Author Yetong |Chain Hill Capital,Co-author Carrie |Chain Hill Capital
In this article, we performed several models to capture the characteristics of Bitcoin Dominance and verified the existence of the downward trend and the seasonality features of Bitcoin Dominance. Meanwhile, we made interpretations and suggestions based on our findings.
TL;DR
According to the result of the significance test, we confirmed the second half of the year BTCD was significantly higher than the first half of the year in history, while ETHD showed the opposite trend, which is clear evidence of sector rotation of the market. The possible reason is that investors are chasing higher returns during a rising market cycle. Meanwhile, from the time series models above, we found significant seasonal characteristics, that is, the BTCD in the same month of last year would significantly affect the BTCD in the same month of this year, therefore we suggest investors adjust their portfolio positions based on the sector rotation and seasonality.
Since BTCD had a significant long-term downward trend, we think, compared to Bitcoin, other projects at the early stage may create a higher return in the long term.
The periods followed by a downward trend had smaller prediction errors than the periods followed by an upward trend. The possible reason is that the time series models in this article have captured the long-term downward trend of BTCD, so when BTCD has a downward trend, the prediction will be more accurate. Besides, when the short-term BTCD deviates from its forecasting path, we strongly suggest that investors need to combine more market information to manage the portfolio risks.
1.Introduction
Bitcoin Dominance (BTCD) or Bitcoin Market Cap Dominance is described as the ratio between the market cap of Bitcoin to the total market cap of the cryptocurrency markets. By observing the historical data of BTCD, we proposed two hypotheses: 1) Long-term downward trend of BTCD; 2) Seasonal characteristics of BTCD.
Through establishing the test of significance and building the time-series models, we found the existence of two characteristics above. Based on the time-series prediction model, after 4 weeks, BTCD will be 45.1261%, and after 24 months, it will be 32.7914%. At the same time, we found the prediction models were more valid in the short term, and the 75th percentile of forecast error for 1 to 4 weeks’ predictions was 3.4808%. At last, further interpretations and conclusions on the model results will be made.
Notice, the models and results in this article were based on the data before 11/01/2021.
2.Background
Between 2013 and 2021, the total cryptocurrency markets have grown from over 1 billion dollars to more than 2 trillion dollars (source: CoinMarketCap). At the same time, it developed into a disruptive innovation market that contains over ten thousand projects.
With the development of the underlying technologies and applications, more and more projects are coming up in this market. Among all the up-and-coming projects, though Bitcoin supremacy is unshaken for most of the time, the long-term declining trend along with the development of the entire industry can be observed from the graph below which shows the BTCD data from 2013 to 2021. Based on the observation, we proposed Hypothesis 1 of this article: Long-term downward trend of BTCD.
Furthermore, using data from 2016 onwards, we draw a heat map of the changes of monthly average BTCD, ETHD (ratio between the market cap of Ethereum to the total market cap of the cryptocurrency markets), ALTD (ratio between the market cap of all projects excluding Bitcoin and Ethereum to the total market cap of the cryptocurrency markets). It seems BTCD had more positive monthly changes in the second half of the year than in the first, while ETHD and ALTD showed the opposite trend. Based on this observation, we proposed Hypothesis 2: Seasonal characteristics of BTCD.
3.Significance Test
Before we tested Hypothesis 1 and 2, we would like to conduct the significance test to verify the statement that we made in the previous section: ‘BTCD had more positive monthly changes in the second half of the year than in the first, while ETHD and ALTD showed the opposite trend’.
At first, we tested the normality of the datasets that we used. If the data is normally distributed, the parametric test will be conducted. Otherwise, a non-parametric test will be used.
The three tables above showed the normality tests results of the changes of monthly average BTCD, ETHD, and ALTD (using data from 2016 to now), we noticed that Pr < W were all < 0.05, therefore, we rejected the null hypothesis at 5% significance level, which means the changes of monthly average BTCD, ETHD, and ALTD were not normally distributed.
