Estimation of mean squared error of X-11-ARIMA and other estimators of time series components

This article considers the familiar but very important problem of how to estimate the mean squared error (MSE) of seasonally adjusted and trend estimators produced by X-11-ARIMA or other decomposition methods. The MSE estimators are obtained by defining the unknown target components such as the trend and seasonal effects to be the hypothetical X-11 estimates of them that would be obtained if there were no sampling errors and the series were sufficiently long to allow the use of the symmetric filters embedded in the programme, which are time invariant. This definition of the component series conforms to the classical definition of the target parameters in design-based survey sampling theory, so that users should find it comfortable to adjust to this definition. The performance of the MSE estimators is assessed by a simulation study and by application to real series obtained from an establishment survey carried out by the Bureau of Labor Statistics in the U.S.A