A new state space approach is proposed to model the time-dependence in an extreme
value process. The generalized extreme value distribution is extended to incorporate the
time-dependence using a state space representation where the state variables either fol-
low an autoregressive (AR) process or a moving average (MA) process with innovations
arising from a Gumbel distribution. Using a Bayesian approach, an efficient algorithm
is proposed to implement Markov chain Monte Carlo method where we exploit an accu-
rate approximation of the Gumbel distribution by a ten-component mixture of normal
distributions. The methodology is illustrated using extreme returns of daily stock data.
The model is tted to a monthly series of minimum returns and the empirical results
support strong evidence of time-dependence among the observed minimum returns.