Financial volatility estimation using functional gradient descent algorithm

Issue title: Statistical Models in Finance and Insurance

Guest editors: Arkady Shemyakin and Vladimir Ladyzhets

Article type: Research Article

Authors: Chung, Steve S.^{a; *} | Niu, Xu-Feng^b

Affiliations: [a] Department of Mathematics, California State University, Fresno, CA 93740-8001, USA | [b] Department of Statistics, Florida State University, Tallahassee, FL 32306-4330, USA

Correspondence: [*] Corresponding author: Steve S. Chung, Department of Mathematics, California State University, Fresno 5245 N. Backer Ave M/S PB 108, Fresno, CA 93740-8001, USA. Tel.: +1 559 278 2462; Fax: +1 559 278 2872; E-mail: schung@csufresno.edu.

Abstract: In this paper, we propose a semiparametric method for modeling the volatility in financial time series. The aim is to improve the forecasting capabilities of the most popular parametric volatility models and we also compare our approach to two recent semiparametric models in the literature. Our method is based on the bivariate Bernstein basis polynomials and the functional gradient descent (FGD) algorithm. We evaluate our method through simulated and real datasets. The results demonstrate its good predictive potential for financial volatility.

Keywords: Financial time series, volatility, functional gradient descent, GARCH, e-GARCH, GJR-GARCH, bivariate Bernstein basis polynomials

DOI: 10.3233/MAS-170406

Journal: Model Assisted Statistics and Applications, vol. 12, no. 4, pp. 305-319, 2017