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ABSENCE OF CHAOS AND 1/f SPECTRA, BUT EVIDENCE OF TAR NONLINEARITIES, IN THE CANADIAN EXCHANGE RATE

Published online by Cambridge University Press:  01 September 2004

APOSTOLOS SERLETIS  and
ASGHAR SHAHMORADI
APOSTOLOS SERLETIS
Affiliation:
University of Calgary
ASGHAR SHAHMORADI
Affiliation:
University of Calgary
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Abstract

This paper uses daily observations for the Canadian dollar–U.S. dollar exchange rate over the recent flexible exchange-rate period (from January 2, 1974, to October 28, 2002), and various tests from dynamical systems theory, such as a chaos test, a self-organized criticality test, and a threshold effects test, to support a stochastic nonlinear origin for the series.

Keywords

Threshold EffectsSelf-Organized CriticalityLyapunov Exponent
Type
NOTE
Information
Macroeconomic Dynamics , Volume 8 , Issue 4 , September 2004 , pp. 543 - 551
Copyright
© 2004 Cambridge University Press

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References

Andrews D.W.K. 1991 Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817– 858.Google Scholar
Bailey B.A. 1996 Local Lyapunov exponents: Predictability depends on where you are. In W.A. Barnett, A.P. Kirman, & M. Salmon (eds.), Nonlinear Dynamics and Economics, pp. 345– 359. Cambridge, UK: Cambridge University Press.
Bak P., C. Tang & K. Wiesenfeld 1987 Self-organized criticality: An explanation of 1/f noise. Physical Review Letters 59, 381– 384.Google Scholar
Bak P., C. Tang & K. Wiesenfeld 1988 Self-organized criticality. Physical Review A 38, 364– 374.Google Scholar
Dickey D.A. & W.A. Fuller 1981 Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica 49, 1057– 1072.Google Scholar
Eckmann J.-P. & D. Ruelle 1985 Ergodic theory of chaos and strange attractors. Reviews of Modern Physics 57, 617– 656.Google Scholar
Eckmann J.-P., S.O. Kamphorst, D. Ruelle & S. Ciliberto 1986 Liapunov exponents from time series. Physical Review A 34, 4971– 4979.Google Scholar
Hansen B.E. 1996 Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 64, 413– 430.Google Scholar
Kwiatkowski D., P.C.B. Phillips, P. Schmidt & Y. Shin 1992 Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics 54, 159– 178.Google Scholar
Li W. 1991 Absence of 1/f Spectra in Dow Jones Average. International Journal of Bifurcation and Chaos 1, 583– 597.Google Scholar
Linton O. & M. Shintani 2003 Is there chaos in the world economy? A nonparametric test using consistent standard errors. International Economic Review 44, 331– 358.Google Scholar
MacKinnon J.G. 1994 Approximate asymptotic distribution functions for unit-root and cointegration tests. Journal of Business and Economic Statistics 12, 167– 176.Google Scholar
Nychka D.W., S. Ellner, A.R. Gallant & D. McCaffrey 1992 Finding chaos in noisy systems. Journal of the Royal Statistical Society B 54, 399– 426.Google Scholar
Pantula S.G., G. Gonzalez-Farias & W. Fuller 1994 A comparison of unit-root test criteria. Journal of Business and Economic Statistics 12, 449– 459.Google Scholar
Phillips P.C.B. 1987 Time series regression with a unit root. Econometrica 55, 277– 301.Google Scholar
Phillips P.C.B. & P. Perron 1988 Testing for a unit root in time series regression. Biometrica 75, 335– 346.Google Scholar
Potter S.M. 1995 A nonlinear approach to US GNP. Journal of Applied Econometrics 10, 109– 125.Google Scholar
Serletis A. & M. Shintani 2003 No evidence of chaos but some evidence of dependence in the U.S. stock market. Chaos, Solitons & Fractals 17, 449– 454.Google Scholar
Shintani M. & O. Linton (forthcoming) Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos. Journal of Econometrics.
Tong H. 1990 Non-Linear Time Series: A Dynamical System Approach. New York: Oxford University Press.
Whang Y.-J. & O. Linton 1999 The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series. Journal of Econometrics 91, 1– 42.Google Scholar