On the Impact of the Boundary on Dynamics: Anti-Persistence in the Case of the HKD Exchange Rate Corridor

Abstract

This paper studies the features of the USD/HKD exchange rate process by assessing the conformity of its dynamics to that of a random walk. This is not a trivial task since we consider the period within which the rate is confined to a specified corridor. This is achieved via analysis of its fractal dimension by means of the Hurst exponent as estimated using the rescaled range method. The conformity can be quantified by the difference between the estimated Hurst exponent and the random walk Hurst exponent of ½. At least two distinct Hurst exponents are identified, one corresponding to a random walk while the other, to an anti-persistent process. Partitioning the rate in state space associates the anti-persistence with proximity to the lower boundary of the corridor so the rate can be modeled using a random walk when sufficiently distant from the boundary.