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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Statistical Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of Business &Economic Statistics.New techniques for the analysis of stochastic volatility models in which the logarithm of conditional variance follows an autoregressive model are developed. A cyclic Metropolis algorithm is used to construct a Markov-chain simulation tool. Simulations from this Markov chain converge in distribution to draws from the posterior distribution enabling exact finite-sample inference. The exact solution to the filtering/smoothing problem of inferring about the unobserved variance states is a by-product of our Markov-chain method. In addition, multistep-ahead predictive densities can be constructed that reflect both inherent model variability and parameter uncertainty. We illustrate our method by analyzing both daily and weekly data on stock returns and exchange rates. Sampling experiments are conducted to compare the performance of Bayes estimators to method of moments and quasi-maximum likelihood estimators proposed in the literature. In both parameter estimation and filtering, the Bayes estimators outperform these other approaches. KEY WORDS: Bayesian inference; Markov-chainMonte Carlo; Method of moments; Nonlinear filtering; Quasi-maximum likelihood; Stochastic volatility. Interest in models with stochastic volatility dates at least to the work of Clark (1973), who proposed an iid mixture model for the distribution of stock-price changes. Unobservable information flow produces a random volume of trade in the Clark approach. Tauchen and Pitts (1983) and Gallant, Hsieh, and Tauchen (1991) noted that if the information flows are autocorrelated, then a stochastic volatility model with time-varying and autocorrelated conditional variance might be appropriate for price-change series. Stochastic volatility models also arise as discrete approximations to various diffusion processes of interest in the continuous-time asset-pricing literature (Hull and White 1987; Melino and Turnbull 1990; Wiggins 1987). The purpose of this article is to develop new methods for inference and prediction in a simple class of stochastic volatility models in which logarithm of conditional volatility follows an autoregressive (AR) times series model. Unlike the autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH (GARCH) models [see Bollerslev, Chou, and Kroner (1992) for a survey of ARCH modeling], both the mean and log-volatility equations have separate error terms.The ease of evaluating the ARCH likelihood function and the ability of the ARCH specification to accommodate the timevarying volatility found in many economic time series has fostered an ...

This paper develops a simulation-based approach for performing maximum likelihood estimation in latent state variable models using Markov Chain Monte Carlo methods (MCMC). The MCMC algorithm simultaneously computes (by numerical integration) and optimizes the marginal likelihood function. The approach relies on data augmentation, combining the insights of simulated annealing and evolutionary or "genetic" algorithms. We prove a limit theorem in the degree of data augmentation and use this to provide standard errors and convergence diagnostics.The estimator inherits all of the usual sampling asymptotic properties of maximum likelihood estimators. We demonstrate the approach on two latent state models central to financial econometrics: a stochastic volatility model and a multivariate jump-diffusion model. * Jacquier is at HEC Montreal and CIRANO, eric.jacquier@hec.ca. Johannes is at the Graduate School of Business, Columbia University, 3022 Broadway, NY, NY, 10027, mj335@columbia.edu. Polson is at the Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago IL 60637, ngp@gsb.uchicago.edu. We would like thank Ron Gallant for his discussion of the paper, Lars Hansen for his comments, and seminar participants at the 2003 Montreal Financial Econometrics Conference and Columbia University for helpful comments. 1 MCMC Maximum Likelihood For Latent State ModelsJEL Classification: C1, C11, C15, G1

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Speculative efficiency often requires that future changes in a series cannot be forecast. In contrast, series with a cyclical component would seem to be forecastable with decreases, possibly relative to a trend, during the upper part of the cycle and increases during the lower part. On the basis of autoregressive model (AR) estimates, it is considered that there is strong evidence of cycles in insurance underwriting performance as measured by the premium‐to‐loss ratio. Indeed, a large literature attempts to explain this documented cyclicality. First, we show that the parameter estimates from AR models do not lead to any such inference and that in the contrary, the evidence in the data is consistent with no cyclicality at all. Second, we show that a number of different filters lead to the same conclusion: that there is no evidence of in‐sample or out‐of‐sample predictability in annual insurance underwriting performance in the United States.