Analysis of Cryptocurrency Data

Introduction

A Cryptocurrency is a digital asset, which is designed to be a medium of exchange and who’s records are saved in a digital format using strong cryptographic algorithms. In lay man’s terms, it is money which only exists only in the digital form.

In this project, the stock prices of 12 major cryptocurrencies including the daily volume traded and their respective market capitalization is analyzed using the base R programming language and its some of its popular libraries like t Tidyverse and Quantmod. All visualizations are constructed using GGplot and Plotly libraries

Mission Outline

1. The Dataset
2. Initial View
3. Description, Slicing and New feature
4. Prices, Market Capitalization and Volume.
5. Distribution and Correlation of Volume
6. Central Limit Theorem
7. Sampling Methods

1. The Dataset

The Dataset consists of daily stock prices of 12 major cryptocurrencies from April of 2013 to December 2019. The data has the following features -

1. Currency Name
2. Date
3. Open (Opening Price)
4. Close (Closing Price)
5. High (Highest Price of the stock on a given day)
6. Low (Lowest Price of the stock on a given day)
7. Volume (Total Volume of Stock Traded by day)
8. Market Cap (Total Market Value of the coin by day)

2. Initial View

library(quantmod)
library(gridExtra)
library(Hmisc)
library(plotly)
library(sampling)
library(ggplotlyExtra)
library(ggplot2)
library(tidyverse)
options(scipen=999)
cd = read.csv("C:/Users/adety/Desktop/Courses/544/Project/consolidated_coin_data.csv")

head(cd)

##   Currency         Date Open High  Low Close     Volume  Market.Cap
## 1    tezos Dec 04, 2019 1.29 1.32 1.25  1.25 46,048,752 824,588,509
## 2    tezos Dec 03, 2019 1.24 1.32 1.21  1.29 41,462,224 853,213,342
## 3    tezos Dec 02, 2019 1.25 1.26 1.20  1.24 27,574,097 817,872,179
## 4    tezos Dec 01, 2019 1.33 1.34 1.25  1.25 24,127,567 828,296,390
## 5    tezos Nov 30, 2019 1.31 1.37 1.31  1.33 28,706,667 879,181,680
## 6    tezos Nov 29, 2019 1.28 1.34 1.28  1.31 32,270,224 867,085,098

tail(cd)

##         Currency         Date Open High  Low Close Volume Market.Cap
## 28939 bitcoin-sv May 03, 2013 3.39 3.45 2.40  3.04      0 52,694,847
## 28940 bitcoin-sv May 02, 2013 3.78 4.04 3.01  3.37      0 58,287,979
## 28941 bitcoin-sv May 01, 2013 4.29 4.36 3.52  3.80      0 65,604,596
## 28942 bitcoin-sv Apr 30, 2013 4.40 4.57 4.17  4.30      0 74,020,918
## 28943 bitcoin-sv Apr 29, 2013 4.37 4.57 4.23  4.38      0 75,388,964
## 28944 bitcoin-sv Apr 28, 2013 4.30 4.40 4.18  4.35      0 74,636,938

summary(cd)

##    Currency             Date               Open               High          
##  Length:28944       Length:28944       Length:28944       Length:28944      
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##      Low               Close              Volume           Market.Cap       
##  Length:28944       Length:28944       Length:28944       Length:28944      
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character

The Dataset is read into R and the initial view of the dataset shows that both - numeric and non-numeric features, are saved in the character format. Therefore, at first all features need to be converted to their respective types from the character format.

3. Description, Slicing and New features

The Currency feature is left as character, the Date variable is converted to Date type, also, a new feature ‘year’ is added to the dataset. All other features are then converted to numeric types. The summary function is used to check the data again after conversion.

The Summary function reveals that the Data set has 28944 rows and other various summarizations for the numerical features.

cd$Date = as.Date(cd$Date, '%b %d, %Y')
cd$Open = as.numeric(gsub(pattern = ',','',cd$Open))
cd$High = as.numeric(gsub(pattern = ',','',cd$High))
cd$Low = as.numeric(gsub(pattern = ',','',cd$Low))
cd$Close = as.numeric(gsub(pattern = ',','',cd$Close))
cd$Volume = as.numeric(gsub(pattern = ',','',cd$Volume))
cd$Market.Cap = as.numeric(gsub(pattern = ',','',cd$Market.Cap))
cd$year = as.numeric(format(cd$Date,"%Y"))
cd$Currency = capitalize(cd$Currency)
summary(cd)

##    Currency              Date                 Open          
##  Length:28944       Min.   :2013-04-28   Min.   :    0.001  
##  Class :character   1st Qu.:2014-12-21   1st Qu.:    0.205  
##  Mode  :character   Median :2016-08-15   Median :    2.995  
##                     Mean   :2016-08-15   Mean   :  300.720  
##                     3rd Qu.:2018-04-10   3rd Qu.:   24.430  
##                     Max.   :2019-12-04   Max.   :19475.800  
##       High                Low                Close          
##  Min.   :    0.002   Min.   :    0.001   Min.   :    0.001  
##  1st Qu.:    0.212   1st Qu.:    0.197   1st Qu.:    0.205  
##  Median :    3.090   Median :    2.880   Median :    2.980  
##  Mean   :  309.833   Mean   :  290.859   Mean   :  300.948  
##  3rd Qu.:   25.530   3rd Qu.:   23.270   3rd Qu.:   24.430  
##  Max.   :20089.000   Max.   :18974.100   Max.   :19497.400  
##      Volume              Market.Cap                year     
##  Min.   :          0   Min.   :           0   Min.   :2013  
##  1st Qu.:     241870   1st Qu.:    63451426   1st Qu.:2014  
##  Median :    5212684   Median :   345367261   Median :2016  
##  Mean   :  813305774   Mean   :  7194826310   Mean   :2016  
##  3rd Qu.:  155476420   3rd Qu.:  3422402834   3rd Qu.:2018  
##  Max.   :53509128965   Max.   :326502485530   Max.   :2019

