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Bayesian Inference for ARFIMA Models
Author(s) -
Durham Garland,
Geweke John,
PorterHudak Susan,
Sowell Fallaw
Publication year - 2019
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12443
Subject(s) - autoregressive fractionally integrated moving average , likelihood function , markov chain monte carlo , bayesian inference , approximate bayesian computation , bayesian probability , inference , algorithm , mathematics , computer science , monte carlo method , autoregressive model , series (stratigraphy) , econometrics , artificial intelligence , statistics , estimation theory , volatility (finance) , paleontology , long memory , biology
This article develops practical methods for Bayesian inference in the autoregressive fractionally integrated moving average (ARFIMA) model using the exact likelihood function, any proper prior distribution, and time series that may have thousands of observations. These methods utilize sequentially adaptive Bayesian learning, a sequential Monte Carlo algorithm that can exploit massively parallel desktop computing with graphics processing units (GPUs). The article identifies and solves several problems in the computation of the likelihood function that apparently have not been addressed in the literature. Four applications illustrate the utility of the approach. The most ambitious is an ARFIMA(2,d,2) model for the Campito tree ring time series (length 5405), for which the methods developed in the article provide an essentially uncorrelated sample of size 16,384 from the exact posterior distribution in under four hours. Less ambitious applications take as little as 4 minutes without exploiting GPUs.