goftest.hill.ts: Goodness of fit test statistics for time series

Description

Give the results of the goodness of fit test for testing the null hypothesis that the tail is fitted by a Pareto distribution starting from the adaptive threshold (for more details see pages 447 and 448 of Durrieu et al. (2015)).

Usage

# S3 method for hill.ts
goftest(object, X, t, plot = FALSE, ...)

Arguments

object

output of the hill.ts function.

a vector of the observed values.

a vector of time covariates which should have the same length as X.

plot

If TRUE, the test statistic are plotted.

...

further arguments passed to or from other methods.

Value

TS.window

the maximum value of test statistics inside the window for each t in Tgrid (see help(hill.ts) ).

TS.max

the maximum value of test statistics for each t in Tgrid (see help(hill.ts) ).

CritVal

the critical value of the test.

References

Grama, I. and Spokoiny, V. (2008). Statistics of extremes by oracle estimation. Ann. of Statist., 36, 1619-1648.

Durrieu, G. and Grama, I. and Pham, Q. and Tricot, J.- M (2015). Nonparametric adaptive estimator of extreme conditional tail probabilities quantiles. Extremes, 18, 437-478.

Examples

Run this code

# NOT RUN {
theta<-function(t){0.5+0.25*sin(2*pi*t)}
n<-5000
t<-1:n/n
Theta<-theta(t)
Data<-NULL
Tgrid<-seq(0.01,0.99,0.01)
#example with fixed bandwidth
for(i in 1:n){Data[i]<-rparetomix(1,a=1/Theta[i],b=5/Theta[i]+5,c=0.75,precision=10^(-5))}
# }
# NOT RUN {
 #For computing time purpose
  #example
  hgrid <- bandwidth.grid(0.009, 0.2, 20, type = "geometric")
  TgridCV <- seq(0.01, 0.99, 0.1)
  hcv <- bandwidth.CV(Data, t, TgridCV, hgrid, pcv = 0.99,
         TruncGauss.kernel, kpar = c(sigma = 1), CritVal = 3.6, plot = TRUE)

  Tgrid <- seq(0.01,0.99,0.01)
  hillTs <- hill.ts(Data, t, Tgrid, h = hcv$h.cv, TruncGauss.kernel, kpar = c(sigma = 1),
                   CritVal = 3.6, gridlen = 100, initprop = 1/10, r1 = 1/4, r2 = 1/20)
  goftest(hillTs, Data, t, plot = TRUE)

  # we observe that for this data, the null hypothesis that the tail
  # is fitted by a Pareto distribution is not rejected
  # for all points on the Tgrid

# }
# NOT RUN {

# }