B0482
Title: Approximate Bayesian computation for long memory processes
Authors: Clara Grazian - University of Sydney (Australia) [presenting]
Abstract: A Bayesian approach is investigated for estimating the parameters of long memory models, in particular ARFIMA models. Long memory, i.e. the phenomena of hyperbolic autocorrelation decay in series, has attracted much attention, since in many situations the assumption of short memory, for example, the Markovian assumption, can be considered too strong. Applications can be easily found in astronomy, finance, and environmental sciences; however, current parametric and semiparametric approaches to long-memory modelling present difficulties, especially in the estimation procedure. A novel approach is presented to approximating the joint posterior distributions of ARFIMA model parameters using approximate Bayesian computation (ABC), which allows the approximation of the posterior distributions of the parameters given the observed finite series, without making use of asymptotic arguments. Acceptance of simulated long-memory parameters is based on the periodogram: an estimate of the spectral density which captures the dominance of long-term non-negligible correlations, characteristic of long-memory ARFIMA processes. A simulation study and an example of daily log returns for Standard and Poor's 500 index will show the advantages of the proposed approach.
