  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.
