Factors that influence the volatility of stock prices

cvfitABSalpha0.2<-cv.biglasso(finalcut, yABS, alpha = 0.2)

elasticnetABSalpha0.2 <- biglasso(finalcut, yABS, alpha = 0.2 , lambda = cvfitABSalpha0.2$lambda.min)

cvfitABSalpha0.3<-cv.biglasso(finalcut, yABS, alpha = 0.3)

elasticnetABSalpha0.3 <- biglasso(finalcut, yABS, alpha = 0.3 , lambda = cvfitABSalpha0.3$lambda.min)

cvfitABSalpha0.4<-cv.biglasso(finalcut, yABS, alpha = 0.4)

elasticnetABSalpha0.4 <- biglasso(finalcut, yABS, alpha = 0.4 , lambda = cvfitABSalpha0.4$lambda.min)

cvfitABSalpha0<-cv.biglasso(finalcut, yABS, alpha = 0)

elasticnetABSalpha0 <- biglasso(finalcut, yABS, alpha = 0 , lambda = cvfitABSalpha0$lambda.min)

cvfitABSalpha0.6<-cv.biglasso(finalcut, yABS, alpha = 0.6)

elasticnetABSalpha0.6 <- biglasso(finalcut, yABS, alpha = 0.6 , lambda = cvfitABSalpha0.6$lambda.min)

cvfitABSalpha0.7<-cv.biglasso(finalcut, yABS, alpha = 0.7)

elasticnetABSalpha0.7 <- biglasso(finalcut, yABS, alpha = 0.7 , lambda = cvfitABSalpha0.7$lambda.min)

cvfitABSalpha0.8<-cv.biglasso(finalcut, yABS, alpha = 0.8)

elasticnetABSalpha0.8 <- biglasso(finalcut, yABS, alpha = 0.8 , lambda = cvfitABSalpha0.8$lambda.min)

cvfitABSalpha0.9<-cv.biglasso(finalcut, yABS, alpha = 0.9)

elasticnetABSalpha0.9 <- biglasso(finalcut, yABS, alpha = 0.9 , lambda = cvfitABSalpha0.9$lambda.min)

cvfitABSalpha1<-cv.biglasso(finalcut, yABS, alpha = 1)

elasticnetABSalpha1 <- biglasso(finalcut, yABS, alpha = 1 , lambda = cvfitABSalpha1$lambda.min)

ELASTICNETbetaABS=matrix(nrow=357, ncol=11)

ELASTICNETbetaABS[,1] <- elasticnetABSalpha0$beta[,1]

ELASTICNETbetaABS[,2] <- elasticnetABSalpha0.1$beta[,1]

ELASTICNETbetaABS[,3]<- elasticnetABSalpha0.2$beta[,1]

ELASTICNETbetaABS[,4] <- elasticnetABSalpha0.3$beta[,1]

ELASTICNETbetaABS[,5] <- elasticnetABSalpha0.4$beta[,1]

ELASTICNETbetaABS[,6] <- elasticnetABS$beta[,1]

ELASTICNETbetaABS[,7]<- elasticnetABSalpha0.6$beta[,1]

ELASTICNETbetaABS[,8] <- elasticnetABSalpha0.7$beta[,1]

ELASTICNETbetaABS[,9] <- elasticnetABSalpha0.8$beta[,1]

ELASTICNETbetaABS[,10] <- elasticnetABSalpha0.9$beta[,1]

ELASTICNETbetaABS[,11] <- elasticnetABSalpha1$beta[,1]

cvfitSQ <- cv.biglasso(finalcut,ySQ, eval.metric = c("default", "MAPE"), alpha = 0.5)

elasticnetSQ <- biglasso(finalcut, ySQ, penalty = c("enet"), alpha = 0.5, lambda = cvfitSQ$lambda.min)

cvfitSQalpha0.1<- cv.biglasso(finalcut, ySQ, eval.metric = c("default"), alpha = 0.1)

elasticnetSQalpha0.1 <- biglasso(finalcut, ySQ, alpha = 0.1 , lambda = cvfitSQalpha0.1$lambda.min)

cvfitSQalpha0.2<-cv.biglasso(finalcut, ySQ, alpha = 0.2)

elasticnetSQalpha0.2 <- biglasso(finalcut, ySQ, alpha = 0.2 , lambda = cvfitSQalpha0.2$lambda.min)

cvfitSQalpha0.3<-cv.biglasso(finalcut, ySQ, alpha = 0.3)

elasticnetSQalpha0.3 <- biglasso(finalcut, ySQ, alpha = 0.3 , lambda = cvfitSQalpha0.3$lambda.min)

cvfitSQalpha0.4<-cv.biglasso(finalcut, ySQ, alpha = 0.4)

elasticnetSQalpha0.4 <- biglasso(finalcut, ySQ, alpha = 0.4 , lambda = cvfitSQalpha0.4$lambda.min)

cvfitSQalpha0<-cv.biglasso(finalcut, ySQ, alpha = 0)

elasticnetSQalpha0 <- biglasso(finalcut, ySQ, alpha = 0 , lambda = cvfitSQalpha0$lambda.min)

cvfitSQalpha0.6<-cv.biglasso(finalcut, ySQ, alpha = 0.6)