Before we run the non-parametric test, we used the Box-Cox method to convert non-normal distributed data to normally distributed data. After the Box-Cox method transformation, the results tables below of tests for normality showed that Pr < W were all > 0.05, which means we successfully converted the changes of monthly average BTCD, ETHD, and ALTD to normally distributed data. Therefore, a parametric test could be performed.
The one-sided test hypothesis was:
3.1.BTCD Results
The three tables above showed: 1) Basic statistics; 2) Homogeneity of variance test results; 3) T-test results. The Pr > F of homogeneity of variance test was larger than 0.05, so the assumption of homogeneity of variance had not been violated. Furthermore, the Pr < t of the T-test was smaller than 0.05, which means the null hypothesis should be rejected and proved BTCD had more positive monthly changes in the second half of the year than in the first.
3.2.ETHD Result
Similarly, the tables above showed the test results for ETHD, and the Pr > F of homogeneity of variance test was larger than 0.05, so the data passed the assumption of homogeneity of variance. Meanwhile, the Pr < t of the T-test was smaller than 0.05, which means that ETHD had more positive monthly changes in the first half of the year than in the second.
3.3.ALTD Results
For the ALTD, though the assumption of homogeneity of variance had not been violated, the Pr < t of the T-test was larger than 0.05. Therefore, the null hypothesis should not be rejected, which means there were no differences between the first half of the year and the second half for the monthly average of ALTD.
4.Time Series Model Fitting with Monthly data
4.1.Curve fitting
To test Hypothesis 1, we considered time-series data as a dependent variable and BTCD as an independent variable to capture the long-term downward trend of BTCD.
The above table showed the curve fitting model results, and it is obvious that the coefficient of time-series data was negative. At the same time, the p-value of the coefficient was smaller than 0.0001, which means that BTCD had a statistically significant downward trend.
4.2.Autoregressive Moving Average Model (ARMA)
4.2.1.Unit Root Test & White Noise Test
The first step for building the time series model is conducting the unit root test and white noise test for the monthly BTCD data. The chart and tables below showed the: 1) Trend graph of BTCD; 2) Unit root test results; 3) White Noise Test results. In the previous section, we proved the significant downward trend of BTCD, and the Pr < Tau of unit root test were all larger than 0.05, the null hypothesis should not be rejected. Therefore, the monthly BTCD was a nonstationary sequence. Meanwhile, the Pr < ChiSq of white noise test were all smaller than 0.0001, which means BTCD was not white noise data.
4.2.2.First Order Difference
Since the monthly BTCD was a nonstationary and non-white noise sequence, we made the first-order difference of the original data. The test results chart and tables were shown above. It should be clear that the first-order difference of monthly BTCD was stationary and non-white noise sequence, which means a valid model can be conducted now.
4.2.3.AMRA (p, q)
Through the SAS SCAN algorithm which can provide the best option of p and q, p = 2 and q = 0 were chosen for the model.
4.2.4.Regression Results
By constructing ARIMA (2, 1, 0) model (1 in the middle means the first-order difference), we got the regression results table above. At the 10% significance level, all AR coefficients were statistically significant, and the Pr > ChiSq of autocorrelation check for residuals were all larger than 0.05, which means the model we established was at the condition with sufficient information extraction. Therefore, ARIMA (2, 1, 0) model was qualified.
The model was as follows:
4.2.5.Model Forecasting
In the previous section, we concluded that ARIMA (2, 1, 0) model was qualified, so we used the same model to predict the BTCD in this section. We predicted BTCD would be 32.7914% after 24 months.
We calculated that the adjusted R square of the model was 95.7%, which means 95.7% of characteristics of BTCD can be explained by this regression model.
4.3.Seasonal ARMA Model
The characteristics of any time-series sequence are Trend characteristics, Periodicity characteristics, and Random characteristics. To study the periodicity characteristics of BTCD, we established the seasonal ARMA model. The periodicity characteristics here we were talking about were referring to the seasonal characteristics, which is not the same as periodicity characteristics. The time intervals of seasonal features are consistent, while the time intervals of periodic features are not necessarily consistent.
