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

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  • Clifford Ball
  • Antonio Roma

Abstract

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.

Suggested Citation

  • Clifford Ball & Antonio Roma, 1998. "Detecting mean reversion within reflecting barriers: application to the European Exchange Rate Mechanism," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(1), pages 1-15.
  • Handle: RePEc:taf:apmtfi:v:5:y:1998:i:1:p:1-15
    DOI: 10.1080/135048698334709
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    References listed on IDEAS

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    1. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(02), pages 231-247, August.
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    8. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    9. Paul R. Krugman, 1991. "Target Zones and Exchange Rate Dynamics," The Quarterly Journal of Economics, Oxford University Press, vol. 106(3), pages 669-682.
    10. Flood, Robert P. & Rose, Andrew K. & Mathieson, Donald J., 1991. "An empirical exploration of exchange-rate target-zones," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 35(1), pages 7-65, January.
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    Cited by:

    1. Hui, C.H. & Lo, C.F., 2009. "A note on estimating realignment probabilities - A first-passage-time approach," Journal of International Money and Finance, Elsevier, vol. 28(5), pages 804-812, September.
    2. Fernando Alvarez & Robert Shimer, 2011. "Search and Rest Unemployment," Econometrica, Econometric Society, vol. 79(1), pages 75-122, January.
    3. Cho-Hoi Hui & Chi-Fai Lo, 2008. "A Note on Estimating Realignment Probabilities -- A First-Passage-Time Approach," Working Papers 0809, Hong Kong Monetary Authority.

    More about this item

    Keywords

    C51; F33;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • F33 - International Economics - - International Finance - - - International Monetary Arrangements and Institutions

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