A Random Forest Test For Jumps

server.R

# Load packages ----
library(shiny)
library(quantmod)
library(randomForest)

### The simulation functions

simulateJump=function(mu_,ss_,lambda_,mu2_,sigma_,TotalTime,delta,compare,size)
{
  Sn=0
  times <- c(0)
  while(Sn <= TotalTime)
  {
    n <- length(times)
    u <- runif(1)
    expon <- -log(u)/lambda_
    Sn <- times[n]+expon
    times <- c(times, Sn)
  }
  times=times[-length(times)]                  #the last time is beyond TotalTime, so i delete from the vector times
  indicator=seq(from=0,to=0,length=TotalTime)  # if there are jumps or not between two times
  jumpSize=seq(from=0,to=0,length=TotalTime)   # stores the size of the jump
  
  delta=1/252
  t=(0:(length=(TotalTime)-1))
  for(m in 2:length(times))
  {
    for(k in 2: length(t))
    {
      if( t[k-1]<=times[m] && times[m]<=t[k])
      {
        indicator[k]=1
        
        if(compare)
        {
          u = runif(1,0,1)
          signA=1          
          if(u<=0.5)
          { signA=-1}
          
          jumpSize[k]=ss_*size*signA
        }
        else
        {
          jumpSize[k]=rnorm(1,mean=mu2_,sd=sigma_)
        }
      }
    }
  }
  
  stock=seq(from=0,to=0,length=TotalTime)
  stock[1]=10
  
  for(i in 2:TotalTime)
  {
    stock[i]=stock[i-1]+(mu_-0.5*ss_^2)*delta+ss_*sqrt(delta)*rnorm(1)+jumpSize[i]*indicator[i]
  }
  
  final=cbind(stock)
  return(final)
}


simulateGBM=function(mu_,ss_,TotalTime,delta)
{
  
  
  stock=seq(from=0,to=0,length=TotalTime)
  stock[1]=10
  
  for(i in 2:TotalTime)
  {
    stock[i]=stock[i-1]+(mu_-0.5*ss_^2)*delta+ss_*sqrt(delta)*rnorm(1)
  }
  
  final=cbind(stock)
  return(final)
}

### Generate the traning data

trainingData<-function(sampleSize)
{
  
  trainingdata=matrix(0,nrow=sampleSize,ncol=9)
  
  for(i in 1:sampleSize)
  {
    
    mu=runif(1,-1,1)
    s=runif(1,0.01,0.7)
    lam=runif(1,1,252)/252
    mu_jump=runif(1,-1,1)
    s_jump=runif(1,0.01,0.5)
    delta=1/252
    TotalTime=252*5
    
    u = runif(1,0,1)
    if(u<=0.5)
    {
      data=simulateJump(mu,s,lam,mu_jump,s_jump,TotalTime,delta,FALSE,1)
      X= data[,1]#X is already log form
      jump=1
    }
    else
    {    
      data=simulateGBM(mu,s,TotalTime,delta) 
      X= data[,1]#X is already log form
      jump=0
    }
    
    FirstMoment= mean(diff(X)^1)
    SecondMoment= mean((diff(X)-FirstMoment)^2)
    Skewness=mean((diff(X)-FirstMoment)^3)/SecondMoment^(3/2)
    Kurtosis = (3-mean((diff(X)-FirstMoment)^4)/SecondMoment^2)/10
    FirthMoment= mean((diff(X)-FirstMoment)^5)
    SixthMoment= mean((diff(X)-FirstMoment)^6)
    SeventhMoment= mean((diff(X)-FirstMoment)^7)
    EigthMoment= mean((diff(X)-FirstMoment)^8)
    
    #Column bind the data into one variable
    trainingdata[i,]= cbind(FirstMoment,SecondMoment,Skewness,Kurtosis,
                            FirthMoment,SixthMoment,SeventhMoment,EigthMoment,jump)
    cat("Iteration Number:\t",i, "\n")
    
  }
  colnames(trainingdata) <- c("FirstMoment", "SecondMoment","Skewness","Kurtosis",
                              "FirthMoment", "SixthMoment","SeventhMoment","EigthMoment","jump")
  trainingdata
  
}

### Beging the Server Function

server <- function(input, output) {
  
  data=trainingData(50)
  
  randomForestModel <- randomForest(as.factor(data[,9]) ~ ., data=data, importance=TRUE,
                                    proximity=TRUE)
  
  dataInput <- reactive({
    getSymbols(input$symb, src = "google", 
               from = input$dates[1],
               to = input$dates[2],
               auto.assign = FALSE)
  })
  
  output$plotLevels <- renderPlot({
    
    X=dataInput()
    if(input$use_log=="YES")
    { X=log(X[,4])}
    else
    {
      X=(X[,4])
    }
    SharePrice=tail((X),-1)
    
    plot(SharePrice,main="Share Price Level",col="blue")
    
    })
  
  output$plotReturns <- renderPlot({
    
    X=dataInput()
    X=log(X[,4])
    logReturns=tail(diff(X),-1)
    
    plot(logReturns,main="Log Returns",col="green")
    
  })
  
  output$JumpTest <- renderText(
    
    { 
      X=dataInput()
      X=X[,4]
      Y=tail(diff(X),-1)
      
      length(Y)
      
      FirstMoment= mean(Y^1)
      SecondMoment= mean((Y-FirstMoment)^2)
      Skewness=mean((Y-FirstMoment)^3)/SecondMoment^(3/2)
      Kurtosis = (3-mean((Y-FirstMoment)^4)/SecondMoment^2)/10
      FirthMoment= mean((Y-FirstMoment)^5)
      SixthMoment= mean((Y-FirstMoment)^6)
      SeventhMoment= mean((Y-FirstMoment)^7)
      EigthMoment= mean((Y-FirstMoment)^8)
      jump=0
      
      #Column bind the data into one variable
      test= cbind(FirstMoment,SecondMoment,Skewness,Kurtosis,
                  FirthMoment,SixthMoment,SeventhMoment,EigthMoment,(jump))
      
      colnames(test) <- c("FirstMoment", "SecondMoment","Skewness","Kurtosis",
                          "FirthMoment", "SixthMoment","SeventhMoment","EigthMoment","jump")
  
      pred <- predict(randomForestModel, test)
      
     if(pred==1)
      {"   Jump Test Result: This share has Jumps"}
      else
      {
        "   Jump Test Result: This share has NO Jumps"
      }
      
      
      })
  
  
  
  
  
  
  
  
  
  
  
  
}

ur.R

library(shiny)

shinyUI( fluidPage(
  
  titlePanel("Random Forest Test For Jumps"),
  
  fluidRow(
    column(12, helpText("Select the share that you want to test for Jumps (Exchange:Symbol).Note that the share price information will be obtained from Google Finance."))),
  
  
  fluidRow(
    column(4, textInput("symb", "Share Symbol", "JSE:MTN")),
    
    column(4, dateRangeInput("dates", 
                             "Date Range",
                             start = "2015-01-01", 
                             end = as.character(Sys.Date()))),
           
    column(4, selectInput("use_log", 
                          label = "Use Log Scale?",
                          choices = list("YES", "NO"),
                          selected = "YES")
           )  
           ),
    
    fluidRow(
      column(4, textOutput("JumpTest"))
      ),
    
  fluidRow(
   # textOutput("JumpTest"),
    plotOutput("plotLevels"),
    plotOutput("plotReturns")
  )
  
))