Joint Mean-Vector and Var-Matrix estimation for Locally Stationary VAR(1) processes

TL;DR

This paper introduces a method for jointly estimating time-varying mean vectors and VAR matrices in locally stationary VAR(1) processes using kernel-weighted least squares, with demonstrated simulation performance.

Contribution

It develops a joint estimation approach for both mean and VAR parameters in locally stationary VAR(1) models, allowing for smoothly changing coefficients and means.

Findings

Simulation results show accurate estimation of time-varying parameters.

The method effectively captures smooth changes in the VAR model.

Closed-form expressions for the local-linear weighting matrix are provided.

Abstract

During the last two decades, locally stationary processes have been widely studied in the time series literature. In this paper we consider the locally-stationary vector-auto-regression model of order one, or LS-VAR(1), and estimate its parameters by weighted least squares. The LS-VAR(1) we consider allows for a smoothly time-varying non-diagonal VAR matrix, as well as for a smoothly time-varying non-zero mean. The weighting scheme is based on kernel smoothers. The time-varying mean and the time-varying VAR matrix are estimated jointly, and the definition of the local-linear weighting matrix is provided in closed-from. The quality of the estimated curves is illustrated through simulation results.