Adaptive filtering on forecasting financial derivatives indices

Abstract

The application of machine learning techniques for market predictions has been broadly established in the scientific community. Developing high-performance techniques for predicting financial time series is a crucial problem for economists, investigators and analysts. The traditional statistical methods used by economists in the past years seem to fail to capture the discontinuities, nonlinearities and high complexity of the financial time series. Complex machine learning techniques have been used so far to predict the trends of the financial time series. Three major examples are the artificial neural networks (Holland et al., 1995), the random forests (Breiman et al., 2001) and the support vector machines (SVMs) (Vapnik and Cortes, 1995). They provide enough learning capacity and are more likely to capture the complex non-linear models which are dominant in the financial markets. Although machine learning techniques have been widely used in financial indexes forecasting, adaptive filtering techniques have rarely been used. In the present chapter, we achieved high-performance predictions of the trends of the three indexes of DAX30, CAC40 and Euronext with classifiers built based on adaptive filtering techniques. Adaptive filtering techniques do not require previous knowledge of the signal statistics, have a small computational complexity per iteration and converge to a neighbourhood of the optimal solution. Moreover, adaptive filtering techniques are suitable for non-stationary signals and systems, and the trend of a financial index can be characterized as such. Three classical parameter estimation algorithms (least mean squares (LMS), recursive least squares (RLS) and Kalman filter) and one gain adaptation algorithm (incremental delta-bar-delta (IDBD)) were considered. The gain adaptation algorithms have been shown to perform comparably to the best algorithms (Kalman and RLS), but they have a lower complexity (Diniz, 2002). Overall, the adaptive filtering techniques used in this survey are the LMS (Widrow and Hoff, 1960), the RLS (Goodwin and Payne, 1977), the extended Kalman filtering method (EKF ) (Welch and Bishop, 1995) and the IDBD (Sutton, 1992). We use as benchmark/comparative methods the well-known naive strategy, buy and hold strategy, ARMA model and MACD model. Theadaptive filtering techniques have proved to perform significantly better that the classical benchmark techniques. Four different evaluation criteria are used to confirm this superiority (annualized return, information gain, maximal drawdown and correct bidirectional change). The rest of the chapter is organized as follows: In Section 2 a description of the three financial indices is given, and all the traditional and machine learning techniques used are briefly described. In Section 3 the comparative results of the methods are presented and discussed, and in Section 4 some future research directions are proposed.