The live method for generalized additive volatility models

We investigate a new separable nonparametric model for time series, which includes many autoregressive conditional heteroskedastic (ARCH) models and autoregressive (AR) models already discussed in the literature. We also propose a new estimation procedure called LIVE, or local instrumental variable estimation, that is based on a localization of the classical instrumental variable method. Our method has considerable computational advantages over the competing marginal integration or projection method. We also consider a more efficient two-step likelihood-based procedure and show that this yields both asymptotic and finite-sample performance gains.