sigma_hat {rlfsm}

Statistical estimator for sigma

Description

Statistical estimator for sigma

Usage

sigma_hat(t1, k, path, alpha, H, freq)

Arguments

t1

real number such that t1 > 0

k

increment order

path

sample path of lfsm on which the inference is to be performed

alpha

self-similarity parameter of alpha stable random motion.

H

Hurst parameter

freq

Frequency of the motion. It can take two values: "H" for high frequency and "L" for the low frequency setting.

Examples

m<-45; M<-60; N<-2^14-M
alpha<-1.8; H<-0.8; sigma<-0.3
freq='H'
r=1; k=2; p=0.4; t1=1; t2=2

# Reproducing the work of ContinEstim
# in high frequency case
lfsm<-path(N=N,m=m,M=M,alpha=alpha,H=H,
           sigma=sigma,freq='L',disable_X=FALSE,seed=1)$lfsm

H_est<-H_hat(p=p,k=k,path=lfsm)
H_est
alpha_est<-alpha_hat(t1=t1,t2=t2,k=k,path=lfsm,H=H_est,freq=freq)
alpha_est

sigma_est<-tryCatch(
                    sigma_hat(t1=t1,k=k,path=lfsm,
                    alpha=alpha_est,H=H_est,freq=freq),
                    error=function(c) 'Impossible to compute sigma_est')
sigma_est