4.3.1.First Order 12-Month Difference
From section 4.2.1., we know the monthly BTCD was a nonstationary and non-white noise sequence, and to study the seasonal features, we made the first-order 12-month difference of the original data.
From the test results tables above, we figured out that after making the first-order 12-month difference of the original data, we got stationary and non-white noise sequence, which means a valid model could be conducted.
4.3.2.AMRA (p, q)
Through the graphs above which showed the Autocorrelation function (ACF) coefficient and the Partial autocorrelation function (PACF) coefficient after making the first-order 12-month difference, the ACF coefficient was significant in 12th order and the PACF coefficient was significant in both 12th and 24th order. Therefore, we used ARMA (0, 1)12 to capture the seasonal features of BTCD, and ARMA (0, 1) to capture the short-term correlation. The final seasonal ARMA model in this section was ARIMA (0, 1, 1) * ARIMA (0, 1, 1)12.
Meanwhile, since the ACF coefficient was significant in the 12th order and the PACF coefficient was significant in both 12th and 24th order, we can conclude that the BTCD in the same month of last year would significantly affect the BTCD in the same month of this year, which proves the existence of seasonal characteristics of BTCD.
4.3.3.Regression Results
Through constructing ARIMA (0, 1, 1) * ARIMA (0, 1, 1)12 model, we got the regression results table above. All MA coefficients were statistically significant, and the Pr > ChiSq of autocorrelation check for residuals were all larger than 0.05, which means the model we established was at the condition with sufficient information extraction. Therefore, ARIMA (0, 1, 1) * ARIMA (0, 1, 1)12 model was qualified.
The model was as follows:
4.3.4.Model Forecasting
Since ARIMA (0, 1, 1) * ARIMA (0, 1, 1)12 was qualified, we would like to use the same model to predict the BTCD in this section. We predicted BTCD would be 31.6735% after 24 months.
We calculated that the adjusted R square of the model was 94.3947%, which means the regression model can explain 94.3947% of characteristics of BTCD.
5.Time Series Model Fitting with Weekly Data
5.1.ARMA Model
5.1.1.Unit Root Test & White Noise Test
Similar to the time series model in section 4, the first step is conducting the unit root test and white noise test for the weekly BTCD data. The chart and tables below showed the: 1) Trend graph of BTCD; 2) Unit root test results; 3) White Noise Test results. The Pr < Tau of unit root test were all larger than 0.05, the null hypothesis should be rejected. Therefore, the monthly BTCD was a nonstationary sequence. Meanwhile, the Pr < ChiSq of white noise test were all smaller than 0.0001, which means BTCD was not white noise data.
5.1.2.First Order Difference
Since the weekly BTCD was a nonstationary and non-white noise sequence, we made the first-order difference of the original data. The test results chart and tables were shown above. It should be clear that the first-order difference of monthly BTCD was stationary and non-white noise sequence.
5.1.3.AMRA (p, q)
Through the SAS SCAN algorithm which can provide the best option of p and q, p = 1 and q = 0 were chosen for the model.
5.1.4.Regression Results
By constructing ARIMA (1, 1, 0) model, we got the regression results table above. The AR coefficient was statistically significant, and the Pr > ChiSq of autocorrelation check for residuals were all larger than 0.05, which means the model we established was at the condition with sufficient information extraction. Therefore, ARIMA
(1, 1, 0) model was qualified.
The model is as follows:
5.1.5.Model Forecasting
In the previous section, we concluded that ARIMA (1, 1, 0) model was qualified, so we used the same model to predict the BTCD in this section. We predicted BTCD would be 45.1261% after 4 weeks, and 34.2524% after 104 weeks (about 24 months) which is slightly higher than the 32.7914% predicted by the monthly data model.
We calculated that the adjusted R square of the model was 97.03%, so the regression model explained 97.03% of characteristics of BTCD.
5.2.Seasonal ARMA Model
5.2.1.First Order 4-Week Difference
From section 5.1., we know the weekly BTCD was a nonstationary and non-white noise sequence, and to study the seasonal features based on weekly data, we made the first-order 4-week difference of the original data.
