Approximation with ergodic processes and testability Academic Article uri icon

Abstract

  • We show that stationary time series can be uniformly approximated over all finite time intervals by mixing processes, non-ergodic processes, and non-mean-ergodic processes. Therefore, the ergodic hypothesis---that time averages will converge to their statistical counterparts---and several adjacent hypotheses are not testable in the nonparametric case. A similar approximation result is provided for codings of aperiodic time series. Further Baire category implications are also explored.

Publication Date

  • 2024-01-01