R/roll.win.rmse.wge.R

In tswge: Time Series for Data Science

#Rolling Window RMSE Function
# series is the array of the series
# horizon is how far you want to predict into the future
# d is the order of the differencing: (1-B^)^d
# s is the order of the seasonality: (1-B^s)
# phi = coefficients of the stationary AR term
# theta = coefficients of the invertible MA term

# It simply takes the given horizon and the model in the form of s,d,phis and 
# thetas and figures out how many windows it can create in the data (series) and then calculates the ASE for each window.  
#The output is the average off all the ASEs from each individual window.  

roll.win.rmse.wge = function(series, horizon = 2, s = 0, d = 0, phi = 0, theta = 0)
{

  
  #DEFINE fore.arma.wge2
  
  fore.arma.wge2=function(x,phi=0,theta=0,n.ahead=5,lastn=FALSE, plot=FALSE,alpha=.05,limits=TRUE, xbar2 = NULL)
  {
    # lastn=TRUE indicates that the last n data values are to be forecast
    # lastn=FALSE (default) indicates we want foreacts for n values beyond the end of the realization
    n=length(x)
    p=length(phi)
    if(sum(phi^2)==0) {p=0}
    q=length(theta)
    if(sum(theta^2)==0) {q=0}
    #resid=rep(0,n)
    npn.ahead=n+n.ahead
    xhat=rep(0,npn.ahead)
    if(is.null(xbar2))
    {
      xbar=mean(x)
    }
    else
    {
      xbar = xbar2
    }
    
    const=1
    if (p > 0) {for(jp in 1:p) {const=const-phi[jp]}}
    #
    #
    # Calculate Box-Jenkins Forecasts
    #
    #
    #Calculating Residuals
    #
    resid=backcast.wge(x,phi,theta,n.back=50)
    #
    #
    #maconst=const*xbar
    #p1=max(p+1,q+1)
    #for (i in p1:n) {resid[i]=x[i]
    #   if ( p > 0) {for (jp in 1:p) {resid[i]=resid[i]-phi[jp]*x[i-jp]}}
    #   if (q > 0) {for (jq in 1:q) {resid[i]=resid[i]+theta[jq]*resid[i-jq]}}
    #                   resid[i]=resid[i]-maconst}
    #
    # Calculating Forecasts
    #
    #
    npn.ahead=n+n.ahead
    xhat=rep(0,npn.ahead)
    mm=n
    #
    #lastn = TRUE
    #
    if(lastn==TRUE) {mm=n-n.ahead}
    #
    #
    for (i in 1:mm) {xhat[i]=x[i]}
    for (h in 1:n.ahead) {
      if (p > 0) {for (jp in 1:p) {xhat[mm+h]=xhat[mm+h]+phi[jp]*xhat[mm+h-jp]}}
      if ((h<=q)&(h>0)) {for(jq in h:q) {xhat[mm+h]=xhat[mm+h]-theta[jq]*resid[mm+h-jq]}}
      xhat[mm+h]=xhat[mm+h]+xbar*const}
    #
    #
    #   Calculate psi weights for forecasts limits
    #
    #
    xi=psi.weights.wge(phi,theta,lag.max=n.ahead)
    #
    #
    #
    #Setting up for plots
    nap1=n.ahead+1
    fplot=rep(0,nap1)
    maxh=mm+n.ahead
    llplot=rep(0,nap1)
    ulplot=rep(0,nap1)
    f=rep(0,nap1)
    ll=rep(0,nap1)
    ul=rep(0,nap1)
    wnv=0
    xisq=rep(0,n.ahead)
    se=rep(0,n.ahead)
    se0=1
    for (i in 1:n) {wnv=wnv+resid[i]**2}
    wnv=wnv/n
    xisq[1]=1
    for (i in 2:n.ahead) {xisq[i]=xisq[i-1]+xi[i-1]^2}
    for (i in 1:n.ahead) {se[i]=sqrt(wnv*xisq[i])}
    fplot[1]=x[mm]
    for (i in 1:n.ahead) {fplot[i+1]=xhat[mm+i]}
    ulplot[1]=x[mm]
    #for (i in 1:n.ahead) { ulplot[i+1]=fplot[i+1]+1.96*se[i]}
    for (i in 1:n.ahead) { ulplot[i+1]=fplot[i+1]-qnorm(alpha/2)*se[i]}
    llplot[1]=x[mm]
    #for (i in 1:n.ahead) { llplot[i+1]=fplot[i+1]-1.96*se[i]}
    for (i in 1:n.ahead) { llplot[i+1]=fplot[i+1]+qnorm(alpha/2)*se[i]}
    #
    if(limits==FALSE) {
      if(lastn==TRUE) {max=max(x,xhat[1:n])
      min=min(x,xhat[1:n])}
      else            {max=max(x,xhat)
      min=min(x,xhat)}}
    if(limits==TRUE) {min=min(x,llplot)
    max=max(x,ulplot)}
    #numrows <- 1
    #numcols <- 1
    timelab <- 'Time'
    valuelab <- ''
    #fig.width <- 5
    #fig.height <- 2.5
    cex.labs <- c(.8,.7,.8)
    #par(mfrow=c(numrows,numcols),mar=c(6,2,3,1))
    t<-1:n;
    np1=n+1
    np.ahead=mm+n.ahead
    tf<-mm:np.ahead
    #if (plot=='TRUE') {
      #fig.width <- 5
      #fig.height <- 2.5
      #cex.labs <- c(1.2,1.2,1.2)
      #par(mfrow=c(numrows,numcols),mar=c(9,4,3,2))
      #plot(t,x,type='o',xaxt='n',yaxt='n',cex=.8,pch=16,cex.lab=1,cex.axis=1,lwd=1,xlab='',ylab='',xlim=c(1,maxh),ylim=c(min,max),col=1)
      #axis(side=1,cex.axis=1.1,mgp=c(3,0.15,0),tcl=-.3);
      #axis(side=2,las=1,cex.axis=1.1,mgp=c(3,.4,0),tcl=-.3)
      #abline=mean(x)
      #mtext(side=c(1,2,1),cex=cex.labs,text=c(timelab,valuelab,""),line=c(1.2,2.1,1.8))
      #points(tf,fplot,type='o',lty=1,cex=.6,lwd=1,pch=1,col=2);
      #if(limits=='TRUE') {points(tf,ulplot,type='l',lty=2,cex=0.6,lwd=.75,pch=1,col=4)
        #points(tf,llplot,type='l',lty=3,cex=0.6,lwd=.75,pch=1,col=4)
     # }
    #}
    np1=n+1
    nap1=n.ahead+1
    f=fplot[2:nap1]
    # Calculate RMSE and MAD
    if(lastn==TRUE){
      t.start=n-n.ahead
      sum.rmse=0
      sum.mad=0
      for(i in 1:n.ahead) {sum.rmse=sum.rmse+(f[i]-x[t.start+i])^2
      sum.mad=sum.mad+abs(f[i]-x[t.start+i])}
      mse=sum.rmse/n.ahead
      rmse=sqrt(mse)
      mad=sum.mad/n.ahead
    }
    ll=llplot[2:nap1]
    ul=ulplot[2:nap1]
    if(lastn==TRUE){out1=list(f=f)}
    if(lastn==FALSE){out1=list(f=f)}
    return(out1)
  }

