NSGEV

The NSGEV R package is devoted to some Non-Stationary Extreme Value models.

The main function of the package is TVGEV which creates an object with class "TVGEV" representing a Time-Varying model with GEV margins depending on the time. This kind of model is especially useful to study block maxima, usually annual maxima. This kind of models could be used with CRAN packages such as extRemes, yet NSGEV makes it easier to cope with bases of functions. It also brings some new things such as the profile likelihood confidence intervals on the return levels or on the quantile of the maximum on an arbitrary period.

Example

In this example we use the annual maxima of the daily maximal temperature (TX) in Dijon (France) provided as the TXMax_Dijon data frame. Note that the warnings and messages will not be shown in this example.

The annual maxima in Celsius are given in in the column TXMax

library(NSGEV)
head(TXMax_Dijon)
#>   Year TXMax
#> 1 1921    NA
#> 2 1922    NA
#> 3 1923    NA
#> 4 1924  33.6
#> 5 1925  34.2
#> 6 1926  34.8

A TVGEV model requires a date variable indicating the beginnings of the annual blocks. This variable can be easily created from the Year variable

df <- within(TXMax_Dijon, Date <- as.Date(paste0(Year, "-01-01")))
fit0 <- TVGEV(data = df, response = "TXMax", date = "Date",
              loc = ~ 1)
coef(fit0)
#>     mu_0  sigma_0     xi_0 
#> 32.94616  1.87935 -0.19645
autoplot(fit0)

We can fit a model with a linear time trend. A possibility is to use the polynomX function that creates a basis of polynomial functions for a given degree. This makes a variable t1 available for the fit

fit1 <- TVGEV(data = df, response = "TXMax", date = "Date",
              design = polynomX(date = Date, degree = 1),
              loc = ~ t1)
autoplot(fit1)

coef(fit1)
#>        mu_0       mu_t1     sigma_0        xi_0 
#> 32.93752186  0.01527735  1.84567285 -0.20471258

The predict method can be used to compute conditional return levels corresponding to a given year, be it a past or future year. Since a TVGEV object keeps trace of the design function(s) used the prediction does not require a data preparation step. By default the “new” dates at which the return levels are computed are those in the data frame used to fit the model

pred <- predict(fit1)
autoplot(pred)

autoplot(predict(fit1, confint = "proflik", trace = 0))

autoplot(predict(fit1, newdate = "2040-01-01", confint = "proflik", trace = 0))

The default confidence intervals are obtained by using the “delta method” but profile likelihood intervals can be obtained as well by using the confintMethod argument (possibly abbreviated as confint of conf). Note that the autoplot method is to be used rather than the plot method, because the **ggplot2* package is used.

Rather than the maximum on a specific block, one can consider the maximum $M$ on a larger period as sometimes called a design life period. The distribution of $M$ is then no longer a GEV but the its quantiles can be computed with confidence intervals

date <- as.Date(paste0(2025:2040, "-01-01"))
qm <- quantMax(fit1, date = date, confint = "proflik", trace = 0)
autoplot(qm) + ggtitle("Quantile of the maximum on 2025-2040")

By changing the value of the design argument one can different use basis functions such as splines with given knots.

INSTALLATION

library(remotes)
install_github("IRSN/NSGEV", dependencies = TRUE)

install_github("IRSN/NSGEV", dependencies = TRUE, build_vignettes = TRUE)