Elsevier

Pattern Recognition Letters

Volume 26, Issue 13, 1 October 2005, Pages 2093-2103
Pattern Recognition Letters

A comparison of global, recurrent and smoothed-piecewise neural models for Istanbul stock exchange (ISE) prediction

https://doi.org/10.1016/j.patrec.2005.03.026Get rights and content

Abstract

This paper makes a comparison of global, feedback and smoothed-piecewise neural prediction models for financial time series (FTS) prediction problem. Each model is implemented by various neural network (NN) architectures: global model by a multilayer perceptron (MLP), feedback model by a recurrent neural network (RNN) and smoothed-piecewise model by a mixture of experts (MoE) structure. The advantages and disadvantages of each model are discussed by using real world finance data: 12 years data of Istanbul stock exchange (ISE) index (XU100) from 1990 to 2002. A conventional exponential generalized autoregressive conditional heteroskedasticity (EGARCH) volatility model is also implemented for comparison purpose. The comparison for each model is done based on well-known criterions of index return series of market: hit rate (HR), positive hit rate (HR+), negative hit rate (HR-), mean squared error (MSE), mean absolute error (MAE) and correlation (ζ). Finally, it is observed that the smoothed-piecewise neural model becomes advantageous in capturing volatility in index return series when it is compared to global and feedback neural model, and also the conventional EGARCH volatility model.

Introduction

Recently, mixture of models and multiple models have become popular research areas in machine learning and related fields. Generally in this field, there has been a special interest in the development of clustering, classification, regression, prediction and parameter estimation algorithms for time series (dynamics) problems. Remarkable efforts include the directions such as support vector machines (SVM), Bayesian networks, mixture of experts, ensembles of neural networks, fuzzy models, etc. (Shafer and Vovk, 2001, Petridis and Kehagias, 1998, Petridis et al., 2001, Rao et al., 1997, Castillo and Melin, 2002, Shawe-Taylor and Cristianini, 2004, Heckerman, 1999). These ideas have further led to reinterpretation of existing network structures; proposals of new network structures; and novel learning algorithms based on optimization techniques, principles, and criteria from these areas.

This study addresses the problem of application of global, feedback and piecewise neural models to financial time series (FTS) prediction (Yümlü et al., 2003, Yümlü et al., 2004). It is an example case of choosing the proper model for a specific application of FTS prediction. Furthermore, a conventional exponential generalized autoregressive conditional heteroskedasticity (EGARCH) model is employed for comparison. A multilayer perceptron (MLP) is employed as a global predictor of FTS that uses the training samples obtained from each local part of the time series. Here, the MLP is trained with these local, fixed-size samples to receive the overall picture of the series, and then make a prediction. A recurrent neural net (RNN) is used as a feedback predictor that introduces a memory between parts of local series. In this case, a number of weighted feedback connections are added to the feedforward structure of a MLP, so it can encode the relationship of a number of partially local series better in the weights. Finally, smoothed-piecewise predictors such as mixture of experts (MoE) structure are used to summarize the localized series with a number of statistics such as mean, variance values and then, obtain an overall prediction smoothed by conditional probability values of each local series or local expert.

The global, feedback and smoothed-piecewise neural models are employed for the prediction of volatilities of certain assets in Istanbul stock exchange (ISE) index (XU100) from Turkey from years of 1990s to 2002s. The real world finance data is divided into two parts: (a) 12 years data from 1990 to 2002 and (b) 4 years data from 1998 to 2002. There is an important reason behind this separation: ISE shows different distributional effects between 1990 and 1998 because of the indeterminate economical structure, so we have decided to test our models with a smaller and more predictable data set from 01/01/1998 to 04/04/2002.

Financial markets (ISE) in Turkey have various instability sources of the economical infrastructure. Any news or rumor may cause changes in volatile movements, as a result, forecasting the volatility of the market becomes an important issue. With the described features (Table 1), we try to measure the effectiveness of above models in the prediction. No previous work has been reported in the area.

We try to make a comparison of the well-known neural models for the case of ISE data in our study: these models are global model with a MLP example, feedback model with a RNN example (Elman’s model with feedback from hidden units), smoothed-piecewise model with MoE example and a well-known, conventional EGARCH model. We furthermore mention piecewise models (individual local experts) such as linear predictors (LP) and polynomial predictors (PP) and the reasons of not using them in our case. Even though a combination of various models such as neural and EGARCH models can also be considered, in this study we limit our attention to performances of above models and describe their effectiveness in the case of ISE data.

The rest of the paper is organized as follows: Section 2 introduces predictor models. Section 3 introduces volatility forecasting and the characteristics of the stock market FTS. Section 4 describes global, feedback and smoothed-piecewise neural prediction models. Section 5 mentions the implementation issues of neural models and the experiments. Section 6 presents results with discussions. Final section concludes the study with future work.

Section snippets

Predictor models

In general for a time series (TS) prediction problem, a predictor fits a model to given data and finds an approximate mapping function between the input and the output values (Shafer and Vovk, 2001, Petridis and Kehagias, 1998, Petridis et al., 2001). Thus, the proposed model predicts underlying patterns, trends and cycles using historical and currently observable data. A time series xt, t = 1, 2, 3, …; for simplicity xt is taken to be scalar but vector-valued time series are also used. Among a

Financial time series problem and volatility

Generally, FTS prediction (Shafer and Vovk, 2001, Petridis and Kehagias, 1998, Petridis et al., 2001) is a difficult problem that has hidden variables and lacks observable data for determining the underlying structure of the series, if one exists. Our study uses conditional variance (volatility) that is time-dependent heteroskedastic variance and it is not a directly observable feature. A well-known approach of financial markets is efficient market hypothesis (EMH) in which the current market

Global, feedback, smoothed-piecewise neural prediction models

In this paper, we interpret global, feedback and smoothed-piecewise neural prediction models for the ISE with two FTS examples. The task of a neural prediction model can be described as follows: given a set of input–output pairs T = {(xi, yi)}, where xiεRn, xiεRm are drawn from an unknown distribution, design a mapping f : Rn  Rm that minimizes the expected prediction error, in the case of squared error, given by E[(y  f(x, w))2]. The function f(x, w) defines corresponding mapping for the predictor. The

Implementation issues of neural models and experiments

In this section, we describe ISE data and then use it for the prediction of risk in index return series by using MLP, RNN, MoE and conventional EGARCH structures. Data consists of 2946 daily observations of ISE 100 index (Turkey) (Fig. 4). Data covers a 12-year period, from 12 January 1990 to 26 April 2002. We use two portions: (a) 12 years data and (b) 4 years data from 1998 to 2002. Besides the index close series, we have studied four supporting series: USD dollar series, two interest rate

Results

Generally, the performance of a model is dependent on the quality and relevance of the data that it represents. Thus, the data selection becomes an important component of a prediction. Here, we consider four different series besides ISE 100 close price series. Sliding windows technique, taking the last n elements in the series as input, is only applied to ISE 100 and USD series. Among the various sizes of hidden units, the best performance given size was used for structures. All the series are

Future work and conclusion

In this study, we interpret and discuss the application of global, feedback and smoothed-piecewise, neural MoE structure. By using the assumption that is against the EMH hypothesis, experimental results on ISE data suggest that MoE structure specifically introduces a powerful model to predict the volatility of FTS data. In our work, we consider ISE XU100 and observe the prediction of volatilities (conditional variances) instead of return index prices makes a valuable contribution to this area.

Acknowledgement

We express our thanks to Boğaziçi University Research Fund due to their support (BAP 04A103 project).

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