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A Consistent Test of Stationary Ergodicity

Domowitz, Ian and El-gamal, Mahmoud A. (1993) A Consistent Test of Stationary Ergodicity. Social Science Working Paper, 794. California Institute of Technology , Pasadena, CA. (Unpublished)

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A formal statistical test of stationary-ergodicity is developed for known Markovian processes on R^d. 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.

Item Type:Report or Paper (Working Paper)
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Additional Information:Revised version. Original dated to April 1992. This is a completely different version of an earlier paper ([9], based on Chapter 4 of [11]) that was presented in the 1988 North American Summer Meetings of the Econometric Society. We thank Lars Peter Hansen, Bo Honoré, Dale Mortensen, Adrian Pagan, Mark Watson, Jeffrey Wooldridge, and two anonymous referees and participants in the econometrics workshops at Northwestern, Rochester, and Yale for their helpful comments and suggestions. We particularly want to express our thanks to Donald W. K. Andrews for going well beyond the line of duty in offering a series of very useful suggestions which resulted in a significantly improved paper. Financial support from the NSF is gratefully acknowledged. We thank the Jet Propulsion Laboratory for giving us access to their Cray YMP2E/116. Any remaining flaws are, of course, our own. Published as Domowitz, Ian, and Mahmoud A. El-Gamal. "A consistent test of stationary-ergodicity." Econometric Theory 9, no. 4 (1993): 589-601.
Group:Social Science Working Papers
Funding AgencyGrant Number
Subject Keywords:Ergodic theory, Density, Statistical estimation, Laws of Motion, Null hypothesis, Economic models, Statistics, Goodness of fit, Mathematical vectors, Test theory
Series Name:Social Science Working Paper
Issue or Number:794
Record Number:CaltechAUTHORS:20170829-151422958
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80924
Deposited By: Jacquelyn Bussone
Deposited On:30 Aug 2017 17:35
Last Modified:03 Oct 2019 18:36

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