KFAS (version 1.0.3)

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

Description

Function approxSMM computes the linear Gaussian approximation of a state space model where observations follow an exponential family distribution.

Usage

approxSSM(model, theta, maxiter = 25, tol = 1e-08)

Arguments

model

A non-Gaussian state space model object of class SSModel.

theta

Initial values for conditional mode theta.

maxiter

The maximum number of iterations used in linearisation. Default is 25.

tol

Tolerance parameter for convergence checks. Iterations are continued until $tol>sum(abs(theta_{new}-theta_{old})/(abs(theta_{old})+0.1))/(n*p)$.

Value

• An object which contains the approximating Gaussian state space model with following additional components:
• thetahat
  mode of $p(\theta|y)$.
• iterations
  number of iterations used.

Details

The linear Gaussian approximating model is 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 $\tilde H$ are 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 a same curvature at the mode. The linearization of the exponential family state space model is based on iterative weighted least squares method, see McCullagh and Nelder (1983) p.31 and Durbin Koopman (2012) p. 243.

See Also

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