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Detecting mean reversion within reflecting barriers: application to the European Exchange Rate Mechanism

  • Clifford Ball
  • Antonio Roma
Registered author(s):

    This paper derives a statistical test, based on the first-order autocorrelation, to ascertain whether a stochastic process evolving within reflecting barriers is mean reverting. Under these conditions the standard unit root analysis does not apply. Since the presence of reflecting barriers per se will induce mean reverting behaviour, the detection of mean reversion inside the two boundaries requires that the effect of reflection be properly accounted for. This statistical procedure may be useful in a number of economic applications which involve an assesment on the dynamics of bounded variables: e.g. the estimation of the mean reversion of ratios in capital structure theory, market share analysis, or the empirical testing of target zones models for exchange rates. We exemplify the inappropriateness of standard unit root analysis in these situations using European Monetary System exchange rate data. Our methodology is helpful in deciding whether the mean reverting behaviour of these exchange rates is due solely to local behaviour at the barriers, or whether a more complex interpretation is warranted. We apply our test to the target zone model introduced by Krugman where the intervention bands are credible. We study bilateral exchange rates of currencies party to the European Monetary System during a period of sustained stability consistent with the credible band assumption. Our results are consistent with those obtained employing significantly more complex maximum likelihood procedures.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334709
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    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 5 (1998)
    Issue (Month): 1 ()
    Pages: 1-15

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    Handle: RePEc:taf:apmtfi:v:5:y:1998:i:1:p:1-15
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    1. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
    2. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    3. Krugman, Paul R, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, MIT Press, vol. 106(3), pages 669-82, August.
    4. Donald J. Mathieson & Robert P. Flood & Andrew K. Rose, 1991. "An Empirical Exploration of Exchange Rate Target-Zones," IMF Working Papers 91/15, International Monetary Fund.
    5. Andrew W. Lo, 1986. "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," NBER Technical Working Papers 0059, National Bureau of Economic Research, Inc.
    6. 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.
    7. Ball, Clifford A. & Roma, Antonio, 1994. "Target zone modelling and estimation for European Monetary System exchange rates," Journal of Empirical Finance, Elsevier, vol. 1(3-4), pages 385-420, July.
    8. Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
    9. Peter C.B. Phillips, 1986. "Regression Theory for Near-Integrated Time Series," Cowles Foundation Discussion Papers 781R, Cowles Foundation for Research in Economics, Yale University, revised Jan 1987.
    10. Ball, Clifford A. & Roma, Antonio, 1993. "A jump diffusion model for the European monetary system," Journal of International Money and Finance, Elsevier, vol. 12(5), pages 475-492, October.
    11. Edison, Hali J. & Fisher, Eric O'N, 1991. "A long-run view of the European monetary system," Journal of International Money and Finance, Elsevier, vol. 10(1), pages 53-70, March.
    12. Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
    13. Paul Krugman & Marcus Miller, 1992. "Exchange Rate Targets and Currency Bands," NBER Books, National Bureau of Economic Research, Inc, number krug92-1, June.
    14. Lindbecg, H. Soderlind, P., 1992. "Target Zone Models and the Intervention Policy; The Swedish Case," Papers 496, Stockholm - International Economic Studies.
    15. 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 1057-72, June.
    16. Meese, Richard A & Singleton, Kenneth J, 1982. " On Unit Roots and the Empirical Modeling of Exchange Rates," Journal of Finance, American Finance Association, vol. 37(4), pages 1029-35, September.
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