Semi‐ and Nonparametric ARCH Processes | Zendy

Oliver B. Linton | Zendy; Yang Yan | Zendy

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Semi‐ and Nonparametric ARCH Processes

Author(s) -

Oliver B. Linton,

Yang Yan

Publication year - 2010

Publication title -

journal of probability and statistics

Language(s) - English

Resource type - Journals

eISSN - 1687-9538

pISSN - 1687-952X

DOI - 10.1155/2011/906212

Subject(s) - arch , autoregressive conditional heteroskedasticity , econometrics , univariate , nonparametric statistics , volatility (finance) , mathematics , multivariate statistics , semiparametric model , variance (accounting) , statistics , economics , geography , accounting , archaeology

ARCH/GARCH modelling has been successfully applied in empirical finance for many years. This paper surveys the semiparametric and nonparametric methods in univariate and multivariate ARCH/GARCH models. First, we introduce some specific semiparametric models and investigate the semiparametric and nonparametrics estimation techniques applied to: the error density, the functional form of the volatility function, the relationship between mean and variance, long memory processes, locally stationary processes, continuous time processes and multivariate models. The second part of the paper is about the general properties of such processes, including stationary conditions, ergodic conditions and mixing conditions. The last part is on the estimation methods in ARCH/GARCH processes

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