Forecasting Currency Exchange Rates: Neural Networks and the Random Walk Model

quantitative methods used to forecast the behaviour of financial markets often produce unsatisfactory if not dismal results given the complex interactions between a given market's behaviour and other economic phenomena. Part of the problem lies in the fact that the relationships existing between financial markets and the economy as a whole are often poorly understood. On top of this there are also a variety of political and psychological factors influencing the dynamics of the markets over time. Neural networks may provide some hope of producing a suitable methodology for overcoming some of these difficulties. This work provides an evaluation of the use of neural networks as a technique for forecasting currency exchange rates. Recently, successful attempts at forecasting exchange rates such as the US$ DM and US$ SF have been reported in the literature (i.e. Refenes et al (1993, Weigend et al (1992))) but their methodologies have been less than stringent leaving them open to accusations of data mining. The work presented here will attempt to replicate some of this previous work and then subjugate the resulting neural network forecasts to a more stringent level of analysis. More specifically, standard backpropagated feedforward networks will be used to forecast the US$ DM exchange rate 1, 5, and 20 trading days into the future with the resulting performances compared to the random walk forecasting model and to an autoregressve forecasting model. The experimental techniques used here are also proposed as a general framework which should be followed when making claims of the successful application of neural networks to financial time series generally seen as unforecastable. A number of successful claims of using neural network based market forecasting systems have been published. Unfortunately, much of this work suffers from inadequate documentation regarding methodology (Binks and Allinson (1991), Collard (1991), Lee and Park, (1992)) or claims of positive results not backed up by comparisons with other relevant forecasting techniques (Binks and Allinson (1991), Lee and Park, (1992), Collard (1991) Weigend et al (1992)). This makes it difficult to both replicate previous work and obtain an accurate assessment of just how well connectionist techniques really perform in comparison to other forecasting techniques. What previous work has been done using connectionist approaches to market forecasting can be roughly categorised based on how a forecast is being extracted from the input data with the neural network INTRODUCTION One of the more difficult problems in economics is the forecasting of financial markets. Traditional model. Most have attempted to extrapolate the future behaviour of a market with a neural network based times series analysis by having the network output some value representing the future behaviour of the market (i.e. forecasting the price, expected return or degree of change etc...). This is usually done by giving the network information about the market's past behaviour (Refenes et al (1993)) or information about its past behaviour in conjunction with the dynamics of a variety of other economic variables used as additional input (Weigend et al (1992), Lee and Park (1992) and Hutchinson (1994)). Others have tried to train the network to recognise known market patterns (Binks and Allinson, (1991)) or attempt to train the network to learn an optimised trading strategy (Collard (1991) and Kimoto et al (1990)). current price changes are independent of past price changes. In other words, univariate forecasting should be impossible as past price changes do not offer any clues to what form the future behaviour of prices might take. Since price changes in efficient markets such as exchange rates are assumed to be a random distribution with 0 mean (see Pindyck and Rubinfeld (1991)) the best forecast one can make for any amount of time in the future is to assume the future price will be the same as today's price. As previous claims of success with univariate forecasting of the US$ DM exchange rate contradict the random walk model, the random walk model is the most appropriate to base a comparison with neural networks with1 in this instance. Second, when claiming positive results steps should be taken to guard against accusations of data mining. It will be shown here that spurious results are not difficult to obtain in some instances. To help circumvent this problem, the approach taken here is to run our simulations on multiple portions of the data set to guard against the possibility of chance results. This report will attempt to apply a connectionist approach to the forecasting of a notoriously "unpredictable" financial market currency exchange rates. Some relatively straight foreword methods of using standard backpropagated feedforward neural networks to forecast the US$ DM exchange rate will be analysed and compared with other forecasting models. These experiments will include univariate forecasting of the exchange rate at 1, 5 and 20 days in advance and multivariate forecasts at 1 and 5 days in advance. METHODS This study consists of five main experiments intended to examine the relative performance of neural networks and the random walk model in forecasting the US$ DM exchange rate. The first experiment attempts to use a feedforward backpropagated network to forecast the US$ DM exchange rate one trading day in advance using input consisting solely of daily US$ DM data in much the same way as Refenes et al (1993). The second experiment attempts to fit the random walk model to the exchange rate data to more accurately ascertain the appropriateness of the random walk model as an explanation for the behaviour of the price changes in the exchange rate. The third experiment will use an identical technique as In addition, a methodological framework is also proposed for the use of neural networks in financial forecasting. The framework is quite simple and consists of two basic techniques. First, the performance of neural networks should be compared with other relevant forecasting models. Simply demonstrating that neural network based methods "work" is not enough as this does not shed any light on their relative performance to potentially simpler and more accurate forecasting methods. For this work, the random walk forecasting model will be use as the primary comparison model as currency exchange rates are widely viewed to be best explained as random walks (Diebold and Nason, (1990)). The random walk model simply states that due to market efficiency, 1Note that the random walk model only refers to univariate or "technical" forecasting. It does not state that price changes in particular markets that follow random walks are also operating independent of other variables. the first experiment to forecast 5 trading days (one week) and 20 trading days (one month) in advance. The fourth experiment will conclude the univariate forecasting by taking a multistep approach to forecasting. In multistep forecasting the output from the network after presentation of the final training pattern is taken as input to the network for the next forecast step. This process is then repeated for the entire length of the forecast lead period. Finally, the last experiment will attempt one and five trading day forecasts using multivariate input incorporating interest rates and other currencies. M e a n S q . E rr o r 0 0.002 0.004 0.006 0.008 AR(2) S LP