  Robust time series analysis is an important subject in statistical modeling.
Models based on Gaussian distribution are sensitive to outliers, which may
imply in a significant degradation in estimation performance as well as in
prediction accuracy. State-space models, also referred as Dynamic Models, is a
very useful way to describe the evolution of a time series variable through a
structured latent evolution system. Integrated Nested Laplace Approximation
(INLA) is a recent approach proposed to perform fast Bayesian inference in
Latent Gaussian Models which naturally comprises Dynamic Models. We present how
to perform fast and accurate non-Gaussian dynamic modeling with INLA and show
how these models can provide a more robust time series analysis when compared
with standard dynamic models based on Gaussian distributions. We formalize the
framework used to fit complex non-Gaussian space-state models using the R
package INLA and illustrate our approach in both a simulation study and on the
brazilian homicide rate dataset.
