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Applied Bayesian Modelling, 2nd Edition by Peter Congdon

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6.4 Dynamic linear and general linear models

In contrast to ARMA methods, dynamic linear models and their extensions (e.g. Durbin and Koopman, 2000; Harvey et al., 2004; Petris et al., 2009; Fahrmeir and Kneib, 2011; West, 2013) based on state space priors aim to directly capture features of time series, such as trend and seasonality. Such models are also useful in representing volatility and time varying regression relationships. Dynamic linear models represent observed time series c06-math-0636 as conditional on unobserved continuous states c06-math-0637 (at the second stage of a hierarchical prior) which in turn condition on hyperparameters such as variance of the states, regression parameters, etc. The observation c06-math-0638 is assumed independent of the past observations given the knowledge of c06-math-0639, so that temporal dynamics are represented by the state parameters. Both observations and states may be multivariate, and a univariate outcome may be represented in terms of multivariate states.

Such models consist of two sets of equations, a measurement or observation equation linking the observations to unobserved state variables, ...

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