by Nalini Ravishanker, Bonnie K. Ray
ftp://merlot.stat.uconn.edu/pub/papers/tr95/tr9526.ps
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Abstract:
We present a general framework for Bayesian inference of multivariate time series exhibiting both long and short memory behavior. The series are modeled using a multivariate autoregressive fractionally integrated moving average (MVARFIMA) process, which can capture both the short and long memory characteristics of the individual series, as well as interdependence and feedback relationships between the series. To facilitate a sampling-based Bayesian approach, we derive the exact joint posterior density for the parameters in a form that is computationally feasible and use a modified Gibbs sampling algorithm to generate samples from the complete conditional distribution associated with each parameter. We also show how an approximate form of the joint posterior density may be used for long time series. The procedure is illustrated using sea surface temperatures measured at three locations along the central California coast. These series are believed to be interdependent due to similarities in local atmospheric conditions at the different locations, and previous studies have found that they exhibit long memory when studied individually. Our approach will enable us to investigate the effect of the interdependence between the series on model estimation.
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