On time series of observations from exponential family distributions

ABRIL, JUAN CARLOS

PAKISTAN JOURNAL OF STATISTICS

ISOSS PUBL

Lugar: Lahore; Año: 2001 vol. 17 p. 235 - 248

1012-9367

In this work a general method is developed for handling non-Gaussian observations in linear state space time series models and this is applied to the special case in which the observations come from exponential family distributions. The method is based on the idea of estimating the state vector by its posterior mode. Let be the vector and let be the conditional density of given the whole sample . The posterior mode estimate (PME) of is defined to be the value of that maximises . When the model is linear and Gaussian, . When the observations are non-Gaussian, however, is generally difficult or impossible to compute and to use the mode instead is a natural alternative. More than that, it can be argued that in the non-Gaussian case the PME is preferable to since it is the value of which is the most probable given the data. In this respect it can be thought of analogous to the maximum likelihood estimate of a fixed parameter vector. The question of calculating suitable starting values for the state iteration is considered and the estimation of the hyperparameters is investigated in the work.