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BAYESIAN ANALYSIS OF VECTOR ARFIMA PROCESSES
Author(s) -
Ravishanker Nalini,
Ray Bonnie K.
Publication year - 1997
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1997.tb00693.x
Subject(s) - autoregressive fractionally integrated moving average , series (stratigraphy) , autoregressive model , bayesian inference , gibbs sampling , range (aeronautics) , bayesian probability , mathematics , sampling (signal processing) , posterior probability , inference , statistics , computer science , econometrics , artificial intelligence , long memory , detector , materials science , composite material , biology , telecommunications , volatility (finance) , paleontology
Summary A general framework is presented for Bayesian inference of multivariate time series exhibiting long‐range dependence. The series are modelled using a vector autoregressive fractionally integrated moving‐average (VARFIMA) process, which can capture both short‐term correlation structure and long‐range dependence characteristics of the individual series, as well as interdependence and feedback relationships between the series. To facilitate a sampling‐based Bayesian approach, the exact joint posterior density is derived for the parameters, in a form that is computationally simpler than direct evaluation of the likelihood, and a modified Gibbs sampling algorithm is used to generate samples from the complete conditional distribution associated with each parameter. The paper also shows 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. The approach adopted here permits investigation of the effects on model estimation of the interdependence and feedback relationships between the series.