The Plot below shows the names of the 12 currencies represented in the dataset. It also shows that each currency has equal representation of 2412 rows of information and it also further verifies, that there is no missing data in the dataset.

plot_ly(as.data.frame(cd$Currency),labels = cd$Currency,type = 'pie',hole = 0.6) %>%
  layout(xaxis = list(showgrid = FALSE, zeroline = FALSE, showticklabels = FALSE),
         yaxis = list(showgrid = FALSE, zeroline = FALSE, showticklabels = FALSE))

As mentioned earlier, this is huge data set with a large number of rows. To make it easier to navigate through the Data, the dataset is divided into 12 subsets of each currency. The Date column henceforth, is converted to index of the Data making it easier to plot the values. Also, the currency name column for the subsequent currencies is dropped with data frame name being the identifier of the subsetted data.

As The subsetted data is in the form ‘OHLC’ (open,High,Low,Close) it is in the ideal format to work with the Quantmod library and hence is converted to XTS type.

Bitcoin_sv = subset(cd,cd$Currency == 'Bitcoin-sv')
Bitcoin_sv$Currency = NULL
colnames(Bitcoin_sv) = c('Bitcoin_svDate','Bitcoin_svOpen','Bitcoin_svHigh',
                         'Bitcoin_svLow','Bitcoin_svClose','Bitcoin_svVolume',
                         'Bitcoin_svMarket.Cap')
Bitcoin_sv = xts(Bitcoin_sv[,-1], order.by=Bitcoin_sv[,1])

Bitcoin_cash = subset(cd,cd$Currency == 'Bitcoin-cash')
Bitcoin_cash$Currency = NULL
colnames(Bitcoin_cash) = c('Bitcoin_cashDate','Bitcoin_cashOpen','Bitcoin_cashHigh',
                         'Bitcoin_cashLow','Bitcoin_cashClose','Bitcoin_cashVolume',
                         'Bitcoin_cashMarket.Cap')
Bitcoin_cash = xts(Bitcoin_cash[,-1], order.by=Bitcoin_cash[,1])

Bitcoin = subset(cd,cd$Currency == 'Bitcoin')
Bitcoin$Currency = NULL
colnames(Bitcoin) = c('BitcoinDate','BitcoinOpen','BitcoinHigh',
                           'BitcoinLow','BitcoinClose','BitcoinVolume',
                           'BitcoinMarket.Cap')
Bitcoin = xts(Bitcoin[,-1], order.by=Bitcoin[,1])

Cardano = subset(cd,cd$Currency == 'Cardano')
Cardano$Currency = NULL
colnames(Cardano) = c('CardanoDate','CardanoOpen','CardanoHigh',
                      'CardanoLow','CardanoClose','CardanoVolume',
                      'CardanoMarket.Cap')
Cardano = xts(Cardano[,-1], order.by=Cardano[,1])

Eos = subset(cd,cd$Currency == 'Eos')
Eos$Currency = NULL
colnames(Eos) = c('EosDate','EosOpen','EosHigh',
                      'EosLow','EosClose','EosVolume',
                      'EosMarket.Cap')
Eos = xts(Eos[,-1], order.by=Eos[,1])

Ethereum = subset(cd,cd$Currency == 'Ethereum')
Ethereum$Currency = NULL
colnames(Ethereum) = c('EthereumDate','EthereumOpen','EthereumHigh',
                  'EthereumLow','EthereumClose','EthereumVolume',
                  'EthereumMarket.Cap')
Ethereum = xts(Ethereum[,-1], order.by=Ethereum[,1])

Litecoin = subset(cd,cd$Currency == 'Litecoin')
Litecoin$Currency = NULL
colnames(Litecoin) = c('LitecoinDate','LitecoinOpen','LitecoinHigh',
                       'LitecoinLow','LitecoinClose','LitecoinVolume',
                       'LitecoinMarket.Cap')
Litecoin = xts(Litecoin[,-1], order.by=Litecoin[,1])

Stellar = subset(cd,cd$Currency == 'Stellar')
Stellar$Currency = NULL
colnames(Stellar) = c('StellarDate','StellarOpen','StellarHigh',
                       'StellarLow','StellarClose','StellarVolume',
                       'StellarMarket.Cap')
Stellar = xts(Stellar[,-1], order.by=Stellar[,1])

Tether = subset(cd,cd$Currency == 'Tether')
Tether$Currency = NULL
colnames(Tether) = c('TetherDate','TetherOpen','TetherHigh',
                      'TetherLow','TetherClose','TetherVolume',
                      'TetherMarket.Cap')
Tether = xts(Tether[,-1], order.by=Tether[,1])

Tezos = subset(cd,cd$Currency == 'Tezos')
Tezos$Currency = NULL
colnames(Tezos) = c('TezosDate','TezosOpen','TezosHigh',
                     'TezosLow','TezosClose','TezosVolume',
                     'TezosMarket.Cap')
Tezos = xts(Tezos[,-1], order.by=Tezos[,1])

Xrp = subset(cd,cd$Currency == 'Xrp')
Xrp$Currency = NULL
colnames(Xrp) = c('XrpDate','XrpOpen','XrpHigh',
                    'XrpLow','XrpClose','XrpVolume',
                    'XrpMarket.Cap')
Xrp = xts(Xrp[,-1], order.by=Xrp[,1])

Binance_coin = subset(cd,cd$Currency == 'Binance-coin')
Binance_coin$Currency = NULL
colnames(Binance_coin) = c('Binance_coinDate','Binance_coinOpen','Binance_coinHigh',
                  'Binance_coinLow','Binance_coinClose','Binance_coinVolume',
                  'Binance_coinMarket.Cap')
Binance_coin = xts(Binance_coin[,-1], order.by=Binance_coin[,1])

4. Prices, Market Capitalization and Volume.

The Opening prices of all currencies by date is presented in this plot. It can be clearly seen that the prices of all currencies actually didn’t start picking up until the later half of 2017.there was some interest in Ethereum in the beginning, however,
that died down quickly after the first two years of its inception. It is now known that 2017 was the year when digital currency formally joined the financial markets.