elasticnetSQalpha0.6 <- biglasso(finalcut, ySQ, alpha = 0.6 , lambda = cvfitSQalpha0.6$lambda.min)

cvfitSQalpha0.7<-cv.biglasso(finalcut, ySQ, alpha = 0.7)

elasticnetSQalpha0.7 <- biglasso(finalcut, ySQ, alpha = 0.7 , lambda = cvfitSQalpha0.7$lambda.min)

cvfitSQalpha0.8<-cv.biglasso(finalcut, ySQ, alpha = 0.8)

elasticnetSQalpha0.8 <- biglasso(finalcut, ySQ, alpha = 0.8 , lambda = cvfitSQalpha0.8$lambda.min)

cvfitSQalpha0.9<-cv.biglasso(finalcut, ySQ, alpha = 0.9)

elasticnetSQalpha0.9 <- biglasso(finalcut, ySQ, alpha = 0.9 , lambda = cvfitSQalpha0.9$lambda.min)

cvfitSQalpha1<-cv.biglasso(finalcut, ySQ, alpha = 1)

elasticnetSQalpha1 <- biglasso(finalcut, ySQ, alpha = 1 , lambda = cvfitSQalpha1$lambda.min)

ELASTICNETbetaSQ=matrix(nrow=357, ncol=11)

ELASTICNETbetaSQ[,1] <- elasticnetSQalpha0$beta[,1]

ELASTICNETbetaSQ[,2] <- elasticnetSQalpha0.1$beta[,1]

ELASTICNETbetaSQ[,3]<- elasticnetSQalpha0.2$beta[,1]

ELASTICNETbetaSQ[,4] <- elasticnetSQalpha0.3$beta[,1]

ELASTICNETbetaSQ[,5] <- elasticnetSQalpha0.4$beta[,1]

ELASTICNETbetaSQ[,6] <- elasticnetSQ$beta[,1]

ELASTICNETbetaSQ[,7]<- elasticnetSQalpha0.6$beta[,1]

ELASTICNETbetaSQ[,8] <- elasticnetSQalpha0.7$beta[,1]

ELASTICNETbetaSQ[,9] <- elasticnetSQalpha0.8$beta[,1]

ELASTICNETbetaSQ[,10] <- elasticnetSQalpha0.9$beta[,1]

ELASTICNETbetaSQ[,11] <- elasticnetSQalpha1$beta[,1]

cvfitRB <- cv.biglasso(finalcut,yRB, eval.metric = c("default", "MAPE"), alpha = 0.5)

elasticnetRB <- biglasso(finalcut, yRB, penalty = c("enet"), alpha = 0.5, lambda = cvfitRB$lambda.min)

cvfitRBalpha0.1<-cv.biglasso(finalcut, yRB, alpha = 0.1)

elasticnetRBalpha0.1 <- biglasso(finalcut, yRB, alpha = 0.1 , lambda = cvfitRBalpha0.1$lambda.min)

cvfitABSalpha0.2<-cv.biglasso(finalcut, yABS, alpha = 0.2)

elasticnetRBalpha0.2 <- biglasso(finalcut, yRB, alpha = 0.2 , lambda = cvfitRBalpha0.2$lambda.min)

cvfitRBalpha0.3<-cv.biglasso(finalcut, yRB, alpha = 0.3)

elasticnetRBalpha0.3 <- biglasso(finalcut, yRB, alpha = 0.3 , lambda = cvfitRBalpha0.3$lambda.min)

cvfitRBalpha0.4<-cv.biglasso(finalcut, yRB, alpha = 0.4)

elasticnetRBalpha0.4 <- biglasso(finalcut, yRB, alpha = 0.4 , lambda = cvfitRBalpha0.4$lambda.min)

cvfitRBalpha0<-cv.biglasso(finalcut, yRB, alpha = 0)

elasticnetRBalpha0 <- biglasso(finalcut, yRB, alpha = 0 , lambda = cvfitRBalpha0$lambda.min)

cvfitRBalpha0.6<-cv.biglasso(finalcut, yRB, alpha = 0.6)

elasticnetRBalpha0.6 <- biglasso(finalcut, yRB, alpha = 0.6 , lambda = cvfitRBalpha0.6$lambda.min)

cvfitRBalpha0.7<-cv.biglasso(finalcut, yRB, alpha = 0.7)

elasticnetRBalpha0.7 <- biglasso(finalcut, yRB, alpha = 0.7 , lambda = cvfitRBalpha0.7$lambda.min)

cvfitRBalpha0.8<-cv.biglasso(finalcut, yRB, alpha = 0.8)

elasticnetRBalpha0.8 <- biglasso(finalcut, yRB, alpha = 0.8 , lambda = cvfitRBalpha0.8$lambda.min)

cvfitRBalpha0.9<-cv.biglasso(finalcut, yRB, alpha = 0.9)

elasticnetRBalpha0.9 <- biglasso(finalcut, yRB, alpha = 0.9 , lambda = cvfitRBalpha0.9$lambda.min)

cvfitRBalpha1<-cv.biglasso(finalcut, yRB, alpha = 1)

elasticnetRBalpha1 <- biglasso(finalcut, yRB, alpha = 1 , lambda = cvfitRBalpha1$lambda.min)

