• X-13arima
• X-13arima-seats

X-13ARIMA-SEATS Binary for R. This package provides an installer for R to access prebuilt binaries of X-13ARIMA-SEATS from the sibbling repository x13prebuilt. This allows for fully automated installation of a X-13ARIMA-SEATS binary simply by adding Depends: x13binary to your R package. X-13ARIMA-SEATS Binary for R. This package provides an installer for R to access prebuilt binaries of X-13ARIMA-SEATS from the sibbling repository x13prebuilt.This allows for fully automated installation of a X-13ARIMA-SEATS binary simply by adding Depends: x13binary to your R package. As the package is on CRAN, the usual procedure applies. Seasonal Adjustment by X-13ARIMA-SEATS in R Christoph Sax University of Basel Dirk Eddelbuettel University of Illinois at Urbana-Champaign Abstract seasonal is a powerful interface between R and X-13ARIMA-SEATS, the seasonal ad-justment software developed by the United States Census Bureau. It o ers access to. The US Census Bureau provides a seasonal adjustment program now called 'X-13ARIMA-SEATS' building on both earlier programs called X-11 and X-12 as well as the SEATS program by the Bank of Spain. The US Census Bureau offers both source and binary versions – which this package integrates for use by other R packages.

X-13ARIMA-SEATS, successor to X-12-ARIMA and X-11, is a set of statistical methods for seasonal adjustment and other descriptive analysis of time series data that are implemented in the U.S. Census Bureau's software package.^[3] These methods are or have been used by Statistics Canada, Australian Bureau of Statistics, and the statistical offices of many other countries.^[4][5]

X-12-ARIMA can be used together with many statistical packages, such as SAS in its econometric and time series (ETS) package, R in its (seasonal) package,^[6]Gretl or EViews which provides a graphical user interface for X-12-ARIMA, and NumXL which avails X-12-ARIMA functionality in Microsoft Excel.^[7] There is also a version for Matlab.^[8]

Notable statistical agencies presently using X-12-ARIMA for seasonal adjustment include Statistics Canada,^[9] the U.S. Bureau of Labor Statistics^[10] and Census and Statistics Department (Hong Kong).^[11] The Brazilian Institute of Geography and Statistics uses X-13-ARIMA.^[12]

X-12-ARIMA was the successor to X-11-ARIMA; the current version is X-13ARIMA-SEATS.^[13]

X-13-ARIMA-SEATS's source code can be found on the Census Bureau's website.^[14]

Methods[edit]

The default method for seasonal adjustment is based on the X-11 algorithm. It is assumed that the observations in a time series, ${\displaystyle Y_t}$, can be decomposed additively,

or multiplicatively,

In this decomposition, ${\displaystyle T_t}$ is the trend (or the 'trend cycle' because it also includes cyclical movements such as business cycles) component, ${\displaystyle S_t}$ is the seasonal component, and ${\displaystyle I_t}$ is the irregular (or random) component. The goal is to estimate each of the three components and then remove the seasonal component from the time series, producing a seasonally adjusted time series.^[15]

The decomposition is accomplished through the iterative application of centered moving averages. For an additive decomposition of a monthly time series, for example, the algorithm follows the following pattern:

1. An initial estimate of the trend is obtained by calculating centered moving averages for 13 observations (from ${\displaystyle t-6}$ to ${\displaystyle t+6}$).
2. Subtract the initial estimate of the trend series from the original series, leaving the seasonal and irregular components (SI).
3. Calculate an initial estimate of the seasonal component using a centered moving average of the SI series at seasonal frequencies, such as ${\displaystyle t-24,t-12,t,t+12,t+24}$
4. Calculate an initial seasonally adjusted series by subtracting the initial seasonal component from the original series.
5. Calculate another estimate of the trend using a different set of weights (known as 'Henderson weights').
6. Remove the trend again and calculate another estimate of the seasonal factor.
7. Seasonally adjust the series again with the new seasonal factors.
8. Calculate the final trend and irregular components from the seasonally adjusted series.

The method also includes a number of tests, diagnostics and other statistics for evaluating the quality of the seasonal adjustments.

See also[edit]

References[edit]

1. ^https://www.census.gov/srd/www/x13as/x13down_unix.html
2. ^https://www.census.gov/srd/www/disclaimer.html
3. ^'X-13ARIMA-SEATS Seasonal Adjustment Program'. United States Census Bureau. Retrieved March 24, 2021.
4. ^'Time Series Analysis: Seasonal Adjustment Methods'. November 14, 2005.
5. ^Susie Fortier and Guy Gellatly. 'Seasonally adjusted data – Frequently asked questions'. Retrieved March 24, 2021.CS1 maint: uses authors parameter (link)
6. ^'seasonal: R Interface to X-13-ARIMA-SEATS version 1.8.2 from CRAN'. rdrr.io. Retrieved 2021-05-25.
7. ^'Implementation of the X-11 Seasonal Adjustment Method'.
8. ^'X-13 Toolbox for Seasonal Filtering'. www.mathworks.com. Retrieved 2021-05-25.
9. ^http://www.statcan.gc.ca/pub/12-539-x/2009001/seasonal-saisonnal-eng.htm
10. ^http://www.bls.gov/cpi/cpisahoma.htm
11. ^https://www.censtatd.gov.hk/hkstat/sub/sc30.jsp
12. ^ftp://ftp.ibge.gov.br/Contas_Nacionais/Contas_Nacionais_Trimestrais/Ajuste_Sazonal/X13_NasContasTrimestrais.pdf
13. ^https://www.census.gov/srd/www/x13as/
14. ^https://www.census.gov/srd/www/x13as/x13down_unix.html
15. ^Findley, David F.; Monsell, Brian C.; Bell, William R.; Otto, Mark C.; Chen, Bor-Chung (1998), 'New Capabilities and Methods of the X-12-ARIMA Seasonal Adjustment Program'(PDF), Journal of Business and Economic Statistics, 16

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