|
Abstract:
|
We develop a Bayesian procedure for analyzing stationary long-range dependent processes. Specifically, we consider the fractional exponential model (FEXP) to estimate the memory parameter of a stationary long-memory Gaussian time series. In particular, we propose a hierarchical Bayesian model and make it fully adaptive by imposing a prior distribution on the model order. Further, we describe a reversible jump Markov chain Monte Carlo algorithm for variable dimension estimation and show that, in our context, the algorithm provides a consistent method of model selection. Therefore, through an application of Bayesian model averaging, we incorporate all possible models from the FEXP class (up to a given finite order). As a result we reduce the underestimation of uncertainty at the model-selection stage as well as achieve better estimates of the long memory parameter.
|
