Abstract
This paper introduces a new class of estimates for estimating the parameters of a vector autoregressive time series. The estimates minimize a sum of weighted pairwise Euclidean distances and extend the univariate GR-estimates of Terpstra et al. (Statist. Probab. Lett. 51 (2001) 165; Statist. Inference Stochastic Process. 4 (2001) 155) to the multivariate model. Asymptotic linearity properties are derived for the so called MGR-estimate. Based on these properties, the MGR-estimate is shown to be asymptotically normal at rate n 1/2.
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