rlfsm-deprecated: The function explores numerical properties of statistical...

Description Usage Arguments Details Value

Description

The function is left for backward compatibility. The newer version of it is MCestimLFSM. The function is useful, for instance, when one needs to compute standard deviation of \widehat α_{high} estimator given a fixed set of parameters.

Usage

1
CLT(Nmc, s, m, M, alpha, H, sigma, fr, Inference, ...)

Arguments

Nmc

Number of Monte Carlo repetitions

s

sequence of path lengths

m

discretization. A number of points between two nearby motion points

M

truncation parameter. A number of points at which the integral representing the definition of lfsm is calculated. So, after M points back we consider the rest of the integral to be 0.

alpha

self-similarity parameter of alpha stable random motion.

H

Hurst parameter

sigma

Scale parameter of lfsm

fr

frequency. Either "H" or "L"

Inference

statistical function to apply to sample paths

...

parameters to pass to Inference

Details

CLT performs Monte-Carlo experiments to compute parameters according to procedure Inference. More specifically, for each element of s it generates Nmc lfsm sample paths with length equal to s[i], performs the statistical inference on each, obtaining the estimates, and then returns their different statistics. It is vital that the estimator returns a list of named parameters (one or several of 'sigma', 'alpha' and 'H'). CLT uses the names to lookup the true parameter value and compute its bias.

For sample path generation CLT uses a light-weight version of path, path_fast. In order to be applied, function Inference must accept argument 'path' as a sample path.

Value

It returns a list containing the following components:

CLT_dataset

a data frame, standardized values of the estimates depending on path length s

BSdM

a data frame, means, biases and standard deviations depending on s

Inference

a closure used to obtain estimates

alpha, H, sigma

the parameters for which CLT performs path generation

freq

frequency, either 'L' for low- or 'H' for high frequency


rlfsm documentation built on April 16, 2021, 5:06 p.m.