Title: Volatility estimation when observations are missing
Authors: Genaro Sucarrat - BI Norwegian Business School (Norway) [presenting]
Natalia Bahamonde - Pontificia Universidad Catolica de Valparaiso (Chile)
Hamdi Raissi - PUCV (Chile)
Abstract: In empirical practice observations are often missing. This invalidates standard estimation methods of Generalised Autoregressive Conditional Heteroscedasticity (GARCH) models because of a repeated invertibility problem induced at each missing location. To sidestep this problem we propose a log-ARCH model -- i.e.\ no GARCH-terms -- with stochastic conditioning covariates (e.g.\ volatility proxies) that can be estimated with least squares methods. Apart from omitted GARCH terms, however, the model is very general and flexible: It is asymmetric, multivariate, allows for (unknown) Dynamic Conditional Correlations (DCCs), and non-negativity constraints are not needed on the parameters nor on the covariates. We derive a least squares equation-by-equation estimator of the model, and prove its Consistency and Asymptotic Normality (CAN) when the missing data process is stationary, unknown and not necessarily independent of the log-ARCH process itself. Our results are illustrated in a simulation study, and in an empirical application.