phi {rlfsm}

Phi

Description

Defined as

\varphi_{\textnormal{high}}(t; H,k)_n := V_{\textnormal{high}}(\psi_t; k)_n \qquad \textnormal{and} \qquad \varphi_{\textnormal{low}}(t; k)_n := V_{\textnormal{low}}(\psi_t; k)_n

, where \psi_t(x):=cos(tx)

Usage

phi(t, k, path, H, freq)

Arguments

t

positive real number

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.

Details

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.

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.