Detecting mean reversion within reflecting barriers: application to the European Exchange Rate Mechanism
AbstractThis 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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Bibliographic InfoArticle provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.
Volume (Year): 5 (1998)
Issue (Month): 1 ()
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Find related papers by 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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- Paul Krugman & Marcus Miller, 1992. "Exchange Rate Targets and Currency Bands," NBER Books, National Bureau of Economic Research, Inc, number krug92-1, octubre-d.
- 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.
- G. William Schwert, 1988.
"Tests For Unit Roots: A Monte Carlo Investigation,"
NBER Technical Working Papers
0073, National Bureau of Economic Research, Inc.
- 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.
- Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
- Paul R. Krugman, 1988.
"Target Zones and Exchange Rate Dynamics,"
NBER Working Papers
2481, National Bureau of Economic Research, Inc.
- Evans, G B A & Savin, N E, 1981. "Testing for Unit Roots: 1," Econometrica, Econometric Society, vol. 49(3), pages 753-79, May.
- Perron, Pierre, 1989.
"The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,"
Econometric Society, vol. 57(6), pages 1361-1401, November.
- Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
- Lindbecg, H. Soderlind, P., 1992. "Target Zone Models and the Intervention Policy; The Swedish Case," Papers 496, Stockholm - International Economic Studies.
- 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.
- 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.
- Andrew W. Lo, . "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," Rodney L. White Center for Financial Research Working Papers 15-86, Wharton School Rodney L. White Center for Financial Research.
- 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.
- Phillips, P C B, 1987.
"Time Series Regression with a Unit Root,"
Econometric Society, vol. 55(2), pages 277-301, March.
- Peter C.B. Phillips, 1985. "Time Series Regression with a Unit Root," Cowles Foundation Discussion Papers 740R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1986.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
- 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.
- Robert P. Flood & Andrew K. Rose & Donald J. Mathieson, 1990. "An Empirical Exploration of Exchange Rate Target-Zones," NBER Working Papers 3543, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Hali J. Edison & Eric Fisher, 1989.
"A long-run view of the european monetary system,"
International Finance Discussion Papers
339, Board of Governors of the Federal Reserve System (U.S.).
- 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.
- Evans, G B A & Savin, N E, 1984. "Testing for Unit Roots: 2," Econometrica, Econometric Society, vol. 52(5), pages 1241-69, September.
- 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.
- Fernando Alvarez & Robert Shimer, 2011.
"Search and Rest Unemployment,"
Econometric Society, vol. 79(1), pages 75-122, 01.
- Fernando Alvarez & Robert Shimer, 2008. "Search and Rest Unemployment," EIEF Working Papers Series 0809, Einaudi Institute for Economics and Finance (EIEF), revised Jan 2008.
- Fernando Alvarez & Robert Shimer, 2008. "Search and Rest Unemployment," NBER Working Papers 13772, National Bureau of Economic Research, Inc.
- 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.
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