Difference-based (auto)covariance/correlation estimation in change point regression with stationary errors.
Provides bias-reducing methods for (auto)covariance-correlation estimation in change point regression with stationary \(m\)-dependent errors without having to pre-estimate the underlying signal of the observations. In the same spirit, provides a robust estimator of the autorregressive coefficient in change point regression with stationary, \(AR(1)\) errors. It also includes a general projection-based method for covariance matrix estimation.
dbacf returns and plots by default (auto)covariance/correlation
estimates without pre-estimating the underlying not necessarily smooth
signal of observations with stationary \(m\)-dependent errors. The corresponding
plot method plot.dbacf allows for adjusting graphical
parameters to users' liking. This method is based on plot.acf.
dbacf_AR1 returns (auto)covariance/correlation estimates while
circumventing the difficult estimation of the underlying change point regression
function from observations with stationary \(AR(1)\) errors.
Given a matrix estimate, not necessarily positive definite, of
the covariance matrix of a stationary process,
nearPDToeplitz returns the nearest, in the Frobenius norm,
covariance matrix to the initial estimate. See projectToeplitz
for the projection of a given symmetric matrix onto the space of Toeplitz matrices.
See also symBandedToeplitz for creating a (stationary process'
large covariance) matrix by specifying its dimension and values of its
autocovariance function.
Tecuapetla-Gómez, I. itecuap@conabio.gob.mx
Grigoriadis, K.M., Frazho, A., Skelton, R. (1994). Application of alternating convex projection methods for computation of positive Toeplitz matrices, IEEE Transactions on signal processing 42(7), 1873--1875.
N. Higham (2002). Computing the nearest correlation matrix - a problem from finance, Journal of Numerical Analysis 22, 329--343.
Tecuapetla-Gómez, I and Munk, A. (2017). Autocovariance estimation in regression with a discontinuous signal and \(m\)-dependent errors: A difference-based approach. Scandinavian Journal of Statistics, 44(2), 346--368.
Levine, M. and Tecuapetla-Gómez, I. (2023). Autocovariance function estimation via difference schemes for a semiparametric change point model with \(m\)-dependent errors. Submitted.