Richard Gerlach

Efficient Bayesian Inference for Dynamic Mixture Models

Abstract A Bayesian approach is presented for estimating a mixture of linear Gaussian state-space models. Such models are used to model interventions in time series and nonparametric regression. Markov chain Monte Carlo sampling is usually necessary to obtain the posterior distributions of such mixture models, because it is difficult to obtain them analytically. The methodological contribution of the article is to derive a set of recursions for dynamic mixture models that efficiently implement a Markov chain Monte Carlo sampling scheme that converges rapidly to the posterior distribution. The methodology is illustrated by fitting an autoregressive model subject to interventions to zinc concentration in sludge.

Structural breaks and diversification: The impact of the 1997 Asian financial crisis on the integration of Asia-Pacific real estate markets

Abstract Currently, there exists relatively little research on the influence that the 1997 Asian financial crisis has had upon capital flows within the property market and the associated long-run implications of it. This paper examines the impact that the crisis has had upon the integration and dynamic links between a number of Asia-Pacific real estate markets. The results show that Asia-Pacific property markets are integrated, despite a structural shift occurring at the time of the crisis. These results are a particularly important finding for fund managers concerned with the impact of globalization on the performance of their real estate portfolios, showing that in the Asia-Pacific region diversification benefits are actually less than that suggested by an analysis incorrectly ignoring the crisis.

Bayesian time-varying quantile forecasting for Value-at-Risk in financial markets

Recently, advances in time-varying quantile modeling have proven effective in financial Value-at-Risk forecasting. Some well-known dynamic conditional autoregressive quantile models are generalized to a fully nonlinear family. The Bayesian solution to the general quantile regression problem, via the Skewed-Laplace distribution, is adapted and designed for parameter estimation in this model family via an adaptive Markov chain Monte Carlo sampling scheme. A simulation study illustrates favorable precision in estimation, compared to the standard numerical optimization method. The proposed model family is clearly favored in an empirical study of 10 major stock markets. The results that show the proposed model is more accurate at Value-at-Risk forecasting over a two-year period, when compared to a range of existing alternative models and methods.

Bayesian Value-at-Risk and expected shortfall forecasting via the asymmetric Laplace distribution

A parametric approach to estimating and forecasting Value-at-Risk (VaR) and expected shortfall (ES) for a heteroscedastic financial return series is proposed. The well-known GJR-GARCH form models the volatility process, capturing the leverage effect. To capture potential skewness and heavy tails, the model assumes an asymmetric Laplace form as the conditional distribution of the series. Furthermore, dynamics in higher moments are modeled by allowing the shape parameter in this distribution to be time-varying. Estimation is via an adaptive Markov chain Monte Carlo (MCMC) sampling scheme, employing the Metropolis-Hastings (MH) algorithm with a mixture of Gaussian proposal distributions. A simulation study highlights accurate estimation and improved inference compared to a single-Gaussian-proposal MH method. The model is illustrated by applying it to four international stock market indices and two exchange rates, generating one-step-ahead forecasts of VaR and ES. Standard and non-standard tests are applied to these forecasts, and the finding is that the proposed model performs favourably compared to some popular competitors: in particular it is the only conservative model of risk over the period studied, which includes the recent global financial crisis.

Optimal dynamic hedging via copula-threshold-GARCH models

The contribution of this paper is twofold. First, we exploit copula methodology, with two threshold GARCH models as marginals, to construct a bivariate copula-threshold-GARCH model, simultaneously capturing asymmetric nonlinear behaviour in univariate stock returns of spot and futures markets and bivariate dependency, in a flexible manner. Two elliptical copulas (Gaussian and Students-t) and three Archimedean copulas (Clayton, Gumbel and the Mixture of Clayton and Gumbel) are utilized. Second, we employ the presenting models to investigate the hedging performance for five East Asian spot and futures stock markets: Hong Kong, Japan, Korea, Singapore and Taiwan. Compared with conventional hedging strategies, including Engles dynamic conditional correlation GARCH model, the results show that hedge ratios constructed by a Gaussian or Mixture copula are the best-performed in variance reduction for all markets except Japan and Singapore, and provide close to the best returns on a hedging portfolio over the sample period.

