A NEW ESTIMATION PROCEDURE USING A REVERSIBLE JUMP MCMC ALGORITHM FOR AR MODELS OF EXPONENTIAL WHITE NOISE

Abstract

The autoregressive model generally has a Gaussian error. If an autoregressive model that has a
Gaussian error is used to model data, the assumption of normality is often not obeyed by the data. In addition,
the parameters of the autoregressive model are generally unknown. The parameters of the autoregressive
model include order model, model coefficient, error mean and error variance. This paper aims to determine
the parameter estimation procedure of an autoregressive model that has an exponential error. In this paper,
the autoregressive model parameter estimation is worked out in a hierarchical Bayesian framework. Since the
autoregressive order is also part of the model parameter, the Bayes estimator has a complex form so that the
Bayes estimator cannot be explicitly calculated. To solve the problem, the reversible jump MCMC is
implemented. The results show that model order, model coefficient, error mean and error variance can be
calculated simultaneously. In addition, the resulting autoregressive model is always a stationary
autoregressive model.