1st Jan 2018

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.

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:

- Cryptos are unlikely to go mainstream as they are too technical
- 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

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 closing prices

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

BTC price change % by year

2014 is a bad year for BTC.

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 day of month

BTC lag plot

The correlation decreases when the lag increases, as expected.

BTC daily ACF & 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

- 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.

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

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:

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 closing prices

ETH price change % by year

ETH increases steadily over the years.

ETH price change % by quarter

ETH price change % by month

ETH price change % by day of month

ETH lag plot

ETH daily ACF & 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

- 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

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

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.