extremefit (version 1.0.2)

predict.hill.ts: Predict the adaptive survival or quantile function for a time serie

Description

Give the adaptive survival function or quantile function of a time serie

Usage

# S3 method for hill.ts
predict(object, newdata = NULL, type = "quantile",
  input = NULL, ...)

Value

p

the input vector of probabilities.

x

the input vector of values.

Tgrid

Tgrid output of the function hill.ts.

quantiles

the estimted quantiles assiociated to newdata.

survival

the estimated survival function assiociated to newdata.

Arguments

object

output object of the function hill.ts.

newdata

optionally, a data frame or a vector with which to predict. If omitted, the original data points are used.

type

either "quantile" or "survival".

input

optionnaly, the name of the variable to estimate.

...

further arguments passed to or from other methods.

Details

If type = "quantile", \(newdata\) must be between 0 and 1. If type = "survival", \(newdata\) must be in the domain of the data from the function hill.ts. If \(newdata\) is a data frame, the variable from which to predict must be the first one or its name must start with a "p" if type = "quantile" and "x" if type = "survival". The name of the variable from which to predict can also be written as \(input\).

References

Durrieu, G. and Grama, I. and Jaunatre, K. and Pham, Q.-K. and Tricot, J.-M. (2018). extremefit: A Package for Extreme Quantiles. Journal of Statistical Software, 87, 1--20.

See Also

hill.ts

Examples

#Generate a pareto mixture sample of size n with a time varying parameter
theta <- function(t){
   0.5+0.25*sin(2*pi*t)
 }
n <- 4000
t <- 1:n/n
Theta <- theta(t)
Data <- NULL
set.seed(1240)
for(i in 1:n){
   Data[i] <- rparetomix(1, a = 1/Theta[i], b = 1/Theta[i]+5, c = 0.75, precision = 10^(-5))
 }
if (FALSE)  #For computing time purpose
  #choose the bandwidth by cross validation
  Tgrid <- seq(0, 1, 0.1)#few points to improve the computing time
  hgrid <- bandwidth.grid(0.01, 0.2, 20, type = "geometric")
  hcv <- bandwidth.CV(Data, t, Tgrid, hgrid, TruncGauss.kernel,
         kpar = c(sigma = 1), pcv = 0.99, CritVal = 3.6, plot = TRUE)
  h.cv <- hcv$h.cv

  #we modify the Tgrid to cover the data set
  Tgrid <- seq(0, 1, 0.02)
  hillTs <- hill.ts(Data, t, Tgrid, h = h.cv, TruncGauss.kernel, kpar = c(sigma = 1),
           CritVal = 3.6, gridlen = 100, initprop = 1/10, r1 = 1/4, r2 = 1/20)
  p <- c(0.999)
  pred.quantile.ts <- predict(hillTs, newdata = p, type = "quantile")
  true.quantile <- NULL
  for(i in 1:n){
     true.quantile[i] <- qparetomix(p, a = 1/Theta[i], b = 1/Theta[i]+5, c = 0.75)
   }
  plot(Tgrid, log(as.numeric(pred.quantile.ts$y)),
       ylim = c(0, max(log(as.numeric(pred.quantile.ts$y)))), ylab = "log(0.999-quantiles)")
  lines(t, log(true.quantile), col = "red")
  lines(t, log(Data), col = "blue")


  #comparison with other fixed bandwidths

  plot(Tgrid, log(as.numeric(pred.quantile.ts$y)),
       ylim = c(0, max(log(as.numeric(pred.quantile.ts$y)))), ylab = "log(0.999-quantiles)")
  lines(t, log(true.quantile), col = "red")

  hillTs <- hill.ts(Data, t, Tgrid, h = 0.1, TruncGauss.kernel, kpar = c(sigma = 1),
                    CritVal = 3.6, gridlen = 100,initprop = 1/10, r1 = 1/4, r2 = 1/20)
  pred.quantile.ts <- predict(hillTs, p, type = "quantile")
  lines(Tgrid, log(as.numeric(pred.quantile.ts$y)), col = "green")


  hillTs <- hill.ts(Data, t, Tgrid, h = 0.3, TruncGauss.kernel, kpar = c(sigma = 1),
               CritVal = 3.6, gridlen = 100, initprop = 1/10, r1 = 1/4, r2 = 1/20)
  pred.quantile.ts <- predict(hillTs, p, type = "quantile")
  lines(Tgrid, log(as.numeric(pred.quantile.ts$y)), col = "blue")


  hillTs <- hill.ts(Data, t, Tgrid, h = 0.04, TruncGauss.kernel, kpar = c(sigma = 1),
             CritVal = 3.6, gridlen = 100, initprop = 1/10, r1 = 1/4, r2 = 1/20)
  pred.quantile.ts <- predict(hillTs ,p, type = "quantile")
  lines(Tgrid, log(as.numeric(pred.quantile.ts$y)), col = "magenta")