Bayesian unit-root tests for Stochastic Volatility models

Journal of Business & Economic Statistics, 1999

2008

Statistics & probability letters, 2005

In the present paper we compare some stochastic volatility models recently pro- posed in financial literature by using a Bayesian criterion. The models considered for this anal- ysis have been estimated through an adaptive Markov chain Monte Carlo procedure, while the marginal likelihood necessary to evaluate the Bayes Factor is computed by using an auxiliary

2004

Journal of Econometrics, 1991

2001

Stochastic volatility (SV) models usually assume that the distribution of asset returns conditional on the latent volatility is normal. This article analyzes SV models with the Student-t distribution or generalized error distribution (GED). A Bayesian method via Markov-chain Monte Carlo (MCMC) techniques is used to estimate parameters and Bayes factors are calculated to compare the fit of distributions. Our method is illustrated by analyzing daily data from the Yen/Dollar exchange rate and the TOPIX. According to Bayes factors, it is found that the SV-t model fits the both data better than the SV-normal and the SV-GED. The effects of the specification of error distributions on the autocorrelation functions of squared returns and the Bayesian confidence intervals of future returns are also examined.

Journal of Econometrics, 2009

We study the problem of testing hypotheses on the parameters of one- and two-factor stochastic volatility models (SV), allowing for the possible presence of non-regularities such as singular moment conditions and unidentified parameters, which can lead to non-standard asymptotic distributions. We focus on the development of simulation-based exact procedures–whose level can be controlled in finite samples–as well as on large-sample procedures which remain valid under non-regular conditions. We consider Wald-type, score-type and likelihood-ratio-type tests based on a simple moment estimator, which can be easily simulated. We also propose a C(α)C(α)-type test which is very easy to implement and exhibits relatively good size and power properties. Besides usual linear restrictions on the SV model coefficients, the problems studied include testing homoskedasticity against a SV alternative (which involves singular moment conditions under the null hypothesis) and testing the null hypothesis of one factor driving the dynamics of the volatility process against two factors (which raises identification difficulties). Three ways of implementing the tests based on alternative statistics are compared: asymptotic critical values (when available), a local Monte Carlo (or parametric bootstrap) test procedure, and a maximized Monte Carlo (MMC) procedure. The size and power properties of the proposed tests are examined in a simulation experiment. The results indicate that the C(α)C(α)-based tests (built upon the simple moment estimator available in closed form) have good size and power properties for regular hypotheses, while Monte Carlo tests are much more reliable than those based on asymptotic critical values. Further, in cases where the parametric bootstrap appears to fail (for example, in the presence of identification problems), the MMC procedure easily controls the level of the tests. Moreover, MMC-based tests exhibit relatively good power performance despite the conservative feature of the procedure. Finally, we present an application to a time series of returns on the Standard and Poor’s Composite Price Index.

Economia Aplicada, 2014

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