Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T05:27:39.320Z Has data issue: false hasContentIssue false
  • English
  • Français

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

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

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

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