Maximum Likelihood Estimation via Toeplitz Gaussian Likelihood

Estimates the spectral basis coefficients that maximize the Gaussian log-likelihood of a univariate time series with autocovariance structure modeled by B-spline basis functions.

Usage

optim_toeplitz_mle(c_init, knots, k, y)

Arguments

c_init

A numeric vector of positive initial values for the coefficients.

knots

A numeric vector of knot locations defining the B-spline basis.

k

The degree of the B-spline basis functions.

y

A numeric vector representing the observed time series.

Value

An object of class optim, containing the MLE estimates (on the log scale), convergence diagnostics, and gradient information.

Details

This function uses optim with the BFGS method to maximize the log-likelihood under a Gaussian process model with a Toeplitz covariance matrix, using compute_toeplitz_loglik and compute_toeplitz_loglik_grad. The optimization is unconstrained by reparameterizing c on the log scale.

The final estimates (in log-scale) are returned in $par, and can be transformed back via exp(result$par).

See also

compute_toeplitz_loglik, compute_toeplitz_loglik_grad, optim