Work with interactive mapping tools from across the Census Bureau.
Collection of audio features and sound bites.
The Census Bureau packages data and information into easy-to-understand visuals.
Browse Census Bureau images.
Read briefs and reports from Census Bureau experts.
Watch Census Bureau vignettes, testimonials, and video files.
Read research analyses from Census Bureau experts.
Developer portal to access services and documentation for the Census Bureau's APIs.
Explore Census Bureau data on your mobile device with interactive tools.
Find a multitude of DVDs, CDs and publications in print by topic.
These external sites provide more data.
Download extraction tools to help you get the in-depth data you need.
Explore Census data with interactive visualizations covering a broad range of topics.
How we provide the best mix of timeliness, relevancy, quality, and cost for the data we collect.
Learn about other opportunities to collaborate with us.
Explore the rich historical background of an organization with roots almost as old as the nation.
Explore prospective positions available at the Census Bureau.
Explore Census programs targeted for particular needs.
Discover the latest in Census Bureau data releases, reports, and events.
The Census Bureau's Director writes on how we measure America's people, places and economy.
Find interesting and quirky statistics regarding national celebrations and major events.
Listen to audio files on fun facts, historical figures, and celebrations of the month.
Find media toolkits, advisories, and all the latest Census news.
See what's coming up in releases and reports.
While it is typical in the econometric signal extraction literature to assume that the unobserved signal and noise components are uncorrelated, there is nevertheless an interest among econometricians in the hypothesis of hysteresis, i.e., that major movements in the economy are fundamentally linked. While specific models involving correlated signal and noise innovation sequences have been developed and applied using state space methods, there is no systematic treatment of optimal signal extraction with correlated components. This paper provides the Mean Square Error optimal formulas for both finite samples and bi-infinite samples, and furthermore relates these filters to the more well-known Wiener-Kolmogorov (WK) and Beveridge-Nelson (BN) signal extraction formulas in the case of ARIMA component models. Then we obtain the result that the optimal filter for correlated components can be viewed as a weighted linear combination of the WK and BN filters. The gain and phase functions of the resulting filters are plotted for some standard cases. Some discussion of estimation of hysteresis models is presented, along with empirical results on several economic time series. Comparisons are made between signal extraction estimates from traditional WK filters and those arising from the hysteresis models.
ARIMA, Nonstationary, Seasonality, Time Series
This symbol 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.