Academia Datathon: DAB PANDA The A.I. Crypto Trader (Part 2.1)

3. Modeling

1. Prelude to modeling

Initially we look at different models that would be appropriate for the respective price series.

library(astsa)
library(forecast)
orig1 <- orig
orig1[,1]=as.POSIXct(orig[,1])
orig2 <- as.ts(orig1, order.by = more_coins$time)
# functions used
# z=1
# for(q in 0:7){
#   for(p in 0:7){
#     
#     if(p+z+q<=7){
#       model <- arima(x=log(orig$Neo), order = c((p),z,(q)))
#       pval <- Box.test(model$residuals, lag=log(length(model$residuals)))
#       sse <- sum(model$residuals^2)
#       cat(p,d,q,'AIC=', model$aic, ' SSE=',sse,' p-VALUE=', pval$p.value,'\n')
#     }
#   }
# }

Residuals for all coins for model ARIMA (0, 1, 6)

residuals = matrix(nrow = 18752, ncol = 21)
for (i in 2:21){
  order = c(0,1,6)
  model = arima(log(orig2[,i]), order = order)
  residuals[,i] = model$residuals
}
residuals = residuals[,2:21]
# Change column names
colnames(residuals) <- c('Bitcoin', 'Bitcoin Cash', 'Bitcoin Gold', 'Cardano', 'Dash',
                         'Nem', 'Eos', 'Ethereum', 'Ethereum Classic', 'Iota', 'Lisk', 
                         'Litecoin', 'Monero', 'Neo', 'Ripple', 'Stellar', 'Tether',
                         'Tron', 'Zcash', 'Dogecoin')

Plot ACF and PACF of the residuals:

for (i in 1:20){
  acf2((residuals[,i]),main=paste("ACF/PACF of residuals:", colnames(residuals)[i]))
}

Plot ACF and PACF of squared residuals:

for (i in 1:20){
  acf2(((residuals[,i])^2),main=paste("ACF/PACF of squared residuals:", colnames(residuals)[i]))
}

