carx (version 0.7.1)

predict.carx: Prediction with a fitted carx object

Description

Predict the future values of an fitted carx object. If the model has non-null covariate x other than the constant mean, the new observations in x must be supplied via newxreg. The model prediction is done in a similar way as in fitted.carx by identifying the latest \(p\) consecutive observed responses in the data used to estimate model, then compute the mean of the conditional distribution of the future values given the information since the latest p consecutive observed values and the supplied new covariate values. For more details, see Wang and Chan (2017).

Usage

# S3 method for carx
predict(object, newxreg = NULL, n.ahead = 1,
  CI.level = 0.95, nRep = 1000, na.action = NULL,
  useSimulatedResidual = FALSE, ...)

Arguments

object

a fitted carx object.

newxreg

the new observations for the coverates x, default=NULL. If there is no covariate, the value can be assigned to be NULL. Otherwise, a matrix of new observations is required to compute predictions. Default=NULL.

n.ahead

the number of steps ahead to predict, default = 1.

CI.level

the CI.level to construct the confidence interval, default = 0.95.

nRep

the number of replications to be performed in the bootstrap for prediction confidence intervals when censoring exists in the last p observations, default = 1000.

na.action

how should model.frame deal with NA values.

useSimulatedResidual

if True, the innovation sequence will be sampled from the simulated residuals, otherwise, they will be sampled from normal distribution with mean 0 and standard deviation object$sigma. Set it TRUE if the normal distribution may be too restrictive. Default = FALSE.

...

not used.

Value

A list consisting of fit, se.fit, and ci representing the predictions, standard errors of predictions, and confidence intervals respectively.

References

Wang C, Chan KS (2017). "Quasi-likelihood estimation of a censored autoregressive model with exogenous variables." Journal of the American Statistical Association. 2017 Mar 20(just-accepted).

Examples

# NOT RUN {
 #This is the function to run a simulation study about the empirical coverage rate of 
 #the predictive confidence intervals,
 runSimPredCR <- function(nRep=200,nObs=200,n.ahead=10,
                          saveRslt=FALSE,saveDir='./testPredictCR',
                          seed=NULL)
 {
   if(!is.null(seed))
     set.seed(seed)
   crMat = matrix(nrow=n.ahead,ncol=nRep)
   if(saveRslt)
   {
     dir.create(saveDir,showWarnings=FALSE,recursive=TRUE)
   }

   replication = list()
   simSingle <- function(iRep)
   {
     message(sprintf("iRep: %04d",iRep))
     sdata = carxSim(nObs=nObs+n.ahead)
     trainingData = sdata[1:nObs,]
     testData = sdata[-(1:nObs),]
     mdl = carx(y~X1+X2-1,data=trainingData,p=2)
     newxreg = testData[,c('X1','X2')]
     predVal = predict(mdl,newxreg=newxreg,n.ahead=n.ahead)
     crInd = (predVal$ci[,1] <= testData$y) & (predVal$ci[,2] >= testData$y)
     crMat[,iRep] = crInd
     list(trainingData=trainingData,
          testData=testData,
          fitted=mdl,
          predVal = predVal,
          crInd= crInd)
   }
   replication = lapply(1:nRep,simSingle)
   crMat = sapply(replication,FUN=function(x){x$crInd})
   print(crMat)
   crPred = apply(crMat,1,mean)
   message("empirical coverage rate:")
   print(crPred)
   if(saveRslt)
   { 
     save(replication,file=paste0(saveDir,'/replication.RData'))
     save(crMat,file=paste0(saveDir,'/crMat.RData'))
     save(crPred,file=paste0(saveDir,'/crPred.RData'))
   }

   list(replication=replication,crMat=crMat,meanCR=crPred)
 }
 #note that nRep=2 is for illustration only, for more stable result, use nRep>=500.
 simPredCR = runSimPredCR(nRep=2,nObs=100)
 
# }
# NOT RUN {
   # for more stable simulation result, run with nRep = 500.
   simPredCR = runSimPredCR(nRep=500,nObs=100)
   message("Empirical coverage rate:")
   print(simPredCR$meanCR)
 
# }