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