Neural network modelling procedure

Conforming to standard heuristics, the training, test and validation sets were partitioned as approximately |, \ and respectively. The training set runs from 17 October 1994 to 8 April 1999 (1169 observations), the test set runs from 9 April 1999 to 18 May 2000 (290 observations), and the validation set runs from 19 May 2000 to 3 July 2001 (290 observations), reserved for out-of-sample forecasting and evaluation, identical to the out-of-sample period for the benchmark models.

To start, traditional linear cross-correlation analysis helped establish the existence of a relationship between EUR/USD returns and potential explanatory variables. Although NNR models attempt to map nonlinearities, linear cross-correlation analysis can give some indication of which variables to include in a model, or at least a starting point to the analysis (Diekmann and Gutjahr, 1998; Dunis and Huang, 2002).

The analysis was performed for all potential explanatory variables. Lagged terms that were most significant as determined via the cross-correlation analysis are presented in Table 1.12.

The lagged terms SPCOMP(—1) and US_yc(—1) could not be used because of time-zone differences between London and the USA, as discussed at the beginning of Section 1.3. As an initial substitute SPCOMP(—2) and US_yc(—2) were used. In addition, various lagged terms of the EUR/USD returns were included as explanatory variables.

Variable selection was achieved via a forward stepwise NNR procedure, namely potential explanatory variables were progressively added to the network. If adding a new variable improved the level of explained variance (EV) over the previous "best" network, the pool of explanatory variables was updated.15 Since the aim of the model-building

14 The problem of convergence did not occur within this research; as a result, a learning rate of 0.1 and momentum of zero were used exclusively.

15 EV is an approximation of the coefficient of determination, R2, in traditional regression techniques.

Table 1.12 Most significant lag of each potential explanatory variable (in returns)


Best lag

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