Bayesian Seasonal Adjustment for Survey Time Series

Seasonal adjustment procedures used by national statistical offices -- X-11 and X-12-ARIMA -- treat each survey estimate as an exact observation, discarding the accompanying standard errors that survey methodologists routinely compute.

This paper closes that gap by embedding time-varying sampling error variances into a Basic Structural Model (BSM), extending a recently proposed Dynamic Mini-Max (DMM) Bayesian framework for survey estimation.

Via the Harvey-Todd equivalence, BSM with zero measurement error variance reduces to X-11-style seasonal adjustment, so DMM-BSM is a principled Bayesian generalisation of existing practice rather than a departure from it.

A two-block Gibbs sampler delivers the full joint smoothing posterior of the latent state trajectory.

Exact credible intervals for the trend level, k-step trend movements (k=1,2,...), and seasonally adjusted estimates follow directly, together with posterior probabilities of directional change -- outputs that X-11 cannot provide.

Simulation studies with within-replication parameter estimation confirm substantially higher credible interval coverage than the X-11-equivalent model across both large and small survey domains.

Applied to 120 months of Australian Bureau of Statistics Labour Force Survey data, once sampling variance is modelled the maximum likelihood estimate of stochastic seasonal variance collapses to zero -- evidence that apparent seasonal fluctuations in the published series are largely attributable to measurement noise rather than genuine seasonal drift, a distinction X-11 cannot make.