Design of a Wavelet Inspired Neuro-Fuzzy Approach to Forecast Financial Data

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1 74 Design of a Wavelet Inspired Neuro-Fuzzy Approach to Forecast Financial Data Priyanka Student, SE, PDM College Of Engineering, Bahadurgarh, Haryana ABSTRACT The prediction algorithm always has their advantage in each field. While working with financial areas the importance of such approach significantly improve. The prediction algorithm basically reduces the risk factor. But main concern here is the accuracy level of the prediction, as the wrong prediction can be disaster for the investor. The proposed work is about to predict or forecast the financial outcome based on available statistics. Here we are using a neuro-fuzzy approach to predict the change in financial terms. While only briefly discussing neural network theory, this research will determine the feasibility and practicality of using neural networks as a forecasting tool for the individual investor. The general methodology required to build, train, and test a neural network using commercially available software. In this research, network models will be validated using recent data and provided a benchmark for further improvement. Here we are implementing the fuzzy logic as the final decision making. The work is about to optimize the prediction results. Keywords Neural Network, Fuzzy Logic, Prediction, Financial, Forecast, back propagation 1.INTRODUCTION The principal motivation for the neural network approach in prediction is 1. In conventional time series analysis instructions and rules are central. A mathematical formula defines the dynamics. One picks a model that is assumed to be applicable for the present task, e.g. the well known Auto Regressive Moving Average (ARMA) model 2. Data is highly complex and hard to model, therefore a non-linear model is beneficial 3. A large set t of interacting input series is often required to explain specific values, which suites neural networks A. Neural Network Forecasting Model One of the widely used ANN models, the backpropagation neural network (BPNN) is used for time series forecasting. The main reason is that the BPNN with an identity transfer function in the output unit and logistic functions in the middle-layer units can approximate any continuous function arbitrarily well given a sufficient amount of middle-layer units It also found that BPNN has been one popular model that can approximate various nonlinearities in the data series. Generally, the BPNN can be trained by the historical data of a time series in order to capture the non-linear characteristics of the specific time series. The model parameters (connection weights and node biases) will be adjusted iteratively by a process of minimizing the forecasting errors. For time series forecasting, according to the previous computation process the relationship between the output (yt) and the inputs (yt 1,yt 2,, yt p) has the following mathematical representation. where a j (j = 0, 1, 2,, q) is a bias on the jth unit, and wij (i = 0, 1, 2,, p; j = 0, 1, 2,, q) is the connection weights between layers of the model, f( ) is the transfer function of the hidden layer, p is the number of input nodes and q is the number of hidden nodes. Actually, the BPNN model performs a nonlinear functional mapping from the past observation (yt 1, yt 2,, yt p). to the future value (yt), i.e., where w is a vector of all parameters and φ is a function determined by the network structure and connection weights. Thus, in some senses, the BPNN model is equivalent to a nonlinear autoregressive (NAR) model. Multilayer Perceptron For the task of predicting the indexes, we'll be using the so called multilayer feed forward network which is the best choice for this type of application. In a feed

2 75 forward neural network, neurons are only connected forward. Each layer of the neural network contains connections to the next layer, but there are no connections back. Typically, the network consists of a set of sensory units (source nodes) that constitute the input layer, one or more hidden layers of computation nodes, and an output layer of computation nodes. In its common use, most neural networks will have one hidden layer, and it's very rare for a neural network to have more than two hidden layers. The input signal propagates through the network in a forward direction, on a layer by layer basis. These neural networks are commonly referred as multilayer perceptrons (MLPs). Shown below is a simple MLP with 4 inputs, 1 output, and 1 hidden layer. outputs. They can capture the nonlinear characteristics of time series well. B.Financial Analysis One of the primary objectives of this project is to also provide financial analysts with a tool with which they can predict movements of stocks in a certain direction. The ability of the network to keep updating it with historical information will allow it to predict the data even more accurately and thus aim to increase the profitability for the investors and the users of this application. Some aspects that we aim at achieving is this regard are to: To aid the users of the software to make valuable decisions. Help the investors to generate and maximize their profits out of the investments they make in the stock market. Reduce the risk involved when investing in stocks. Support the users in an efficient portfolio management. To detect the changes in the stock prices and to make the network learn the trends in order to predict the future prices with as much accuracy as possible, long periods (about one