Models with the highest p-values

# bitcoin arima(0,1,6) AIC= -163146.9  SSE= 0.1827101  p-VALUE= 0.8898061
# bitcoin cash arima (0,1,6) AIC= -148875.8  SSE= 0.3909791  p-VALUE= 0.9844488
# bitcoin cash arima (6,1,0) AIC= -148874  SSE= 0.3910169  p-VALUE= 0.9196427
# bitcoin gold arima 5 1 0 AIC= -139988.1  SSE= 0.6280686  p-VALUE= 0.9285041
# bitcoin gold arima 0 1 5 AIC= -139988  SSE= 0.6280735  p-VALUE= 0.9194634
# bitcoin gold arima 0 1 6 AIC= -139987  SSE= 0.6280371  p-VALUE= 0.9671026
# bitcoin gold arima 0 1 6 AIC= -139987  SSE= 0.6280371  p-VALUE= 0.9671026
# cardano arima 0 1 6 AIC= -134310.3  SSE= 0.8500523  p-VALUE= 0.8903308
# cardano arima 0 1 5 AIC= -134311.8  SSE= 0.8500761  p-VALUE= 0.8507009
# cardano arima 5 1 0 AIC= -134311.7  SSE= 0.8500809  p-VALUE= 0.842242 
# cardano arima 6 1 0 AIC= -134310.2  SSE= 0.8500576  p-VALUE= 0.8826964
# dash arima 6 1 0 AIC= -151438.9  SSE= 0.3410233  p-VALUE= 0.0146797
# dash arima 5 1 0 AIC= -151431.9  SSE= 0.3411868  p-VALUE= 0.0004798259
# dash arima 1 1 5 AIC= -151440.4  SSE= 0.3409961  p-VALUE= 0.01534037 
# dash arima 0 1 6 AIC= -151440.8  SSE= 0.3409897  p-VALUE= 0.01704869 
# nem arima 0 1 5 AIC= -128251.3  SSE= 1.174429  p-VALUE= 0.603514
# nem arima 0 1 6 AIC= -128252.5  SSE= 1.174226  p-VALUE= 0.8934795 
# nem arima 6 1 0 AIC= -128253.3  SSE= 1.174176  p-VALUE= 0.9439804
# eos arima 5 1 0 AIC= -141334.1  SSE= 0.5845431  p-VALUE= 0.910631 
# eos arima 6 1 0 AIC= -141332.6  SSE= 0.5845274  p-VALUE= 0.9378108
# eos arima 0 1 5 AIC= -141334.3  SSE= 0.5845383  p-VALUE= 0.9192631 
# eos arima 1 1 5 AIC= -141332.3  SSE= 0.5845389  p-VALUE= 0.9182253 
# eos arima 0 1 6 AIC= -141332.4  SSE= 0.5845351  p-VALUE= 0.9250239
# etherium arima  6 1 0 AIC= -154959.9  SSE= 0.2826508  p-VALUE= 0.1889165
# etherium arima 0 1 6 AIC= -154961  SSE= 0.2826346  p-VALUE= 0.2142195
# etherium classic 0 1 6 AIC= -143172.9  SSE= 0.5298932  p-VALUE= 0.8009095
# etherium classic 6 1 0 AIC= -143171.6  SSE= 0.5299287  p-VALUE= 0.7044136
# iota arima 0 1 6 AIC= -135322.1  SSE= 0.8054028  p-VALUE= 0.8211937
# iota arima 6 1 0 AIC= -135322.1  SSE= 0.8053994  p-VALUE= 0.8354789
# lisk arima 0 1 5 AIC= -133271.1  SSE= 0.8985987  p-VALUE= 0.300508 
# lisk arima 1 1 5 AIC= -133269.2  SSE= 0.8985939  p-VALUE= 0.3066513 
# lisk arima 0 1 6 AIC= -133269.4  SSE= 0.8985846  p-VALUE= 0.3175778
# litecoin arima 0 1 6 AIC= -147684.7  SSE= 0.4165891  p-VALUE= 0.002356966
# monero  arima 0 1 6 AIC= -145422.5  SSE= 0.4700091  p-VALUE= 0.4633666
# neo arima 0 1 6 AIC= -137683.7  SSE= 0.7101156  p-VALUE= 0.2783678
#Dogecoin 6 1 0 AIC= -134235.4  SSE= 0.8534827  p-VALUE= 0.2259134
#Dogecoin 0 1 6 AIC= -134236  SSE= 0.8534515  p-VALUE= 0.2605084
#Zcash 0 1 6 AIC= -147257.9  SSE= 0.4261904  p-VALUE= 0.563043 
#Tron 0 1 6 AIC= -132231.9  SSE= 0.9497042  p-VALUE= 0.07077541
#Tron 5 1 1 AIC= -132232.1  SSE= 0.9496931  p-VALUE= 0.08028114
#Tether 0 1 6 AIC= -144870.1  SSE= 0.4840216  p-VALUE= 0.01319184
#Tether 1 1 5 AIC= -144870.3  SSE= 0.4840165  p-VALUE= 0.0144533
#Tether 3 1 1 AIC= -144874.8  SSE= 0.4840031  p-VALUE= 0.01522452
#Stellar 0 1 6 AIC= -131486.6  SSE= 0.9882045  p-VALUE= 0.9684533
#Ripple 6 1 0 AIC= -137749.8  SSE= 0.7075952  p-VALUE= 0.9969477
#Ripple 1 1 5 AIC= -137748.8  SSE= 0.7076322  p-VALUE= 0.9825528 
#Ripple 0 1 6 AIC= -137749.9  SSE= 0.7075889  p-VALUE= 0.9976909

Code for rolling window for Dash

# x=orig[,6]
# x=log((x))
# mm=list()
# 
# for (i in 1:(length(x)-2016+1)){
#   mm[[i]]=arima(x[i:(i+2015)], order=c(0,1,6))
# }
# f=list()
# ff=rep(0,length(x))
# for (i in 1:(length(x)-2016+1)){
#   f[[i]]=predict(mm[[i]],n.ahead = 1)
#   ff[2016+i]=f[[i]]$pred[1]
# }

par2 <- par(mfrow=c(2, 1))
plot(x,col="blue",type="l",lwd=0.75, main="Dash orginal price series")
plot(ff[2017:length(ff)],col="red",type="l", lwd=0.75, main="Dash prediction price series")
sqrt(mean((x[2017:length(x)]-ff[2017:length(x)])^2))

[1] 0.004110244

# We see a difference in the fifth digit after the decimal point
mean(ff[2017:length(ff)])  # [1] 6.362825

[1] 6.362825

mean(x[2017:length(x)])    # [1] 6.362806

[1] 6.362806

# We see a difference in the fifth third digit after the decimal point
sd(ff[2017:length(ff)])  # [1] 0.2070071

[1] 0.2070071

sd(x[2017:length(x)])    # [1] 0.2069952

[1] 0.2069952