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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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File URL: http://www.ssc.wisc.edu/econ/archive/wp9716.pdf
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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
Contact details of provider: Postal: UNIVERSITY OF WISCONSIN MADISON, SOCIAL SYSTEMS RESEARCH INSTITUTE(S.S.R.I.), MADISON WISCONSIN 53706 U.S.A.

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  1. Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
  2. Friedman, Benjamin M, 1988. "Lessons on Monetary Policy from the 1980s," Journal of Economic Perspectives, American Economic Association, vol. 2(3), pages 51-72, Summer.
  3. Schwert, G William, 1989. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(2), pages 147-59, April.
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  5. 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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  10. Norman R. Swanson, 2010. "Further Developments in the Study of Cointegrated Variables," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 8(2), pages 187-190, spring.
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  12. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
  13. Martin Feldstein, 1992. "The Recent Failure of U.S. Monetary Policy," NBER Working Papers 4236, National Bureau of Economic Research, Inc.
  14. Steven N. Durlauf & Paul A. Johnson, 1992. "Local Versus Global Convergence Across National Economies," NBER Working Papers 3996, National Bureau of Economic Research, Inc.
  15. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-78, September.
  16. 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.
  17. 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.
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  19. Bierens, H.J., 1989. "A consistent conditional moment test of functional form," Serie Research Memoranda 0064, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  20. El-Gamal, Mahmoud A, 1991. "Non-parametric Estimation of Deterministically Chaotic Systems," Economic Theory, Springer, vol. 1(2), pages 147-67, April.
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  22. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
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  24. Danny Quah, 1992. "Empirical cross-section dynamics in economic growth," Discussion Paper / Institute for Empirical Macroeconomics 75, Federal Reserve Bank of Minneapolis.
  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. Eckstein, Zvi & Foulides, Costas & Kollintzas, Tryphon, 1991. "On the Many Kinds of Growth," CEPR Discussion Papers 592, C.E.P.R. Discussion Papers.
  28. Friedman, Benjamin M & Kuttner, Kenneth N, 1992. "Money, Income, Prices, and Interest Rates," American Economic Review, American Economic Association, vol. 82(3), pages 472-92, June.
  29. George Roussas, 1969. "Nonparametric estimation in Markov processes," Annals of the Institute of Statistical Mathematics, Springer, vol. 21(1), pages 73-87, December.
  30. Durlauf, S.M. & Johnson, P.A., 1995. "Multiple Regimes and Cross-Country Growth Behavior," Working papers 9419r, Wisconsin Madison - Social Systems.
  31. Engel, Charles & Hamilton, James D, 1990. "Long Swings in the Dollar: Are They in the Data and Do Markets Know It?," American Economic Review, American Economic Association, vol. 80(4), pages 689-713, September.
  32. 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.
  33. Schwert, G. William, 1987. "Effects of model specification on tests for unit roots in macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 20(1), pages 73-103, July.
  34. Catherine Bonser-Neal, 1996. "Does central bank intervention stabilize foreign exchange rates?," Economic Review, Federal Reserve Bank of Kansas City, issue Q I, pages 43-57.
  35. Duffie, Darrell, et al, 1994. "Stationary Markov Equilibria," Econometrica, Econometric Society, vol. 62(4), pages 745-81, July.
  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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