An official website of the United States government
Here’s how you know
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
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 the mean squared error optimal linear estimate of the signal given 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.
Share
Related Information
Some content on this site is available in several different electronic formats. Some of the files may require a plug-in or additional software to view.
Top