The reason of sudden interest in Bitcoin in the mid of 2017 is still unknown, however, it is wildly speculated that a single ‘whale’( entity or a person who owns a large amount of stock of a single company) manipulated the price of Bitcoin causing it to flare up and hence generating large scale interest in the currency. Upon which, the financial world sort of opened its eyes towards digital currencies and almost all currencies saw a jump in their prices with Bitcoin emerging as the strongest and the most popular currency of the competition.

ggplot(Bitcoin, aes(x = index(Bitcoin),y = Bitcoin[,1]/100,color = 'Bitcoin')) + 
  geom_line() + 
  ggtitle("All Crypto Opening price series") + 
  theme(legend.position = "top") + 
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
  labs(
    x = "Date",
    y = "Opening Prices",
    color = "Currencies",
    caption = "Adi") +
  scale_x_date(date_labels = "%b %y", date_breaks = "6 months") + 
    theme(plot.title = element_text(hjust = 0.5)) +
  theme(plot.subtitle = element_text(hjust = 0.5)) +
  theme(legend.key.width = unit(2,"cm")) +
  geom_line(aes(y = Xrp[,1],color = 'Xrp')) +
  geom_line(aes(y = Cardano[,1],,color = 'Cardano')) + 
  geom_line(aes(y = Tezos[,1],color = 'Tezos')) +
  geom_line(aes(y = Binance_coin[,1],color = 'Binance_coin')) +
  geom_line(aes(y = Eos[,1],color = 'Eos')) +
  geom_line(aes(y = Tether[,1],color = 'Tether')) +
  geom_line(aes(y = Bitcoin_cash[,1],color = 'Bitcoin_cash')) +
  geom_line(aes(y = Stellar[,1],color = 'Stellar')) +
  geom_line(aes(y = Litecoin[,1],color = 'Litecoin')) + 
  geom_line(aes(y = Ethereum[,1],color = 'Ethereum')) +
  geom_line(aes(y = Bitcoin_sv[,1],color = 'Bitcoin_sv'))

The four price indicators namely, Daily Opening, Closing, High and Low, by currency are presented here in boxplots to better understand the price ranges of different currencies. The plot shows the Data for the years 2017 to 2019.

From the graph one can easily derive, that apart from Bitcoin, no other currency was traded for more than a $1000 consistently in the two years. Most currencies traded for below $500 and currencies like Tether and Cardano stayed under a dollar.

cd %>%
  filter(year == '2018'| year == '2019' | year == '2019') %>%
  plot_ly(type = 'box',x = ~High,transforms = list(list(type = 'filter',
                                                        target = ~Currency,
                                                        operation = '=',
              value = unique(cd$Currency)[1])),name="High") %>%
  add_boxplot(x = ~Low,name = 'Low') %>%
  add_boxplot(x = ~Open,name = 'Open') %>%
  add_boxplot(x = ~Close,name = 'Close') %>%
  
  layout(title = 'All Price Indicators of all Currencies',
         xaxis = list(title = 'Value'), 
         updatemenus = list(list(type = 'dropdown',buttons = list(
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[1]),
         label = unique(cd$Currency)[1]),
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[2]),
         label = unique(cd$Currency)[2]),
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[3]),
         label = unique(cd$Currency)[3]),
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[4]),
         label = unique(cd$Currency)[4]),
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[5]),
         label = unique(cd$Currency)[5]),
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[6]),
         label = unique(cd$Currency)[6]),
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[7]),
         label = unique(cd$Currency)[7]),
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[8]),
         label = unique(cd$Currency)[8]),
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[9]),
         label = unique(cd$Currency)[9]),
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[10]),
         label = unique(cd$Currency)[10]),
    list(method = "restyle",args = list("transforms[0].value", unique(cd$Currency)[11]),
         label = unique(cd$Currency)[11]),list(method = "restyle",
                            args = list("transforms[0].value", unique(cd$Currency)[12]),
         label = unique(cd$Currency)[12]))))) %>%
  layout(annotations = list(list(text = "For the years 2017-19",  xref = "paper", yref = "paper",
                            yanchor = "bottom",xanchor = "center", align = "center",
                            x = 0.5, y = .97, showarrow = FALSE)))

As seen with the prices, the same can be said about the Market capitalization of all the currencies. After the mid of 2017, when the prices started going up, so did the market value of all the currencies, and with Bitcoin again leading the competition by a huge margin.

