Local Instrumental Variable (LIVE) Method For The Generalized Additive-Interactive Nonlinear Volatility Model

In this article we consider a new separable nonparametric volatility model related to the GANARCH model of Kim and Linton (2004) [24]. Unlike the GANARCH model, it does not assume the known link function but includes second-order inter-action terms in both mean and variance functions instead. The assumption of the known link function implies knowing the distribution of the data. The exact data distribution is often not so easy to verify, especially in the multivariate case; thus, it can be said that our model imposes fewer difficult to verify assumptions. Moti-vated by the local instrumental variable estimation method introduced by Kim and Linton (2004)[24], we propose an instrumental variable-based estimation method of both additive and interactive mean and variance component functions for this model. This method is computationally more effective than most other nonparametric esti-mation methods that can potentially be used to estimate components of such a model. Asymptotic behavior of the resulting estimators is investigated and their asymptotic normality is established. Explicit expressions for asymptotic means and variances of these estimators are also obtained. Simulation experiments provide strong evidence that these estimators are well-behaved in finite samples as well.