year) of reliable stock price data have to be available. A relatively long period of impact monitoring is also required if accurate deductions, on the impacts, are to be made. Research is needed in order to analyze the records and to make projections into the future and on the details of the response mechanisms which will be required in order to adapt to and mitigate price change. The input layer is the conduit through which the external environment presents a pattern to the neural network. Once a pattern is presented to the input layer, the output layer will produce another pattern. In essence, this is all the neural network does - it matches the input pattern to one which best fits the training's output. It is important to remember that the inputs to the neural network are floating point numbers, represented as C# double type (most of the time you'll be limited to this type). The output layer of the neural network is what actually presents a pattern to the external environment (the result of the computation). The number of output neurons should be directly related to the type of work that the neural network is to perform. A major advantage of neural networks is their ability to provide flexible nonlinear mapping between inputs and 2. EXISTING WORK Smolensky, Mozer, and Rumelhart provide Weigand s thoughts on time series analysis and prediction. Although extremely technical, it touches on financial market prediction and provides a good overview of time series analysis. He breaks time series analysis into forecasting and modeling. Forecasting is short-term prediction while modeling tries to identify features that accurately predict long term trends. Wiegand states that these can be quite different and that the laws governing a short-term forecast may not substantially relate to the long-term model or the actual characteristics of the system. More specifically, Weigand claims that the complexity of a model useful for forecasting may not be related to the actual complexity of the system. Potentially models can accurately predict markets where they are substantially less complex than the

3 76 market itself. Lowe (1994) focuses on portfolio optimization and short term equity forecasting. Some believe that efficient market theory causes predictions based upon historical price patterns to be valueless. However, Lowe (1994) postulates that A system which is apparently random could have significant deterministic components embedded in its data. He states that a neural network s ability to create nonlinear approximations to the underlying generators of data may be exploited. Lowe (1994) concludes that it would be possible to develop an automated trading system based entirely upon quantitative pattern processing techniques capable of consistently outperforming professional traders. Lederman and Klein provide Jurik s thoughts on trading system development. Although Jurik does not provide specific examples of trading systems, he provides a wealth of advice on data preprocessing techniques. He states, Strive for simple models having only a few choice input variables. He supports this by explaining that as the number of model inputs increase, the degrees of freedom of the governing equation also increases. While equations with high degrees of freedom have the capability to model the training data effectively, they fail miserably when given test data. This is because models with fewer degrees of freedom do not try to trace the data s random scattering but only follow the general trend. Jurik also states that When trying to remove unimportant variables, sensitivity analysis of nonstationary or nonlinear models has dubious practical value. This is extremely important because this is one of the standard techniques used in regression analysis. If applied to a neural network model it could seriously fail. Jurik states there are only two ways to correctly remove unimportant variables. The first is to use a genetic algorithm to develop multiple combinations of input variables while only letting the most accurate survive. The second is a manual method of systematically removing one variable at a time and recording network accuracy. This technique is repeated until the accuracy of the model starts decreasing. While these entire authors hint at the capability of neural networks in forecasting financial markets, the researcher found only one text that meticulously tracks the development of the neural network from data gathering and preprocessing to training and application of the net. This research uses techniques for developing a model to predict future price of the dollar. Build a model that is slightly improved methods for forecasting. Additionally and potentially most importantly for the investor, model accuracy probabilities were generated. This was done by combining historical market movement probabilities with the model accuracy probability. This conditional probability could prove to be a vital tool for investment decision making. 