ggplot(Bitcoin, aes(x = index(Bitcoin),y = Bitcoin[,6]/100000000,color = 'Bitcoin')) + 
  geom_line() + 
  ggtitle("All Crypto Market Cap") + 
  theme(legend.position = "top") + 
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
  labs(
    x = "Date",
    y = "Total Mean Capital",
    color = "Curriencies",
    title = "All Currencies Market Capatalization",
    subtitle = "in 100 millions",
    caption = "Adi") +
  scale_x_date(date_labels = "%b %y", date_breaks = "6 months") +
    theme(plot.title = element_text(hjust = 0.5)) +
  theme(plot.subtitle = element_text(hjust = 0.5)) +
  theme(legend.key.width = unit(2,"cm")) +
  geom_line(aes(y = Xrp[,6]/100000000,color = 'Xrp')) +
  geom_line(aes(y = Cardano[,6]/100000000,,color = 'Cardano')) + 
  geom_line(aes(y = Tezos[,6]/100000000,color = 'Tezos')) +
  geom_line(aes(y = Binance_coin[,6]/100000000,color = 'Binance_coin')) +
  geom_line(aes(y = Eos[,6]/100000000,color = 'Eos')) +
  geom_line(aes(y = Tether[,6]/100000000,color = 'Tether')) +
  geom_line(aes(y = Bitcoin_cash[,6]/100000000,color = 'Bitcoin_cash')) +
  geom_line(aes(y = Stellar[,6]/100000000,color = 'Stellar')) +
  geom_line(aes(y = Litecoin[,6]/100000000,color = 'Litecoin')) + 
  geom_line(aes(y = Ethereum[,6]/100000000,color = 'Ethereum')) +
  geom_line(aes(y = Bitcoin_sv[,6]/100000000,color = 'Bitcoin_sv'))

The plot below shows the progress of Bitcoin’s market capitalization over the years. it is interesting to see that in the early years Bitcoin and Ethereum were almost neck to neck when it came to market capitalization. However, as Bitcoin gained popularity over the years, its value increased many a folds.

What led to the sudden interest and explosion in the value of digital currencies 10 years after their inception, including that Bitcoin past 2017, is as mentioned earlier still a bit of a mystery, however some of the main reasons are -

1. Digital Currencies are not extensively regulated:

Unlike decree currencies like the US Dollar or the Euro, digital currencies are not regulated, which means that any central bank or any particular government of any country doesn’t control them as much as they do other financial instruments.

It is important to remember here, that when ‘Satoshi Nakamoto’ - the creator of Bitcoin - wrote those lines of code to bring Bitcoin into existence back in 2009, the world was going through the banking crises of 2008. Digital currencies were born somewhat due the requirement of alternative to fiat currencies which were prone to a lot of regulation and financial market’s manupliative forces.

2. They are very discrete:

Cryptocurrencies offer a lot more privacy than bank accounts or other money keeping instruments. The account numbers or ‘addresses’ of cryptocurrencies are in alpha-numeric format type, which are used as pointers to digital wallets and are not related to the personal information of the entity or individual which owns the wallet. and thus, digital currencies provide a much greater sense of security against fraud and financial watchdog regulations.

3. Short and stable supply:

In the case of Bitcoin, it has a very limited supply of only twenty million Bitcoins, and is unlikely to change in the near future.distinctively from normal currencies, Bitcoins cannot be manufactured in a money mint in unlimited quantities in the wake of a global catastrophe or a financial crisis. This not only makes the existing Bitcoins more valuable as the time passes but also provides solidarity to their monetary values.

cd %>%
  plot_ly(labels = ~Currency,values = ~Market.Cap, type = 'pie',
          transforms = list(list(type = 'filter',target = ~year,operation = '=',
                          value = unique(cd$year)[1])),name="2013") %>%
  layout(title = "Currency Yearly Market Capatalization Representation",
         xaxis = list(title = 'Value'), 
updatemenus = list(list(type = 'dropdown',buttons = list(
  list(method = "restyle",args = list("transforms[0].value", unique(cd$year)[1]),
       label = unique(cd$year)[1]),
  list(method = "restyle",args = list("transforms[0].value", unique(cd$year)[2]),
       label = unique(cd$year)[2]),
  list(method = "restyle",args = list("transforms[0].value", unique(cd$year)[3]),
       label = unique(cd$year)[3]),
  list(method = "restyle",args = list("transforms[0].value", unique(cd$year)[4]),
       label = unique(cd$year)[4]),
  list(method = "restyle",args = list("transforms[0].value", unique(cd$year)[5]),
       label = unique(cd$year)[5]),
  list(method = "restyle",args = list("transforms[0].value", unique(cd$year)[6]),
       label = unique(cd$year)[6]),
  list(method = "restyle",args = list("transforms[0].value", unique(cd$year)[7]),
       label = unique(cd$year)[7])))))

As there was hardly any interest in digital money before 2017, the 2017 onward volume traded data is presented here. It is evident that higher amount of market interest after the mid of 2017, resulted in large amounts of volume being traded in the financial markets across the world.

However, it is also quite interesting to note that even though currency Tether, which was nowhere near the price range(96 cents to $ 1.04 of Tether vs 4k to 18k of Bitcoin) or the market capitalization of the Bitcoin,it rivals and sometimes even goes past Bitcoin in the amount of volume traded.

ggplot(Bitcoin['2017-08/'], aes(x = index(Bitcoin['2017-08/']),
                                y = Bitcoin['2017-08/'][,5]/100000000,
                                color = 'Bitcoin')) + 
  geom_line() + 
  ggtitle("All Crypto Volume Traded") + 
  theme(legend.position = "top") + 
  labs(
    x = "Date",
    y = "Total Mean Volume",
    color = "Curriencies",
    subtitle = "in 100 millions",
    caption = "Adi") +
  scale_x_date(date_labels = "%b %y", date_breaks = "6 months") +
    theme(plot.title = element_text(hjust = 0.5)) +
  theme(plot.subtitle = element_text(hjust = 0.5)) +
  theme(legend.key.width = unit(2,"cm")) +
  geom_line(aes(y = Xrp['2017-08/'][,5]/100000000,color = 'Xrp')) +
  geom_line(aes(y = Cardano['2017-08/'][,5]/100000000,color = 'Cardano')) + 
  geom_line(aes(y = Tezos['2017-08/'][,5]/100000000,color = 'Tezos')) +
  geom_line(aes(y = Binance_coin['2017-08/'][,5]/100000000,color = 'Binance_coin')) +
  geom_line(aes(y = Eos['2017-08/'][,5]/100000000,color = 'Eos')) +
  geom_line(aes(y = Tether['2017-08/'][,5]/100000000,color = 'Tether')) +
  geom_line(aes(y = Bitcoin_cash['2017-08/'][,5]/100000000,color = 'Bitcoin_cash')) +
  geom_line(aes(y = Stellar['2017-08/'][,5]/100000000,color = 'Stellar')) +
  geom_line(aes(y = Litecoin['2017-08/'][,5]/100000000,color = 'Litecoin')) + 
  geom_line(aes(y = Ethereum['2017-08/'][,5]/100000000,color = 'Ethereum')) +
  geom_line(aes(y = Bitcoin_sv['2017-08/'][,5]/100000000,color = 'Bitcoin_sv'))

