Abstract
This paper describes a procedure for testing the presence of a pure feedback loop in a transfer function model for a multivariate discrete dynamic stochastic system. A modification of the portmanteau statistic based on sample cross-covariance matrices of the prewhitened series is proposed. The statistic is shown to be asymptotically distributed according to a % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gaeq4Xdm2aaWbaaSqabeaacaaIYaaaaaaa!3E0C!\[\chi ^2 \]-distribution with certain degrees of freedom under some pure feedback assumptions. Some numerical results are given to show the behavior of the proposed method.
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Nakano, J., Tagami, S. A test for the presence of pure feedback in multivariate dynamic stochastic systems. Ann Inst Stat Math 41, 765–779 (1989). https://doi.org/10.1007/BF00057740
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DOI: https://doi.org/10.1007/BF00057740