding chi-square test statistics with the degrees of freedom. The null hypothesis for Granger causality based on the table VIII can then be interpreted as: the lags of the predictor in the second column do not ‘Granger-cause’ the variable in the first column.
There are 4 dependent variables that ‘Granger-cause’ bitcoin. Ethereum, Tether, Chainlink and EOS all produce a chi-square statistic that is statistically significant at a 10 percent level or lower. Hence, Ethereum, Tether, Chainlink and EOS are said to ‘Granger-cause’ bitcoin and have a causal effect on Bitcoin’s return. Tether and EOS even produce statistically significant values at a 1 percent significance level. The overall results that are provided in appendix VII show how the cryptocurrencies are interconnected. Every
cryptocurrency has at least two cryptocurrencies that have a causal effect on the particular cryptocurrency. Litecoin has the highest amount of statistically significant predictors in the Granger causality test. 6 (included are a combination of all the cryptocurrencies) out of the 10 predictors have a statistically significant causal effect on Litecoin’s return. Whereas Ethereum has the least amount of predictors that produce a statistically significant causal effect.
‘
Table VIII
Granger causality results
This table documents the results of the Granger causality test for Bitcoin
Dependent variable Excluded chi2 df
Bitcoin Ethereum 4.7352* 2
Bitcoin Tether 9.7062*** 2
Bitcoin Ripple 3.612 2
Bitcoin Bitcoin Cash 3.166 2
32 6. Conclusion
In this paper we enlarged the literature regarding the predictability of cryptocurrencies. A bivariate predictive regression is employed to test and analyse 67 technical trading rules for ten of the highest ranked cryptocurrencies based on market capitalisation (BTC, ETH, USDT, XRP, BCH, Link), BNB, LTC, ADA, and EOS). A VAR(p) model was also employed to examine connections between the cryptocurrencies themselves. The returns of the cryptocurrencies all displayed a stationary process, i.e. a unit root was not present in the returns. Hence, the use of a VAR(p) model was justified.
This paper examines whether technical trading rules have predictable power in the cryptocurrency market. The results indicate that the technical trading rules employed in this paper do indeed have predictable power for cryptocurrencies. The technical trading rules produce statistically significant positive coefficients for all ten cryptocurrencies. Tether appeared to be the most predictable by the technical trading rules, which can partly be devoted to Tether’s price development during the timespan of the sample. The moment rule and the exponential moving average rule appeared to be the most successful to produce statistically significant positive coefficients. Followed by the filter trading rules. Interestingly, by examining the individual technical trading rules per cryptocurrencies, the channel
breakout rules appeared to be the best-performing rules.
This study also explores whether cryptocurrencies are interconnected. Both the substitution effect and the whole market effect imply connections between
cryptocurrencies. The former effect would imply negative coefficients and the latter effect would predict positive coefficients. The VAR model employed in this paper resulted in both positive and negative statistically significant coefficients. Other possible explanation for the connections between cryptocurrencies are the trading pairs that are present in the
cryptocurrency market and herding behaviour for investors.
In this paper, we also show proof of causal effects between the ten cryptocurrencies. We established causal effects between every cryptocurrencies. Ethereum, Tether, Chainlink and EOS have a causal effect on Bitcoin’s return. Litecoin appeared to have the most causal effects with other cryptocurrencies.
33
relationship amongst themselves. The results can be used to invest, diversify risk and hedging.
