GenHighEstim {rlfsm}

High frequency estimation procedure for lfsm.

Description

General estimation procedure for high frequency case when 1/alpha is not a natural number. "Unnecessary" parameter freq is preserved to allow for investigation of the inference procedure in low frequency case

Usage

GenHighEstim(p, p_prime, path, freq, low_bound = 0.01, up_bound = 4)

Arguments

p

power

p_prime

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.

low_bound

positive real number

up_bound

positive real number

Details

In this algorithm the preliminary estimate of alpha is found via using uniroot function. The latter is given the lower and the upper bounds for alpha via low_bound and up_bound parameters. It is not possible to pass 0 as the lower bound because there are numerical limitations on the alpha estimate, caused by the length of the sample path and by numerical errors. p and p_prime must belong to the interval (0,1/2) (in the notation kept in rlfsm package) The two powers cannot be equal.

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<-0.2; p_prime<-0.4

#### 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

GenHighEstim(p=p,p_prime=p_prime,path=lfsm,freq="H")

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

GenHighEstim(p=p,p_prime=p_prime,path=lfsm,freq="H")