dbacf-package {dbacf}

Autocovariance function estimation via difference-based methods

Description

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.

Autocovariance 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.

Covariance Matrix Estimation

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.

Author(s)

Tecuapetla-Gómez, I. [e-mail]

References

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.