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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 ...