Self-Organizing Time Series Model

  • Tomoyuki Higuchi
Part of the Statistics for Engineering and Information Science book series (ISS)


The generalised state-space model (GSSM) that we deal with in this study is defined by a set of two equations,
$$system\;\bmod el\quad {x_t} = f({x_{t - 1}},{v_t})$$
$$observation\;\bmod el\quad {y_t} \sim r( \cdot |{x_t},{\theta _{obs}})$$
where x t is an n x × 1 vector of unobserved sate variables, and y t is an n y dimensional vector observation. \( {\mathbb{R}^{{n_x}}} \times {\mathbb{R}^{{n_v}}} \to {\mathbb{R}^{{n_x}}} \) is a given function. {v t } is an independent and identically distributed (i.i.d.) random process with v t ~ q(v|θ sys ). r is the conditional distribution of y t given x t q(∙|∙) and r(∙|∙) are, in general, non-Gaussian densities specified by the unknown parameter vectors, θ sys and θ obs respectively. In this study, we set θ = [θ sys ,θ obs ]′. The initial state x 0 is distributed according to the density p 0(x).


Roulette Wheel Roulette Wheel Selection Marginal Posterior Distribution Spiral Density Wave Deterministic Sampling 


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Copyright information

© Springer Science+Business Media New York 2001

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  • Tomoyuki Higuchi

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