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A Consistent Nonparametric Test of Ergodicity for Time Series with Applications

  • Domowitz, I.
  • El-Gamal, M.A.

We propose a set of algorithms for testing the ergodicity of empirical time series, without reliance on a specific parametric framework. It is shown that the resulting test asymptotically obtains the correct size for stationary and nonstationary processes, and maximal power against non-ergodic but stationary alternatives. The test will not reject in the presence of nonstationarity that does not lead to ergodic failure. The work is linked to recent research on reformulations of the concept of integrated processes of order zero, and we demonstrate the means to operationalize new concepts of "short memory" for economic time series. Limited Monte Carlo evidence is provided with respect to power against the non-stationary and non-ergodic alternative of unit root processes. The method is used to investigate debates over stability of monetary aggregates relative to GDP, and the mean reversion hypothesis with respect to high frequency data on exchange rates.

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Paper provided by Wisconsin Madison - Social Systems in its series Working papers with number 9716.

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Length: 36 pages
Date of creation: 1997
Date of revision:
Handle: RePEc:att:wimass:9716

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  1. Robert P. Flood & Peter M. Garber, 1981. "A Model of Stochastic Process Switching," NBER Working Papers 0626, National Bureau of Economic Research, Inc.
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  10. Peter C.B. Phillips, 1993. "Fully Modified Least Squares and Vector Autoregression," Cowles Foundation Discussion Papers 1047, Cowles Foundation for Research in Economics, Yale University.
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  13. George Roussas, 1969. "Nonparametric estimation in Markov processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 21(1), pages 73-87, December.
  14. John Y. Campbell & Pierre Perron, 1991. "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Chapters, in: NBER Macroeconomics Annual 1991, Volume 6, pages 141-220 National Bureau of Economic Research, Inc.
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  25. Bleaney, Michael & Mizen, Paul, 1996. "Nonlinearities in Exchange-Rate Dynamics: Evidence from Five Currencies, 1973-94," The Economic Record, The Economic Society of Australia, vol. 72(216), pages 36-45, March.
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  27. Arthur, W Brian, 1989. "Competing Technologies, Increasing Returns, and Lock-In by Historical Events," Economic Journal, Royal Economic Society, vol. 99(394), pages 116-31, March.
  28. Domowitz, Ian & El-Gamal, Mahmoud A., 1993. "A Consistent Test of Stationary-Ergodicity," Econometric Theory, Cambridge University Press, vol. 9(04), pages 589-601, August.
  29. Eckstein, Zvi & Foulides, Costas & Kollintzas, Tryphon, 1991. "On the Many Kinds of Growth," CEPR Discussion Papers 592, C.E.P.R. Discussion Papers.
  30. Durlauf, S.M. & Johnson, P.A., 1995. "Multiple Regimes and Cross-Country Growth Behavior," Working papers 9419r, Wisconsin Madison - Social Systems.
  31. Bollerslev, Tim & Domowitz, Ian, 1993. " Trading Patterns and Prices in the Interbank Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 48(4), pages 1421-43, September.
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  35. Martin Feldstein & James H. Stock, 1994. "The Use of a Monetary Aggregate to Target Nominal GDP," NBER Chapters, in: Monetary Policy, pages 7-69 National Bureau of Economic Research, Inc.
  36. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March.
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