As suspected, the graphical representation below proves, that the volume traded of Tether currency in the financial markets was actually higher than that of Bitcoin in the year 2019.

The reasons for the same are later explored in the project and the correlation between market capitalization and volume traded of the two currencies is also scrutinized.

Bitcoin$year = as.numeric(format(index(Bitcoin),"%Y"))
Tether$year = as.numeric(format(index(Tether),"%Y"))

Vol_yrly_BT = aggregate(BitcoinVolume ~ year, data=Bitcoin , FUN= mean)
Vol_yrly_BT$TetherVolume = aggregate(TetherVolume ~ year, data=Tether , FUN= mean)[2]

Vol_yrly_BT$TetherVolume = as.numeric(unlist(Vol_yrly_BT$TetherVolume))

plot_ly(Vol_yrly_BT,x =~year ,y = ~BitcoinVolume, type = 'bar',name = 'Bitcoin Volume',
        marker = list(color = 'rgb(49,130,189)')) %>%
  add_trace(y = ~TetherVolume, name = 'Tether Volume',
            marker = list(color = 'rgb(204,204,204)')) %>%
  layout(title = 'Yearly Volume Traded by Bitcoin & Tether',
         xaxis = list(title = 'Years',tickangle = -45),
         yaxis = list(title = 'Total Volume Traded'),
         margin = list(b=100),
         barmode = 'group')

5. Distribution & Correlation of Volume

In the below graphs we look at the distribution of volume variable of Tether and Bitcoin Currencies. As is evident from the graph, it is a right skewed distribution. Which means they are both positively skewed. The means and Standard Deviations of the Data are also marked.

As it can be seen quite clearly, that mean is a lot lower than the median in both cases. This can mean there are a lot of outliers on the left of the data.

Bitcoin1819 = subset(Bitcoin,year == '2018' | year == '2019')
Tether1819  = subset(Tether,year == '2018' | year == '2019')

ggplot(Bitcoin1819,aes(x = BitcoinVolume/100000000, fill = cut(BitcoinVolume,30))) +
  geom_histogram(show.legend = FALSE,bins = 50,color = 'black') + 
  scale_fill_discrete(h = c(240,10)) + 
  theme_minimal() +
  labs(x = 'Bitcoin Volume', y = 'Frequency',title = 'Bitcoin Volume for 2018-19',
  subtitle = 'in Hundred Millions',caption = "Adi" ) +
  theme(axis.text.x = element_text(angle=65, vjust=0.6)) +
  theme(plot.title = element_text(hjust = 0.5)) +
  theme(plot.subtitle = element_text(hjust = 0.5)) +
  annotate("text", x=303, y=92, label= paste("Mean =",round(mean(Bitcoin1819$BitcoinVolume/100000000),2))) +
  annotate("text", x=303, y=97, label= paste("SD =",round(sd(Bitcoin1819$BitcoinVolume/100000000),2))) +
  annotate("text", x=300, y=87, label= paste("Median =",round(median(Bitcoin1819$BitcoinVolume/100000000),2))) +
  scale_x_continuous(breaks = seq(0, 500, 50)) +
  scale_y_continuous(limits = c(0, 100))+
  geom_vline(aes(xintercept = mean(Bitcoin1819$BitcoinVolume/100000000)), linetype = "dashed")

ggplot(Tether1819,aes(TetherVolume/100000000, fill = cut(TetherVolume,30))) + 
  geom_histogram(show.legend = FALSE,bins = 50,color = 'black',size = .001) + 
  scale_fill_discrete(h = c(240,10)) + 
  theme_minimal() +
  labs(x = 'Tether Volume', y = 'Frequency',title = 'Tether Volume for 2018-19',
  subtitle = 'in Hundred Millions' ) +
  theme(axis.text.x = element_text(angle=65, vjust=0.6)) +
  theme(plot.title = element_text(hjust = 0.5)) +
  theme(plot.subtitle = element_text(hjust = 0.5)) +
  scale_x_continuous(breaks = seq(0, 500, 50)) +
  annotate("text", x=452, y=95, label= paste("Mean =",round(mean(Tether1819$TetherVolume/100000000),2))) +
  annotate("text", x=454, y=100, label= paste("SD =",round(sd(Tether1819$TetherVolume/100000000),2))) +
  annotate("text", x=450, y=90, label= paste("Median =",round(median(Tether1819$TetherVolume/100000000),2))) +
  scale_y_continuous(limits = c(0, 100)) +
  geom_vline(aes(xintercept = mean(Tether1819$TetherVolume/100000000)), linetype = "dashed") 

In the plot below, we examine the correlation between market capitalization and Volume traded for Currencies Tether and Bitcoin. Both Currencies show a positive correlation with Tether showing a higher correlation of 0.77 whereas Bitcoin shows comparatively lower, but still very strong correlation of 0.52 between its Volume Traded and Market Capitalization.

