AI 中文总结
研究针对国家统计局季节调整程序忽略调查估计标准误差的问题，将时变抽样误差方差嵌入基本结构模型，扩展DMM贝叶斯框架，通过双块吉布斯采样器得出相关后验及可信区间等，模拟和应用表明其优于X-11，能区分测量噪声与真正季节漂移。
AI 中文摘要
国家统计局使用的季节调整程序——X-11和X-12-ARIMA，将每个调查估计值视为精确观测值，而忽略了调查方法学家通常计算的伴随标准误差。本文通过将时变抽样误差方差嵌入基本结构模型（BSM）来弥补这一差距，扩展了最近提出的用于调查估计的动态最小-最大（DMM）贝叶斯框架。通过哈维-托德等价关系，测量误差方差为零的BSM简化为X-11式季节调整，因此DMM-BSM是现有实践的有原则的贝叶斯推广。一个双块吉布斯采样器给出了潜在状态轨迹的完整联合平滑后验。趋势水平、k步趋势变化（k=1,2,...）和季节调整估计的精确可信区间直接得出，以及方向变化的后验概率——这是X-11无法提供的输出。模拟研究表明，在大小调查域中，DMM-BSM的可信区间覆盖率都比X-11等效模型高得多。应用于澳大利亚统计局劳动力调查的120个月数据，一旦对抽样方差进行建模，随机季节方差的最大似然估计就会降至零，这表明已发布序列中的明显季节波动很大程度上归因于测量噪声而非真正的季节漂移，这是X-11无法区分的。
英文摘要
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.
Comments23 pages, 12 figures
