cov_GHBMP: Covariance of Gaussian Haar-based multifractional processes

In Rmfrac: Simulation and Statistical Analysis of Multifractional Processes

Covariance of Gaussian Haar-based multifractional processes

Description

Computes the theoretical covariance matrix of a Gaussian Haar-based multifractional process.

Usage

cov_GHBMP(
  t,
  H,
  J = 8,
  theta = NULL,
  plot = FALSE,
  num.cores = availableCores(omit = 1)
)

Arguments

t	Time point or time sequence on the interval [0,1].
H	Hurst function H(t) which depends on t.
J	Positive integer. For large J values could be rather time consuming. Default is set to 8.
theta	Optional: Smoothing parameter.
plot	Logical: If TRUE, a 3D surface plot of the covariance function is plotted in interactive sessions.
num.cores	Number of cores to set up the clusters for parallel computing.

Details

To make it comparable with the empirical covariance function the same smoothing parameter theta can be used if needed.

Value

An m \times m matrix, where m is the length of t.

References

Ayache, A., Olenko, A. and Samarakoon, N. (2025). On Construction, Properties and Simulation of Haar-Based Multifractional Processes. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.48550/arXiv.2503.07286")}. (submitted).

See Also

GHBMP, est_cov

Examples

t <- seq(0, 1, by = 0.01)
H <- function(t) {return(0.5 - 0.4 * sin(6 * 3.14 * t))}

#Smoothed covariance function
cov_GHBMP(t, H, theta = 0.1, plot = TRUE)

#Non-smoothed covariance function
cov_GHBMP(t, H, plot = TRUE)

Rmfrac documentation built on Sept. 10, 2025, 10:31 a.m.