This paper proposes a new methodology to estimate a simple spot and forward exchange rates model. The method is inspired by the recent development in Independent Component Analysis (ICA) and it allows the identification and estimation of efficient exchange rate (exchange rate when market is efficient) and external market influences (market noise). Consider the linear equation y(t) = Ax(t), where y(t) and x(t) are k x 1 vectors of observable and unobservable random variables, respectively, and A is a k x k matrix. Under the assumption that each element in x(t) is independent to each other and x(t) consists of no more than one normal variate, then Independent Component Analysis (ICA) provides a convenient framework to recover the mixing matrix A, subject to scaling and permutation, by utilising the independence and non-normality nature of x(t). Subsequently, it is also possible to recover x(t) based on the observations of y(t), subject to scaling and permutation. Let y(t) denotes a k x 1 vector of co-integrated I (1) variables, then following the Granger's Representation Theorem and the Phillips' Triangular Representation, there exists a k x k matrix, A, and a k x 1 vector, x(t), such that y(t) = Ax(t). Moreover, there are exactly r I (0) elements and k - r I (1) elements in x(t). This paper shows that, under the same assumptions of ICA, it is possible to estimate A, and recover the unobserved random variables, x(t), based solely on the observations of y(t). In order words, this paper proposes a new test of co-cointegration based on ICA. This is particularly useful as standard co-integration analysis assumes normality which is unlikely to be true for most high frequency financial time series. Thus, the proposed technique is particularly suitable for analysing high frequency financial time series data, such as stock prices and exchange rates. The paper then proposes a simple model of spot and forward exchange rates which assumes that both rates are linear combinations of two unobserved components, namely, efficient exchange rate and market noise. The paper shows that the proposed co-integration test can be applied to the model in order to differentiate the efficient exchange rate and the market noise. This paper applies the proposed method to the daily US/Australia spot and forward exchange rates. By analysing the dynamics in the efficient rates and market noise, this paper obtains evidence against some of the standard assumptions underlying conventional exchange rate models and market micro-structure noise.
