No. 181 - Mean Reversion Tests with Reflecting Barriers: An Application to European Monetary System Exchange Rates

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. The test is applied to the exchange rate in terms of Deutsche Marks of five currencies participating in the European Monetary System. Our methodology is helpful in deciding whether the behaviour of these exchange rates inside the barriers may be modeled as a simple reflected Brownian motion, or whether a more complex model is warranted.