RDP 8612: A Weekly Model of the Floating Australian Dollar 1. Introduction

The Australian dollar became a market determined currency on 14 December 1983. With respect to the US dollar it depreciated about 5 per cent in its first year of floating and about 25 per cent in its second. The variance of the spot rate increased by nearly 40 per cent in its first year of floating, relative to the previous year of managed rates, and by a further 100 per cent in its second. The level and change in the logarithm of the spot rate are shown in Figure 1. The apparent drift in the level and the variability of the exchange rate need to be verified by empirical time series analysis. Once the univariate time series properties of the exchange rate have been established, a question worth addressing is whether a multivariate model can be found to encompass the univariate one.

The empirical exchange rate literature does not give much comfort to any particular exchange rate theory that has been postulated. Any success achieved usually turns out to be episodal and the particular model tends to do no better at out-of-sample forecasting than a random walk.^[1] Mussa (1979) contended that flexible exchange rates, in common with other asset prices, generally behave largely like a random walk (with drift). A random walk is a sufficient condition for a series to be non-stationary. If this is true, inferences from the estimates of the parameters of a model of that series will need to account for that non-stationarity, or else transforms of the series (say, by differencing) are needed to obtain stationarity and the right to use classical distribution theory. Meese and Singleton (1982) establish the non-stationarity of the US dollar vis a vis the Swiss Franc, the Canadian dollar and the Deutschemark. This paper follows their lead, testing for the non-stationarity of the Australian dollar, but also taking into account the possible heteroscedasticity and non-normality of the error process, suggested by the facts in the first paragraph.

If a random walk with drift can be verified, a multivariate model can be postulated to try to find an explanation of the drift from the expected or actual values of other variables, and to try to reduce the noise process by substituting in the effects of unexpected values of these other variables. With such a short length of data accumulated since the float,^[2] this exercise cannot be expected to be more than indicative of possible directions for future research.

Whenever an economic system underdoes a major regime switch, econometric modellers and forecasters have to wait patiently for enough data to accumulate so that they have sufficient degrees of freedom to be able to estimate the fundamentals of that system. Even though asset prices, such as the exchange rate, can be observed continuously, the essentially exogenous variables that are generally thought to be important influences on them are often only published monthly, or even quarterly and always with a substantial publication lag. Yet market determined asset prices are formed by market participants who have to continuously make conjectures about current and future fundamentals. All previously announced observations of fundamental variables contain information than can help to make these conjectures. It seems decidedly wasteful to throw out all but (say) quarterly information on all variables. If one can find a satisfactory method of modelling conjectures on a continuous, rather than discrete basis, one will not be constrained by the longest publication period amongst the fundamentals. In this paper, a method due to Muth (1961) is used to this end. A variable, or its rate of growth is assumed to be composed of unobservable permanent and transitory components. The permanent element is modelled as a random walk. All future forecasts are based on the current estimate of this element, and it is this feature which delivers the required property. Attempts are made to explain the exchange rate using these generated regressors. The obvious loss in efficiency from this procedure is hopefully more than balanced by the gain from using a larger sample.

Models with future price expectations that are determined rationally display the well-known problem of multiple solutions. This occurs because the future expectation is an additional endogenous variable in a system that has no extra equations. There are two strategies that one can adopt to solve the problem of non-uniqueness.

The first and least restrictive approach makes the weak rational expectations assumption that the actual expectational error of an asset price is only due to new information that arrived after the expectation was formed. This knowledge is known to the model builder, and can be used to eliminate expectational variables in the underlying model. The model to be estimated becomes a multivariate autoregressive moving average (ARMA) one with orders at least one higher than the original and can be estimated using a minimum distance procedure which is a good approximation to FIML with a small number of parameters. The estimated parameters then provide a unique solution. This solution can be analytically solved and the result may contain non-fundamental or bubble solutions. The second strategy is the standard method of finding a solution for the convergence of the series of future expectations. This latter problem is deterministic and is akin to that of finding the saddlepath in perfect foresight models.

In Section 2, the univariate time series properties of the exchange rate are investigated and a benchmark random walk model is established. The conclusions from this section are used to restrict the multivariate analysis in Section 3. Monetarist and Keynesian error correction models are set up to compete with the random walk benchmark. Section 4 offers some conclusions.

Footnotes

Meese and Rogoff (1985) show that random walks have at least as much success as other theories. [1]

Information about the exchange rate system can be gleaned from the study of arbitrage equations. Tease (1986) established inefficiency in the Australian foreign exchange market by testing whether the difference between the forward and the appropriate future spot rate is orthogonal to known information. Trevor and Donald (1986) use VAR estimation methods on daily data of the trade-weighted exchange rate index and international interest rates for Australia, U.S., Japan and West Germany. The Australian dollar appeared to be unaffected by Australian interest rates. [2]