fitlm_GPD

Fits the three-parameter Generalised Pareto distribution to an xts series by the method of L-moments. Parameters are obtained in closed form via pelgpa, which matches the sample L-moment ratios to the theoretical L-moment ratios of the GPD. If bound is supplied the location is fixed; otherwise all three parameters are free. The shape parameter governs tail behaviour: values greater than -1/2 are required for finite variance, greater than -1/3 for finite skewness, and greater than -1/4 for finite kurtosis. Zero values below zero_threshold may be excluded via ignore_zeros. Goodness-of-fit is assessed via GOF_tests.

Usage

fitlm_GPD(x, bound = NULL, ignore_zeros = FALSE, zero_threshold = 0.01)

Arguments

x

An xts object containing the time series data.

bound

Numeric or NULL. Optional fixed lower bound (location). Default NULL.

ignore_zeros

Logical. If TRUE, values below zero_threshold are excluded. Default FALSE.

zero_threshold

Numeric. Threshold below which values are treated as zero. Default 0.01.

Value

A list with elements Distribution, Param (named list of fitted parameters), TheorLMom (theoretical L-moments), DataLMom (sample L-moments), and GoF (goodness-of-fit metrics).

Examples

x <- xts::xts(rgpd(365, location = 0, scale = 1, shape = -0.2),
              order.by = as.Date("2020-01-01") + 0:364)
fit <- fitlm_GPD(x)
#> [1] "Shape parameter must be >-1/2 for finite variance"
#> [1] "Shape parameter must be >-1/3 for finite skewness"
#> [1] "Shape parameter must be >-1/4 for finite kurtosis"
fit$Param
#> $location
#> [1] -0.01926867
#> 
#> $scale
#> [1] 1.10862
#> 
#> $shape
#> [1] -0.1187803
#>