The investigation is based on the London daily closing prices for the EUR/USD
exchange rate. In the absence of an indisputable theory of exchange rate determination,
we assumed that the EUR/USD exchange rate could be explained by that rate's
recent evolution, volatility spillovers from other financial markets, and macro economic
and monetary policy expectations.
With this in mind it seemed reasonable to include,
as potential inputs, other leading traded exchange rates, the evolution of important stock
and commodity prices, and, as a measure of macro economic and monetary policy expectations,
the evolution of the yield curve. The data retained is presented in Table 1.1
along with the relevant Datastream mnemonics, and can be reviewed in Sheet 1 of the
DataAppendix·xls Excel spreadsheet.
All the series span the period from 17 October 1994 to 3 July 2001, totalling 1749
trading days. The data is divided into two periods: the first period runs from 17 October
1994 to 18 May 2000 (1459 observations) used for model estimation and is classified
in sample, while the second period from 19 May 2000 to 3 July 2001 (290 observations)
is reserved for out of sample forecasting and evaluation. The division amounts to
approximately 17% being retained for out of sample purposes.
Over the review period there has been an overall appreciation of the USD against
the euro, as presented in Figure 1.1. The summary statistics of the EUR/USD for the
examined period are presented in Figure 1.2, highlighting a slight skewness and low
kurtosis. The Jarque Bera statistic confirms that the EUR/USD series is non-normal at the
99% confidence interval. Therefore, the indication is that the series requires some type of
transformation. The use of data in levels in the FX market has many problems, "FX price
movements are generally non stationary and quite random in nature, and therefore not very
suitable for learning purposes. . . Therefore for most neural network studies and analysis
concerned with the FX market, price inputs are not a desirable set" (Mehta, 1995: 191).
To overcome these problems, the EUR/USD series is transformed into rates of return.
Given the price level P1, P2, ... , Pt , the rate of return at time t is formed by:
An example of this transformation can be reviewed in Sheet 1 column C of the
oos Naive·xls Excel spreadsheet, and is also presented in Figure 1.5. See also the comment
in cell C4 for an explanation of the calculations within this column.
An advantage of using a returns series is that it helps in making the time series stationary,
a useful statistical property.
Formal confirmation that the EUR/USD returns series is stationary is confirmed at the
1% significance level by both the Augmented Dickey Fuller (ADF) and Phillips–Perron
(PP) test statistics, the results of which are presented in Tables 1.2 and 1.3.
The EUR/USD returns series is presented in Figure 1.3. Transformation into returns
often creates a noisy time series. Formal confirmation through testing the significance of
the autocorrelation coefficients reveals that the EUR/USD returns series is white noise
at the 99% confidence interval, the results of which are presented in Table 1.4. For such
series the best predictor of a future value is zero. In addition, very noisy data often makes
forecasting difficult.