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Modelling long-term investment returns via Bayesian infinite mixture time series models

Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/137373

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Title: Modelling long-term investment returns via Bayesian infinite mixture time series models
Related: Scandinavian actuarial journal, Vol. 2008, Issue 4, (2008), p.243-282
DOI: 10.1080/03461230701862889
Publisher: Taylor & Francis
Date: 2008
FoR/RFCD Code(s): 010200 Applied Mathematics
Author/Creator: Lau, John W
Author/Creator: Siu, Tak Kuen
Description: This paper introduces the class of Bayesian infinite mixture time series models first proposed in Lau & So (2004) for modelling long-term investment returns. It is a flexible class of time series models and provides a flexible way to incorporate full information contained in all autoregressive components with various orders by utilizing the idea of Bayesian averaging or mixing. We adopt a Bayesian sampling scheme based on a weighted Chinese restaurant process for generating partitions of investment returns to estimate the Bayesian infinite mixture time series models. Instead of using the point estimates, as in the classical or non-Bayesian approach, the estimation in this paper is performed by the full Bayesian approach, utilizing the idea of Bayesian averaging to incorporate all information contained in the posterior distributions of the random parameters. This provides a natural way to incorporate model risk or uncertainty. The proposed models can also be used to perform clustering of investment returns and detect outliers of returns. We employ the monthly data from the Toronto Stock Exchange 300 (TSE 300) indices to illustrate the implementation of our models and compare the simulated results from the estimated models with the empirical characteristics of the TSE 300 data. We apply the Bayesian predictive distribution of the logarithmic returns obtained by the Bayesian averaging or mixing to evaluate the quantile-based and conditional tail expectation risk measures for segregated fund contracts via stochastic simulation. We compare the risk measures evaluated from our models with those from some well-known and important models in the literature, and highlight some features that can be obtained from our models.
Description: 40 page(s)
Subject Keyword: 010200 Applied Mathematics
Subject Keyword: Bayesian MAR models
Subject Keyword: Bayesian mixture AR-ARCH models
Subject Keyword: Weighted Chinese restaurant process
Subject Keyword: Clustering of returns
Subject Keyword: Outliers detection
Subject Keyword: Dirichlet prior process
Subject Keyword: Quantile-based risk measures
Subject Keyword: Conditional tail expectation
Resource Type: journal article
Organisation: Macquarie University. Dept. of Actuarial Studies

Identifier: http://hdl.handle.net/1959.14/137373
Identifier: ISSN:0346-1238
Identifier: mq-rm-2009000233
Language: eng
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