Data Liberation Initiative Seasonal Adjustment

1. Data Liberation Initiative Seasonal Adjustment Gylliane Gervais March 2009

2. Why seasonal adjustment? • Many human and economic activities are seasonal, i.e. vary with the season • The seasonality present in a time series obscures its fundamental trend • Without seasonal adjustment, it would be impossible to make comparisons with previous month or quarter • Therefore, it would be impossible to identify • Recessions • Turning points in the economic cycle

3. Time series and their components • Time series: a sequence of values of one variable taken at equally spaced time intervals • Time interval: weekly, monthly, quarterly • Variable: Employment, retail sales, GDP, etc • Virtually all time series contain some seasonality • Even births! • Virtually all time series are seasonally adjusted at STC • Index of industrial production, first published in 1926, was seasonally adjusted • Exceptions: most financial series, most price indexes

4. Time series and their components • Trend: long-term upward (downward) movement observed in the data over several decades • Cycle: sequence of smooth fluctuations around the long-term trend with alternating periods of expansion and contraction • Trading-day effect • Number of working or trading days in month varies with calendar • Seasonality: Intra-year (monthly, quarterly) fluctuations which repeat more or less regularly from year to year • Moving holidays: Easter, Ramadan • Irregular component: Strikes, hurricanes, etc.

9. What is seasonal adjustment? • To seasonally adjust a series is to decompose it into its components in order to remove seasonality and all other calendar related effects: • Seasonal component • Trading day effect • Moving holidays • Programs currently used for this purpose • X-11-ARIMA (developed at Statistics Canada) • X-12-ARIMA (developed at U.S. Bureau of Labor Statistics)

10. Causes of seasonality • Climatic seasonality • Due to seasonal variations in the climate • Example: Consumption of heating oil • Institutional seasonality • Due to social conventions and administrative rules • Example: Effect of Christmas on retail sales • Induced seasonality • Due to seasonality in other activities • Example: output of the food processing industry • In most cases, combined result of all three types • Example: employment

11. Causes of evolving seasonality • Technological change • Ex.: development of construction materials and techniques better adapted to winter • Institutional change • Ex.: Extension of store hours and opening days  • Change in the composition of series • Ex.: provincial employment becoming more industrialized and less dependent on primary industries (e.g. fishing, agriculture) which typically display more seasonality • Seasonality tends to be less pronounced over time on account of technological and institutional changes

12. Seasonal adjustment at STC • Done with X-11-ARIMA (old) or X-12-ARIMA (new) • X-12-ARIMA deemed superior, also more flexible • Adoption of X-12-ARIMA results in minor revisions • Programs already switched to X-12-ARIMA • Retail and wholesale, manufacturing, services, tourism • Programs switching to X-12-ARIMA in near future • Quarterly GDP, income and expenditure accounts: June 2009 • Monthly GDP by industry: October 2009 • International trade: January 2010 • Labour Force Survey: January 2010

13. Seasonal adjustment in national accounts Series are published in 2 formats: • Unadjusted (without seasonal adjustment, or ‘raw’) • Quarterly GDP is about 25% of level of annual GDP • Seasonally adjusted “at annual rates” • In the U.S. also, but generally not • So beware when making international comparisons! • “At annual rates” means converted to annual level • Monthly series are multiplied by 12, quarterly series by 4 • Comparable in level to counterpart annual series • Official estimates are the seasonally adjusted ones