  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.
