Bayesian analysis of nonlinear and non-Gaussian state space models via multiple-try sampling methods

We develop in this paper three multiple-try blocking schemes for Bayesian analysis of nonlinear and non-Gaussian state space models. To reduce the correlations between successive iterates and to avoid getting trapped in a local maximum, we construct Markov chains by drawing state variables in blocks with multiple trial points. The first and second methods adopt autoregressive and independent kernels to produce the trial points, while the third method uses samples along suitable directions. Using the time series structure of the state space models, the three sampling schemes can be implemented efficiently. In our multimodal examples, the three multiple-try samplers are able to generate the desired posterior sample, whereas existing methods fail to do so

A multivariate long memory stochastic volatility model

This paper develops a multivariate long-memory stochastic volatility model which allows the multi-asset long-range dependence in the volatility process. The motivation is from the fact that both autocorrelations and cross-correlations of some proxies of exchange rate volatility exhibit strong evidence of long-memory behavior. The statistical properties of the new stochastic volatility model provide theoretical explanation to the common findings that long memory volatility properties are more apparent if we use absolute return as a volatility proxy than squared return. Results of the real data application show that our model outperforms an existing multivariate stochastic volatility model. (c) 2005 Elsevier B.V. All rights reserved

On a threshold heteroscedastic model

This paper proposes a threshold heteroscedastic model which integrates threshold nonlinearity and GARCH-type conditional variance for modeling mean and volatility asymmetries in financial markets. The main feature of this model is that the threshold variable for regime switching is formulated as a weighted average of important auxiliary variables. Estimation and diagnostic checks are performed using Markov chain Monte Carlo methods. Forecasts of volatility and value at risk can also be generated from predictive distributions. The proposed methodology is illustrated using both simulated and actual international market index data. Empirical results show higher average volatility and more persistent volatility when bad news arrives. While the domestic return is the major determinant of the regimes, both the SP 500 and Nikkei 225 indices also impact the dynamic structure of domestic market returns. (c) 2005 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved

Bayesian unit-root testing in stochastic volatility models

This article uses a Bayesian unit-foot test in stochastic volatility models. The time series of interest is the volatility that is unobservable. The unit-root testing is based on the posterior odds ratio, which is approximated by Markov-chain Monte Carlo methods. Simulations show that the testing procedure is efficient for moderate sample size. The unit-root hypothesis is rejected in seven market indexes, and some evidence of nonstationarity is observed in the TWSI of Taiwan

Estimation of multiple period expected shortfall and median shortfall for risk management

With the regulatory requirements for risk management, Value at Risk (VaR) has become an essential tool in determining capital reserves to protect the risk induced by adverse market movements. The fact that VaR is not coherent has motivated the industry to explore alternative risk measures such as expected shortfall. The first objective of this paper is to propose statistical methods for estimating multiple-period expected shortfall under GARCH models. In addition to the expected shortfall, we investigate a new tool called median shortfall to measure risk. The second objective of this paper is to develop backtesting methods for assessing the performance of expected shortfall and median shortfall estimators from statistical and financial perspectives. By applying our expected shortfall estimators and other existing approaches to seven international markets, we demonstrate the superiority of our methods with respect to statistical and practical evaluations. Our expected shortfall estimators likely provide an unbiased reference for setting the minimum capital required for safeguarding against expected loss

A threshold stochastic volatility model

This article introduces a new model to capture simultaneously the mean and variance asymmetries in time series. Threshold non-linearity is incorporated into the mean and variance specifications of a stochastic volatility model. Bayesian methods are adopted for parameter estimation. Forecasts of volatility and Value-at-Risk can also be obtained by sampling from suitable predictive distributions. Simulations demonstrate that the apparent variance asymmetry documented in the literature can be due to the neglect of mean asymmetry. Strong evidence of the mean and variance asymmetries was detected in US and Hong Kong data. Asymmetry in the variance persistence was also discovered in the Hong Kong stock market. Copyright © 2002 John Wiley & Sons, Ltd.link_to_subscribed_fulltex

A stochastic volatility model with Markov switching

This article presents a new way of modeling time-varying volatility. We generalize the usual stochastic volatility models to encompass regime-switching properties. The unobserved state variables are governed by a first-order Markov process. Bayesian estimators are constructed by Gibbs sampling. High-, medium- and low-volatility stares are identified for the Standard and Poor's 500 weekly return data. Persistence in volatility is explained by the persistence in the low-and the medium-volatility states. The high-volatility regime is able to capture the 1987 crash and overlap considerably with four U.S. economic recession periods

Forecasting exchange rate volatility using autoregressive random variance model

Recently, as an alternative to the GARCH model, the autoregressive random variance (ARV) model has been gaining popularity in the modelling of changing volatility, mainly because of the capability in capturing the stochastic nature of volatility. This article highlights the ARV model as an alternative to the GARCH model in modelling volatility. The main focus is to compare the two models in forecasting exchange rate volatility. Although the two approaches generally give close forecasting performance, the ARV method provides a notable improvement in Canadian/ Dollar and Australian/Dollar. The outstanding performance seems to be related to the 'volatility of volatility', i.e. the volatility changes from day to day.link_to_subscribed_fulltex