MinContrastEstim {rlfsm}R Documentation

Statistical estimator of sigma, alpha and H in low frequency setting based on minimal contrast estimation comparing the empirical characteristic function with the true one

Description

Estimates H using the H_hat function while sigma and alpha are obtained via

\arg\min_{σ, α} \int_{0}^{∞} (\varphi_n(t) - \varphi_{σ, α, H_{hat}}(t))^2 \exp(-t^2/2) d t

, where \varphi_n is the empirical characteristic function, see phi, and \varphi_{σ, α, H_{hat}} is the characteristic function of the kth order increment wrt the parameters σ, α, H_{hat}, see also increment.

Usage

MinContrastEstim(path, k, p, order_GH)

Arguments

path

low frequency sample path from which the parameters should be estimated.

k

order of increments.

p

any real number, the power used for H_hat.

order_GH

number of weights in the Gauss-Hermite approximation of the integral, see the gauss.hermite function from the spatstat package.

Details

This algorithm approximates the above integral using Gauss-Hermite quadrature and uses the L-BFGS-B method from the optim function to minimize over the parameters sigma and alpha. Due to numerical problems estimation of sigma below 0.01 and alpha or H below 0.05 is currently not possible.

References

Ljungdahl MM, Podolskij M (2019). “A Minimal Contrast Estimator for the Linear Fractional Stable Motion.” To be submitted.

Examples

m0 = 256
M0 = 600
alpha0 = 1.8
H0 = 0.8
sigma0 = 0.3
n = 100
X <- path(N = n, m = m0, M = M0, alpha = alpha0, H = H0, sigma = sigma0, freq = 'L')$lfsm
MinContrastEstim(path = X, k = 2, p = 0.4, order_GH = 8)


[Package rlfsm version 1.0.0 Index]