splines_est: Compute the Splines Estimator.

In CovEsts: Nonparametric Estimators for Covariance Functions

Compute the Splines Estimator.

Description

Compute the estimated covariance function by using the method from Choi, Li & Wang (2013, pp. 614-617).

C(\tau) = \sum_{j = 1}^{m + p} \beta_{j} f_{j}^{(p-1)}(\tau^{2}),

where m is the number of nonboundary knots, p is the order of the splines, \tau is the isotropic distance, \beta_{j} are nonnegative weights and f_{j}^{(p)} are basis functions of order p. For optimisation, the Nelder-Mead and L-BFGS-B methods are used, the one which selects parameters which minimises the objective function is chosen.

Usage

splines_est(
  X,
  x,
  estCov,
  p,
  m,
  maxLag = length(X) - 1,
  type = "autocovariance",
  inital_pars = c(),
  control = list(maxit = 1000)
)

Arguments

X	A vector representing observed values of the time series.
x	A vector of lags.
estCov	An estimated autocovariance function to fit to (a vector).
p	The order of the splines.
m	The number of nonboundary knots.
maxLag	An optional parameter that determines the maximum lag to compute the estimated autocovariance function at. Defaults to length(X) - 1.
type	Compute either the 'autocovariance' or 'autocorrelation'. Defaults to 'autocovariance'.
inital_pars	An optional vector of parameters - can be used to fine tune the fit. By default, it is a vector of 0.5 whose length is m+p.
control	An optional list of optimisation parameters used in the optimisation process, see control in stats::optim.

Value

A vector whose values are the spline autocovariance estimates.

References

Choi, I., Li, B. & Wang, X. (2013). Nonparametric Estimation of Spatial and Space-Time Covariance Function. JABES 18, 611-630. https://doi.org/10.1007/s13253-013-0152-z

Examples

X <- rnorm(100)
x <- seq(0, 5, by = 0.25)
maxLag <- 5
estCov <- standard_est(X, maxLag = maxLag)
estimated <- splines_est(X, x, estCov, 3, 2, maxLag = maxLag)
estimated

CovEsts documentation built on Sept. 10, 2025, 10:39 a.m.