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36 Appendix
38 Appendix II. Bivariate regression results
Rule Coefficient Robust standard error t-value P > (t)
RSI(7) v=20 0.004 0.002 2.270 0.024 RSI (7) v=25 0.005 0.004 1.220 0.223 RSI (7) v=30 0.004 0.003 1.320 0.188 RSI (14) v=20 0.007 0.004 1.830 0.067 RSI (14) v=25 0.008 0.006 1.460 0.144 RSI (14) v=30 0.029 0.022 1.280 0.202 MA (1,25) -0.003 0.003 -1.340 0.181 MA (1,50) 0.005 0.003 1.870 0.061 MA (1,100) 0.003 0.002 1.050 0.295 MA (2,25) 0.005 0.003 2.030 0.043 MA (2,50) 0.004 0.003 1.420 0.157 MA (2,100) 0.002 0.002 0.720 0.473 MA (5,25) 0.005 0.003 1.780 0.075 MA (5,50) 0.003 0.003 1.270 0.204 MA (5,100) 0.003 0.002 1.190 0.233 MA (10,25) 0.005 0.003 2.150 0.032 MA(10,50 0.003 0.003 1.000 0.318 MA (10,100) 0.000 0.002 0.150 0.882 EMA (5,12) 0.006 0.003 2.240 0.025 Filter (0.5,1) 0.002 0.001 1.160 0.245 Filter(0.5,2) 0.004 0.001 2.760 0.006 Filter(0.5,5) 0.004 0.002 2.220 0.026 Filter(0.5,10) 0.004 0.002 1.640 0.101 Filter (1,1) 0.002 0.002 1.030 0.302 Filter(1,2) 0.004 0.001 2.540 0.011 Filter(1,5) 0.004 0.002 2.330 0.020 Filter(1,10) 0.004 0.002 2.040 0.041 Filter(5,1) -0.004 0.004 -0.950 0.340 Filter(5,2) 0.001 0.003 0.200 0.844 Filter(5,5) 0.003 0.002 2.070 0.038 Filter(5,10) 0.004 0.002 2.660 0.008 Filter(10,1) -0.012 0.010 -1.230 0.219 Filter(10,2) -0.006 0.005 -1.230 0.221 Filter(10,5) 0.003 0.003 0.990 0.321 Filter(10,10) 0.004 0.002 1.600 0.110 Support-resistance (1,1) 0.002 0.002 1.030 0.302 Support-resistance (1,5) 0.004 0.002 1.880 0.060 Support-resistance (1,10) 0.003 0.003 1.060 0.289 Support-resistance (1,20) 0.005 0.004 1.370 0.171 Support-resistance (5,1) -0.004 0.004 -0.950 0.340 Support-resistance (5,5 0.000 0.006 0.030 0.978 Support-resistance (5,10) -0.001 0.007 -0.210 0.831 Support-resistance (5,20) 0.001 0.008 0.170 0.861 Support-resistance (10,1) -0.012 0.010 -1.230 0.219 Support-resistance (10,5) -0.010 0.016 -0.610 0.541 Support-resistance (10,10) -0.015 0.020 -0.720 0.470 Support-resistance (10,20) -0.012 0.024 -0.490 0.624 Channel breakout (5,1,0.5) Channel breakout (5,1,1) 0.023 0.022 1.050 0.292 Channel breakout (5,1,5) 0.017 0.001 13.630 0.000 Channel breakout (5,5,0.5) 0.004 0.003 1.430 0.154 Channel breakout (5,5,1) 0.004 0.003 1.130 0.258 Channel breakout (5,5,5) 0.008 0.006 1.230 0.221 Channel breakout (5,10,0.5) 0.005 0.002 2.510 0.012 Channel breakout (5,10,1) 0.006 0.003 2.260 0.024 Channel breakout (5,10,5) 0.010 0.006 1.640 0.102 Channel breakout (20,1,0.5) Channel breakout (20,1,1) Channel breakout (20,1,5) Channel breakout (20,5,0.5) 0.000 0.004 0.070 0.945 Channel breakout (20,5,1) 0.007 0.004 1.450 0.146 Channel breakout (20,5,5) 0.017 0.001 13.310 0.000 Channel breakout (20,10,0.5) 0.018 0.007 2.450 0.015 Channel breakout (20,10,1) 0.022 0.009 2.630 0.009 Channel breakout (20,10,5) 0.004 0.006 0.750 0.451 Momentum (9) 0.003 0.003 1.160 0.248 Momentum (12) 0.005 0.003 1.960 0.050 Bitcoin
