GARCH model evaluation: strength and initial values

• Grant number: 17/10262-3
• Support type: Scholarships in Brazil - Scientific Initiation
• Effective date (Start): June 01, 2017
• Effective date (End): December 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Statistics
• Principal researcher: Luiz Koodi Hotta
• Grantee: Sérgio Henrique Andrade de Azevedo
• Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 13/00506-1 - Time series, wavelets and functional data analysis, AP.TEM

Abstract

The generalized autoregressive conditional heteroskedasticity (GARCH) model has been the most used model to model volatility series of returns of prices of financial assets. Its popularity is due to the fact that the model can explain the main characteristics of interest found in these series and because its likelihood can be calculated in a simple way, when conditioned to an initial value of the volatility. Therefore, in this approach the maximum likelihood estimator depends on the initial value of the volatility. In the project the student is going to study the GARCH model, maximum likelihood estimators of the GARCH model and use simulation to study properties of estimators. Several choices of the initial value of volatility will be considered and the simulation will be used to study their properties. (AU)