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Approximation with ergodic processes and testability
Published online by Cambridge University Press: 23 January 2024
Abstract
We show that stationary time series can be uniformly approximated over all finite time intervals by mixing, non-ergodic, non-mean-ergodic, and periodic processes, and by codings of aperiodic processes. A corollary is that the ergodic hypothesis—that time averages will converge to their statistical counterparts—and several adjacent hypotheses are not testable in the non-parametric case. Further Baire category implications are also explored.
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust