Data Liberation Initiative Seasonal Adjustment Gylliane Gervais March 2009

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

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

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.

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)

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

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

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

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