![]() ![]() Support vector methods, such as other nonparametric statistical analysis techniques, tend to be useful tools of nonlinear forecasting, as they do not presume the linearity of the data-generating process but let the data speak for themselves. Many empirical studies have shown that the dynamics of financial processes can be nonlinear (see, e.g., and references therein). The econometric literature extensively discusses the empirical properties of financial time series, which include volatility clustering, weak autocorrelation of returns, occurrence of an asymmetric impact of positive and negative shocks on conditional volatility (the so-called leverage effect), long memory, existence of strong dependencies between returns of various financial instruments, and some characteristics of return distributions, such as fat tails, leptokurtosis and asymmetry. In the literature, the term SVM is typically applied in the context of classification problems, while the term support vector regression (SVR) is used to describe regression with support vector methods. Originally, the SVM method was developed to solve classification problems later, however, it was extended to the domain of regression problems. In particular, new methodological approaches, including some modifications of the original SVM models or specific SVM-based hybrid models, have been proposed (e.g., ). The literature on SVM has been systematically expanding, both in the area of methodology and practical applications. This method, applied to solve both classification and regression problems, is designed to have good generalisability and an overall stable behaviour, implying good out-of-sample performance. One of them is the support vector machine (SVM) method proposed by Vapnik. In recent years, several ML methods have been successfully used for forecasting purposes. These data-driven, self-adaptive techniques require very few assumptions about the models used for the investigated data. Generally, machine learning includes methods that help computer systems automatically improve their performance with experience. In the context of financial data analysis, one of the most relevant AI methods is machine learning (ML). The advantage of the suggested procedure is higher during turbulent periods, i.e., when forecasting is the most difficult and accurate forecasts matter most.Īrtificial intelligence (AI) offers new approaches to modelling and forecasting real-time data. ![]() ![]() The second contribution of the paper is to show with an example of the exchange rates from the forex market that the covariance matrix forecasts calculated using the proposed approach are more accurate than the forecasts from the benchmark dynamic conditional correlation model. The methodology guarantees the positive definiteness of the forecasted covariance matrices and is flexible, as it can be applied to different dependence patterns. Such prices are most often available with closing prices for many financial series and contain more information about volatility and relationships between returns. The procedure is applied to range-based covariance matrices of returns, which are estimated on the basis of low and high prices. ![]() The first main contribution of this paper is to propose a methodology for dynamic modelling and forecasting covariance matrices based on support vector regression using the Cholesky decomposition. Recent studies have shown that it can describe the dynamic characteristics of financial processes and make more accurate forecasts than other machine learning techniques. Support vector regression is a promising method for time-series prediction, as it has good generalisability and an overall stable behaviour. ![]()
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