  Dependent generalized extreme value (dGEV) models have attracted much
attention due to the dependency structure that often appears in real datasets.
To construct a dGEV model, a natural approach is to assume that some parameters
in the model are time-varying. A previous study has shown that a dependent
Gumbel process can be naturally incorporated into a GEV model. The model is a
nonlinear state space model with a hidden state that follows a Markov process,
with its innovation following a Gumbel distribution. Inference may be made for
the model using Bayesian methods, sampling the hidden process from a mixture
normal distribution, used to approximate the Gumbel distribution. Thus the
response follows an approximate GEV model. We propose a new model in which each
marginal distribution is an exact GEV distribution. We use a variable
transformation to combine the marginal CDF of a Gumbel distribution with the
standard normal copula. Then our model is a nonlinear state space model in
which the hidden state equation is Gaussian. We analyze this model using
Bayesian methods, and sample the elements of the state vector using particle
Gibbs with ancestor sampling (PGAS). The PGAS algorithm turns out to be very
efficient in solving nonlinear state space models. We also show our model is
flexible enough to incorporate seasonality.