From the test results tables above, it is obvious that after making the first-order 4-week difference of the original data, we got stationary and non-white noise sequences.
5.2.2.AMRA (p, q)
The graphs above which showed the ACF coefficient and the PACF coefficient after making the first-order 4-week difference. The ACF coefficient was significant in the 4th order and the PACF coefficient was significant in the 4th, 5th, 8th, and 9th order. Therefore, we used ARMA (0, 1)4 to capture the seasonal features of BTCD, and ARMA (0, 1) to capture the short-term correlation. The final seasonal ARMA model in this section was ARIMA (0, 1, 1) * ARIMA (0, 1, 1)4.
Meanwhile, since the ACF coefficient was significant in 4th order and the PACF coefficient was significant in the 4th, 5th, 8th, and 9th order, we concluded that the BTCD in the same week of last month would significantly affect the BTCD in the same week of this month, which proves the existence of seasonal characteristics of BTCD.
5.2.3.Regression Results
Through constructing ARIMA (0, 1, 1) * ARIMA (0, 1, 1)4 model, we got the regression results table above. All MA coefficients were statistically significant, and the Pr > ChiSq of autocorrelation check for residuals were all larger than 0.05, which means the model we established was at the condition with sufficient information extraction. Therefore, ARIMA (0, 1, 1) * ARIMA (0, 1, 1)4 model was qualified.
The model was as follows:
5.2.4.Model Forecasting
Since ARIMA (0, 1, 1) * ARIMA (0, 1, 1)4 was qualified, we would like to use the same model to predict the BTCD in this section. We predicted BTCD would be 45.4403% after 4 weeks, and 38.3482% after 104 weeks (about 24 months) which is slightly higher than the 31.6735% predicted by the monthly data model.
We calculated that the adjusted R square of the model was 85.7922%, so the regression model explained 85.7922% of characteristics of BTCD. Compare to the time series model in the previous section, the adjusted R square is lower. The possible reason is that 4 weeks are not strictly a month, and we can see it from the ACF coefficient and the PACF coefficient graphs, the ACF coefficient was significant in the 4th order and PACF was significant in the 4th, 5th, 8th, and 9th order.
6.Forecasting Model Comparison
To evaluate the forecasting models, we used the data from different periods to establish the models. In this section, all models were based on weekly BTCD data.
6.1.2013/04–2018/12
The same as previous sections, we made the first-order difference at first, then determined the value of p and q. The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 51.8077% after 4 weeks (52.7309% in real data), 50.9666% after 10 weeks (52.0026% in real data), 49.5602% after 20 weeks (58.1098% in real data).
6.2.2013/04–2019/03
The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 50.1506% after 4 weeks (54.4983% in real data), 49.3105% after 10 weeks (55.7968% in real data), 47.9095% after 20 weeks (68.1467% in real data).
6.3.2013/04–2019/06
The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 60.7912% after 4 weeks (65.4735% in real data), 60.1716% after 10 weeks (70.2934% in real data), 59.1505% after 20 weeks (65.3576% in real data).
6.4.2013/04–2019/09
The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 66.5799% after 4 weeks (67.1689% in real data), 66.0919% after 10 weeks (65.8393% in real data), 65.2822% after 20 weeks (62.8051% in real data).
6.5.2013/04–2019/12
The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 68.0411% after 4 weeks (65.7814% in real data), 67.5962% after 10 weeks (63.2734% in real data), 66.8553% after 20 weeks (68.5355% in real data).
6.6.2013/04–2020/03
The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 66.3810% after 4 weeks (66.3168% in real data), 65.9247% after 10 weeks (64.9024% in real data), 65.1669% after 20 weeks (59.8290% in real data).
6.7.2013/04–2020/06
The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 64.8677% after 4 weeks (64.0777% in real data), 64.4042% after 10 weeks (57.4548% in real data), 63.6325% after 20 weeks (68.9859% in real data).
