alpha_hat {rlfsm} | R Documentation |
Defined for the two frequencies as
\widehat α_{high} := \frac{\log | \log \varphi_{high} (t_2; \widehat H_{high} (p,k)_n, k)_n| - \log | \log \varphi_{high} (t_1; \widehat H_{high} (p,k)_n, k)_n|}{\log t_2 - \log t_1}
\widehat α_{low} := \frac{\log | \log \varphi_{low} (t_2;k)_n| - \log | \log \varphi_{low} (t_1; k)_n|}{\log t_2 - \log t_1}
alpha_hat(t1, t2, k, path, H, freq)
t1 |
real number such that t2 > t1 > 0 |
t2 |
real number such that t2 > t1 > 0 |
k |
increment order |
path |
sample path of lfsm on which the inference is to be performed |
H |
Hurst parameter |
freq |
Frequency of the motion. It can take two values: "H" for high frequency and "L" for the low frequency setting. |
The function triggers function phi
, thus Hurst parameter is required only in high frequency case. In the low frequency, there is no need to assign H a value because it will not be evaluated.
Mazur S, Otryakhin D, Podolskij M (2018). “Estimation of the linear fractional stable motion.” Aarhus University.
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 # Estimating alpha in the high frequency case # using preliminary estimation of H lfsm<-path(N=N,m=m,M=M,alpha=alpha,H=H, sigma=sigma,freq='L',disable_X=FALSE,seed=3)$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