Skip Main Navigation Skip To Navigation Content

Research Reports

You are here: Census.govSubjects A to ZResearch Reports Sorted by Year › Abstract of RRS2007/15
Skip top of page navigation

A Nonparametric Method for Asymmetrically Extending Signal Extraction Filters

Tucker McElroy

KEY WORDS: ARIMA model, Nonstationary time series, Seasonal adjustment, X-11


Two important problems in the X-11 seasonal adjustment methodology are the construction of standard errors and the handling of the boundaries. We adapt the ``implied model approach" of Kaiser and Maravall to achieve both objectives in a nonparametric fashion. The frequency response function of an X-11 linear filter is used, together with the periodogram of the differenced data, to define spectral density estimates for signal and noise. These spectra are then used to define a matrix smoother, which in turn generates an estimate of the signal that is linear in the data. Estimates of the signal are provided at all time points in the sample, and the associated time-varying signal extraction mean squared errors are a by-product of the matrix smoother theory. After explaining our method, it is applied to popular nonparametric filters such as the Hodrick-Prescott (HP), the Henderson Trend, and Ideal Low-Pass and Band-Pass filters, as well as X-11 seasonal adjustment, trend, and irregular filters. Finally, we illustrate the method on a single time series and provide comparisons with X-11-ARIMA seasonal adjustments.


Source: U.S. Census Bureau, Statistical Research Division

Created: November 13, 2007
Last revised: November 13, 2007

[PDF] or PDF denotes a file in Adobe’s Portable Document Format. To view the file, you will need the Adobe® Reader® Off Site available free from Adobe.

This symbol Off Site indicates a link to a non-government web site. Our linking to these sites does not constitute an endorsement of any products, services or the information found on them. Once you link to another site you are subject to the policies of the new site.

Source: U.S. Census Bureau | Statistical Research Division | (301) 763-3215 (or |   Last Revised: October 08, 2010