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A new recursive method is proposed for fitting multivariate ARX models and testing their stability from impulse response and output covariance information. This recursive algorithm, differing from that of Mullis and Roberts, consists of two types of recurrences, one of which is related to updating AR orders and the other to updating MA orders. It offers more computational convenience especially in case of choosing the correct orders of ARX models. It is further shown that "Burg identities" are also proved crucial in deducing some important relations between the resulting polynomial matrices as in the case of the multivariate autoregression. These realtions together with the generalized Rouche 's theorem are applied to testing stability of the fitted ARX models at each step of the recursion.