Errors in variables and seasonal adjustment procedures

Seasonal adjustment procedures attempt to estimate the sample realizations of an unobservable economic time series in the presence of both seasonal and irregular factors. In this article, we consider a factor that has not been considered explicitly in previous treatments of seasonal adjustment: measurement error. Because of the sample design used in the Current Population Survey, measurement error will not be a white-noise process, but instead it will be characterized by serial correlation of a known form. We first consider what effect the serially correlated measurement error has on estimation of the nonseasonal component in seasonal adjustment models. We also consider the effect of measurement error on the widely used seasonal adjustment process X-11. Estimated unobserved-components models are used to estimate the precision (root mean squared error) of the official and optimal seasonally adjusted data.