Question

I need to run a bootstrap on a time series with non-standard dependence. So to do this I need to create a function that simulates the time series by making time by time adjustments.

testing<-function(){
  sampleData<-as.zoo(data.frame(index=1:1000,vol=(rnorm(1000))^2,x=NA))
  sampleData[,"x"]<-sampleData[,"vol"]+rnorm(1000) #treat this is completely exognenous and unknown in connection to vol
  sampleData<-cbind(sampleData,mean=rollmean(sampleData[,"vol"],k=3,align="right"))
  sampleData<-cbind(sampleData,vol1=lag(sampleData[,"vol"],k=-1),x1=lag(sampleData[,"x"],k=-1),mean1=lag(sampleData[,"mean"],k=-1))

  #get estimate
  mod<-lm(vol~vol1+x1+mean1,data=sampleData)

  res<-mod$residuals

  for(i in 5:1000){
    #recursively estimate
    sampleData[i,"vol"]<-as.numeric(predict(mod,newdata=data.frame(sampleData[i-1,])))+res[i-3]

    #now must update other paramaters
      #first our rolled average
      sampleData[i,"mean"]<-mean(sampleData[(i-3):i,"vol"])

      #reupdate our lagged variables
      sampleData[i,"vol1"]<-sampleData[i-1,"vol"]
      sampleData[i,"mean1"]<-sampleData[i-1,"mean"]

  }

  lm(vol~vol1+x1+mean1,data=sampleData)
}

When I run this code and measure the run time I get

system.time(testing())
user  system elapsed 
2.711   0.201   2.915 

This is a slight problem for me as a will be integrating this code to construct a bootstrap. This means any time taken here is multiplied by about 100 for each step. And I am updating this at a few thousand times. That means a single run will take hours (to days) to run.

Is there anyway to speed this code up?

Kind regards,

Matthew

Answer 1

Here’s how to avoid the overhead of predict.lm. Also note that I used a matrix instead of a zoo object, which would be a tiny bit slower. You can see just how much this slowed down your code. That’s the price you pay for convenience.

testing.jmu <- function() {
  if(!require(xts)) stop("xts package not installed")
  set.seed(21)  # for reproducibility
  sampleData <- .xts(data.frame(vol=(rnorm(1000))^2,x=NA), 1:1000)
  sampleData$x <- sampleData$vol+rnorm(1000)
  sampleData$mean <- rollmean(sampleData$vol, k=3, align="right")
  sampleData$vol1 <- lag(sampleData$vol,k=1)
  sampleData$x1 <- lag(sampleData$x,k=1)
  sampleData$mean1 <- lag(sampleData$mean,k=1)

  sampleMatrix <- na.omit(cbind(as.matrix(sampleData),constant=1))
  mod.fit <- lm.fit(sampleMatrix[,c("constant","vol1","x1","mean1")],
                    sampleMatrix[,"vol"])
  res.fit <- mod.fit$residuals

  for(i in 5:nrow(sampleMatrix)){
    sampleMatrix[i,"vol"] <-
      sum(sampleMatrix[i-1,c("constant","vol1","x1","mean1")] *
          mod.fit$coefficients)+res.fit[i-3]
    sampleMatrix[i,"mean"] <- mean(sampleMatrix[(i-3):i,"vol"])
    sampleMatrix[i,c("vol1","mean1")] <- sampleMatrix[i-1,c("vol","mean")]
  }

  lm.fit(sampleMatrix[,c("constant","vol1","x1","mean1")], sampleMatrix[,"vol"])
}
system.time(out <- testing.jmu())
#    user  system elapsed 
#    0.05    0.00    0.05 
coef(out)
#    constant        vol1          x1       mean1 
#  1.08787779 -0.06487441  0.03416802 -0.02757601

Add the set.seed(21) call to your function and you’ll see that my function returns the same coefficients as yours.