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A Consistent Test of Stationary-Ergodicity

Published online by Cambridge University Press:  11 February 2009

Ian Domowitz  and
Mahmoud A. El-Gamal
Ian Domowitz
Affiliation:
Northwestern University
Mahmoud A. El-Gamal
Affiliation:
California Institute of Technology
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Abstract

A formal statistical test of stationary-ergodicity is developed for known Markovian processes on ℝd This makes it applicable to testing models and algorithms, as well as estimated time series processes ignoring the estimation error. The analysis is conducted by examining the asymptotic properties of the Markov operator on density space generated by the transition in the state space. The test is developed under the null of stationary-ergodicity, and it is shown to be consistent against the alternative of nonstationary-ergodicity. The test can be easily performed using any of a number of standard statistical and mathematical computer packages.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 4 , August 1993 , pp. 589 - 601
Copyright
Copyright © Cambridge University Press 1993

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