This basically means that the Market Capitalization for currencies (Tether more than Bitcoin) directly influences the volume traded. Which is not very surprising since it is the public sentiment of trust(among other things) which largely influence the market capitalization of a product/company. For example, stock of prices Mordena and other pharmaceutical companies shot up really high when the news of them finding a possible vaccine for Covid-19 came out. Even though there was no proof or conclusive tests in the beginning.

However, we are still looking for the answer to the question as to why the volume traded of Tether is almost similar to Bitcoin even though it is so far behind on all other factors.

ggplot(Tether1819, aes(x=scale(TetherMarket.Cap), y=scale(TetherVolume))) + 
  geom_point() +
  geom_smooth(method=lm, se=FALSE, fullrange=TRUE,color = 'red') + 
  geom_rug()+
  theme(plot.title = element_text(hjust = 0.5)) +
  theme(plot.subtitle = element_text(hjust = 0.5)) +
  labs(x = 'Scaled Tether Market Capatalization ', y = 'Scaled Tether Volume',
       title = 'Tether Volume and Market Capatalization for 2018-19',
       subtitle = 'Scaled',caption = "Adi" ) +
  theme(panel.background = element_rect(colour = "orange",size = 2,linetype = "solid")) +
  annotate("text", x=-1.20, y=4,size = 5, label= paste("Correlation =",
            round(cor(Tether1819$TetherVolume,Tether1819$TetherMarket.Cap),2)))

ggplot(Bitcoin1819, aes(x=scale(BitcoinMarket.Cap), y=scale(BitcoinVolume))) + 
  geom_point() +
  geom_smooth(method=lm, se=FALSE, fullrange=TRUE,color = 'red') + 
  geom_rug()+
  theme(plot.title = element_text(hjust = 0.5)) +
  theme(plot.subtitle = element_text(hjust = 0.5)) +
  labs(x = 'Scaled Bitcoin Market Capatalization ', y = 'Scaled Bitcoin Volume',
       title = 'Bitcoin Volume and Market Capatalization for 2018-19',
       subtitle = 'Scaled',caption = "Adi" ) +
  theme(panel.background = element_rect(colour = 'orange',size = 2, 
                                        linetype = "solid"))+
  annotate("text", x=-1, y=3.7,size = 5, label= paste("Correlation =",
        round(cor(Bitcoin1819$BitcoinVolume,Bitcoin1819$BitcoinMarket.Cap),2)))

The answers to the question above lies in the closing prices of the two currencies as shown in the below graphical representation.

One of the biggest contributing factor to such high confidence levels of trade of Tether is the price volatility of Bitcoin. Notice from the below graph that within two years, Bitcoin’s pricing has gone down from less than 4000 to almost upwards of 18000. However, in case of Tether, the price difference has not been more than a mere 6 cents.

Another reason behind such high volume of trade for Tether is the base price of the stock. The price of Tether is so low that people who are not avid investors and also low risk mutual fund companies who want to get into the digital currency market can get in through Tether without too taking too much risk. This, however also leads to very low reward when compared to Bitcoin as reward is always proportional to the risk factor

However, this does lead to the question as to why Tether and not any other currency with low price volatility and low base price competes with Bitcoin. the answer to this question is that Tether is the only cryptocurrency which is backed by US dollar. No other currency is backed by physical currency, which leads to further investor trust in the stock.

bitcoin_close = plot_ly(as.data.frame(Bitcoin1819),y = ~BitcoinClose, x = ~index(Bitcoin1819), 
        type = 'scatter',mode = 'lines',name = 'Bitcoin Closing Price') %>%
layout(xaxis = list(title = 'Years',tickangle = -45,tickfont = list(size = 20)),
       yaxis = list(title = 'Price Range',tickfont = list(size = 20)))

tether_close = plot_ly(as.data.frame(Tether1819),y = ~TetherClose, x = ~index(Tether1819), 
        type = 'scatter',mode = 'lines',name = 'Tether Closing Price') %>%
    layout(xaxis = list(title = 'Years',tickangle = 45,tickfont = list(size = 20)),
           yaxis = list(title = 'Price Range',tickfont = list(size = 20)))

subplot(bitcoin_close, tether_close) %>% layout(title="Closing Prices of Bitcoin and Tether",font = 20)

6. Central Limit Theorm

The Central limit theorem application is shown by taking 5000 samples of sizes 10, 40 and 100 of Bitcoin volume traded for the last two years. It can be clearly seen that the distributions follows a normal curve with a mean of around 110 (scaled). As the sample size increases, the standard deviation keeps decreasing resulting in a more compact distribution.

xbar10 = c()

for (i in 1:5000) {
  xbar10[i] = mean(sample(x = Bitcoin1819$BitcoinVolume,size = 10,replace = TRUE))
}
xbar10 = as.numeric(unlist(xbar10))

p1 = ggplot(mapping = aes(xbar10/100000000, fill = cut(xbar10,30))) + 
  geom_histogram(show.legend = FALSE,color = 'black',,bins = 30,size = .001) + 
  scale_fill_discrete(h = c(240,10)) + 
  theme_minimal() +
  labs(x = 'Sample Bitcoin Volume', y = 'Frequency',title = 'Sample Bitcoin Volume for 2018-19',
       subtitle = 'in Hundred Millions/ Sample of 10') +
  theme(axis.text.x = element_text(angle=65, vjust=0.6)) +
  theme(plot.title = element_text(hjust = 0.5)) +
  theme(plot.subtitle = element_text(hjust = 0.5)) +
  annotate("text", x=130, y=500, label= paste("Mean =",round(mean(xbar10/100000000),2))) +
  annotate("text", x=130, y=520, label= paste("SD =",round(sd(xbar10/100000000),2)))

xbar40 = c()