ELASTICNETbetaRB = matrix(nrow=357, ncol=11)

ELASTICNETbetaRB[,1] <- elasticnetRBalpha0$beta[,1]

ELASTICNETbetaRB[,2] <- elasticnetRBalpha0.1$beta[,1]

ELASTICNETbetaRB[,3]<- elasticnetRBalpha0.2$beta[,1]

ELASTICNETbetaRB[,4] <- elasticnetRBalpha0.3$beta[,1]

ELASTICNETbetaRB[,5] <- elasticnetRBalpha0.4$beta[,1]

ELASTICNETbetaRB[,6] <- elasticnetRB$beta[,1]

ELASTICNETbetaRB[,7]<- elasticnetRBalpha0.6$beta[,1]

ELASTICNETbetaRB[,8] <- elasticnetRBalpha0.7$beta[,1]

ELASTICNETbetaRB[,9] <- elasticnetRBalpha0.8$beta[,1]

ELASTICNETbetaRB[,10] <- elasticnetRBalpha0.9$beta[,1]

ELASTICNETbetaRB[,11] <- elasticnetRBalpha1$beta[,1]

grid <- seq( from = 0, to = 1, by = 0.1)

colnames(ELASTICNETbetaABS) <- grid

Intercept <- data.frame(filtered_names="INTERCEPT",filtered_class= 0)

names <- rbind(Intercept,names_f)

rownames(ELASTICNETbetaABS) <- names$filtered_names

colnames(ELASTICNETbetaSQ) <- grid

rownames(ELASTICNETbetaSQ) <- names$filtered_names

colnames(ELASTICNETbetaRB) <- grid

rownames(ELASTICNETbetaRB) <- names$filtered_names

colnames(ELASTICNETbetaVAR) <- grid

rownames(ELASTICNETbetaVAR) <- names$filtered_names

library(ddalpha)

library(caret)

library(lars)

library(tidyverse)

#larscvABS <- trainControl(finalcut, yABS , method = "lars")

print(lars)

#Linear Regression with Stepwise Selection (method = 'leapSeq')

#Linear Regression with Forward Selection (method = 'leapForward')

#Least Angle Regression (method = 'lars')For regression using package lars with tuning parameters:Fraction (fraction)

#Least Angle Regression (method = 'lars2') For regression using package lars with tuning parameters:Number of Steps (step)

ctrl <- trainControl(method = "cv", savePred=T, number=T)

#fold.ids <- createMultiFolds(yABS,k=10,times=3)

#fitControl <- trainControl(method = "repeatedcv", number = 10,repeats = 3,returnResamp = "final",index = fold.ids,summaryFunction = defaultSummary,selectionFunction = "oneSE")

yandxABC <- cbind(yABS, finalcutNOTBIG)

yandxABC <- as.data.frame(lapply(yandxABC, function(x) as.numeric(as.character(x))))

yandxSQ <- cbind(ySQ, finalcutNOTBIG)

yandxSQ <- as.data.frame(lapply(yandxSQ, function(x) as.numeric(as.character(x))))

yandxVAR <- cbind(yVARna, finalcutNOTBIGVAR)

yandxVAR <- as.data.frame(lapply(yandxVAR, function(x) as.numeric(as.character(x))))

yandxRB <- cbind(yRB, finalcutNOTBIG)

yandxRB <- as.data.frame(lapply(yandxRB, function(x) as.numeric(as.character(x))))

#ctrl <- trainControl(method = "cv", savePred=T, number=T)

library(xgboost)

set.seed(100) # For reproducibility

inTrainABS <- createDataPartition(y = yandxABC$weekly.returns, list = FALSE) #p = 0.8

trainingABS <- yandxABC[inTrainABS, ]

testingABS <- yandxABC[-inTrainABS,]

#for ABS

X_trainABS = xgb.DMatrix(as.matrix(trainingABS %>% select(-weekly.returns)))

y_trainABS = trainingABS$weekly.returns

X_testABS = xgb.DMatrix(as.matrix(testingABS %>% select(-weekly.returns)))

y_testABS = testingABS$weekly.returns

xgb_trcontrol = trainControl(method = "cv",number = 5,allowParallel = TRUE,verboseIter = FALSE,returnData = FALSE, initialWindow = 240,

horizon = 1,

fixedWindow = FALSE)

# by default parameters

xgbGrid <- expand.grid(nrounds = c(200), max_depth = c(15), colsample_bytree = (0.6),eta = 0.1, gamma=0, min_child_weight = 1,subsample = 1)

xgb_modelABS = train( X_trainABS, y_trainABS,trControl = xgb_trcontrol,tuneGrid = xgbGrid, method = "xgbTree")

#best valuesfor hyperparameters

xgb_modelABS$bestTune

xgbGridbest <- expand.grid(nrounds = 200, max_depth = 15, colsample_bytree = 0.6,eta = 0.1, gamma=0, min_child_weight = 1,subsample = 1)

xgb_modelABSbest = train( X_trainABS, y_trainABS,trControl = xgb_trcontrol,tuneGrid = xgbGridbest, method = "xgbTree")

predictedABS = predict(xgb_modelABS, X_testABS) #or

#predictedABS = predict(xgb_modelbestABS, X_testABS)

residualsABS = y_testABS - predictedABS

RMSEabs = sqrt(mean(residualsABS^2))

cat('The root mean square error of the test data is ', round(RMSEabs,3),'\n')

