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Bootstrap prediction in univariate and multivariate volatility models

Grant number: 12/09596-0
Support Opportunities:Scholarships in Brazil - Doctorate
Effective date (Start): August 01, 2012
Effective date (End): August 31, 2016
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Statistics
Principal Investigator:Luiz Koodi Hotta
Grantee:Carlos Cesar Trucios Maza
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated scholarship(s):13/23524-5 - Bootstrap prediction intervals to forecast portfolio value-at-risk, BE.EP.DR


The goals of the thesis aims is to propose, based on existing procedures for the univariate case, procedures for bootstrap prediction intervals in multivariate volatility models (multivariate GARCH and multivariate stochastic volatility models, with and without leverage effect). The interest in multivariate models comes from the fact that, as it is known in financial literature, there is a dependency structure between the financial series, since the volatility of different assets from the same or different markets move together. The interest in the multivariate models with leverage effect, in turn, stems from the fact that, as is well known in financial markets, the negative returns have greater influence on volatility than positive returns of the same magnitude. The project considers several multivariate GARCH models, generalizations of the models leverage GARCH, EGARCH and GJR for the multivariate case and multivariate stochastic volatility model. The thesis will present the algorithms for each model as well as a study, through simulations, the behavior of the proposed procedure for assessing the quality of the prediction intervals obtained for the returns of the individual series and an investment portfolio. Applications will also be conducted with a series of Brazilian and non-Brazilian financial series.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
TRUCIOS, CARLOS; HOTTA, LUIZ K.; RUIZ, ESTHER. Robust bootstrap forecast densities for GARCH returns and volatilities. JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, v. 87, n. 16, p. 3152-3174, . (13/00506-1, 13/23524-5, 12/09596-0)
TRUCIOS, CARLOS; HOTTA, LUIZ K.. Bootstrap prediction in univariate volatility models with leverage effect. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 120, p. 91-103, . (13/00506-1, 12/09596-0)
TRUCIOS, CARLOS; HOTTA, LUIZ K.; RUIZ, ESTHER. Robust bootstrap densities for dynamic conditional correlations: implications for portfolio selection and Value-at-Risk. JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, v. 88, n. 10, SI, p. 1976-2000, . (13/00506-1, 12/09596-0)
Academic Publications
(References retrieved automatically from State of São Paulo Research Institutions)
MAZA, Carlos Cesar Trucios. Densidades de previsões bootstrap em modelos de volatilidade univaridos e multivariados. 2016. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.

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