Semiparametric Volatility Model with Varying Frequencies

Abstract

In extracting time series data from various sources, it is inevitable to compile variables measured at varying frequencies as this is often dependent on the source. Modeling from these data can be facilitated by aggregating high frequency data to match the relatively lower frequencies of the rest of the variables. This however, can easily loss vital information that characterizes the system ought to be modelled. Two semiparametric volatility models are postulated to account for covariates of varying frequencies without aggregation of the data to lower frequencies. First is an extension of the autoregressive integrated moving average with explanatory variable (ARMAX) model, it integrates high frequency data into the mean equation (VF-ARMA). Second is an extension of the Glosten, Jagannathan and Rankle (GJR) model that incorporates the high frequency data into the variance equation (VF-GARCH). In both models, high frequency data was introduced as a nonparametric function in the model. Both models are estimated using a hybrid estimation procedure that benefits from the additive nature of the models. Simulation studies illustrate the advantages of postulated models in terms of predictive ability compared to generalized autoregressive conditionally heteroscedastic (GARCH) and GJR models that simply aggregates high frequency covariates to the same frequency as the output variable. Furthermore, VF-ARMA is superior to VF-GARCH since it exhibits some degree of robustness in a wide range of scenarios.