Abstract: Time series models of sampling error, true unobserved rates, and covariates can be used to pool data across time and space to reduce variance in a subnational estimator. We present such models along with associated hierarchical Bayesian analyses. Specifically, we present a joint time series model for a 51 U.S. state labor force series in a Bayesian framework. Data are input in the form of optimal composite estimates from a sampling error model. The basic time series model is constructed from fractional Gaussian noise processes. Covariation of the true series across states is modeled by having a common national component modified by individual state components. Markov chain Monte Carlo methods are applied to develop samplers for a high-dimensional system of 105 parameters. The results indicate substantial gains in the efficient use of CPS data for U.S. state employment and unemployment rates series.
Key words and phrases: Bayesian inference, long memory process, Markov chain Monte Carlo, small area estimation, unemployment rates.