Continuous-Time Linear Models

On Bayesian analysis of non-linear continuous-time autoregression models

This paper introduces a method for performing fully Bayesian inference for non-linear conditional autoregressive continuous-time models, based on a finite skeleton of observations. Our approach uses MCMC and involves imputing data from times at which observations are not made. It uses a reparameterisation technique for the missing data, and due to the non-Markovian nature of the models, it is n...

Prediction Formulas for Continuous Time Linear Rational Expectations Models

l1li' 11' In this note we derive optimal prediction formulas to be used in solving continuous time rational expectations models. In these derivations we employ Laplace transforms in a manner analogous to the use of z transforms for solving discrete time optimal prediction problems in Hansen and Sargent (1980a, Appendix A). The formulas are intended to play the same role for continuous time mode...

Models of Continuous-Time Linear Time-Varying Systems with Fully Adaptable System Modes

Estimating Continuous-Time Income Models

While earning processes are commonly unobservable income flows which evolve in continuous time, observable income data are usually discrete, having been aggregated over time. We consider continuous-time earning processes, specifically (non-linearly) transformed Ornstein-Uhlenbeck processes, and the associated integrated, i.e. time aggregated process. Both processes are characterised, and we sho...

Continuous - Time Short Rate Models

These notes provide an overview of singleand multi-factor models of the short rate. We will begin with a generic single-factor model where the dynamics of rt under the physical measure, P , are given. Following the approach of Vasicek, we then derive the PDE that must be satisfied by derivative security prices. We then use the martingale approach to give an alternative (and familiar) expression...