BitCoin - Analysis
5/2/2018
Overview of Bitcoin data analysis using GARCH
library(ggplot2)
library(caTools)
library(dygraphs)
library(xts)
library(forecast)
library(fGarch)
library(tseries)Importing Data
getwd()## [1] "C:/Users/abhil/Desktop/Rfiles"setwd ("C:/Users/abhil/Desktop/Rfiles")
data=read.csv("BTC_USD Bitfinex Historical Data.csv", header = TRUE)Dropping price and change for candlestick chart.
df=data
df =df[,-c(2,7)]
# Formating Dates.
df=xts(df[,-1],order.by=as.Date(df[,1],"%m/%d/%Y"))
# Creating candlestick chart.
m <- head(df, n=39)
dygraph(m) %>%
dyCandlestick()da=data.frame(data$Date,data$Price)
class(da$data.Price)## [1] "integer"da$data.Date = as.Date(da$data.Date, '%m/%d/%Y')
ggplot(data=da, aes(data.Date,as.numeric(data.Price))) + geom_line()
## TimeSeries Plot
The data will be skewed data. There is so much variance/volatility coming towards the end.
da$logPrice= log(as.numeric(da$data.Price))
ggplot(data=da, aes(data.Date,as.numeric(logPrice))) + geom_line()
# log of price
(Trying to make teh data stationary using various methods)
da$sqrt= sqrt(da$logPrice)
ggplot(data=da, aes(data.Date,as.numeric(sqrt))) + geom_line()
#SQRT of LogPrice
since there is still a lot of raneg in y axis, let us use the square root function to the data
diffPrice=diff(da$logPrice)
newFrame=da[-c(1),]
acf(diffPrice)
ggplot(data=newFrame, aes(data.Date,diffPrice)) + geom_line()
# diff of sqrt
Using diff once makes the data more stationary.
adf.test(diffPrice)##
## Augmented Dickey-Fuller Test
##
## data: diffPrice
## Dickey-Fuller = -11.304, Lag order = 11, p-value = 0.01
## alternative hypothesis: stationaryThe data is Stationary
fit1 = auto.arima(da$sqrt, trace = TRUE, test = "kpss", ic = "bic")##
## Fitting models using approximations to speed things up...
##
## ARIMA(2,2,2) : Inf
## ARIMA(0,2,0) : -9484.479
## ARIMA(1,2,0) : -9928.875
## ARIMA(0,2,1) : -10592.62
## ARIMA(1,2,1) : -10588.41
## ARIMA(0,2,2) : -10590.17
## ARIMA(1,2,2) : -10583.28
##
## Now re-fitting the best model(s) without approximations...
##
## ARIMA(0,2,1) : Inf
## ARIMA(0,2,2) : Inf
## ARIMA(1,2,1) : Inf
## ARIMA(1,2,2) : Inf
## ARIMA(1,2,0) : -9947.43
##
## Best model: ARIMA(1,2,0)Box.test(fit1$residuals, lag = 12, type = "Ljung-Box")##
## Box-Ljung test
##
## data: fit1$residuals
## X-squared = 286.35, df = 12, p-value < 2.2e-16acf(fit1$residuals^2)
tsdisplay(fit1$residuals)
tsdiag(fit1)
#### Model arima(1,0) will be selecte dfor GARCH analysis and the diff data is used for GARCH analysis
# garch effect is there
model=garchFit(~arma(1,0)+garch(1,1), data=diff(da$sqrt), trace=F, cond.dist ='std')
