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The exact likelihood for a state space model with stochastic inputs

✍ Scribed by J. Casals; S. Sotoca

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
547 KB
Volume
42
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this work, we derive exact and approximate expressions for the conditional mean and variance of the initial state of a state space model, allowing for unit roots and stochastic inputs. These results provide adequate initial conditions to compute the exact likelihood using the Kalman filter. The exact conditional moments axe the best choice when the stochastic structure of the inputs is known. If this is not the case, the approximate expressions axe a good alternative, as some simulation results illustrate.

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## Abstract The cornerstone of the theory of discrete‐space single‐input–single‐output linear systems is the idea that every such system has an input–output map that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which, for t