Particle filtering for Gumbel-distributed daily maxima of methane and nitrous oxide.

In atmospheric chemistry, daily maxima concentrations capture information about the variability among peak values. Statistically, they can often be modeled by a Gumbel distribution. This is the case for two very important greenhouse gases methane and nitrous oxide maxima when they are measured at our site of interest, Gif-sur-Yvette, a city south west of Paris. In practice, those two daily concentrations are not always recorded during the same period, and it would be of interest to reconstruct one from the other one. Such a type of inference can be handled within a state space modeling framework, but state space models are not tailored to represent the dynamics among Gumbel-distributed maxima. By building on our previous work, which made a link between linear autoregressive time series and Gumbel-distributed maxima, we propose and study such a state space model. It has the advantages of being linear and of preserving the Gumbel characteristic in both the state and observational equations. Concerning the inference of the hidden maxima at the state equation level, we derive the optimal weights of the auxiliary particle filtering approach of Pitt and Shephard. A simulation study indicates that our approach offers a gain over the Kalman filter, the bootstrap filter, and the nonmodified version of the Pitt and Shephard auxiliary filter. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]