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Predecitve model for Stock Return forecast (future prediction) for FTS100 Tech-Mark Series (top technical firms) in UK listed on London Stock Exchange

ARIMA Model

install.packages("quantmod") library(quantmod)

Input the Stock Variables for required firms predective analysis (SGE.L,SN.L,BA.L,CCC.L,GNS.L,QQ.L,FLTR.L,RWS.L,SPT.L,SXS.L) ( This is the Dataset, that will change accordingly when you input different Stock symbols or ticker symbols of Respective companies and you can also change the time set )

data<-getSymbols("SN.L", src = "yahoo",from=as.Date("2015-01-01"),to=as.Date("2022-12-31"),auto.assign = FALSE) #Daily Data data View(data) #Used For forecating Monthly data #data<-to.monthly(data) #Used For forecasting Weekly data #data<-to.weekly(data)

Construct only the closing price of stocks for forecasting

CLOSEPRICE<-data[,4] CLOSEPRICE<-na.omit(CLOSEPRICE) View(CLOSEPRICE)

summary(CLOSEPRICE) sd(CLOSEPRICE) skewness(CLOSEPRICE) kurtosis(CLOSEPRICE) sum(!complete.cases(CLOSEPRICE)) View(CLOSEPRICE) #Visulise the data chart_Series(CLOSEPRICE, col = "black") add_SMA(n = 100, on = 1, col = "red") add_SMA(n = 20, on = 1, col = "black") add_RSI(n = 14, maType = "SMA") add_BBands(n = 20, maType = "SMA", sd = 1, on = -1) add_MACD(fast = 12, slow = 25, signal = 9, maType = "SMA", histogram = TRUE) View(CLOSEPRICE)

Set the training (JAN 2015- DEC 2020) and testing (JAN 2021-DEC 2022) dataset

set.seed(123) train<-CLOSEPRICE[1:1518] testa<-CLOSEPRICE[1519:2021] plot(CLOSEPRICE,main="STOCK CLOSE PRICE,2015-2022",ylab="Price",xlab="Days") lines(train,col="blue") lines(testa,col="green") legend("bottomright",col=c("blue","green"),lty=1,legend=c("Training","Testing"))

ADF Test for Stationrity

library(tseries) adf<-adf.test(train) adf #ACF and PACF Plots acf(train) pacf(train) diff_train<-diff(train) diff_train<-diff_train[-1,] adf.test(diff_train) par(mfrow=c(1,1)) acf(diff_train) pacf(diff_train) library(caTools) library(forecast) #Fitting the ARIMA Model fitA<-arima(train,order=c(2,1,2)) fitA tsdisplay(residuals(fitA),lag.max = 40) checkresiduals(fitA) fitb<-arima(train,order = c(3,1,2)) fitb BIC(fitb) tsdisplay(residuals(fitb),lag.max = 40) checkresiduals(fitb) fitc<-arima(train,order = c(3,1,2)) fitc tsdisplay(residuals(fitc),lag.max = 40) checkresiduals(fitc) fitd<-arima(train,order=c(2,1,2)) fitd tsdisplay(residuals(fitd),lag.max = 40) checkresiduals(fitd) fite<-arima(train,order=c(2,1,2)) fite tsdisplay(residuals(fite),lag.max = 40) checkresiduals(fite) #Forecasting the future values for stock returns

"forecasta, forecastb, forecastc, forecastd,forecaste" is the predicted values of future stock prices of respective companies

forecasta<-forecast(fitA,h=503) plot(forecasta) forecasta forecastb<-forecast(fitb,h=503) plot(forecastb) forecastb forecastc<-forecast(fitc,h=503) plot(forecastc) forecastc forecastd<-forecast(fitd,h=503) plot(forecastd) forecaste<-forecast(fite,h=503) plot(forecaste)

Evaluate the best ARIMA model for forecasting on the basis of forecast accuracy measures

accuracy(forecasta) accuracy(forecastb) accuracy(forecastc) accuracy(forecasta) accuracy(forecasta) #Estimate the performance of the best ARIMA model with the available testing model accuracy(forecasta,testa)

#GARCH MODEL

Libraries

library(quantmod) library(xts) library(PerformanceAnalytics) library(rugarch) library(tseries)

# Input the Stock Variables for required firms predective analysis (SGE.L,SN.L,BA.L,CCC.L,GNS.L,QQ.L,FLTR.L,RNS.L,SPT.L,SXS.L) ( This is the Dataset, that will change accordingly when you input different Stock symbols or ticker symbols of Respective companies and you can also change the time set )

datag<-getSymbols("SN.L" ,src = "yahoo",from=as.Date("2015-01-01"),to=as.Date("2022-12-31"),auto.assign = FALSE) #For Daily Data View(datag) 0 #Used For Monthly data #datag<-to.monthly(datag) #Used For Weekly data #datag<-to.weekly(datag)

