Variance Estimation for Noise Components in Time Series from a Survey

Daniell Toth and Stuart Scott


Models for economic time series of the form y=trend + seasonal + irregular typically assume each term is stochastic with a noise component. A fourth noise component enters the picture when the series is observed from a survey. Chen, Wong, Morry, and Fung (2003) compared method of moments and spectral estimates of "combined error" autocovariances in X-11 seasonal adjustment. This paper revisits the topic both with and without the use of external sampling error information. For comparison, we use simulated data generated from structural models— -as done by Chen et al.—-and sampling error models—-suggested by the Bureau of Labor Statistics employment and unemployment series. We investigate whether prior smoothing in this system adds stability to the estimation. We also address selecting a "cutoff" value for the number of autocovariance terms needed.