#the root mean square error of the test data is 353.346

y_test_meanABS = mean(y_testABS)

# Calculate total sum of squares

tssABS = sum((y_testABS - y_test_meanABS)^2 )

# Calculate residual sum of squares

rssABS = sum(residualsABS^2)

# Calculate R-squared

rsqABS = 1 - (rssABS/tssABS)

cat('The R-square of the test data is ', round(rsqABS,3), '\n')

#The R-square of the test data is 0.129

#PLOT ACTUAL WITH PREDICTED

options(repr.plot.width=8, repr.plot.height=4)

my_dataABS = as.data.frame(cbind(predicted = predictedABS,

observed = y_testABS))

# Plot predictions vs test data

ggplot(my_dataABS,aes(predicted, observed)) + geom_point(color = "darkred", alpha = 0.5) +

geom_smooth(method=lm)+ ggtitle('Linear Regression ') + ggtitle("Extreme Gradient Boosting: Prediction vs Test Data") +

xlab("Predecited Volatility ") + ylab("Observed Volatility") +

theme(plot.title = element_text(color="darkgreen",size=16,hjust = 0.5),

axis.text.y = element_text(size=12), axis.text.x = element_text(size=12,hjust=.5),

axis.title.x = element_text(size=14), axis.title.y = element_text(size=14))

#OR IF XGBLINEAR

xgbGrid <- expand.grid(nrounds = c(100,200), lambda=0,eta = 0.1, alpha=1)

xgbABSlin_model = train( X_trainABS, y_trainABS,trControl = xgb_trcontrol,tuneGrid = xgbGrid, label = TRUE,method = "xgbLinear")

xgbABSlin_model$bestTune

#xgbABSlinGridbest <- expand.grid(nrounds = 200, lambda = 0 , eta = 0.1, alpha =1 )

#xgb_modelABSlinbest = train( X_trainABS, y_trainABS,trControl = xgb_trcontrol,tuneGrid = xgbABSlinGridbest, method = "xgbLinear")

predictedABSlin = predict(xgbABSlin_model, X_testABS) #or

#predictedABSlin = predict(xgb_modelbestABSlinbest, X_testABS)

residualsABSlin = y_testABS - predictedABSlin

RMSEabslin = sqrt(mean(residualsABSlin^2))

cat('The root mean square error of the test data is ', round(RMSEabslin,3),'\n')

#the root mean square error of the test data is 148.203

y_test_meanABS = mean(y_testABS)

# Calculate total sum of squares

tssABS = sum((y_testABS - y_test_meanABS)^2 )

# Calculate residual sum of squares

rssABSlin = sum(residualsABSlin^2)

# Calculate R-squared

rsqABSlin = 1 - (rssABS/tssABS)

cat('The R-square of the test data is ', round(rsqABSlin,3),'\n')

#The R-square of the test data is 0.847

#PLOT ACTUAL WITH PREDICTED

options(repr.plot.width=8, repr.plot.height=4)

my_dataABSlin = as.data.frame(cbind(predicted = predictedABSlin,

observed = y_testABS))

# Plot predictions vs test data

ggplot(my_dataABSlin,aes(predicted, observed)) + geom_point(color = "darkred", alpha = 0.5) +

geom_smooth(method=lm)+ ggtitle('Linear Regression ') + ggtitle("Extreme Gradient Boosting: Prediction vs Test Data") +

xlab("Predecited Volatility ") + ylab("Observed Volatility") +

theme(plot.title = element_text(color="darkgreen",size=16,hjust = 0.5),

axis.text.y = element_text(size=12), axis.text.x = element_text(size=12,hjust=.5),

axis.title.x = element_text(size=14), axis.title.y = element_text(size=14))

#for SQ

inTrainSQ <- createDataPartition(y = yandxSQ$weekly.returns, list = FALSE) #p = 0.8

trainingSQ <- yandxSQ[inTrainSQ, ]

testingSQ <- yandxSQ[-inTrainSQ,]

X_trainSQ = xgb.DMatrix(as.matrix(trainingSQ %>% select(-weekly.returns)))

y_trainSQ = trainingSQ$weekly.returns

X_testSQ = xgb.DMatrix(as.matrix(testingSQ %>% select(-weekly.returns)))

y_testSQ = testingSQ$weekly.returns

xgb_trcontrol = trainControl(method = "cv",number = 5,allowParallel = TRUE,verboseIter = FALSE,returnData = FALSE)

# by default parameters

xgbGrid <- expand.grid(nrounds = c(100,200), max_depth = c(10, 15, 20, 25), colsample_bytree = seq(0.5, 0.9, length.out = 5),eta = 0.1, gamma=0, min_child_weight = 1,subsample = 1)

xgb_modelSQ = train( X_trainSQ, y_trainSQ,trControl = xgb_trcontrol,tuneGrid = xgbGrid, method = "xgbTree", label = yandxABC$s)