  
  numwindows = 0
  RMSEHolder = numeric()

  
if(s == 0 & d == 0)
{
  
  trainingSize = max(length(phi),length(theta)) + 1 # The plus 1 is for the backcast residuals which helps with ARMA model with q > 0
  numwindows = length(series)-(trainingSize + horizon) + 1   
  RMSEHolder = numeric(numwindows)

  print(paste("Please Hold For a Moment, TSWGE is processing the Rolling Window RMSE with", numwindows, "windows."))
  
  for( i in 1:numwindows)
  {
    forecasts <- fore.arma.wge2(series[i:(i+(trainingSize-1))], plot = TRUE, phi = phi, theta = theta,n.ahead = horizon, xbar = mean(series))

    RMSE = sqrt(mean((series[(trainingSize+i):(trainingSize+ i + (horizon) - 1)] - forecasts$f)^2))
    
    RMSEHolder[i] = RMSE
  }
}
else
  {
    trainingSize = sum(length(phi),length(theta),s, d) + 1 # sum and plus one is to help backcast.wge, lag.max and ylim plotting issue in fore.arima.wge
    numwindows = length(series)-(trainingSize + horizon) + 1
    RMSEHolder = numeric(numwindows)

    print(paste("Please Hold For a Moment, TSWGE is processing the Rolling Window RMSE with", numwindows, "windows."))
    
    for( i in 1:numwindows)
    {
      #invisible(capture.output(forecasts <- fore.arima.wge(series[i:(i+(trainingSize-1))],phi = phis, theta = thetas, s = s, d = d,n.ahead = horizon)))
      forecasts <- fore.arima.wge(series[i:(i+(trainingSize-1))],phi = phi, s = s, d = d, theta = theta,n.ahead = horizon)
      
      RMSE = sqrt(mean((series[(trainingSize+i):(trainingSize+ i + (horizon) - 1)] - forecasts$f)^2))
      
      RMSEHolder[i] = RMSE
      
    }
  }
  
  
  RMSEHolder
  hist(RMSEHolder, main = "RMSEs for Individual Windows")
  WindowedRMSE = mean(RMSEHolder)
  
  print("The Summary Statistics for the Rolling Window RMSE Are:")
  print(summary(RMSEHolder))
  print(paste("The Rolling Window RMSE is: ",round(WindowedRMSE,3)))

#output
  invisible(list(rwRMSE = WindowedRMSE, trainingSize = trainingSize, numwindows = numwindows, horizon = horizon, s = s, d = d, phi = phi, theta = theta, RMSEs = RMSEHolder))
  
  }