Bitcoin VS Ethereum Analysis

1st Jan 2018

Project background

Bitcoin and Ethereum are the top 2 cryptocurrencies (aka cryptos) in terms of market capitalization.

I am interested to see if I can discover any patterns for these 2 cryptos using time series analysis.

My exposure to cryptos

I was first exposed to cryptos in 2016, at that time, the price of 1 bitcoin is about $500 - $600.

I don't invest in cryptos then because:

  1. Cryptos are unlikely to go mainstream as they are too technical
  2. With the USA's tight financial regulation, there is a potential risk that it may become illegal

If I could time travel, 1 of the things I would do is

Images from the movies: Back to the Future & The Wolf of Wall Street.

Bitcoin (BTC)

First, let's look at BTC from 2013-05-01 to 2017-12-31.

BTC correlations between open, high, low, close prices and market capitalization

BTC correlations

BTC closing prices

In this article, I will be using closing price (USD).

BTC closing prices

BTC price change % by year

BTC price change % by year

2014 is a bad year for BTC.

BTC price change % by quarter

BTC price change % by quarter

In general, quarter 2 will yield better return than 1 and 3.

BTC price change % by month

BTC price change % by month

BTC price change % by day of month

BTC price change % by day of month

BTC lag plot

BTC lag plot

The correlation decreases when the lag increases, as expected.

BTC daily ACF & PACF plot

BTC daily ACF plot
BTC daily PACF plot
  • From ACF plot, it's clear that it's not a white noise process.
  • Using Augmented Dickey-Fuller test, I obtained the p-value of 1. Hence BTC has unit root and is non-stationary and it follows a random walk

BTC returns

BTC returns
BTC returns ACF plot
  • Based on ADF test, with p-value < 0.05, I conclude that BTC returns don't follow random walk process and is stationary
  • This is a close call as based on ACF plot, there are a few lags that seem significant.

BTC returns in calendar heatmap

Days where BTC prices jump by at least 15%:

['2013–05–04', '2013–11–18', '2013–11–21', '2013–11–26', '2013–12–19', '2014–03–03', '2014–04–11', '2014–11–12', '2015–01–15', '2017–07–17', '2017–07–20', '2017–09–15', '2017–12–06', '2017–12–07']

Days where BTC prices drop by at least 15%:

['2013-07-05', '2013-11-19', '2013-12-01', '2013-12-06', '2013-12-07', '2013-12-16', '2013-12-18', '2014-01-07', '2014-03-27', '2014-04-10', '2015-01-13', '2015-01-14', '2015-08-18', '2016-01-15', '2017-09-14']

BTC ARIMA model

Based on the ACF & PACF plot, I managed to determined the ARIMA model order.

ARIMA residual plot
ARIMA residual distribution plot
ARIMA forecast for 292 steps

It's not surprising that the forecast values for 292 steps ahead are off.

ARIMA forecast for 292 steps

The result for 1 step forecast is better than what I expected. It appears that the statistical methods are able to handle the extreme volatility of cryptos:thumbsup:

ARIMA forecast for 292 steps

Ethereum (ETH)

First, let's look at ETH from 2015-08-08 to 2017-12-31.

ETH correlations between open, high, low, close prices and market capitalization

ETH correlations

ETH closing prices

ETH closing prices

ETH price change % by year

ETH price change % by year

ETH increases steadily over the years.

ETH price change % by quarter

ETH price change % by quarter

ETH price change % by month

ETH price change % by month

ETH price change % by day of month

ETH price change % by day of month

ETH lag plot

ETH lag plot

ETH daily ACF & PACF plot

ETH daily ACF plot
ETH daily PACF plot
  • From ACF plot, it's clear that it's not a white noise process.
  • Using Augmented Dickey-Fuller test, I obtained the p-value of 1. Hence ETH has unit root and is non-stationary and it follows a random walk

ETH returns

ETH returns
ETH returns ACF plot
  • Based on ADF test, with p-value < 0.05, I conclude that ETH returns don't follow random walk process and is stationary

ETH returns in calendar heatmap

Days where ETH prices jump by at least 15%:

['2015-08-11', '2015-08-13', '2015-08-19', '2015-08-20', '2015-10-22', '2015-10-26', '2015-10-27', '2015-10-29', '2015-11-01', '2016-01-23', '2016-01-25', '2016-02-07', '2016-02-09', '2016-02-11', '2016-02-18', '2016-02-22', '2016-03-01', '2016-03-09', '2016-03-12', '2016-04-30', '2016-07-22', '2016-08-03', '2016-12-06', '2017-01-03', '2017-01-04', '2017-02-14', '2017-03-13', '2017-03-15', '2017-03-16', '2017-03-19', '2017-03-24', '2017-04-27', '2017-04-30', '2017-05-04', '2017-05-19', '2017-05-21', '2017-05-30', '2017-06-10', '2017-06-12', '2017-07-12', '2017-07-17', '2017-07-18', '2017-09-15', '2017-09-18', '2017-11-24', '2017-12-11', '2017-12-12']

Days where ETH prices drop by at least 15%:

['2015-08-17', '2015-09-11', '2015-09-28', '2015-11-11', '2016-02-16', '2016-03-07', '2016-06-17', '2016-06-18', '2016-08-02', '2017-03-18', '2017-09-04', '2017-09-14', '2017-12-22']

ETH has more days where the prices jump by at least 15%.

ETH ARIMA model

ARIMA residual plot
ARIMA residual distribution plot
ARIMA forecast for 292 steps
ARIMA forecast for 292 steps
ARIMA forecast for 292 steps

Comparing growth rate of BTC & ETH

In order to compare the rate of growth for BTC & ETH, I took the data starting from 2015–08–08 to 2017–12–31 and normalized them.

Between 2015–08–08 and 2017–12–31:

  • ETH grows by 1004 times while BTC grows by 54 times
  • ETH's growth is 18.5 times of BTC's growth

Final thoughts

The result from the one-step forecast model is better than what I expected.

I think the cryptos will have a decent future if they provide anonymity for the users. But based on the current call for regulation, I believe that the current cryptos are the "Friendster", a stepping stone before we have a truly decentralized, anonymous cryptocurrency.