Time-Varying Dispersion Integer-Valued GARCH Models

We propose a general class of INteger-valued Generalized AutoRegressive Conditionally Heteroskedastic (INGARCH) processes by allowing time-varying mean and dispersion parameters, which we call time-varying dispersion INGARCH (tv-DINGARCH) models. More specifically, we consider mixed Poisson INGARCH models and allow for a dynamic modeling of the dispersion parameter (as well as the mean), similarly to the spirit of the ordinary GARCH models. We derive conditions to obtain first and second order stationarity, and ergodicity as well. Estimation of the parameters is addressed and their associated asymptotic properties established as well. A restricted bootstrap procedure is proposed for testing constant dispersion against time-varying dispersion. Monte Carlo simulation studies are presented for checking point estimation, standard errors, and the performance of the restricted bootstrap approach. The inclusion of covariates is also addressed and applied to the daily number of deaths due to COVID-19 in Ireland. Insightful results were obtained in the data analysis, including a superior performance of the tv-DINGARCH processes over the ordinary INGARCH models.Comment: Paper submitted for publicatio

Modeling Price Clustering in High-Frequency Prices

The price clustering phenomenon manifesting itself as an increased occurrence of specific prices is widely observed and well-documented for various financial instruments and markets. In the literature, however, it is rarely incorporated into price models. We consider that there are several types of agents trading only in specific multiples of the tick size resulting in an increased occurrence of these multiples in prices. For example, stocks on the NYSE and NASDAQ exchanges are traded with precision to one cent but multiples of five cents and ten cents occur much more often in prices. To capture this behavior, we propose a discrete price model based on a mixture of double Poisson distributions with dynamic volatility and dynamic proportions of agent types. The model is estimated by the maximum likelihood method. In an empirical study of DJIA stocks, we find that higher instantaneous volatility leads to weaker price clustering at the ultra-high frequency. This is in sharp contrast with results at low frequencies which show that daily realized volatility has a positive impact on price clustering

A model for integer-valued time series with conditional overdispersion

10.1016/j.csda.2012.04.011Computational Statistics and Data Analysis56124229-4242CSDA