Copyright © 2011 Oliver B. Linton and Yang Yan. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.