#best valuesfor hyperparameters

xgb_modelSQ$bestTune #

xgbGridbest <- expand.grid(nrounds = c(200), max_depth = c(10), colsample_bytree = seq(0.8),eta = 0.1, gamma=0, min_child_weight = 1,subsample = 1)

xgb_modelSQbest = train( X_trainSQ, y_trainSQ,trControl = xgb_trcontrol,tuneGrid = xgbGridbest, method = "xgbTree")

predictedSQ = predict(xgb_modelSQ, X_testSQ) #or

#predictedSQ = predict(xgb_modelSQbest, X_testSQ)

residualsSQ = y_testSQ - predictedSQ

RMSEsq = sqrt(mean(residualsSQ^2))

cat('The root mean square error of the test data is ', round(RMSEsq,3),'\n')

#the root mean square error of the test data is 0.002

y_test_meanSQ = mean(y_testSQ)

# Calculate total sum of squares

tssSQ = sum((y_testSQ - y_test_meanSQ)^2 )

# Calculate residual sum of squares

rssSQ = sum(residualsSQ^2)

# Calculate R-squared

rsqSQ = 1 - (rssSQ/tssSQ)

cat('The R-square of the test data is ', round(rsqSQ,3), '\n')

#The R-square of the test data is 0.151

#PLOT ACTUAL WITH PREDICTED

options(repr.plot.width=8, repr.plot.height=4)

my_dataSQ = as.data.frame(cbind(predicted = predictedSQ,

observed = y_testSQ))

# Plot predictions vs test data

ggplot(my_dataSQ,aes(predicted, observed)) + geom_point(color = "darkred", alpha = 0.5) +

geom_smooth(method=lm)+ ggtitle('Linear Regression ') + ggtitle("Extreme Gradient Boosting: Prediction vs Test Data") +

xlab("Predecited Volatility ") + ylab("Observed Volatility") +

theme(plot.title = element_text(color="darkgreen",size=16,hjust = 0.5),

axis.text.y = element_text(size=12), axis.text.x = element_text(size=12,hjust=.5),

axis.title.x = element_text(size=14), axis.title.y = element_text(size=14))

#OR IF XGBLINEAR

xgbGrid <- expand.grid(nrounds = c(100,200), lambda=0,eta = 0.1, alpha=1)

xgbSQlin_model = train( X_trainSQ, y_trainSQ,trControl = xgb_trcontrol,tuneGrid = xgbGrid, method = "xgbLinear")

xgbSQlin_model$bestTune

#xgbSQlinGridbest <- expand.grid(nrounds = 100, lambda =0 , eta = 0.1, alpha =1 )

#xgb_modelSQlinbest = train( X_trainABS, y_trainABS,trControl = xgb_trcontrol,tuneGrid = xgbABSlinGridbest, method = "xgbLinear")

predictedSQlin = predict(xgbSQlin_model, X_testSQ) #or

#predictedSQlin = predict(xgb_modelSQlinbest, X_testSQ)

residualsSQlin = y_testSQ - predictedSQlin

RMSEsqlin = sqrt(mean(residualsSQlin^2))

cat('The root mean square error of the test data is ', round(RMSEsqlin,3),'\n')

#the root mean square error of the test data is 0.003

y_test_meanSQ = mean(y_testSQ)

# Calculate total sum of squares

tssSQ = sum((y_testSQ - y_test_meanSQ)^2 )

# Calculate residual sum of squares

rssSQlin = sum(residualsSQlin^2)

# Calculate R-squared

rsqSQlin = 1 - (rssSQlin/tssSQ)

cat('The R-square of the test data is ', round(rsqSQlin,3), '\n')

#The R-square of the test data is

#PLOT ACTUAL WITH PREDICTED

options(repr.plot.width=8, repr.plot.height=4)

my_dataSQlin = as.data.frame(cbind(predicted = predictedSQlin,

observed = y_testSQ))

# Plot predictions vs test data

ggplot(my_dataSQlin,aes(predicted, observed)) + geom_point(color = "darkred", alpha = 0.5) +

geom_smooth(method=lm)+ ggtitle('Linear Regression ') + ggtitle("Extreme Gradient Boosting: Prediction vs Test Data") +

xlab("Predecited Volatility ") + ylab("Observed Volatility") +

theme(plot.title = element_text(color="darkgreen",size=16,hjust = 0.5),

axis.text.y = element_text(size=12), axis.text.x = element_text(size=12,hjust=.5),

axis.title.x = element_text(size=14), axis.title.y = element_text(size=14))

#for RB

inTrainRB <- createDataPartition(y = yandxRB$SPY.High, list = FALSE) #p = 0.8

trainingRB <- yandxRB[inTrainRB, ]

testingRB <- yandxRB[-inTrainRB,]

X_trainRB = xgb.DMatrix(as.matrix(trainingRB %>% select(-SPY.High)))

y_trainRB = trainingRB$SPY.High

X_testRB = xgb.DMatrix(as.matrix(testingRB %>% select(-SPY.High)))

y_testRB = testingRB$SPY.High

xgb_trcontrol = trainControl(method = "cv",number = 5,allowParallel = TRUE,verboseIter = FALSE,returnData = FALSE)

