Description of Data Set
For this project, I chose and downloaded the data for the historical daily close prices of
the cryptocurrency Ethereum (ETH) in US dollars. I obtained the data from Yahoo Finance and
the dates for this assignment are from December 15, 2018 to December 15, 2019. For the purpose
of the project, I removed the last data point and will be using it again to check the performance of
the forecast intervals later. I will use R for this project and in doing so, will use both “forecast”
and “tseries” libraries to complete my analysis.
Data URL: https://finance.yahoo.com/quote/ETH-USD/history?
period1=1544850000&period2=1576386000&interval=1d&filter=history&frequency=1d
Part 1: Time Series Plot of Ethereum
To start, I plotted the series of the original prices of Ethereum. The time series plot is the
following:
The time series plot has some sharp up and downs throughout the time range. To reduce the
conditional volatility, I took the logarithm of the data. The plot of ACF of log(Price) and PACF of
log(Price) is as follows:
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As shown through the graphs above, the log-price is not stationary because the series is not
mean-reverting, the ACF of log-price stays around 1 and decreases gradually, and the PACF is
almost 1 at lag-1 and cuts off after lag-1. This suggests that the series should be differenced to see
if the difference of log-price is stationary.
The following plots are the first difference of log-price as well as the ACF and PACF.
To determine if I should use the first difference of log-price, I further computed the second
difference of log-price. The second difference of log-price as well as its respective ACF and
PACF are shown below.
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