goftest.hill.ts {extremefit} R Documentation

## 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 class 'hill.ts'
goftest(object, X, t, plot = FALSE, ...)
```

### Arguments

 `object` output of the hill.ts function. `X` a vector of the observed values. `t` 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.

`hill.ts`, `goftest`

### Examples

```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

## End(Not run)

```

[Package extremefit version 1.0.2 Index]