Case Study Australian Forex Market

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In the following, we present a case study to forecast six different currency rates, namely, the U.S. dollar (USD), Great British pound (GBP), Japanese yen (JPY), Singapore dollar (SGD), New Zealand dollar (NZD) and Swiss franc (CHF) against the Australian dollar using their historical exchange rate data. The case study is based on our previous study (Kamruzzaman & Sarker, 2004). In most of the previous studies related to forex forecasting, the neural network algorithms used were: Standard Backpropation (SBP), Radial Basis Function (RBF), or Generalized Regression Neural Network (GRNN). In this case study, we used two other improved feed-forward learning algorithms, namely the Scaled Conjugated Gradient (SCG) and Bayesian Reguralization (BR) algorithms, to build the model and investigate how the algorithms performed compared to standard backpropagation in terms of prediction accuracy and profitability.

Dataset. The data used in this study is the foreign exchange rate of six different currencies against the Australian dollar from January 1991 to July 2002 made available by the Reserve Bank of Australia. A total of 565 weekly data of the previously mentioned currencies were considered, of which first 500 weekly data were used for training and the remaining 65 weekly data for evaluating the model. The plots of historical rates for USD, GBP, SGD, NZD, and CHF are shown in Figure 1(a) and for JPY in Figure 1(b).

Figure 1. Historical exchange rates for (a) USD, GBP, SGD, NZD and CHF and(b) JPN against Australian dollar

20 0

51 101 151 201 251 301 351 401 451 501 551 Week Num ber

20 0

51 101 151 201 251 301 351 401 451 501 551 Week Num ber

51 101 151 201 251 301 351 401 451 501 551 Week Number

Technical Indicators. The time delay moving average is used as a technical indicator. The advantage of the moving average is its tendency to smooth out some of the irregularity that exits between market days. We used moving average values of past weeks to feed to the neural network to predict the following week's rate. The indicators are MA5, MA10, MA20, MA60, MA120, and X., namely, moving average of 1 week, 2 weeks, 1 month, 1 quarter, half year, and last week's closing rate, respectively. The predicted value is X r The model has six inputs for six indicators, one hidden layer, and one output unit to predict exchange rate. It has been reported in another study that increasing the number of inputs does not necessarily improve forecasting performance (Yao & Tan, 2000).

Learning Algorithms. In most of the previous studies, a standard backpropagation algorithm has been investigated. However, backpropagation suffers from slow convergence and sometimes fails to learn the time series within a reasonable computational time limit. A desired neural network model should produce small error not only on sample data but also on out of sample data. In this case study, we investigated with Scaled Conjugated Gradient (Moller, 1993) and Bayesian Reguralization (MacKey, 1992) algorithms that have been reported to produce improved results than the standard backpropagation in a number of other studies. A detailed description of the algorithms is presented in Chapter 1 of this book.

Evaluation ofPrediction Accuracy. The most common measure to evaluate how closely the model is capable of predicting future rate is measured by Normalized Mean-Square Error (NMSE). The other measure important to the trader is correct prediction of movement. We used four other measures, which are: Mean Absolute Error (MAE), Directional Symmetry (DS), Correct Up trend (CU) and Correct Down trend (CD). These criteria are defined in Table 1, where Xk and Xk are the actual and predicted values,

Table 1. Performance metrics to evaluate the forecasting accuracy of the model

N

DS=

N k [0 otherwise

|1 if(xk - Xk-l) > 0, (xk - Xk-l)(Xk - Xk-l) a 0 — 1 [0 otherwise |

[0 otherwise

Lfk k

|1 if (Xk- Xk-l) < 0, (xk- Xk-i) (Xk - Xk-l a 0 — 1

0 otherwise k |

[0 otherwise

respectively. NMSE and MAE measure the deviation between actual and forecast value. Smaller values of these metrics indicate higher accuracy in forecasting. Additional evaluation measures include the calculation of correct matching number of the actual and predicted values with respect to sign and directional change. DS measures correctness in predicted directions while CU and CD measure the correctness of predicted up and down trends, respectively.

Profitability. The traders are more interested in making a profit by buying and selling in forex market. In order to assess the profitability attainable by using the model, we simulated a trading over the forecasted period. Similar simulated trading is also used in another study (Yao & Tan, 2000). Seed money is used to trade according to the following strategy:

At the ending the trading period, the currency is converted to the original seed money. The profit return is then calculated as:

Return=

Money Obtained Seed Money

where Money Obtained is the money at the end of the testing period and wis the number of weeks in the testing period.

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Forex Trading Manual

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