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Bayesian Nonparametric Functional Mixture Estimation for Time-Series Data, With Application to Estimation of State Employment Totals

The U.S. Bureau of Labor Statistics use monthly, by-state employment totals from the Current Population Survey (CPS) as a key input to develop employment estimates for counties within the states. The monthly CPS by-state totals, however, express high levels of volatility that compromise the accuracy of resulting estimates composed for the counties. Typically-employed models for small area estimation produce de-noised, state-level employment estimates by borrowing information over the survey months, but assume independence among the collection of by-state time series, which is typically violated due to similarities in their underlying economies. We construct Gaussian process and Gaussian Markov random field alternative functional prior specifications, each in a mixture of multivariate Gaussian distributions with a Dirichlet process (DP) mixing measure over the parameters of their covariance or precision matrices. Our DP mixture of functions models allow the data to simultaneously estimate a dependence among the months and between states. A feature of our models is that those functions assigned to the same cluster are drawn from a distribution with the same covariance parameters, so that they are similar, but don't have to be identical. We compare the performances of our two alternatives on synthetic data and apply them to recover de-noised, by-state CPS employment totals for data from $2000-2013$.