Fitting State-Space Models

Abstract

This chapter is an overview of methods for using available data to make inferences about states and parameters of a state-space model. We call this “model fitting”, or as Hilborn and Mangel (1997) say, “confronting models with data”. Given a general SSM [Eqs. (3.3)–(3.5)], $$\displaystyle\begin{array}{rcl} \mbox{ Initial state pdf}&:& g_{0}(\mathbf{n}_{0}\vert \boldsymbol{\theta }) {}\\ \mbox{ State $t$ pdf}&:& g_{t}(\mathbf{n}_{t}\vert \mathbf{n}_{t-1},\boldsymbol{\theta }) {}\\ \mbox{ Observation $t$ pdf}&:& f_{t}(\mathbf{y}_{t}\vert \mathbf{n}_{t},\boldsymbol{\psi }), {}\\ \end{array}$$ model fitting is a matter of using the data, y 1: T , to estimate the unknown parameters, \((\boldsymbol{\theta },\boldsymbol{\psi })\) , or the unknown states, n 0: T , or both—the dual estimation problem (Wan and Nelson 2001).