summary (model)##
## Title:
## GARCH Modelling
##
## Call:
## garchFit(formula = ~arma(1, 0) + garch(1, 1), data = diff(da$sqrt),
## cond.dist = "std", trace = F)
##
## Mean and Variance Equation:
## data ~ arma(1, 0) + garch(1, 1)
## <environment: 0x0000000024554e58>
## [data = diff(da$sqrt)]
##
## Conditional Distribution:
## std
##
## Coefficient(s):
## mu ar1 omega alpha1 beta1
## 3.0929e-04 -4.6090e-02 1.1145e-06 2.6999e-01 8.2504e-01
## shape
## 2.7921e+00
##
## Std. Errors:
## based on Hessian
##
## Error Analysis:
## Estimate Std. Error t value Pr(>|t|)
## mu 3.093e-04 1.043e-04 2.965 0.00303 **
## ar1 -4.609e-02 2.444e-02 -1.886 0.05928 .
## omega 1.115e-06 4.805e-07 2.320 0.02037 *
## alpha1 2.700e-01 6.277e-02 4.301 1.7e-05 ***
## beta1 8.250e-01 2.230e-02 36.999 < 2e-16 ***
## shape 2.792e+00 2.374e-01 11.761 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Log Likelihood:
## 5714.605 normalized: 3.65384
##
## Description:
## Thu May 03 15:22:46 2018 by user: abhil
##
##
## Standardised Residuals Tests:
## Statistic p-Value
## Jarque-Bera Test R Chi^2 79774.68 0
## Shapiro-Wilk Test R W 0.8556633 0
## Ljung-Box Test R Q(10) 34.47074 0.0001536681
## Ljung-Box Test R Q(15) 40.46234 0.0003860302
## Ljung-Box Test R Q(20) 49.06471 0.0003010221
## Ljung-Box Test R^2 Q(10) 5.440571 0.8598744
## Ljung-Box Test R^2 Q(15) 5.83996 0.9823124
## Ljung-Box Test R^2 Q(20) 6.275422 0.9984708
## LM Arch Test R TR^2 5.556593 0.9367664
##
## Information Criterion Statistics:
## AIC BIC SIC HQIC
## -7.300007 -7.279464 -7.300036 -7.292370resid=residuals(model, standardize=T)
Box.test(resid)##
## Box-Pierce test
##
## data: resid
## X-squared = 7.7622, df = 1, p-value = 0.005335plot(resid,type='l', main="Residual plot for model") 
Box.test(resid^2)##
## Box-Pierce test
##
## data: resid^2
## X-squared = 7.3318e-07, df = 1, p-value = 0.9993tsdisplay(resid^2)
#### The variables are significant with an AIC of -7.3
pred=predict(model,n.ahead=15,plot=TRUE,crit_val =1)
#plot(forecast(fit1),xlab="Year",ylab="Stock Value")The plot above shows the upper limit, lower limit and the mean values for the differenced data
tail(diff(da$sqrt))## [1] -0.0136927260 0.0073169573 -0.0065344133 0.0077066686 0.0009526415
## [6] -0.0028217341lowerbound = pred$lowerInterval
lowpred = diffinv(lowerbound, xi= 3.021804)
lowpred## [1] 3.021804 3.013562 3.004697 2.995356 2.985512 2.975145 2.964232
## [8] 2.952751 2.940679 2.927988 2.914654 2.900648 2.885941 2.870501
## [15] 2.854297 2.837294actuallow = exp(lowpred^2)
actuallow## [1] 9240.021 8791.655 8334.901 7880.600 7430.009 6984.753 6546.400
## [8] 6116.467 5696.404 5287.583 4891.284 4508.683 4140.841 3788.693
## [15] 3453.040 3134.540midbound = pred$meanForecast
valpred = diffinv(midbound, xi= 3.021804)
valpred## [1] 3.021804 3.022243 3.022532 3.022828 3.023124 3.023420 3.023715
## [8] 3.024011 3.024307 3.024602 3.024898 3.025194 3.025489 3.025785
## [15] 3.026081 3.026376actualval = exp(valpred^2)
actualval## [1] 9240.021 9264.590 9280.791 9297.411 9314.045 9330.711 9347.409
## [8] 9364.138 9380.898 9397.690 9414.514 9431.370 9448.257 9465.177
## [15] 9482.128 9499.112upperbound = pred$upperInterval
uppred = diffinv(upperbound, xi= 3.021804)
uppred## [1] 3.021804 3.030924 3.040367 3.050300 3.060736 3.071695 3.083199
## [8] 3.095271 3.107935 3.121216 3.135142 3.149739 3.165038 3.181069
## [15] 3.197864 3.215459actualup = exp(uppred^2)
actualup## [1] 9240.021 9764.436 10340.601 10985.512 11708.900 12522.836 13441.669
## [8] 14482.567 15666.163 17017.378 18566.477 20350.405 22414.531 24814.893
## [15] 27621.152 30920.465The inverse differenced values are calculated as above
actPrice = data$Price[1300:length(data$Price)]
lPrice = c(actPrice,actuallow)
mPrice=c(actPrice,actualval)
hPrice=(c(actPrice,actualup))
plot.ts(lPrice, main="Forecast plot for Bitcoin for 20 days",col="red")
lines(1:length(hPrice),hPrice,col="Green")
lines(1:length(mPrice),mPrice,col="Blue")
## The forecast values are shown above with the original values. The lower bound and upper bound indicate the range in which the forecast value smight fall.