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Nonparametric estimation of a time-varying GARCH model

In this paper, a non-stationary time-varying GARCH (tvGARCH) model has been introduced by allowing the parameters of a stationary GARCH model to vary as functions of time. It is shown that the tvGARCH process is locally stationary in the sense that it can be locally approximated by stationary GARCH processes at fixed time points. We develop a two-step local polynomial procedure for the estimation of the parameter functions of the proposed model. Several asymptotic properties of the estimators have been established, including the asymptotic optimality. It is found that the tvGARCH model performs better than many of the standard GARCH models for various real data sets.