# by default parameters

xgbGrid <- expand.grid(nrounds = c(100,200), max_depth = c(10, 15, 20, 25), colsample_bytree = seq(0.5, 0.9, length.out = 5),eta = 0.1, gamma=0, min_child_weight = 1,subsample = 1)

xgb_modelRB = train( X_trainRB, y_trainRB,trControl = xgb_trcontrol,tuneGrid = xgbGrid, method = "xgbTree")

#best valuesfor hyperparameters

xgb_modelRB$bestTune

xgbGridbest <- expand.grid(nrounds = c(100), max_depth = c(10), colsample_bytree = seq(0.7),eta = 0.1, gamma=0, min_child_weight = 1,subsample = 1)

xgb_modelRBbest = train( X_trainRB, y_trainRB,trControl = xgb_trcontrol,tuneGrid = xgbGridbest, method = "xgbTree")

predictedRB = predict(xgb_modelRB, X_testRB) #or

predictedRB = predict(xgb_modelRBbest, X_testRB)

residualsRB = y_testRB - predictedRB

RMSErb = sqrt(mean(residualsRB^2))

cat('The root mean square error of the test data is ', round(RMSErb,3),'\n')

#the root mean square error of the test data is 1.765

varImp(xgb_modelRB)

y_test_meanRB = mean(y_testRB)

# Calculate total sum of squares

tssRB = sum((y_testRB - y_test_meanRB)^2 )

# Calculate residual sum of squares

rssRB = sum(residualsRB^2)

# Calculate R-squared

rsqRB = 1 - (rssRB/tssRB)

cat('The R-square of the test data is ', round(rsqRB,3), '\n')

#The R-square of the test data is 0.476

#PLOT ACTUAL WITH PREDICTED

options(repr.plot.width=8, repr.plot.height=4)

my_dataRB = as.data.frame(cbind(predicted = predictedRB,

observed = y_testRB))

# Plot predictions vs test data

ggplot(my_dataRB,aes(predicted, observed)) + geom_point(color = "darkred", alpha = 0.5) +

geom_smooth(method=lm)+ ggtitle('Linear Regression ') + ggtitle("Extreme Gradient Boosting: Prediction vs Test Data") +

xlab("Predecited Volatility ") + ylab("Observed Volatility") +

theme(plot.title = element_text(color="darkgreen",size=16,hjust = 0.5),

axis.text.y = element_text(size=12), axis.text.x = element_text(size=12,hjust=.5),

axis.title.x = element_text(size=14), axis.title.y = element_text(size=14))

#OR IF XGBLINEAR

xgbGrid <- expand.grid(nrounds = c(100,200), lambda=0,eta = 0.1, alpha=1)

xgbRBlin_model = train( X_trainRB, y_trainRB,trControl = xgb_trcontrol,tuneGrid = xgbGrid, method = "xgbLinear")

xgbRBlin_model$bestTune

xgbRBlinGridbest <- expand.grid(nrounds = 100 ,lambda = 0 , eta =0.1 , alpha = 1)

xgb_modelRBlinbest = train( X_trainRB, y_trainRB,trControl = xgb_trcontrol,tuneGrid = xgbRBlinGridbest, method = "xgbLinear")

predictedRBlin = predict(xgbRBlin_model, X_testRB) #or

predictedRBlin = predict(xgb_modelRBlinbest, X_testRB)

residualsRBlin = y_testRB - predictedRBlin

RMSErblin = sqrt(mean(residualsRBlin^2))

cat('The root mean square error of the test data is ', round(RMSErblin,3),'\n')

#the root mean square error of the test data is 1.776

y_test_meanRB = mean(y_testRB)

# Calculate total sum of squares

tssRB = sum((y_testRB - y_test_meanRB)^2 )

# Calculate residual sum of squares

rssRBlin = sum(residualsRBlin^2)

# Calculate R-squared

rsqRBlin = 1 - (rssRBlin/tssRB)

cat('The R-square of the test data is ', round(rsqRBlin,3),'\n')

#The R-square of the test data is 0.47

#PLOT ACTUAL WITH PREDICTED

options(repr.plot.width=8, repr.plot.height=4)

my_dataRBlin = as.data.frame(cbind(predicted = predictedRBlin,

observed = y_testRB))

# Plot predictions vs test data

ggplot(my_dataRBlin,aes(predicted, observed)) + geom_point(color = "darkred", alpha = 0.5) +

geom_smooth(method=lm)+ ggtitle('Linear Regression ') + ggtitle("Extreme Gradient Boosting: Prediction vs Test Data") +

xlab("Predecited Volatility ") + ylab("Observed Volatility") +

theme(plot.title = element_text(color="darkgreen",size=16,hjust = 0.5),

axis.text.y = element_text(size=12), axis.text.x = element_text(size=12,hjust=.5),

axis.title.x = element_text(size=14), axis.title.y = element_text(size=14))

#for VAR

inTrainVAR <- createDataPartition(y = yandxVAR$daily.returns, list = FALSE) #p = 0.8

trainingVAR <- yandxVAR[inTrainVAR, ]

testingVAR <- yandxVAR[-inTrainVAR,]

