Bitcoins Market

Idris_Rasheed_Bitcoins.Rmd

---
title: "Bitcoins Market"
author: "Idris Rasheed"
date: "August 12, 2017"
output: pdf_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

```{r libraries}
library(tseries)
library(qpcR)
library(readxl)
library(forecast)
```

```{r read data}
Bitcoin <- read_excel("~/R/BITCOINWATCH-MINING.xls")
#Pick specific columns
Bitcoin <- subset(Bitcoin, select = c(Date,Total.BTC))
#Start from latest date to most recent
Bitcoin <- Bitcoin[nrow(Bitcoin):1,]
```

```{r ts}
#Make data into time series object
Bit.ts <- ts(Bitcoin$Total.BTC, start = c(2016,1), 
             end = c(2017,5), 
             frequency = 365)
```

```{r ts plot}
ts.plot(Bit.ts, xlab = "Time", ylab = "Total Bitcoins", main = "Bitcoin Time Series")
```

```{r ori var}
print(paste("Variance of original time series = ", var(Bit.ts)))
print(paste("Mean of original time series = ", mean(Bit.ts)))
```

```{r dif 1 var}
Bit.diff1 <- diff(Bit.ts, lag = 1)
print(paste("Variance differenced at lag 1 = ", var(Bit.diff1)))
print(paste("Mean differenced at lag 1 = ", mean(Bit.diff1)))
```

```{r dif 2 var}
Bit.diff2 <- diff(Bit.ts, lag = 2)
print(paste("Variance differenced at lag 2 = ", var(Bit.diff2)))
print(paste("Mean differenced at lag 2 = ", mean(Bit.diff2)))
```

```{r dif plot}
op <- par(mfrow = c(1,2))
ts.plot(Bit.diff1, main = 'Detrended Time Series', ylab = 'Total Bitcoins', xlab = 'Time')
ts.plot(Bit.ts, xlab = "Time", ylab = "Total Bitcoins", main = "Original Time Series")
par(op)
```

ACF and PACF
```{r acf}
#Plot ACF and PACF side by side
op <- par(mfrow = c(1,2))
acf(Bit.diff1, lag.max=20)
pacf(Bit.diff1, lag.max=20)
par(op)
```

```{r fit1}
fit1 <- arima(diff(Bit.ts), order=c(5,1,1))
fit1
print(paste("AICC =", AICc(fit1)))
```

```{r fit2}
fit2 <- arima(diff(Bit.ts), order=c(6,1,1)) 
fit2
print(paste("AICC =", AICc(fit2)))
```

```{r orders}
p = 6
q = 1
h = length(Bit.diff1)
lag = floor(sqrt(h))
```

```{r box-pierce}
#Box-Pierce test
Box.test(residuals(fit2), lag = lag, type = c("Box-Pierce"), fitdf = p+q)
```

```{r box-test}
#Box-Ljung test
Box.test(residuals(fit2), type="Ljung", lag = lag, fitdf = p+q)
```

```{r ljung}
#McLeod-Li test: Ljung-Box for squares
Box.test(residuals(fit2)^2,lag = lag, fitdf = p + q, type = "Ljung-Box")
```

```{r shapiro}
#Normality test
shapiro.test(residuals(fit2))
```

```{r resid ts}
ts.plot(residuals(fit2),main = "Fitted Residuals")
```

```{r dia}
par(mfrow=c(1,2),oma=c(0,0,2,0))
# Plot diagnostics of residuals
op <- par(mfrow=c(2,2))
# acf
acf(residuals(fit2),main = "Autocorrelation")
# pacf
pacf(residuals(fit2),main = "Partial Autocorrelation")
# Histogram
hist(residuals(fit2),main = "Histogram")
# q-q plot
qqnorm(residuals(fit2))
qqline(residuals(fit2),col ="purple")
# Add overall title
title("Fitted Residuals Diagnostics", outer=TRUE)
```

```{r stat}
op <- par(mfrow = c(1,2))
setwd('C:/Users/Aquaria/Documents/R') # path of your working directory
source("plot.roots.R.txt") # read source file from Gaucho Space
#Plot coefficients on unit circle
plot.roots(NULL,polyroot(c(-0.7775,-0.5994, -0.4469, -0.3137, -0.1971, -0.0946)), main="Roots of AR Part")
plot.roots(NULL,polyroot(c(-1)), main="Roots of MA Part")
par(op)
```

```{r Forecast}
#Forecast 20 days into the future
forecast <- forecast(Bit.ts,20)
plot(forecast, main = "Bitcoin Forecast", 
     ylab = "Total Bitcoins", 
     xlab = "Time")
```