Summary
We show that smoothness properties of a spectral density matrix and its optimal factor are closely related when the density satisfies theboundedness condition. This is crucial in proving multivariate generalizations of Baxter's inequality and obtaining rates of convergence of finite predictors. We rely on a technique of Lowdenslager and Rosenblum relating the optimal factor to the spectral density via Toeplitz operators.
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Cheng, R., Pourahmadi, M. Baxter's inequality and convergence of finite predictors of multivariate stochastic processess. Probab. Th. Rel. Fields 95, 115–124 (1993). https://doi.org/10.1007/BF01197341
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DOI: https://doi.org/10.1007/BF01197341
Mathematics Subject Classification (1991)
- 60G25