Bayesian Dependent Functional Mixture Estimation for Area and Time-Indexed Data: An Application for the Prediction of Monthly County Employment

Abstract

The U.S. Bureau of Labor Statistics (BLS) publishes employment totals for all U.S. counties on a monthly basis. BLS use the Quarterly Census of Employment and Wages, where responses are received on a 6–7 month lagged basis and aggregated to county, and apply a time series forecast model to each county and project forward to the current month, which ignores the dependence among counties. Our approach treats these by-county employment time series as a collection of area indexed noisy functions that we co-model. Our model includes predictor, trend and seasonality terms indexed by county. This application is among the first in the U.S. Federal Statistical System to address the joint modeling of a collection of time series expressing heterogenous seasonality patterns between them. We demonstrate that use of a Fourier basis to model seasonality outperforms a locally-adaptive, intrinsic conditional autoregressive construction on our collection of time series where the degree of expressed seasonality varies. County-indexed parameters of the 3 terms are drawn from a dependent Dirichlet process (DDP) prior to allow the borrowing of information. We show that employment of both spatial and industry concentration predictors into the prior probabilities for co-clustering among the counties produces better prediction accuracy. Our DDP prior accounts for the possibility that nearby counties may express distinct underlying economic structures. A feature of our joint modeling framework is that it computes efficiently to support the monthly BLS production cycle. We compare the performances of alternative formulations for the dependent Dirichlet process prior on monthly, county employment data from 2002–2016.