for (i in 1:5000) {
  xbar40[i] = mean(sample(x = Bitcoin1819$BitcoinVolume,size = 40,replace = TRUE))
}
xbar40 = as.numeric(unlist(xbar40))

p2 = ggplot(mapping = aes(xbar40/100000000, fill = cut(xbar40,30))) + 
  geom_histogram(show.legend = FALSE,color = 'black',,bins = 30,size = .001) + 
  scale_fill_discrete(h = c(240,10)) + 
  theme_minimal() +
  labs(x = 'Sample Bitcoin Volume', y = 'Frequency',title = 'Sample Bitcoin Volume for 2018-19',
       subtitle = 'in Hundred Millions/ Sample of 40' ) +
  theme(axis.text.x = element_text(angle=65, vjust=0.6)) +
  theme(plot.title = element_text(hjust = 0.5)) +
  theme(plot.subtitle = element_text(hjust = 0.5)) +
  annotate("text", x=130, y=500, label= paste("Mean =",round(mean(xbar40/100000000),2))) +
  annotate("text", x=130, y=520, label= paste("SD =",round(sd(xbar40/100000000),2)))

xbar100 = c()

for (i in 1:5000) {
  xbar100[i] = mean(sample(x = Bitcoin1819$BitcoinVolume,size = 100,replace = TRUE))
}
xbar100 = as.numeric(unlist(xbar100))

p3 = ggplot(mapping = aes(xbar100/100000000, fill = cut(xbar100,30))) + 
  geom_histogram(show.legend = FALSE,color = 'black',,bins = 30,size = .001) + 
  scale_fill_discrete(h = c(240,10)) + 
  theme_minimal() +
  labs(x = 'Sample Bitcoin Volume', y = 'Frequency',title = 'Sample Bitcoin Volume for 2018-19',
       subtitle = 'in Hundred Millions/ Sample of 100' ) +
  theme(axis.text.x = element_text(angle=65, vjust=0.6)) +
  theme(plot.title = element_text(hjust = 0.5)) +
  theme(plot.subtitle = element_text(hjust = 0.5)) +
  annotate("text", x=128, y=500, label= paste("Mean =",round(mean(xbar100/100000000),2))) +
  annotate("text", x=130, y=520, label= paste("SD =",round(sd(xbar100/100000000),2)))

grid.arrange(p1, p2, p3, nrow = 1)

7. Sampling Methods

Random, Systematic, Stratified and Cluster sampling methods are used to analyze the sampling means to the population mean of all currencies volume data. The below plot shows relative difference between different sampling methods and its comparison to the population mean. A sample of 50 values for each currency was taken to ensure equal representation.

set.seed(100)

Currency_list = c("Tezos","Binance_coin","Eos","Bitcoin","Tether","Xrp","Bitcoin_cash",
                  "Stellar","Litecoin","Ethereum","Cardano","Bitcoin_sv")

random_sampling_means = c()
count = 1

for (i in Currency_list){
  random_sampling_means[count] = mean(get(i)[(srswor(50,nrow(get(i)[,5])))!=0,])
  count = count + 1
}

sampling_DF = as.data.frame(random_sampling_means,Currency_list)

# Systematic Sampling
set.seed(100)

N = nrow(Bitcoin)
n = 50
k = floor(N / n)
r = sample(k, 1)
s = seq(r, by = k, length = n)

systematic_sampling_means = c()
count = 1

for (i in Currency_list){
  systematic_sampling_means[count] = mean(get(i)[s,][,5])
  count = count + 1
}
sampling_DF$systematic_sampling_means = systematic_sampling_means

# Stratified Sampling

# add year coloum to whole data to pick 'year'stratas from each currency

freq = table(cd$Currency, cd$year)
st.sizes =as.vector(t(round((595 * freq / sum(freq))))) # 595 so as to get 50 samples for each currency
st.sizes = st.sizes[st.sizes != 0]

st.3 = strata(cd,stratanames = c('Currency','year'),
              size = st.sizes, method = 'srswor',
              description = FALSE)

stratified_sampling_means = getdata(cd, st.3)
stratified_sampling_means = tapply(stratified_sampling_means$Volume, stratified_sampling_means$Currency, mean)
stratified_sampling_means = as.data.frame(stratified_sampling_means)
sampling_DF$stratified_sampling_means = stratified_sampling_means[c(11,1,6,2,10,12,3,9,8,7,5,4),]

# Cluster

cluster_sampling_means = c()

cd$category = sample(LETTERS[1:12],nrow(cd),replace = TRUE)
cluster_data = getdata(cd,(cluster(cd,c('category'),6,'srswor')))

data_Tezos = cluster_data[cluster_data$Currency == 'Tezos',]
sample_Tezos = srswor(50,nrow(data_Tezos))
cluster_sampling_means[1] = mean(data_Tezos[sample_Tezos != 0,][,7])

data_Binance_coin = cluster_data[cluster_data$Currency == 'Binance-coin',]
sample_Binance_coin = srswor(50,nrow(data_Binance_coin))
cluster_sampling_means[2] = mean(data_Binance_coin[sample_Binance_coin != 0,][,7])

data_Eos = cluster_data[cluster_data$Currency == 'Eos',]
sample_Eos = srswor(50,nrow(data_Eos))
cluster_sampling_means[3] = mean(data_Eos[sample_Eos != 0,][,7])

data_Bitcoin = cluster_data[cluster_data$Currency == 'Bitcoin',]
sample_Bitcoin = srswor(50,nrow(data_Bitcoin))
cluster_sampling_means[4] = mean(data_Bitcoin[sample_Bitcoin != 0,][,7])

