TempStable {TempStable}

TempStable: A collection of methods to estimate parameters of different tempered stable distributions.

Description

A collection of methods to estimate parameters of different tempered stable distributions. Currently, there are three different tempered stable distributions to choose from: Tempered stable subordinator distribution, classical tempered stable distribution, normal tempered stable distribution. The package also provides functions to compute characteristic functions and tools to run Monte Carlo simulations.

Details

The package was developed by Till Massing and Cedric Juessen and is structurally based on the "StableEstim" package by Tarak Kharrat and Georgi N. Boshnakov.

Brief description of functions

TemperedEstim() TemperedEstim()computes all the information about the estimator. It allows the user to choose the preferred method and several related options.

Characteristic function, density function, probability function and other functions for every tempered stable distribution mentioned above. E.g. charTSS(), dCTS(), ...

Monte Carlo simulation: a tool to run a Monte Carlo simulation TemperedEstim_Simulation() is provided and can save output files or produce statistical summary.To parallelize this function, you can use parallelizeMCsimulation().

Examples

## basic example code
# Such a simulation can take a very long time. Therefore, it can make sense
# to parallelize after Monte Carlo runs. Parallelization of the simulation is
# now possible with [parallelizeMCsimulation()].

# For testing purposes, the amount of runs and parameters is greatly reduced.
# Therefore, the result is not meaningful. To start a meaningful simulation,
# the SampleSize could be, for example, 1000 and MCParam also 1000.

thetaT <- c(1.5,1,1,1,1,0)
res_CTS_ML_size4 <- TemperedEstim_Simulation(ParameterMatrix =
                                                rbind(thetaT),
                                              SampleSizes = c(4),
                                              MCparam = 4,
                                              TemperedType = "CTS",
                                              Estimfct = "ML",
                                              saveOutput = FALSE)

colMeans(sweep(res_CTS_ML_size4$outputMat[,9:14],2,thetaT), na.rm = TRUE)