A comparison of Bayes-Laplace, Jeffreys, and other priors: the case of zero events

Beta distributions with both parameters equal to 0, ½, or 1 are the usual choices for “noninformative” priors for Bayesian estimation of the binomial parameter. However, as illustrated by two examples from the Bayesian literature, care needs to be taken with parameter values below 1, both for noninformative and informative priors, as such priors concentrate their mass close to 0 and/or 1 and can suppress the importance of the observed data. These examples concern the case of no successes (or failures) and illustrate the informativeness of the Jeffreys prior usually recommended as the “consensus prior.” In particular, the second example suggests that when the binomial parameter is known to be very small, an informative prior from the beta (1, b) family (b > 1) seems appropriate, while a beta (a, b) with a < 1 can be too informative. It is thus argued that sensitivity analysis of an informative prior should be based on a consensus posterior corresponding to the Bayes–Laplace prior rather than the Jeffreys prior.

The Australian EEG Database

The Australian EEG Database is a web-based de-identified searchable database of 18,500 EEG records recorded at a regional public hospital over an 11-year period. Patients range in age from a premature infant born at 24 weeks gestation, through to people aged over 90 years. This paper will describe the history of the database, the range of patients represented in the database, and the nature of the text-based and digital data contained in the database. Preliminary results of the first two studies undertaken using the database are presented. Plans for sharing data from the Australian EEG database with researchers are discussed. We anticipate that such data will be useful in not only helping to answer clinical questions but also in the field of mathematical modeling of the EEG.

Comparison of nonnested asymmetric heteroskedastic models

The GJR-GARCH model is a popular choice among nonlinear models of the well-known asymmetric volatility phenomenon in financial market data. However, recent work employs double threshold nonlinear models to capture both mean and volatility asymmetry. A Bayesian model comparison procedure is proposed to compare the GJR-GARCH with various double threshold GARCH specifications, by designing a reversible jump Markov chain Monte Carlo algorithm. A simulation experiment illustrates good performance in estimation and model selection over reasonable sample sizes. In a study of seven markets strong evidence is found that the DTGARCH, with US market news as threshold variable, outperforms the GJR-GARCH and traditional self-exciting DTGARCH models. This result was consistent across six markets, excluding Canada.

Bayesian Forecasting for Financial Risk Management, Pre and Post the Global Financial Crisis

Value-at-Risk (VaR) forecasting via a computational Bayesian framework is considered. A range of parametric models are compared, including standard, threshold nonlinear and Markov switching GARCH specifications, plus standard and nonlinear stochastic volatility models, most considering four error probability distributions: Gaussian, Student-t, skewed-t and generalized error distribution. Adaptive Markov chain Monte Carlo methods are employed in estimation and forecasting. A portfolio of four Asia-Pacific stock markets is considered. Two forecasting periods are evaluated in light of the recent global financial crisis. Results reveal that: (i) GARCH models out-performed stochastic volatility models in almost all cases; (ii) asymmetric volatility models were clearly favoured pre-crisis; while at the 1% level during and post-crisis, for a 1 day horizon, models with skewed-t errors ranked best, while IGARCH models were favoured at the 5% level; (iii) all models forecasted VaR less accurately and anti-conservatively post-crisis

Volatility forecasting using threshold heteroskedastic models of the intra-day range

An effective approach for forecasting return volatility via threshold nonlinear heteroskedastic models of the daily asset price range is provided. The range is defined as the difference between the highest and lowest log intra-day asset price. A general model specification is proposed, allowing the intra-day high-low price range to depend nonlinearly on past information, or an exogenous variable such as US market information. The model captures aspects such as sign or size asymmetry and heteroskedasticity, which are commonly observed in financial markets. The focus is on parameter estimation, inference and volatility forecasting in a Bayesian framework. An MCMC sampling scheme is employed for estimation and shown to work well in simulation experiments. Finally, competing range-based and return-based heteroskedastic models are compared via out-of-sample forecast performance. Applied to six international financial market indices, the range-based threshold heteroskedastic models are well supported by the data in terms of finding significant threshold nonlinearity, diagnostic checking and volatility forecast performance under various volatility proxies.