Irregularly Spaced AR and ARCH (ISAR-ARCH) Models

Abstract

High frequency data in finance are time series which are often measured at unequally or irregularly spaced time intervals. This paper suggests a modeling approach by so-called AR response surfaces where the AR coefficients are declining functions in continuous lag time. The irregularly spaced AR-ARCH (ISAR-ARCH) models contain the usual AR-ARCH models as a special case if the time series is equally spaced. The time between observation arrivals is treated as a stochastic time varying process and modeled as a conditional Weibull distribution to capture the stylized fact of duration clustering. For the ISAR-ARCH process and the conditional Weibull duration (CWD) process, we show how to carry out an exact Bayesian analysis using a Markov chain Monte Carlo method. Model selection and forecasting are handled using the predictive density. Finally, we illustrate our methodology with two examples