3. RESEARCH METHODOLOGY Since the stock prices and the currency exchange rates are essentially the time series prediction problem, our project can easily be modified to be used for currency exchange rate predictions. In effect it the prediction problems can be incorporated into a single system, making it a complete portfolio adviser. This will not only improve the market of our product but will also improve the report generation option. Since it will now have more data to use for decision making and analysis. The primary purpose of this work is to accurately state and describe the requirements of software that predicts the fiscal curve of the stock market. Previously it was thought that it was not possible to predict the market trends, this was based on the Efficient Market Hypothesis (EMH). According to (EMH), it is not possible to predict the changes in the price curves for the stock market based on the available data. The primary purpose of this project would be to test the hypothesis of EMH and construct a model to predict the market curves for financial time series data like the stock prices, in Pakistan Stock Market using Statistical Analysis with the help of available data. Artificial Neural Networks are used for predicting this change, a special type of neural net called Recurrent Neural Networks. The stock market predictor s primary aim would be to help investors to get an idea of whether a certain share would be going up (+ve) of down (-ve). By developing this software the following objectives are hoped to be achieved: This is a specialized product which predicts the stock prices using a special kind of Artificial Neural Network (ANN), which at the moment is a major challenge for the stock investors. This is a different kind of product from those present in the market because it uses Recurrent Neural Network for predicting the future trends of the stock market and mainly Haar wavelet transformation to make the data stationary and some more filtering techniques for removing the noise from the signals. This software is independent and totally self-contained. However a completely functional operating system is required. The major problem with applying expert systems to the stock market is the difficultly in formulating knowledge of the markets because we ourselves do not completely understand them. Neural fuzzy networks have an advantage over expert systems because they can extract rules without having them explicitly formalized. It is hard to extract information from experts and formalize it in a way usable by expert systems. Expert systems are only good within their domain of knowledge and do not work well when there is missing or incomplete information. 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4 77 handle dynamic data better and can generalize and make "educated guesses." Thus, neural networks are more suited to the stock market environment than expert systems. In the wide variety of different models presented so far, each model has its own benefits and shortcomings. The best way is that these methods work best when employed together. The major benefit of using a fuzzy neural network then is for the network to learn how to use these methods in combination effectively, and hopefully learn how the market behaves as a factor of our collective consciousness. A. Requirement Phase 4. RESULT ANALYSIS A. Simulation Tool B. Results 1) MATLAB Editor is used for writing the code to implement our algorithm. 2) The result will be shown in the command window of MATLAB In this present work we have implemented the forecasting process on Gold rates. The results obtained from the presented work are given as under During the data requirement phase, we went through three types of things; model input data, calibration data, and verification data. Input data simply consists of the required parameters to run the model, and it typically includes information regarding the closing stock prices of everyday, for each company. Calibration is the process of parameter adjustments to obtain a match between predicted and the actual output. Where as, in verification, we hold the parameters constant and test the calibration on an independent data set. One can say that, calibration is used to estimate the value of these parameters, and verification is used to test the validity of the estimate. B.Algorithm The learning algorithm is used to train the networks. Before learning starts, tolerances are defined for the output units. During learning, the weights are updated only when the output errors exceed the tolerances. The learning data for which the output errors do not exceed the tolerances are eliminated from the training data sets. All the main features of the program: (1) Download historical data from the Internet. (2) Arrange all of data into the format that used for the next step, and insert data into database. (3) Remove the impurities from the dataset such as blank data. (4) Algorithm, which trains the neural networks using the mean square error as stop criterion for learning, while never exceeding the maximum number of cycles which can take testing data from the initial date to the user entered date, and predicts the future stock closing values. (5) Generate the fuzzy rule based on large dataset. (6) Compare the obtained results with this dataset and predict the up or down in the stock market (7) A program is written, which compares the predicted values with real values. Figure 4.1: Gold Price Curve As we can see in figure 4.1, it is showing the variation in gold price over the period. Here x axis represents the period or the time instances and the y axis represents the variation. As we can see as the time instances increases the variation is also increased. Figure 4.2: Efficient Gold Price Curve As we can see in figure 4.2, it is showing the variation in gold price over the period. Here only the curve is shown to shown the variation in better way. Effectively the results of this figure are same as the previous. Here x axis represents the period or the time instances and the y axis represents the variation. As we can see as the time instances increases the variation is also increased.