Rule Coefficient Robust standard error t-value P > (t)
39
Rule Coefficient Robust standard error t-value P > (t)
RSI(7) v=20 0.005 0.001 4.590 0.000 RSI (7) v=25 0.005 0.001 5.460 0.000 RSI (7) v=30 0.005 0.001 5.490 0.000 RSI (14) v=20 0.005 0.001 4.660 0.000 RSI (14) v=25 -0.015 0.009 -1.550 0.121 RSI (14) v=30 -0.017 0.010 -1.730 0.084 MA (1,25) 0.020 0.018 1.090 0.274 MA (1,50) -0.009 0.015 -0.630 0.530 MA (1,100) -0.703 0.001 -1310.130 0.000 MA (2,25) 0.006 0.001 4.780 0.000 MA (2,50) -0.010 0.016 -0.650 0.515 MA (2,100) -0.703 0.001 -1310.130 0.000 MA (5,25) 0.006 0.001 4.750 0.000 MA (5,50) -0.012 0.017 -0.670 0.501 MA (5,100) -0.703 0.001 -1310.130 0.000 MA (10,25) -0.008 0.013 -0.580 0.561 MA(10,50 -0.010 0.016 -0.650 0.516 MA (10,100) -0.703 0.001 -1310.130 0.000 EMA (5,12) 0.006 0.001 5.240 0.000 Filter (0.5,1) Filter(0.5,2) 0.011 0.002 6.500 0.000 Filter(0.5,5) 0.006 0.001 6.550 0.000 Filter(0.5,10) 0.006 0.001 5.580 0.000 Filter (1,1) 0.035 0.005 6.440 0.000 Filter(1,2) 0.020 0.003 6.740 0.000 Filter(1,5) 0.011 0.002 6.060 0.000 Filter(1,10) 0.006 0.001 6.590 0.000 Filter(5,1) 0.117 0.021 5.710 0.000 Filter(5,2) 0.069 0.012 5.900 0.000 Filter(5,5) 0.034 0.005 6.390 0.000 Filter(5,10) 0.019 0.003 6.680 0.000 Filter(10,1) 0.177 0.031 5.720 0.000 Filter(10,2) 0.113 0.020 5.720 0.000 Filter(10,5) 0.059 0.010 6.030 0.000 Filter(10,10) 0.035 0.005 6.350 0.000 Support-resistance (1,1) 0.035 0.005 6.440 0.000 Support-resistance (1,5) 0.036 0.006 6.430 0.000 Support-resistance (1,10) 0.036 0.006 6.440 0.000 Support-resistance (1,20) 0.036 0.006 6.440 0.000 Support-resistance (5,1) 0.117 0.021 5.710 0.000 Support-resistance (5,5 0.117 0.021 5.710 0.000 Support-resistance (5,10) 0.117 0.021 5.710 0.000 Support-resistance (5,20) 0.117 0.021 5.710 0.000 Support-resistance (10,1) 0.177 0.031 5.720 0.000 Support-resistance (10,5) 0.176 0.031 5.720 0.000 Support-resistance (10,10) 0.176 0.031 5.720 0.000 Support-resistance (10,20) 0.176 0.031 5.720 0.000 Channel breakout (5,1,0.5) 0.276 0.016 1.720 0.085 Channel breakout (5,1,1) 0.050 0.001 69.950 0.000 Channel breakout (5,1,5) Channel breakout (5,5,0.5) 0.007 0.003 1.950 0.052 Channel breakout (5,5,1) 0.026 0.018 1.470 0.141 Channel breakout (5,5,5) 0.406 0.001 619.470 0.000 Channel breakout (5,10,0.5) 0.008 0.003 3.100 0.002 Channel breakout (5,10,1) 0.016 0.006 2.610 0.009 Channel breakout (5,10,5) 0.406 0.001 619.470 0.000 Channel breakout (20,1,0.5) 0.050 0.001 69.280 0.000 Channel breakout (20,1,1) 0.050 0.001 69.280 0.000 Channel breakout (20,1,5) Channel breakout (20,5,0.5) 0.038 0.008 4.520 0.000 Channel breakout (20,5,1) 0.038 0.008 4.520 0.000 Channel breakout (20,5,5) Channel breakout (20,10,0.5) 0.123 0.082 1.500 0.135 Channel breakout (20,10,1) 0.123 0.082 1.500 0.135 Channel breakout (20,10,5) 0.405 0.001 612.760 0.000 Momentum (9) 0.007 0.001 5.140 0.000 Momentum (12) 0.007 0.001 4.890 0.000 Tether
Rule Coefficient Robust standard error t-value P > (t)
