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Guide to Seasonal Adjustment with X-12-ARIMA **DRAFT**

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Guide to Seasonal Adjustment with X-12-ARIMA **DRAFT** OONNSS MMeetthhooddoollooggyy aanndd SSttaattiissttiiccaall DDeevveellooppmmeenntt Guide to Seasonal Adjustment with X-12-ARIMA **DRAFT** TSAB March 2007 Guide to Seasonal Adjustment with X12ARIMA TABLE OF CONTENTS 1. Introduction ..................................................................................................................... 1.1 2. Introduction to seasonal adjustment ....................................................................... 2.1 3. Overview of the X12ARIMA Method .......................................................................... 3.1 4. How to run X12ARIMA .................................................................................................. 4.1 7. Length of the series ...................................................................................................... 7.1 8. Consistency across time ............................................................................................. 8.1 9. Aggregate Series ........................................................................................................... 9.1 10 Revisions and updates ..............................................................................................10.1 11. The regARIMA model .................................................................................................11.1 12. Trading day ..................................................................................................................12.1 13. Easter .............................................................................................................................13.1 14. Level Shift and Additive Outliers ...........................................................................14.1 15. Which Seasonal Decomposition Model to Use ..................................................15.1 16. Moving Averages ........................................................................................................16.1 17. Seasonal Breaks .........................................................................................................17.1 18. Existence of Seasonality ..........................................................................................18.1 19. X12ARIMA Standard Output ....................................................................................19.1 20. Graphs and X-12-graph .............................................................................................20.1 21. Sliding Spans ...............................................................................................................21.1 22. History Diagnostics......................................................................................................22.1 23. Composite spec ..........................................................................................................23.1 Table of contents 25. Forecasting ...................................................................................................................25.1 26. Trend Estimation .........................................................................................................26.1 27. Quality Measures .........................................................................................................27.1 Guide to Seasonal Adjustment with X-12-ARIMA 1 INTRODUCTION 1.1 Introduction Seasonal adjustment is widely used in official statistics as a technique for enabling timely interpretation of time series data. The X-12-ARIMA seasonal adjustment package has been chosen from the many available seasonal adjustment methods as the standard one for use in official statistics in the United Kingdom (UK). This was agreed by the National Statistics Quality and Methods Programme Board in 2001, and is in line with European best practice and consistent with the Bank of England. The method is used by most of the leading national statistical institutes across the world. X-12-ARIMA is developed by the United States (US) Bureau of the Census. The software is comprehensive, with many options available for tailoring seasonal adjustment to each individual series. It therefore requires many choices to be made by its users. The main purpose of this guide is to provide practical guidance on seasonal adjustment using X-12- ARIMA. The guide explains what seasonal adjustment means, and addresses many of the statistical, organisational and presentational issues and problems associated with seasonal adjustment. This guide complements the Office for National Statistics (ONS) training courses in seasonal adjustment. A detailed explanation of the X-12-ARIMA method can be found at www.census.gov/srd/www/x12a or in Ladiray and Quenneville (2001). 1.2 What is in this guide The guide starts with a brief introduction to seasonal adjustment and to some of the main associated issues (Chapter 2). It then provides an overview of the X-12-ARIMA method (Chapter 3), and a description of how to run the program (Chapter 4). Chapter 5 describes a procedure that should be used when seasonally adjusting a series using X-12-ARIMA, while the prior considerations that users should address when seasonally adjusting a series are discussed in Chapters 6 to 10. The second part of the guide examines seasonal adjustment in more detail. Here the user will find more detailed descriptions of the regression-ARIMA model, of potential effects such as trading days, and of how X-12-ARIMA deals with them (Chapters 11 to 14). Guidance is also provided on selecting a decomposition model, moving averages, prior adjustments, and on problems such as seasonal breaks (Chapters 15 to 19). The third part of this guide deals with X-12-ARIMA output and with diagnostics or tools that may be useful in seasonal adjustment (Chapters 20 to 25). Chapters 26 to 28 look at alternative uses, other than seasonal adjustment, of the X-12-ARIMA software. 1.3 How to use this guide This guide is not intended to be read from cover to cover. Users are advised to read Part 1 before attempting any seasonal adjustment, and to refer to other parts of the guide as appropriate. Anyone who is responsible for setting up or reviewing seasonal adjustment should attend a training course aimed at seasonal adjustment practitioners. This guide complements, but is not a substitute for, such a training course. ONS provides short training courses for users of seasonal adjustment, and for 27/02/07 1-1 Introduction persons responsible for presenting data in seasonally adjusted form. More information on training courses can be obtained from Time Series Analysis Branch (TSAB). 1.4 What this guide is not This guide does not describe the detailed working of X-12-ARIMA, nor the underlying mathematics. For those who are interested in these matters, the X-12-ARIMA user manual is a good starting point. Additional technical references and papers are listed in the References below. 1.5 What does TSAB do? The Methodology Directorate (MD) provides leadership, and defines best practice for many methodological aspects of ONS work. MD also provides methodological advice to other parts of ONS and, where resources permit, to the rest of the Government Statistical Service (GSS), on methodological issues. TSAB provides expertise in time series analysis issues, and in particular seasonal adjustment. TSAB has produced this guide, and runs regular courses in seasonal adjustment. TSAB is responsible for the quality of all ONS seasonal adjustment, and manages a rolling programme of annual seasonal adjustment reviews of statistical outputs across ONS. Furthermore, TSAB provides support for practitioners and users of seasonal adjustment, and should be the main point of contact for any questions or queries regarding seasonal adjustment. 1.6 Contact details If you have a query related to time series analysis, if you require information on seasonal adjustment training, or if you have any comments on this guidance, we can be contacted at: Office for National Statistics, Time Series Analysis Branch, 1 Drummond Gate, London SW1V 2QQ or by email at: [email protected]. 1.7 Acknowledgements This guide has been developed with input and assistance from the following people: Claudia Annoni, Simon Compton, Duncan Elliott, Lee Howells, Fida Hussain, Peter Kenny, Jim Macey, Craig McLaren, Ross Meader, Nigel Stuttard, Anthony Szary, and Anita Visavadia. Please bring any errors or omissions to our attention. 1-2 27/02/07 Guide to Seasonal Adjustment with X-12-ARIMA 2 INTRODUCTION TO SEASONAL ADJUSTMENT 2.1 What is seasonal adjustment? Data that are collected over time form a time series. Many of the most well known statistics published by the Office for National Statistics are regular time series, including: the claimant count, the Retail Prices Index (RPI), Balance of Payments, and Gross Domestic Product (GDP). Those analysing time series typically seek to establish the general pattern of the data, the long term movements, and whether any unusual occurrences have had major effects on the series. This type of analysis is not straightforward when one is reliant on raw time series data, because there will normally be short-term effects, associated with the time of the year, which obscure or confound other movements. For example, retail sales rise each December due to Christmas. The purpose of seasonal adjustment is to remove systematic calendar related variation associated with the time of the year, i.e. seasonal effects. This facilitates comparisons between consecutive time periods. Figure 2-1 - Non-seasonally adjusted (NSA) and seasonally adjusted (SA) data for United
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