Statistics for Finance

Chapter 14

Inference in partially observed processes

14.1 Introduction

This section concentrates on filtering (state estimation) and prediction theory related to state space models. There are several reasons for considering state space models. The primary reason is probably that the process described by the system equation of the state space model is a (first-order) Markov process (assuming that the Itō interpretation is used). Furthermore, the state space formulation contains a measurement equation which allows for a rather flexible structure of the observations (aggregation of the state variables, missing measurements, etc.).

More specifically we shall assume that the system is described by the continuous-discrete state space model, which will ...