A Fractional Cointegration Approach to Testing Mean Reversion Between Spot and Forward Exchange Rates: A Case of High Frequency Data with Low Frequency Dynamics

Abstract

This paper applies a relatively new but generalised concept of fractional cointegration to shed some light on the validity of a long‐run relationship between high frequency daily spot and the lagged forward Australian‐US dollar exchange rate. An investigation of the stochastic properties of these rates reveals that, while the relationship is not cointegrated in their logs, they appear to be fractionally cointegrated if we allow for mean reverting processes that are CI(1, d) with 0<d<1. The paper demonstrates that relaxing the condition that the residual from the cointegration equation must be a I(0) process, captures a much wider class of mean‐reversion behaviour. This result is interpreted in the context of the speculative EMH between the spot and forward exchanges rates, as having some empirical support. Furthermore, an analysis of the short‐run dynamics propelling the long‐run relationship tends to imply that in both the short‐ and long‐term, the forward rate is led by the spot rate. In the longer term, the spot rate is found to be the initial receptor of any exogenous shock to the equilibrium and it is the forward exchange rate that bears the brunt of short‐run adjustment to re‐establish the long‐run equilibrium relationship. The approach illustrated in this paper is shown to hold enormous potential for tests of mean reversion involving hypotheses popular to financial econometrics in general, where the dynamics of high frequency data are under scrutiny.