GenHighEstim {rlfsm} | R Documentation |
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
GenHighEstim(p, p_prime, path, freq, low_bound = 0.01, up_bound = 4)
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 |
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.
Mazur S, Otryakhin D, Podolskij M (2018). “Estimation of the linear fractional stable motion.” Aarhus University.
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")