Tinge exchange rate model using a new neural network ...



Tenge exchange rate model using new neural network training method

Author1

Author affiliation

Author Email

Author2

Author affiliation

Author Email

Abstract: The paper reports results derived from new robust neural network (RNN) based KZT/USD exchange rate model against AR (2) model. The characteristic of the RNN method is explained followed by comparative study of quarterly KZT/USD models. Diagnostic measure such as mean absolute deviations (MAD), R2 and tracking signals (TS) suggests superiority of the RNN KZT/UDS model. The RNN training methods computes adoptive directional search vectors such that the error function is gradually optimized. The method automatically computes adjustable dynamic learning rates to direct search toward the minimum valley of the error function. The algorithm identifies dynamic adjustable learning rates to generate convergent sequence of the error function. As a result, the training is robust to model exchange rate. The RNN model performs better in MAD, TS and R2 value.

Key-Words- KZT/USD Exchange rate, Robust Neural Networks, Adjustable training, Forecast.

1. Introduction

Due to the exchange rate crisis in the CIS region during the fall of USSR era, many small open economies have adopted flexible exchange rates in combination with some kind of monetary or interest rate mechanism. Volatility of exchange rate in Kazakhstan is significant issue taking account possibility of huge transaction loss induced by volatility exchange rate. Kazakhstan economy highly depends on international trade and FDI (Foreign Direct Investment), exchange rate volatility in Kazakhstan have influence in international trade and FDI. Kazakhstan has consistently achieved moderate growth rate induced by oil export. But international oil price is declining and under such market condition exchange rate could be influenced by several possible macroeconomic factors. USD (dollar) exchange rate trends had grown up to 2003 but dollar’s exchange rate to Tenge has fallen since 2003 (see Table 1). There have been number of attempts to apply neural network (NN) to the task of financial modeling (Cao et al. 2005, Jasic and Wood 2004, Kaastra and Boyd 1995, Lam 2004, Nygren 2004). When it comes to performing a predictive analysis, it is very difficult to build one general model that will fit every market. Such models tend to be specific to markets and asset classes and a general model may not be applicable across markets. Similarly, there may be some temporal changes as well which mean that the models may need to be modified over time in order to preserve their effectiveness (Zhang, et al, 1998). We develop KZT/USD exchange rate forecast model using new RNN training method and brief results are reported to show the superior performance of the model, against AR (2) model.

2 Rationales for Self-Adaptive Training Method

Consider a NN error function with m training weights and the learning rates are identified automatically. For computational convenience, the higher dimensional error function in Em dimension is decomposed into several error functions in lower dimension. Such transformed error function retains the true convex characteristics of the original error function. The gradient information is evaluated and the training method updates all the network weight parameters say wj, j=1,2,…..m, by a factor such that improvement in training is noticed. Each epoch identifies m different learning rates along the training directions. Once the NN training weights are updated, the error function is evaluated to notice the improvement in error function and the rate of convergence. Various form of standard back propagation training method and its variant are not self-adaptive. They are heuristic training method (Ahmed et al 2000a; Haykin, 1999; Weir, 1991; and Kamarthi et al., 1999). The training direction, d k of the error function f (w) is computed using the gradient, ▽f (wk) information from a single training pattern in standard on-line back propagation (Bishop, 1995, Ahmed, et al, 2000b). The fixed value of a learning rate,[pic] does not always lead to a maximum local decrease in function value. The learning rate depends on the shape of the error function (Jacobs, 1988) as it trains from the current epoch [pic] to the next epoch k+1, k+2,… and so on. The constant value of learning rate, η k , can direct the search away from the local minimum during epoch k and the directions dk generated from gradient ▽f (wk) are different for a single weight component in standard back propagation training. Consider a training method, we call RNN, where an iterative algorithm is applied to an error function with an initial arbitrary weight vector wk, at the beginning of iteration k, the algorithm generates a sequence of vectors w k+1, w k+2,.… during epoch k+1, k+2,….,.., and henceforth. The iterative algorithm is globally convergent if the sequence of vectors converges to a solution set Ω. Consider the problem: minimize f (w), subject to: w Є Em. Let, Ω Є Em be the solution set, and let, the application of an algorithmic map, ℬ, generates the sequence w k+1, w k+2,.…, starting with weight vector wk such that (w k, w k+1 , w k+2,.…) Є Ω, then the algorithm converges globally and the algorithmic map is closed over Ω. The following properties are utilized to train the new RNN.

