Dresden 2014 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 41: Poster - Pattern/ Nonlinear Dyn./ Fluids/ Granular/ Critical Phen.
DY 41.14: Poster
Thursday, April 3, 2014, 17:00–19:00, P3
Bayesian Analysis of Non-Gaussian Long-Range Dependent Processes — Tim Graves5, •Nicholas Watkins1,2,3,4,8, Bobby Gramacy6,5, and Christian Franzke7,8 — 1MPIPKS, Dresden, Germany — 2CFSA, Physics, University of Warwick, Coventry, UK — 3MCT, Open University, Milton Keynes, UK — 4CATS, LSE, London, UK — 5Statistics Laboratory, University of Cambridge, Cambridge, UK — 6Booth School of Business, The University of Chicago, Chicago, USA. — 7Meteorologisches Institut, Universität Hamburg, Germany — 8British Antarctic Survey, Cambridge, United Kingdom
We have used MCMC algorithms to perform a Bayesian analysis of Auto-Regressive Fractionally-Integrated Moving-Average ARFIMA(p,d,q) processes, which are capable of modeling LRD [Graves, Ph.D, 2013]. Our principal aim is to obtain inference about the long memory parameter, d, with secondary interest in the scale and location parameters. We have developed a reversible-jump method enabling us to integrate over different model forms for the short memory component. We initially assume Gaussianity, and have tested the method on both synthetic and physical time series. We have extended the ARFIMA model by weakening the Gaussianity assumption, assuming an α-stable distribution for the innovations, and performing joint inference on d and α. We will present a study of the dependence of the posterior variance of the memory parameter d on the length of the time series considered. This will be compared with equivalent error diagnostics for other measures of d.