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

John W. Lau, Tak Kuen Siu

Research output: Contribution to journalArticle

Abstract

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. © 2008 Taylor & Francis.

Original languageEnglish
Pages (from-to)243-282
Number of pages40
JournalScandinavian Actuarial Journal
Issue number4
DOIs
Publication statusPublished - 2008

Fingerprint

Modeling
Time series models
Risk measures
Stock exchange
Predictive distribution
Model risk
Posterior distribution
Bayesian approach
Random parameters
Model uncertainty
Stochastic simulation
Clustering
Conditional tail expectation
Outliers
Sampling
Quantile
Chinese restaurant

Keywords

  • Bayesian MAR models
  • Bayesian mixture AR-ARCH models
  • Clustering of returns
  • Conditional tail expectation
  • Dirichlet prior process
  • Outliers detection
  • Quantile-based risk measures
  • Weighted Chinese restaurant process

Cite this

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Modelling long-term investment returns via Bayesian infinite mixture time series models. / Lau, John W.; Siu, Tak Kuen.

In: Scandinavian Actuarial Journal, No. 4, 2008, p. 243-282.

Research output: Contribution to journalArticle

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