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Chaos, self-organized criticality, and SETAR nonlinearity: An analysis of purchasing power parity between Canada and the United States

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  • Serletis, Apostolos
  • Shahmoradi, Asghar

Abstract

This paper uses monthly observations for the real exchange rate between Canada and the United States over the recent flexible exchange rate period (from January 1, 1973 to August 1, 2004) to test purchasing power parity between Canada and the United States using unit root and stationarity tests. Moreover, given the apparent random walk behavior in the real exchange rate, various tests from dynamical systems theory, such as for example, the Nychka et al. [Nychka DW, Ellner S, Ronald GA, McCaffrey D. Finding chaos in noisy systems. J Roy Stat Soc B 1992;54:399–426] chaos test, the Li [Li W. Absence of 1/f spectra in Dow Jones average. Int J Bifurcat Chaos 1991;1:583–97] self-organized criticality test, and the Hansen [Hansen, B.E. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 1996;64:413–30] threshold effects test are used to distinguish between stochastic and deterministic origin for the real exchange rate.

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  • Serletis, Apostolos & Shahmoradi, Asghar, 2007. "Chaos, self-organized criticality, and SETAR nonlinearity: An analysis of purchasing power parity between Canada and the United States," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1437-1444.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:5:p:1437-1444
    DOI: 10.1016/j.chaos.2006.02.008
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    1. Shintani, Mototsugu & Linton, Oliver, 2004. "Nonparametric neural network estimation of Lyapunov exponents and a direct test for chaos," Journal of Econometrics, Elsevier, vol. 120(1), pages 1-33, May.
    2. Peter C.B. Phillips, 1987. "Multiple Regression with Integrated Time Series," Cowles Foundation Discussion Papers 852, Cowles Foundation for Research in Economics, Yale University.
    3. Perron, Pierre & Vogelsang, Timothy J., "undated". "Level Shifts and Purchasing Power Parity," Instructional Stata datasets for econometrics levshift, Boston College Department of Economics.
    4. Apostolos Serletis, 1994. "Maximum likelihood cointegration tests of purchasing power parity: Evidence from seventeen OECD countries," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 130(3), pages 476-493, September.
    5. Papell, David H. & Theodoridis, Hristos, 1998. "Increasing evidence of purchasing power parity over the current float," Journal of International Money and Finance, Elsevier, vol. 17(1), pages 41-50, February.
    6. Jacob A. Frenkel, 1980. "Exchange Rates, Prices and Money: Lessons from the 1920s," NBER Working Papers 0452, National Bureau of Economic Research, Inc.
    7. Kugler, Peter & Lenz, Carlos, 1993. "Multivariate Cointegration Analysis and the Long-Run Validity of PPP," The Review of Economics and Statistics, MIT Press, vol. 75(1), pages 180-184, February.
    8. Glen, Jack D., 1992. "Real exchange rates in the short, medium, and long run," Journal of International Economics, Elsevier, vol. 33(1-2), pages 147-166, August.
    9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    10. Perron, Pierre & Vogelsang, Timothy J, 1992. "Nonstationarity and Level Shifts with an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 301-320, July.
    11. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    12. Pippenger, Michael K., 1993. "Cointegration tests of purchasing power parity: the case of Swiss exchange rates," Journal of International Money and Finance, Elsevier, vol. 12(1), pages 46-61, February.
    13. Ng, Serena & Perron, Pierre, 1997. "Estimation and inference in nearly unbalanced nearly cointegrated systems," Journal of Econometrics, Elsevier, vol. 79(1), pages 53-81, July.
    14. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-125, April-Jun.
    15. Phylaktis, Kate & Kassimatis, Yiannis, 1994. "Does the real exchange rate follow a random walk? The Pacific Basin perspective," Journal of International Money and Finance, Elsevier, vol. 13(4), pages 476-495, August.
