Continuous Time Series Models for Unequally Spaced Data Applied to Modeling Atomic Clocks

Abstract

State space representations and Kalman filters used to calculate likelihoods have increased the ease and flexibility of fitting time series models to data. When data are unequally spaced with no underlying basic sampling interval, continuous time series models are more natural than discrete time series models. State space representations still provide the flexibility needed to include a large class of models. This paper gives a survey of state space methods for continuous time processes, discusses extensions to multivariate data at unequally spaced time points with missing data within the observation vector, and gives an example of estimating time and model parameters from an ensemble of atomic clocks.