5 78 Figure 4.3: Step Curve As we can see in figure 4.3, it is showing the step change in gold price over the period. As we can see there are three major changes in gold rates, it showing the major variation in gold rates over the period. Figure 4.5: Error Curve As we can see in figure 4.5 it is showing the Error curve. As we can see in this figure as the training process is performed over the time, the error rate is reduced. The result here obtains after the implementation of neuro fuzzy on current dataset. Figure 4.4: Expected Fuzzy Output As we can see in figure 4.4, it is showing the expected variation in the gold rates. As we can see, most of the time the gold rates are stable. The difference between the light and dark green lines shows the fluctuation in rates of gold. Figure 4.6: Expected Fuzzy Output As we can see in figure 4.6, it is showing the expected variation in the gold rates. As we can see, most of the time the cold rates are stable. The difference between the light and dark green lines shows the fluctuation in rates of gold. The result obtained here is after implementation of Neuro Fuzzy.

6 79 software program so that data can be preprocessed efficiently. Study financial market theory so that input data to the neural net is not chosen inappropriately or at random. Obtain a neural network software program to test and evaluate many neural networks. Figure 4.7: Actual Neuro-Fuzzy Output As we can see in figure 4.7, it is showing the prediction error while analyzing the gold rates. The flat surface is the indication of true estimation. Higher is the line, more error in the prediction process. The work is here on the basis of Neuro Fuzzy rule Implementation. 5. CONCLUSION The Proposed System is suitable for financial forecasting and marketing analysis. They can be used for financial time series, such as foreign exchange rates forecasting. Proposed System is successful applied to the problem of forecasting the foreign currency exchange. When applying proposed model in a real application, attention should be taken in every single step. The architecture selection is a result of a long and timeconsuming process of trial-and-error. This process is more an art than a science, more practice than theory. Here the two important soft computing techniques are combined to get the desired results. 6. FUTURE WORK For individual investors to successfully use Neuro fuzzy system to predict financial markets, they must undertake the following s As a minimum, read a basic text on neural networks to understand neural network theory and its limitations. Understand basic statistical measures and probability and become extremely proficient with a spreadsheet Practice by varying inputs and studying the effects on outputs. Once a network is developed, do not blindly follow its advice. As Gately (1996) states, try to verify it with other indicators before taking action. In other words use multiple indicators. This could include using multiple networks incorporating different inputs to predict the same output. Only by meticulously following these recommendations will individual investors improve their potential profits by using neural networks. REFERENCES [1] A. N. Refenes, M. Azema-Barac, L. Chen and S.A. Karoussos, Currency Exchange Rate Prediction and Neural Network Design Strategies, Neural Computing & Applications, 1993 [2] W. Remus, M. O'connor, Neural Networks For Time Series Forecasting, in Principles of Forecasting: A Handbook for Researchers and Practitioners, [3] Shaikh A. Hamid Primer on using neural network for forecasting market variables Associate Professor of Finance Southern New Hampshire University Working Paper No [4] Back, B., Laitinen T., and Sere K. (1996) Neural Networks and Genetic Algorithms for Bankruptcy Predictions. Expert Systems with Applications 11(4): [5] Dropsy, V. (1992) Exchange Rates and Neural Networks. Working Paper 1-92, California State University, Dept. of Economics, Fullerton. [6] Fletcher, D., and Goss, E. (1993) Forecasting With Neural Networks: An Application Using Bankruptcy Data. Information and Management 24(3): [7] Geigle, D.S. and J.E. Aronson (1999) An artificial neural network approach to the valuation of options and forecasting of volatility, Journal of Computational Intelligence in Finance 7:6 (November/December). [8] Gencay, R. (1999) Linear, Nonlinear and Essential Foreign Exchange Rate Prediction with Simple Technical Trading Rules. Journal of International Economics 47:

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