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Approximation with ergodic processes and testability

Part of: Nonparametric inference Ergodic theory

Published online by Cambridge University Press:  23 January 2024

Isaac Loh Open the ORCID record for Isaac Loh [Opens in a new window]
Isaac Loh*
Affiliation:
UNC Wilmington
*
*Postal address: Department of Economics and Finance, UNC Wilmington, 601 South College Road, Wilmington NC 28403. Email: lohi@uncw.edu
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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.

Keywords

Mixingtestabilityergodicity

MSC classification

Primary: 37A50: Relations with probability theory and stochastic processes
Secondary: 62G10: Hypothesis testing
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 20
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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