AbstractIntheparametertrackingoftime-varyingsystems,theordinarymethodisweightedleastsquareswiththerectangularwindowortheexponentialwindow.Inthispaperweproposeanewkindofslidingwindowcalledthemultipleexponentialwindow,andthenuseittofittime-varyingGaussianvectorautoregressivemodels.Theasymptoticbiasandcovarianceoftheestimatoroftheparameterfortime-invariantmodelsarealsoderived.Simulationresultsshowthatthemultipleexponentialwindowshavebetterparametertrackingeffectthanrectangularwindowsandexponentialones.