Construct only the closing price of stocks for forecasting

datag<-datag[,4] CLOSEPRICE<-datag CLOSEPRICET<-CLOSEPRICE[1:1518] CLOSEPRICEF<-CLOSEPRICE[1519:2021] chartSeries(SXS.L) View(CLOSEPRICE)

Calculate Daily returns

returnss <- CalculateReturns(CLOSEPRICE) View(returnss) returnss <- returnss[-1] #Contruct the training (JAN 2015- DEC 2020) and testing (JAN 2021- DEC 2022) dataset return<-returnss[1:1517] test<-returnss[1518:2020] class(test) hist(return) #Visuualise the data chart.Histogram(return, methods = c('add.density', 'add.normal'), colorset = c('blue', 'green', 'red')) chartSeries(CalculatedReturns)

Test for different Garch models

1. sGARCH model with contant mean

s <- ugarchspec(mean.model = list(armaOrder = c(0,0)), variance.model = list(model = "sGARCH"), distribution.model = 'norm') m <- ugarchfit(data = return, spec = s) coef(m) plot(m)

9 0

2. GARCH with sstd

s <- ugarchspec(mean.model = list(armaOrder = c(0,0)), variance.model = list(model = "sGARCH"), distribution.model = 'sstd') m <- ugarchfit(data = return, spec = s) m checkresiduals(m) s <-m@fit$fitted.values kurtosis(s) plot(m) 9 0

GARCH with General Error Distrubution

s <- ugarchspec(mean.model = list(armaOrder = c(0,0)), variance.model = list(model = "sGARCH"), distribution.model = 'ged') m <- ugarchfit(data = return, spec = s) m plot(m) 9 0

3. GJR-GARCH

s <- ugarchspec(mean.model = list(armaOrder = c(0,0)), variance.model = list(model = "gjrGARCH"), distribution.model = 'sstd') m <- ugarchfit(data = return, spec = s) coef(m) checkresiduals(m) s <-m@fit$fitted.values kurtosis(s) plot(m) 9 0

#4. GJR-GARCH in mean s <- ugarchspec(mean.model = list(armaOrder = c(0,0)), variance.model = list(model = "sGARCH"), distribution.model = 'ged') m <- ugarchfit(data = return, spec = s) m plot(m) 9 0

Simulation with the best GARCH model evaluted on the bassis of providing the lowest Akakie

s <- ugarchspec(mean.model = list(armaOrder = c(0,0)), variance.model = list(model = "gjrGARCH"), distribution.model = 'sstd') m <- ugarchfit(data = return, spec = s) m plot(m) 9 0 s sfinal <- s setfixed(sfinal)<-as.list(coef(m))

Forecast the futre returns of the stocks by the GJR-GARCH model( Values for forecasting changes according to the type of dataset choosed)

f <- ugarchforecast(m, n.ahead =503)

f plot(f) 4 0 par(mfrow = c(1,1)) #Showing the volatality of the stock plot(sigma(f)) predictedvalues<- ugarchpath(spec = sfinal, m.sim = 1, n.sim = 503, rseed = 123) plot.zoo(fitted(predictedvalues)) View(fitted(sim)) class(test) sigma(sim) plot.zoo(sigma(predictedvalues)) tail(CLOSEPRICET)

predicted values of stock return (Closing Price) of the firms on each day

#Substitute the last value of Stock close price from the trainiing set in the p variable to predict the future values from the GARCH model p <- 1510*apply(fitted(predictedvalues),1, 'cumsum') +1510

p is the predicted values of future stock prices of respective companies

p View(p) plot(p) table(p) class(p)

ForecastedValues plot(p, type = "l", lwd = 1, main = "Forecasted Values of SN.L by GJR-GARCH(1,1)") plot(p,closepricef, type = "l",lwd = 1) length(p) length(closepricef)

Evaluate the Performance of GJR-Garch Model ,

View(p) p<-as.numeric(p) closepricef<-as.numeric(CLOSEPRICEF$SN.L.Close) accuracy(p,closepricef) p-closepricef

rmse<-sqrt(mean((p)^2)) rmse abs<-abs((closepricef-p)/closepricef)*100

mean(abs) forecastedp<-ts(p,start=1) closepricets<-ts(CLOSEPRICEF$GNS.L.Close,start=1) accuracy(forecastedp) accuracy(forescastdp)

Evaluate the supreme model among ARIMA and GARCH model for being a better fit for the data depending on required time horizon

#ARIMA model accuracy(forecasta,testa) #GARCH model accuracy(forecastedp,closepricets)