Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-28T12:21:34.895Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Ahrens, J. & Dieter, U.. Computer methods for sampling from gamma, beta, poisson and binomial distributions. Computing 12 (1974): 223–246.Google Scholar
2.Bierens, H.ARMAX model specification testing, with an application to unemployment in the Netherlands. Journal of Econometrics 35 (1987): 161–190.CrossRefGoogle Scholar
3.Bierens, H.ARMA Memory index modeling of economic time series (with discussion). Econometric Theory 4 (1988): 35–59.Google Scholar
4.Bierens, H.A Consistent conditional moment test of functional form. Econometrica 58, (1990): 1443–1458.Google Scholar
5.Bierens, H. & Hartog, J.. Non-linear regression with discrete explanatory variables, with an application to the earnings function. Journal of Econometrics 38 (1988): 269–299.Google Scholar
6.Cornfeld, I., Fomin, S. & Sinai, Ya.. Ergodic Theory. Berlin: Springer-Verlag, 1982.Google Scholar
7.Davies, R.Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrica 64 (1977): 247–254.Google Scholar
8.Devroye, L.Non-Uniform Random Variate Generation. New York: Springer-Verlag, 1986.CrossRefGoogle Scholar
9.Domowitz, I. & El-Gamal, M.. A Test of the Harris Ergodicity of Stationary Dynamical Economic Models. RCER working paper #157, University of Rochester, 1988.Google Scholar
10.Doob, J.Stochastic Processes. New York: Wiley, 1953.Google Scholar
11.El-Gamal, M. Estimation in Economic Systems Characterized by Deterministic Chaos. Ph.D. Dissertation, Northwestern University, 1988.Google Scholar
12.Gallant, A.R. & Tauchen, G.. Seminonparametric estimation of conditionally constrained heterogeneous processes. Econometrica 57 (1989).Google Scholar
13.Harris, T.E. The existence of stationary measures for certain Markov processes. In Neyman, J. (ed.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press, 1956.Google Scholar
14.Khmaladze, E.An innovation approach to goodness-of-fit tests in ℝm. The Annals of Statistics 16 (1988): 1503–1516.CrossRefGoogle Scholar
15.Loéve, M.Probability Theory II, 4th Edition. New York: Springer-Verlag, 1978.Google Scholar
16.Piterbarg, V. & Fatalov, V.. Exact asymptotics for probabilities of large deviations for certain Gaussian fields of use in statistics. In Kolmogorov, A.N. (ed.), Probabilistic Methods of Research. Moscow: Moscow University Press, 1983.Google Scholar
17.Press, W.H., Flannery, B.P., Teukolsky, S.A., & Vetterling, W.T.Numerical Recipes in C; The Art of Scientific Computing. Cambridge: Cambridge Univ. Press, 1988.Google Scholar
18.Shorack, G. & Wellner, J.Empirical Processes with Applications to Statistics. New York: Wiley, 1986.Google Scholar