MinContrastEstim {rlfsm} | R Documentation |
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
.
MinContrastEstim(path, k, p, order_GH)
path |
low frequency sample path from which the parameters should be estimated. |
k |
order of increments. |
p |
any real number, the power used for |
order_GH |
number of weights in the Gauss-Hermite approximation of the integral, see the |
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.
Ljungdahl MM, Podolskij M (2019). “A Minimal Contrast Estimator for the Linear Fractional Stable Motion.” To be submitted.
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)