    16. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-879, August.
    17. Whang, Yoon-Jae & Linton, Oliver, 1999. "The asymptotic distribution of nonparametric estimates of the Lyapunov exponent for stochastic time series," Journal of Econometrics, Elsevier, vol. 91(1), pages 1-42, July.
    18. Mototsugu Shintani & Oliver Linton, 2003. "Is There Chaos in the World Economy? A Nonparametric Test Using Consistent Standard Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(1), pages 331-357, February.
    19. MacKinnon, James G, 1994. "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 167-176, April.
    20. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    21. Diebold, Francis X & Husted, Steven & Rush, Mark, 1991. "Real Exchange Rates under the Gold Standard," Journal of Political Economy, University of Chicago Press, vol. 99(6), pages 1252-1271, December.
    22. Serletis, Apostolos & Zimonopoulos, Grigorios, 1997. "Breaking Trend Functions in Real Exchange Rates: Evidence from Seventeen OECD Countries," Journal of Macroeconomics, Elsevier, vol. 19(4), pages 781-802, October.
    23. Barnett, William A. & Serletis, Apostolos, 2000. "Martingales, nonlinearity, and chaos," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 703-724, June.
    24. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    25. Frenkel, Jacob A, 1980. "Exchange Rates, Prices, and Money: Lessons from the 1920's," American Economic Review, American Economic Association, vol. 70(2), pages 235-242, May.
    26. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    27. Grilli, Vittorio & Kaminsky, Graciela, 1991. "Nominal exchange rate regimes and the real exchange rate : Evidence from the United States and Great Britain, 1885-1986," Journal of Monetary Economics, Elsevier, vol. 27(2), pages 191-212, April.
    28. Koedijk, Kees G. & Schotman, Peter C. & Van Dijk, Mathijs A., 1998. "The re-emergence of PPP in the 1990s," Journal of International Money and Finance, Elsevier, vol. 17(1), pages 51-61, February.
    29. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November.
    30. Coe, Patrick J. & Serletis, Apostolos, 2002. "Bounds tests of the theory of purchasing power parity," Journal of Banking & Finance, Elsevier, vol. 26(1), pages 179-199, January.
    31. Adler, Michael & Lehmann, Bruce, 1983. "Deviations from Purchasing Power Parity in the Long Run," Journal of Finance, American Finance Association, vol. 38(5), pages 1471-1487, December.
    32. Pantula, Sastry G & Gonzalez-Farias, Graciela & Fuller, Wayne A, 1994. "A Comparison of Unit-Root Test Criteria," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 449-459, October.
    33. Patel, Jayendu, 1990. "Purchasing Power Parity as a Long-Run Relation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(4), pages 367-379, Oct.-Dec..
    34. Mark, Nelson C., 1990. "Real and nominal exchange rates in the long run: An empirical investigation," Journal of International Economics, Elsevier, vol. 28(1-2), pages 115-136, February.
    35. Lothian, James R & Taylor, Mark P, 1996. "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 488-509, June.
    36. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    37. Cheung, Yin-Wong & Lai, Kon S, 1993. "A Fractional Cointegration Analysis of Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 103-112, January.
    38. Apostolos Serletis & Periklis Gogas, 2000. "Purchasing power parity, nonlinearity and chaos," Applied Financial Economics, Taylor & Francis Journals, vol. 10(6), pages 615-622.
    39. Serletis, Apostolos & Gogas, Periklis, 2004. "Long-horizon regression tests of the theory of purchasing power parity," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1961-1985, August.
    40. Serletis, Apostolos & Shahmoradi, Asghar, 2004. "ABSENCE OF CHAOS AND 1/f SPECTRA, BUT EVIDENCE OF TAR NONLINEARITIES, IN THE CANADIAN EXCHANGE RATE," Macroeconomic Dynamics, Cambridge University Press, vol. 8(04), pages 543-551, September.
    41. Alston Flynn, N. & Boucher, Janice L., 1993. "Tests of long-run Purchasing Power Parity using alternative methodologies," Journal of Macroeconomics, Elsevier, vol. 15(1), pages 109-122.
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