An Exploration of Backpropagation Numerical Algorithms in Modeling US Exchange Rates

An Exploration of Backpropagation Numerical Algorithms in Modeling US Exchange Rates

Salim Lahmiri (ESCA School of Management, Morocco & University of Quebec at Montreal, Canada)
DOI: 10.4018/978-1-4666-7272-7.ch022
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This chapter applies the Backpropagation Neural Network (BPNN) trained with different numerical algorithms and technical analysis indicators as inputs to forecast daily US/Canada, US/Euro, US/Japan, US/Korea, US/Swiss, and US/UK exchange rate future price. The training algorithms are the Fletcher-Reeves, Polak-Ribiére, Powell-Beale, quasi-Newton (Broyden-Fletcher-Goldfarb-Shanno, BFGS), and the Levenberg-Marquardt (LM). The standard Auto Regressive Moving Average (ARMA) process is adopted as a reference model for comparison. The performance of each BPNN and ARMA process is measured by computing the Mean Absolute Error (MAE), Mean Absolute Deviation (MAD), and Mean of Squared Errors (MSE). The simulation results reveal that the LM algorithm is the best performer and show strong evidence of the superiority of the BPNN over ARMA process. In sum, because of the simplicity and effectiveness of the approach, it could be implemented for real business application problems to predict US currency exchange rate future price.
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1. Introduction

Currency exchange rate forecasting is crucial for financial institutions to estimate currency risk, increase profits, and to monitor strategic financial planning. Additionally, active participants in the foreign exchange market such as traders, investors, and speculators continuously make arbitrage and hedging transactions so as to affect financial institutions wealth and national economies. Consequently, all these participants become dependent on the response in the foreign exchange market. Nowadays, governments, economists and participants in the foreign exchange market are increasingly interested in models that allow accurately predicting currency exchange rate. However, currency markets are generally perceived as nonlinear and no stationary systems which are difficult to predict (Majhi et al, 2012).

Statistical models such as the auto regressive moving average (ARMA) (Box et al, 1994) and generalized autoregressive conditional heteroskedasticity (GARCH) (Bollerslev, 1986) models and linear regression methods were largely applied by researchers and scholars in modeling foreign currency exchange rates (Hsieh, 1989; Liu et al, 1994; Brooks, 1996). However, all these linear statistical models require a priori assumptions about the underlying laws governing the data and the model specification. As a result, their applications are restricted to linear specifications of the model. They are also restricted to stationarity and normality distribution of variables and errors. Indeed, these assumptions are not true in real life situations, which lead to poor prediction quality (Hu et al, 1999; Yao & Tan, 2000).

In the last decade, soft computing tools such as multilayer artificial neural networks (ANN) (Rumelhart et al, 1986; Haykin, 2008) were introduced in currency exchange time series forecasting (Hu et al, 1999; Yao & Tan, 2000) since they do not make such assumptions. In addition, they are adaptive and robust to noisy and incomplete data. Furthermore, the ANN employs the traditional empirical risk minimization principle to minimize the error on training data using the backpropagation algorithm. Finally they were proven to be effective and accurate in different time series application problems; including electrical load (Kulkarni, 2013), stock market volatility (Wei, 2013), river flow (Singh & Deo, 2007), car fuel consumption (Wu & Liu, 2012), flood (Feng & Lu, 2010), and rainfall-runoff forecasting (Sedki et al, 2009), in stock market prediction (Lahmiri, 2014; Lahmiri et al, 2014a, 2014b), and also recently in currency exchange rate forecasting (Majhi et al, 2012; Sedki et al, 2009; Majhi et al, 2009; Panda & Narasimhan, 2007; Sermpinis & Laws, 2012; Hussain et al, 2006; Dunis et al, 2011).

Key Terms in this Chapter

ARMA Process: A description of stationary stochastic process in terms of an auto-regression and moving average polynomials.

Genetic Algorithms: A heuristic search algorithm that mimics the process of natural selection used for optimization purpose using mutation, selection, and crossover operators.

Exchange Rate: The rate at which one currency will be exchanged for another.

Forecasting: A prediction process of unobservable events.

Gradient Descent: A first-order optimization algorithm used to find a local minimum of a function by taking steps proportional to the negative of the gradient.

Neural Networks: Biologically inspired computing system based on the neural structure of the brain.

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