6.8.2013/04–2020/09
The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 60.0899% after 4 weeks (64.8300% in real data), 59.5703% after 10 weeks (62.8073% in real data), 58.7028% after 20 weeks (63.6897% in real data).
6.9.2013/04–2020/12
The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 70.9716% after 4 weeks (64.4643% in real data), 70.6244% after 10 weeks (62.5588% in real data), 70.0521% after 20 weeks (41.2876% in real data).
6.10.2013/04–2021/03
The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 59.9858% after 4 weeks (50.9226% in real data), 59.4978% after 10 weeks (44.1656% in real data), 58.6835% after 20 weeks (45.6051% in real data).
6.11.2013/04–2021/06
The model used here was ARIMA (1, 1, 0), and verified the model we established was at the condition with sufficient information extraction. We predicted BTCD would be 47.2849% after 4 weeks (50.6103% in real data), 46.6364% after 10 weeks (42.1630% in real data), 45.7702% after 20 weeks (45.58% in real data).
6.12.Comparison
After using the BTCD data from different periods to evaluate the model, we got the forecasting results and calculated the absolute value of errors. At the same time, we calculated the 75th percentiles of the absolute value of residual for 1st to 4th week periods, 5th to 10th week periods, and 11th to 20th week periods, and draw the table above. We predicted the 75th percentiles of the absolute value of errors were 3.4808% for 1st to 4th week periods, 7.7291% for 5th to 10th week periods, and 10.5359% for 11th to 20th week periods.
By drawing the heat map of the absolute value of errors, we realized that when the absolute value of residual is relatively small in 4 weeks, it is more likely that the residual will be small in the corresponding 20 weeks.
By observing the historical chart of BTCD above, it can be found that when BTCD showed a downward trend, the prediction errors were small. When BTCD was in an upward trend, the prediction errors became larger. For example, using data before December 2018, September 2019, and March 2020 which are all the beginning of the downward trend to conduct prediction model, it was found that the prediction errors were relatively small. If the data before March 2019 and September 2020 were used to predict the BTCD, it was found that the prediction errors were relatively large.
To test the pattern we mentioned above, we divided the period into two groups, the first group consisted of the periods followed by downward trend and the second group consisted of the periods followed by upward trend, and draw the table above. The periods followed by a downward trend had smaller prediction errors than the periods followed by an upward trend.
This section concluded that: 1) Short-term prediction results were more accurate; 2) When BTCD showed a downward trend, the prediction errors were small; when BTCD was in an upward trend, the prediction errors became larger.
7.Model Flaws
In this article, we showed and verified the downward trend and seasonal characteristics of BTCD, and we think the models only can accurately predict the short-term trend of BTCD. If the seasonal time series model based on monthly data is used to predict the long-term trend of BTCD, BTCD will become negative after 90 months; if based on weekly data, BTCD will become negative after 420 weeks, all these predictions become meaningless at that point.
8.Conclusion
After building the test of significance and the time-series models, we found: 1) BTCD had more positive monthly changes in the second half of the year than in the first, while ETHD showed the opposite trend; 2) BTCD had a significant long-term downward trend; 3) BTCD had statistically significant seasonal characteristics; 4) The time series models in this article can only be used to predict the short-term BTCD, and the shorter the prediction period, the more accurate prediction will be; 5) When BTCD showed a downward trend, the prediction errors were smaller, and when BTCD was in an upward trend, the prediction errors became larger.
About Chain Hill Capital
Focusing on value investment in crypto and blockchain space since 2017, our investment philosophy is building a decentralized financial infrastructure and a user value oriented Internet. Based in Hong Kong, our venture capital focuses on areas including web 3.0 applications, DAO tooling, Defi 2.0,and Gamefi, investing in venture equity and early-stage tokens.Our profound blockchain expertise and broad connections in the space allow us to assist projects at different stages from different aspects such as tokenomic design, community development, legal and audit.
Combining the rigorous fundamental research with quantitative models, we also run funds focusing on liquid tokens investment strategies via an actively managed index fund,as well as a discretionary long only alpha fund.