data_Tether = cluster_data[cluster_data$Currency == 'Tether',]
sample_Tether = srswor(50,nrow(data_Tether))
cluster_sampling_means[5] = mean(data_Tether[sample_Tether != 0,][,7])

data_Xrp = cluster_data[cluster_data$Currency == 'Xrp',]
sample_Xrp = srswor(50,nrow(data_Xrp))
cluster_sampling_means[6] = mean(data_Xrp[sample_Xrp != 0,][,7])

data_Bitcoin_cash = cluster_data[cluster_data$Currency == 'Bitcoin-cash',]
sample_Bitcoin_cash  = srswor(50,nrow(data_Bitcoin_cash))
cluster_sampling_means[7] = mean(data_Bitcoin_cash[sample_Bitcoin_cash != 0,][,7])

data_Stellar = cluster_data[cluster_data$Currency == 'Stellar',]
sample_Stellar = srswor(50,nrow(data_Stellar))
cluster_sampling_means[8] = mean(data_Stellar[sample_Stellar != 0,][,7])

data_Litecoin = cluster_data[cluster_data$Currency == 'Litecoin',]
sample_Litecoin = srswor(50,nrow(data_Litecoin))
cluster_sampling_means[9] = mean(data_Litecoin[sample_Litecoin != 0,][,7])

data_Ethereum = cluster_data[cluster_data$Currency == 'Ethereum',]
sample_Ethereum = srswor(50,nrow(data_Ethereum))
cluster_sampling_means[10] = mean(data_Ethereum[sample_Ethereum != 0,][,7])

data_Cardano = cluster_data[cluster_data$Currency == 'Cardano',]
sample_Cardano = srswor(50,nrow(data_Cardano))
cluster_sampling_means[11] = mean(data_Cardano[sample_Cardano != 0,][,7])

data_Bitcoin_sv = cluster_data[cluster_data$Currency == 'Bitcoin-sv',]
sample_Bitcoin_sv = srswor(50,nrow(data_Bitcoin_sv))
cluster_sampling_means[12] = mean(data_Bitcoin_sv[sample_Bitcoin_sv != 0,][,7])

sampling_DF$cluster_sampling_means = cluster_sampling_means

# Population

population_means = c()
count = 1

for (i in Currency_list){
  population_means[count] = mean(get(i)[,5])
  count = count + 1
}

sampling_DF$population_means = population_means

plot_ly(sampling_DF, x = Currency_list, y = ~random_sampling_means, type = 'bar', 
        name = 'Random Sampling Means',texttemplate = '%{y:.2s}', textposition = 'outside') %>% 
   add_trace(y = ~systematic_sampling_means, name = 'Systematic Means') %>%
   add_trace(y = ~stratified_sampling_means, name = 'Stratified Means') %>%
   add_trace(y = ~cluster_sampling_means, name = 'Cluster Means') %>%
   add_trace(y = ~population_means, name = 'Population Means') %>%
   layout(title = 'Means of Volume by Sampling Methods',xaxis = list(tickangle = 45,
                                                    tickfont = list(size = 20)),
         yaxis = list(title = 'Volume Means',tickfont = list(size = 20)))

sampling_DF$percentage_error_rs = round((abs(sampling_DF$population_means - 
         sampling_DF$random_sampling_means) / sampling_DF$random_sampling_means),4) * 100

sampling_DF$percentage_error_systematic = round((abs(sampling_DF$population_means - 
          sampling_DF$systematic_sampling_means) / sampling_DF$systematic_sampling_means),4) * 100

sampling_DF$percentage_error_stratified = round((abs(sampling_DF$population_means - 
          sampling_DF$stratified_sampling_means) / sampling_DF$stratified_sampling_means),4) * 100

sampling_DF$percentage_error_cluster = round((abs(sampling_DF$population_means - 
          sampling_DF$cluster_sampling_means) / sampling_DF$cluster_sampling_means),4) * 100

Random Sampling -

A sample of 50 is selected out of all rows for each currency (50 rows out of 2412 for each currency) the data is randomly selected irrespective of the years and since the data is very heavily left skewed, the random sampling method produce the least reliable results.

Systematic Sampling -

50 rows of data for each currency is again selected without taking into account the years factor. however, the systematic sampling results seem much better than random sampling as systematic sampling is sequence based which means the lower end and the higher end of data has equal representation. Hence, the years from 2013 to mid of 2017 with very less activity are balanced by the later years of high activity.

Stratified Sampling -

The years factor is taken into consideration in stratified sampling. The results seem on par with systematic sampling and much closer to the population means. The Stratified means seem to be lower than population means for almost currencies except Tether.

Cluster Sampling -

The data was first divided into random clusters, as there were no natural divisions in the dataset. Two-stage cluster sampling method was used. Six random clusters were selected from twelve manually created clusters and from those six, 50 rows of data for each currency was selected to arrive at the Cluster means for the currencies. The results seem to be quite close to the population means.

plot_ly(sampling_DF, x = Currency_list, y = ~percentage_error_rs, type = 'bar', 
        name = 'Random Sampling Error %') %>% 
  add_trace(y = ~percentage_error_systematic, name = 'Systematic Means Error %') %>%
  add_trace(y = ~percentage_error_stratified, name = 'Stratified Means Error %') %>%
  add_trace(y = ~percentage_error_cluster, name = 'Cluster Means Error %') %>%
  layout(title = 'Error % of Sampling Methods',xaxis = list(tickangle = 45,tickfont = list(size = 20)),
         yaxis = list(title = 'Percentage',tickfont = list(size = 20)))

In conclusion it is interesting to see that that the random sampling method on an average seems to be the most inaccurate method of sampling for this dataset. Upon investigation it can be concluded that because the data if of all years and that there was hardly any activity in the digital currency financial markets before mid of 2017, could be the reason for such high inaccuracy compared to other methods.