Volatility forecasting from multiscale and high-dimensional market data

Abstract

Advantages and limitations of the existing volatility models for forecasting foreign-exchange and stock market volatility from multiscale and high-dimensional data have been identified. Support vector machines (SVM) have been proposed as a complimentary volatility model that is capable of effectively extracting information from multiscale and high-dimensional market data. SVM-based models can handle both long memory and multiscale effects of inhomogeneous markets without restrictive assumptions and approximations required by other models. Preliminary results with foreign-exchange data suggest that SVM can effectively work with high-dimensional inputs to account for volatility long-memory and multiscale effects. Advantages of the SVM-based models are expected to be of the utmost importance in the emerging field of high-frequency finance and in multivariate models for portfolio risk management.

Introduction

Predictive capabilities of the data-driven models of the systems with complex multiscale dynamics depend on the quality and amount of the available data and on the algorithm used to extract generalized mappings. Availability of the real-time, high-resolution data constantly increases in many fields of practical interest. However, the majority of advanced statistical and machine learning algorithms, including neural networks (NN), can encounter a set of problems called “dimensionality curse” when applied to high-dimensional data [4]. Nonstationarity of the system can also impose significant limitations on the size of a training set which leads to poor generalization ability of the model.

A very promising algorithm that can tolerate high-dimensional and incomplete data is support vector machine (SVM) [43], [44]. SVMs have recently been receiving significant interest due to excellent results in various applications [10]. SVM combines the training efficiency and simplicity of linear algorithms with the accuracy of the best nonlinear techniques, and systematic approach for optimal generalization. In many practical applications SVMs can tolerate high-dimensional and/or incomplete data and often demonstrate performances superior to the best available techniques including NNs [10]. Note that in this article majority of the comparative references to NNs would imply multilayer perceptron (MLP) or similar algorithms and architectures [4], [33]. Recent successful applications of SVM-based adaptive systems include image/object classification [32], face detection and recognition [30], text categorization [22], process identification in high-energy physics [42], cancer diagnostic and prognosis [26], gene classification [8], as well as many other scientific, engineering, medical, and biological applications.

Recently we have also applied SVM to a challenging problem of real-time space weather forecasting [20]. It has been shown that the performance of the SVM-based model for geomagnetic substorm prediction can be comparable (or superior) to that of the best existing models including NNs [19]. The advantages of the SVM-based techniques are expected to be much more pronounced in the next generation of the space-weather forecasting models, which will incorporate many types of high-dimensional, multiscale input data once real-time availability of this information becomes technologically feasible.

Financial time-series forecasting is another challenging area where advantages of the SVM-based systems could be very important. Although some financial applications of the SVM have been reported [13], [16] the full range of potential SVM applications in finance remains largely unexplored. For example, there are no comprehensive studies of the SVM applications to volatility forecasting from multiscale and high-dimensional market data. Exception is a recent work by Van Gestel et al. [41] where new SVM formulation is introduced and applied to financial time series. Encouraging results of the volatility modeling of the daily DAX30 closing pricing have been reported [41].

Volatility of the foreign exchange and stock markets is a very important quantity for option pricing, value-at-risk (VaR) calculations used in portfolio risk management, and for general decision making in real-time trading systems. The empirically confirmed existence of volatility long memory (up to several months) may require high-dimensional inputs in the volatility models. Multivariate structure of the volatility and covariance models used in portfolio risk management further increases dimensionality of the model. Emerging new field of the high-frequency finance [11], dealing with multiscale market data (from several minutes to several months), imposes even more demanding requirements on the dimensionality of the multiscale volatility models.

In this paper we review stylized facts and features of the market data and existing volatility models. Limitations of the known volatility models, especially their ability to handle long memory and multiscale nature of the market data, are identified. SVM-based system is proposed as a complimentary multiscale volatility model. Advantages and potential applications of the new model are discussed. Encouraging preliminary results of the SVM model application to volatility forecasting of foreign exchange market are reported. Although only foreign exchange market examples are considered in this paper, almost all discussion is relevant to stock market data as well. When necessary, specific differences between stock and foreign exchange markets are mentioned.