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.
Many seasonal adjustment procedures decompose time series into trend, seasonal, irregular and other components using simple non-seasonal finnite moving-average trend filters. This report considers the design of such filters, both in the body and at the ends of series, based on specified criteria and simple dynamic models operating locally within the span of the filter.
In the body of the series a flexible family of finite moving-average trend filters is developed from specified smoothness and fidelity criteria. These filters are based on local dynamic models and generalise the standard Macaulay and Henderson filters used in practice. The properties of these central filters are determined and evaluated both in theory and in practice.
At the ends of the series the central moving-average trend filter used in the body needs to be extended to handle missing observations. A family of end filters is constructed using a minimum revisions criterion and based on the local dynamic model operating within the span of the central filter. These end filters are equivalent to evaluating the central filter with unknown observations replaced by constrained optimal linear predictors. Two prediction methods are considered; best linear unbiased prediction (BLUP) and best linear biased prediction where the bias is time invariant (BLIP). The BLIP end filters generalise those developed by Musgrave for the central X-11 Henderson filters and include the BLUP end filters as a special case.
The properties of these end filters are determined both in
theory and practice. In particular, they are compared to the
Musgrave end filters used by X-11 and to the case where the central
filter is evaluated with unknown observations predicted by global
ARIMA models. The latter parallels the forecast extension method
used in X-11-ARIMA.
Moving-average filters; local trend estimation; dynamic models;
fidelity; smoothness; minimum revisions; best linear unbiased
prediction; best linear biased prediction; X-11; seasonal time
series; seasonal adjustment.
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.