X_trainVAR = xgb.DMatrix(as.matrix(trainingVAR %>% select(-daily.returns)))

y_trainVAR = trainingVAR$daily.returns

X_testVAR = xgb.DMatrix(as.matrix(testingVAR %>% select(-daily.returns)))

y_testVAR = testingVAR$daily.returns

xgb_trcontrol = trainControl(method = "cv",number = 5,allowParallel = TRUE,verboseIter = FALSE,returnData = FALSE)

# by default parameters

xgbGrid <- expand.grid(nrounds = c(100,200), max_depth = c(10, 15, 20, 25), colsample_bytree = seq(0.5, 0.9, length.out = 5),eta = 0.1, gamma=0, min_child_weight = 1,subsample = 1)

xgb_modelVAR = train( X_trainVAR, y_trainVAR,trControl = xgb_trcontrol,tuneGrid = xgbGrid, method = "xgbTree")

#best valuesfor hyperparameters

xgb_modelVAR$bestTune

xgbGridbest <- expand.grid(nrounds = c(200), max_depth = c(10), colsample_bytree = seq(0.5),eta = 0.1, gamma=0, min_child_weight = 1,subsample = 1)

xgb_modelVARbest = train( X_trainVAR, y_trainVAR,trControl = xgb_trcontrol,tuneGrid = xgbGridbest, method = "xgbTree")

predictedVAR = predict(xgb_modelVAR, X_testVAR) #or

predictedVAR = predict(xgb_modelVARbest, X_testVAR)

residualsVAR = y_testVAR - predictedVAR

RMSEvar = sqrt(mean(residualsVAR^2))

cat('The root mean square error of the test data is ', round(RMSEvar,3),'\n')

#the root mean square error of the test data is 0

y_test_meanVAR = mean(y_testVAR)

# Calculate total sum of squares

tssVAR = sum((y_testVAR - y_test_meanVAR)^2 )

# Calculate residual sum of squares

rssVAR = sum(residualsVAR^2)

# Calculate R-squared

rsqVAR = 1 - (rssVAR/tssVAR)

cat('The R-square of the test data is ', round(rsqVAR,3), '\n')

#The R-square of the test data is 0.142

#PLOT ACTUAL WITH PREDICTED

options(repr.plot.width=8, repr.plot.height=4)

my_dataVAR = as.data.frame(cbind(predicted = predictedVAR,

observed = y_testVAR))

# Plot predictions vs test data

ggplot(my_dataVAR,aes(predicted, observed)) + geom_point(color = "darkred", alpha = 0.5) +

geom_smooth(method=lm)+ ggtitle('Linear Regression ') + ggtitle("Extreme Gradient Boosting: Prediction vs Test Data") +

xlab("Predecited Volatility ") + ylab("Observed Volatility") +

theme(plot.title = element_text(color="darkgreen",size=16,hjust = 0.5),

axis.text.y = element_text(size=12), axis.text.x = element_text(size=12,hjust=.5),

axis.title.x = element_text(size=14), axis.title.y = element_text(size=14))

#OR IF XGBLINEAR

xgbGrid <- expand.grid(nrounds = c(100,200), lambda=0,eta = 0.1, alpha=1)

xgbVARlin_model = train( X_trainVAR, y_trainVAR,trControl = xgb_trcontrol,tuneGrid = xgbGrid, method = "xgbLinear")

xgbVARlin_model$bestTune

#xgbVARlinGridbest <- expand.grid(nrounds = 100 , lambda = 0, eta =0.1 , alpha = 1)

#xgb_modelVARlinbest = train( X_trainVAR, y_trainVAR,trControl = xgb_trcontrol,tuneGrid = xgbVARlinGridbest, method = "xgbLinear")

predictedVARlin = predict(xgbVARlin_model, X_testVAR) #or

#predictedVARlin = predict(xgb_modelVARlinbest, X_testVAR)

residualsVARlin = y_testVAR - predictedVARlin

RMSEvarlin = sqrt(mean(residualsVARlin^2))

cat('The root mean square error of the test data is ', round(RMSEvarlin,3),'\n')

#the root mean square error of the test data is 0.002

y_test_meanVAR = mean(y_testVAR)

# Calculate total sum of squares

tssVAR = sum((y_testVAR - y_test_meanVAR)^2 )

# Calculate residual sum of squares

rssVARlin = sum(residualsVARlin^2)

# Calculate R-squared

rsqVARlin = 1 - (rssVARlin/tssVAR)

cat('The R-square of the test data is ', round(rsqVARlin,3),'\n')

#The R-square of the test data is -16.321

#PLOT ACTUAL WITH PREDICTED

options(repr.plot.width=8, repr.plot.height=4)

my_dataVARlin = as.data.frame(cbind(predicted = predictedVARlin,

observed = y_testVAR))

