KFAS (version 0.9.9)

approxSSM: Linear Gaussian Approximation for Non-Gaussian State Space Model

Description

Function approxSMM computes the linear Gaussian approximation of a state space model where the observations have a non-Gaussian exponential family distribution. Currently only Poisson and Binomial distributions are supported.

Usage

approxSSM(object, theta = NULL, maxiter = 100)

Arguments

object

Non-Gaussian state space model object of class SSModel.

theta

Initial values for conditional mode theta. Default is log(mean(y/u)) for Poisson and log(mean(y/(u-y))) for Binomial distribution (or log(mean(y)) in case of $u_t-y_t = 0$ for some $t$).

maxiter

Maximum number of iterations used in linearisation. Default is 100.

Value

• An object which contains the approximating Gaussian state space model with additional components original.distribution, original.y, thetahat, and iterations (the number of iterations used).

Details

The linear Gaussian approximating model is a model defined by $$\tilde y_t = Z_t \alpha_t + \epsilon_t, \quad \epsilon_t \sim N(0,\tilde H_t),$$ $$\alpha_{t+1} = T_t \alpha_t + R_t \eta_t, \quad \eta_t \sim N(0,Q_t),$$ and $\alpha_1 \sim N(a_1,P_1)$, where $\tilde y$ and $\tilde H$ is chosen in a way that the linear Gaussian approximating model has the same conditional mode of $\theta=Z\alpha$ given the observations $y$ as the original non-Gaussian model. Models also have same curvature at the mode.

The linearization of the exponential family state space model is based on the first two derivatives of the observational logdensity.

The approximating Gaussian model is used in computation of the log-likelihood of the non-Gaussian model and in importance sampling of non-Gaussian model.

See Also

Importance sampling of non-Gaussian state space models importanceSSM, construct a SSModel object SSModel.