Semiparametric volatility model with varying frequencies

Time series data from various sources usually results to 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 can easily lose vital information that characterizes the system ought to be modeled. 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, integrating high frequency data into the mean equation. Second is an extension of the Glosten, Jagannathan, and Rankle model that incorporates the high frequency data into the variance equation. High frequency data were introduced as a nonparametric function in both models that are then 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 GJR models that aggregates high frequency covariates to the same frequency as the output variable. An illustration is provided with stock return data from the Philippines.