# Plot predictions vs test data

ggplot(my_dataVARlin,aes(predicted, observed)) + geom_point(color = "darkred", alpha = 0.5) +

geom_smooth(method=lm)+ ggtitle('Linear Regression ') + ggtitle("Extreme Gradient Boosting: Prediction vs Test Data") +

xlab("Predecited Volatility ") + ylab("Observed Volatility") +

theme(plot.title = element_text(color="darkgreen",size=16,hjust = 0.5),

axis.text.y = element_text(size=12), axis.text.x = element_text(size=12,hjust=.5),

axis.title.x = element_text(size=14), axis.title.y = element_text(size=14))

varimp <- varImp(xgb_modelSQ, scale = FALSE)

plot(varimp, top = 20)

varImp(xgb_modelVAR, scale = FALSE)

varImp(xgb_modelABS, scale = FALSE)

varImp(xgb_modelRB, scale = FALSE)

varImp(xgb_modelABS, scale = FALSE)

library(corrplot)

correlations = cor(yandxABC)

corrplot(correlations, method="color")

library(fGarch)

garch1 <- garchFit(~ garch(1,1), data = SPYWEEKRETURN)

coef(garch)

predict(garch)

install.packages("rugarch")

library(rugarch)

gspec.ru <- ugarchspec(mean.model=list(armaOrder=c(0,0)), distribution="std")

gfit.ru <- ugarchfit(gspec.ru, SPYWEEKRETURN, n.ahead=1, n.roll = 660)

garch <- ugarchforecast(gfit.ru)

results1 <- garch@forecast$seriesFor[1,] + garch@forecast$sigmaFor[1,]

results2 <- garch@forecast$seriesFor[1,] - garch@forecast$sigmaFor[1,]

#one step ahead forecast

garch@forecast

gfit.ru@fit

sigmagarch <- as.data.frame(gfit.ru@fit[["sigma"]])

sigmagarch <- as.data.frame(gfit.ru@fit[["sigma"]])[660:1315, ]

#with predicted rolling window from 660 obs as training set start

predictedABS <- predictedABS[660:1315, ]

gfit.ru <- ugarchfit(gspec.ru, SPYWEEKRETURN, initialWindow = 660,horizon = 1315, fixedWindow = 1)

#DIEBOLD MARIANO TEST

library(forecast)

PROXYMODUL1 <- PROXYMODUL[660:1315]

PROXYRB1 <- PROXYRB[660:1315]

PROXYSQUARED1 <- PROXYSQUARED[660:1315]

PROXYVARIANCE1 <- PROXYVARIANCEna[657:1312]

ForecastErrorsXgbABS <- (PROXYMODUL1 - predictedABSlin)

ForecastErrorsGARCH <- (PROXYMODUL1 - sigmagarch)#dm test in r require row forecast errors

#MSE = loss

dm.test(ForecastErrorsGARCH, ForecastErrorsXgbABS, alternative = c("greater"))

ForecastErrorsXgbRB <- (PROXYRB1 - predictedRB)

#Diebold-Mariano Test

ForecastErrorsXgbSQ <- (PROXYSQUARED1 - predictedSQ)

ForecastErrorsXgVAR <- (PROXYVARIANCE1 - predictedVAR)

Diebold-Mariano Test

data: ForecastErrorsGARCHForecastErrorsXgb

DM = -4.3037, Forecast horizon = 1, Loss function power = 2, p-value = 1

alternative hypothesis: greater # model 2 is more accurate than 1

Diebold-Mariano Test

data: ForecastErrorsGARCHForecastErrorsXgb

DM = -4.3037, Forecast horizon = 1, Loss function power = 2, p-value =

1.936e-05 = 0

alternative hypothesis: two.sided

dm.test(ForecastErrorsGARCH, ForecastErrorsXgbSQ, alternative = c("greater"))

Diebold-Mariano Test

data: ForecastErrorsGARCHForecastErrorsXgbRB

DM = -4.0937, Forecast horizon = 1, Loss function power = 2, p-value = 1

alternative hypothesis: greater

plot(PROXYMODUL)

plot(PROXYVARIANCE)

plot(PROXYSQUARED)

plot(PROXYRB)

predictedABS2 <- predictedABS^2

normspec <- ugarchspec(mean.model=list(armaOrder=c(1,0)), distribution="norm")

Nmodel = ugarchfit(normspec,SPYWEEKRETURN)

Nfit<- as.data.frame(Nmodel@fit[["sigma"]])[660:1315, ]

Nfit2 <- (Nfit)^2

PROXYMODUL2 <- PROXYMODUL1^2

dm.test(( PROXYMODUL2- Nfit2), (PROXYMODUL2 - predictedABS2 ), alternative = c("greater"), h = 1, power = 2)

#Diebold-Mariano Test

data: (PROXYMODUL2 - Nfit2)(PROXYMODUL2 - predictedABS2)

DM = -2.6094, Forecast horizon = 1, Loss function power = 2, p-value =

0.009278

alternative hypothesis: two.sided



Reference

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3. Chinco, A. M., Clark-Joseph, A. D., & Ye, M. (2017). Sparse signals in the cross-section of returns (No. w23933). National Bureau of Economic Research.

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5. Ghysels, E., Santa-Clara, P., & Valkanov, R. (2006). Predicting volatility: getting the most out of return data sampled at different frequencies. Journal of Econometrics, 131(1-2), 59-95.

6. Jon Kleinberg Himabindu Lakkaraju Jure Leskovec Jens Ludwig Sendhil Mullainathan (2017). HUMAN DECISIONS AND MACHINE PREDICTIONS

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10. Tianqi Chen & Carlos Guestrin. (2017). XGBoost: A Scalable Tree Boosting System

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