estimating.pdf (EC3400)

estimating.pdf (EC3400) - Q U A N T IT A T IV E F I N A N C...

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QUANTITATIVE FINANCE VOLUME 3 (2003) 1–10 R ESEARCH P APER INSTITUTE OF PHYSICS PUBLISHING quant.iop.org Estimating GARCH models using support vector machines* Fernando P´erez-Cruz 1 , Julio A Afonso-Rodr´ ıguez 2 and Javier Giner 3 1 Department of Signal Theory and Communications, University Carlos III, Legan´es, 28911 Madrid, Spain 2 Department of Institutional Economics, Economic Statistics and Econometrics, University of La Laguna, 38071 Tenerife, Canary Islands, Spain 3 Department of Financial Economy and Accounting, University of La Laguna, 38071 Tenerife, Canary Islands, Spain E-mail: fernando@tsc.uc3m.es, jafonsor@ull.es and jginer@ull.es Received 17 February 2002, in ±nal form 20 February 2003 Published Online at stacks.iop.org/Quant/3 Abstract Support vector machines (SVMs) are a new nonparametric tool for regression estimation. We will use this tool to estimate the parameters of a GARCH model for predicting the conditional volatility of stock market returns. GARCH models are usually estimated using maximum likelihood (ML) procedures, assuming that the data are normally distributed. In this paper, we will show that GARCH models can be estimated using SVMs and that such estimates have a higher predicting ability than those obtained via common ML methods. 1. Introduction Financial returns series are mainly characterized by having a zero mean, exhibiting high kurtosis and little, if any, correlation. The squares of these returns often present high correlation and persistence, which makes ARCH-type Q.1 models suitable for estimating the conditional volatility of such processes; see Engle (1982) for the seminal work, Bollerslev et al (1994) for a survey on volatility models and Engle and Patton (2001) for several extensions. The ARCH parameters are usually estimated using maximum likelihood (ML) procedures that are optimal when the data is drawn from a Gaussian distribution. Support vector machines (SVMs) are state-of-the-art tools for linear and nonlinear input–output knowledge discovery (Vapnik 1998, Sch¨olkopf and Smola 2001). SVMs can be employed for solving pattern recognition and regression * Paper presented at Applications of Physics in Financial Analysis (APFA) 3, 5–7 December 2001, Museum of London, UK. estimation problems. SVMs have been developed in the machine learning community and resemble, in some ways, a neural network (NN). But SVMs are superior to most common NNs (such as multi-layered perceptron or radial basis function networks) due to the SVM optimization procedure giving not only the weights of the network but also its architecture. Furthermore, one of the most desirable properties when using a SVM is that its optimizing functional is quadratic and linearly restricted, meaning that it only presents a single minimum without any local undesirable solutions.
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This note was uploaded on 02/28/2010 for the course ECO 211 taught by Professor Gilo during the Spring '10 term at Young Harris.

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estimating.pdf (EC3400) - Q U A N T IT A T IV E F I N A N C...

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