Property 1: Suppose that f: E m → E1 and the gradient of the error function, ▽f (w), is defined then there is a directional vector d such that ▽f (w)T d < 0, and f(w +ηd) < f(w) : (η Є (0, ( ), ( > 0), then the vector d is a descent direction of f (w), where ( is assumed arbitrary positive scalar.

Property 2: Let f: E m → E1 is a descent function. Consider any training weight w Є Em and d Є Em : d ≠0. Then the directional derivative ▽f(w, d) of the error function f(w) in minimum direction d always exists. The expression to update the RNN network weight, wk+1 is given by w k+1 =w k + ηk dk. Here, η k is defined as a minimization problem of the type: η k = {min f(w + ηd)}; subject to : ηk Є L, where, L = (η : η Є E1).

3. Results

The following table shows R2 as well the MAD value for the RNN model is better than the AR (2) model. This confirms the superiority of the KZT/USD exchange model using the new RNN method. The TS vale in both case are within acceptable limits, however, the plot shows that the TS vale in RNN is asymmetrical on the zero level, hence the overall predictability is good with RNN model.

|Model |R2 |MAD |TS |TS Plot |Fitted & Actual Data |

|RNN |0.92 |3.11 |0.051 |[pic] |[pic] |

|AR(2) |0.87 |5.60 |0.002 |[pic] |[pic] |

|Table 1: Performance of RNN and AR (2) model (A=Actual, F=Fitted Quarterly KZT/USD Exchange rate1999 till 2007) |

4. Conclusions

This research examined and analyzed the use of a newly developed neural network model (RNN) in foreign exchange forecasting with KZT against USD. The RNN model gives the evidence that there is possibility of extracting information to forecast exchange rate reliably. The evaluation of the model is based on the estimate of mean absolute error, R2 and tracking signal.

5. References

1] Xxxx, uyyyy (year). Neural Network without Learning Parameter”, xyz 2nd International conference, 2000, xyz Place.

2] vvvvv, cccccc. (Year). “Multi-directional training algorithm for Feed-Forward Neural Network”, Journal xyz, 2000.

3] Bishop, Christopher M. (1995). “Neural Networks for Pattern Recognition”. Oxford, UK: Clarendon.

4] Cao, Q., K.B. Leggio and M.J. Schniederjans (2005), ‘A Comparison Between Fama and French’s Model and Artificial Neural Networks in Predicting the Chinese Stock Market’, Computers and Operations Research, 32: 2499–2512.

5] Haykin, Simon, (1999). “Neural Networks: A Comprehensive Foundation”, Prentice Hall, NJ.

6] Jacobs, R.A. (1988). “Increased Rate of Convergence Through Learning Rate Adaptation”. Neural Networks, 1, 295-307.

7] Jasic, T. and D. Wood (2004), ‘The Profitability of Daily Stock Market Indices Trades Based on Neural Network Predictions: Case Study for the S&P 500, the DAX, the TOPIX and the FTSE in the Period 1965–1999’, Applied Financial Economics, 14(4): 285–297.

8] Kaastra, L. and M. Boyd (1995), ‘Designing a Neural Network for Forecasting Financial and Economic Time Series’, Neurocomputing, 10(3): 215–236.

9] Kamarthi, S.V., and Pittner, S., (1999). “Accelerating Neural Network Training Using Weight Extrapolations”, Neural Networks, 12, 1285-1299.

10] Lam, M. (2004), ‘Neural Network Techniques for Financial Performance Prediction: Integrating Fundamental and Technical Analysis’, Decision Support Systems, 37(4): 567–581.

11] Nygren, K. (2004), Stock Prediction—A Neural Network Approach, Master’s Thesis, Royal Institute of Technology, KTH, Sweden.

12] Weir, M.K., (1991). “A Method for Self-Determination of Adaptive Learning Rates in Back Propagation”. Neural Networks, 4, 371-379.

13] Zhang, G. and M.Y. Hu (1998), ‘Neural Network Forecasting of the British pound/US dollar Exchange Rate’, International Journal of Management Science, 26(4): 495–506.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download