GenLowEstim {rlfsm}

Low frequency estimation procedure for lfsm.

Description

General estimation procedure for low frequency case when 1/alpha is not a natural number.

Usage

GenLowEstim(t1, t2, p, path, freq = "L")

Arguments

t1, t2

real number such that t2 > t1 > 0

p

power

path

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

freq

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

References

Mazur S, Otryakhin D, Podolskij M (2020). “Estimation of the linear fractional stable motion.” Bernoulli, 26(1), 226–252. https://doi.org/10.3150/19-BEJ1124.

Examples

m<-45; M<-60; N<-2^10-M
sigma<-0.3
p<-0.3; k=3; t1=1; t2=2

#### Continuous case
lfsm<-path(N=N,m=m,M=M,alpha=1.8,H=0.8,
           sigma=sigma,freq='L',disable_X=FALSE,seed=3)$lfsm

GenLowEstim(t1=t1,t2=t2,p=p,path=lfsm,freq="L")

#### H-1/alpha<0 case
lfsm<-path(N=N,m=m,M=M,alpha=0.8,H=0.8,
           sigma=sigma,freq='L',disable_X=FALSE,seed=3)$lfsm

GenLowEstim(t1=t1,t2=t2,p=p,path=lfsm,freq="L")

#### The procedure works also for high frequency case
lfsm<-path(N=N,m=m,M=M,alpha=1.8,H=0.8,
           sigma=sigma,freq='H',disable_X=FALSE,seed=3)$lfsm

GenLowEstim(t1=t1,t2=t2,p=p,path=lfsm,freq="H")