Covariance matrix forecasting using support vector regression

Abstract

Support vector regression is a promising method for time-series prediction, as it has good generalisability and an overall stable behaviour. Recent studies have shown that it can describe the dynamic characteristics of financial processes and make more accurate forecasts than other machine learning techniques. 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. The procedure is applied to range-based covariance matrices of returns, which are estimated on the basis of low and high prices. Such prices are most often available with closing prices for many financial series and contain more information about volatility and relationships between returns. The methodology guarantees the positive definiteness of the forecasted covariance matrices and is flexible, as it can be applied to different dependence patterns. 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 advantage of the suggested procedure is higher during turbulent periods, i.e., when forecasting is the most difficult and accurate forecasts matter most.

Forecasting currency covariances using machine learning tree-based algorithms with low and high prices

“…where 𝐻𝐻 𝑃𝑃 and 𝐿𝐿 𝑃𝑃 are the daily high and low prices, respectively. More details about the applied range-based covariance estimator and its properties can be found in Fiszeder and Orzeszko (2021), who employ this estimator in a new methodology for dynamic modeling and forecasting covariance matrices based on support vector regression.…”

“…Fischer et al, 2019). These factors cause machine learning algorithms to outperform most traditional stochastic methods in financial market forecasting (Fiszeder & Orzeszko, 2021;Ryll & Seidens, 2019). The most popular ML approaches in the field of finance are Artificial Neural Network (ANN) and Support Vector Machine (SVM).…”

Estimation of the Cholesky Multivariate Stochastic Volatility Model Using Iterated Filtering

“…Over the last several decades, significant progress has been made in modelling the volatilities of multivariate stock market returns. Nowadays, there are four main approaches: multivariate generalised autoregressive conditional heteroskedasticity (MGARCH) models (Engle, 2002;Engle and Kroner, 1995), multivariate stochastic volatility (MSV) models (Chib et al, 2009) realised covariance models (Bollerslev et al, 2018;Jin and Maheu, 2013), and machine learning (ML) algorithms (Bejger and Fiszeder, 2021;Fiszeder and Orzeszko, 2021). All of these approaches have some strengths and weaknesses, and the choice between them depends on the specific characteristics of the data, the objectives of the analysis, and the trade-offs between modelling flexibility and computational complexity.…”

Nonlinear Causality between Crude Oil Prices and Exchange Rates: Evidence and Forecasting

“…It is designed to have a good power of generalization and an overall stable behavior, which implies a good out-of-sample performance. Many studies in the literature have shown that SVR models can give more accurate forecasts than alternative machine learning methods and can be successfully used to forecast financial time series, such as stock indices, stock prices, future contracts, or exchange rates (see, e.g., [32][33][34][35]). SVR and SVR-based models have also been applied to forecast crude oil prices [36][37][38][39][40][41] or exchange rates [42][43][44][45][46].…”