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## Siem Jan Koopman and Neil Shephard

Print publication date: 2015

Print ISBN-13: 9780199683666

Published to Oxford Scholarship Online: January 2016

DOI: 10.1093/acprof:oso/9780199683666.001.0001

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# Inference for models with asymmetric α -stable noise processes

Chapter:
(p.190) Chapter 9 Inference for models with asymmetric $α$ -stable noise processes
Source:
Unobserved Components and Time Series Econometrics
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199683666.003.0009

This chapter begins with a simple general framework for inference in the presence of α‎-stable processes, where the stable processes are represented as conditionally Gaussian distributions, relying on (exact) series representations of the stable laws and the corresponding stochastic integrations in terms of infinite summations of random Poisson process arrival times. Inference can therefore be carried out using techniques including auxiliary variables, Rao-Blackwellized particle filtering, and Markov chain Monte Carlo. The Poisson series representation is further enhanced by introducing an approximation of the series residual terms based on exact moment calculations. Extensions to the discrete-time asymmetric stable case and to continuous-time are

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