Work with interactive mapping tools from across the Census Bureau.
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.
Information about the U.S. Census Bureau.
Information about what we do at the U.S. Census Bureau.
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 U.S. Census Bureau.
Information about the current field vacancies available at the U.S. Census Bureau Regional Offices.
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.
Find media toolkits, advisories, and all the latest Census news.
See what's coming up in releases and reports.
Business cycle; Gain and phase shift functions; Growth rates; Moving averages.
When a monthly economic indicator series contracts sharply for a few months and then starts to recover, the published annual and monthly growth rates can give conicting signals: the annual growth rate can indicate a decrease and the monthly growth rate an increase or vice versa. This is well known to the seasonal adjustment community, see, for example, Shiskin (1957). In this paper, we revisit, illustrate and then explain this potential for conict more analytically. For example, the annual differences lag the monthly differences by five and a half months because the same-month-year-ago difference is the sum of the current and eleven preceding monthly differences, and the annual sum has a phase shift of five and a half months. Illustrative examples are followed by an elementary formal mathematical derivation using the gain and phase functions of the annual sum.
Benoit Quenneville and David F. Findley. (2012). The Timing and Magnitude Relationships Between Month-to-Month Changes and Year-to-Year Changes That Make Comparing Them Difficult. Center for Statistical Research & Methodology Research Report Series (Statistics #2012-05). U.S. Census Bureau. Available online at <http://www.census.gov/srd/papers/pdf/rrs2012-05.pdf>.
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.