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Monthly and quarterly data (or sub-annual data) are affected by seasonal patterns and require seasonal adjustment. Annual data are not affected by the seasonal pattern that occurs within a year. However, annual totals of seasonally adjusted monthly or quarterly series are affected by shifting seasonal patterns and extra trading days, and may not equal the unadjusted annual total unless it has been specified in the seasonal adjustment program to impose it on the seasonally adjusted data.
According to the “Statistics Canada Quality Guidelines”, Statistics Canada Catalogue no. 12-539, October 2009, (available at /pub/12-539-x/12-539-x2009001-eng.pdf, page 63), climatic and institutional effects are seasonal effects while trading day effects and the movement of Easter between March and April are calendar effects. Together, the seasonal and calendar effects form the combined seasonal effect. In order to avoid confusion in this paper, the climatic and institutional effects are discussed separately, and all references to seasonal factors, seasonal effects, seasonality, seasonal patterns, and seasonal adjustment throughout the paper refer to the combined seasonal effect.
The most important days of the week vary from series to series. In the international merchandise trade import data, Mondays are the busiest days. An additional charge is applied to goods processed by customs on Saturdays and Sundays, which leads some importers to hold their goods until Monday and thus creates a queue.
The Easter effect increases retail sales in the month in which it occurs but reduces the work week (and therefore has a dampening effect) for most other series. Easter in early April also affects retail sales late in March.
The calendar effect tends to be much greater in series such as retail sales and merchandise trade than in labour force survey (LFS) and consumer price index (CPI) data. The LFS and CPI data are collected over a scheduled period each month and do not have a trading day adjustment but rather a reference period adjustment that accounts for holidays in the period in which the data are collected. As a result, the difference between the unadjusted and seasonally adjusted LFS and CPI data is much less than these other series.
This is the case only for series for which a multiplicative model of seasonal adjustment, the most common, applies. An additive model is used for series such as the change in inventories where negative numbers occur.
The seasonal adjustment package that Statistics Canada uses is X-12-ARIMA. This package can be downloaded without charge from the US Census Bureau website.
Yiling Zhang. “Consumer Holiday Shopping Patterns.” Analysis in Brief. December 2004.
Katherine Marshall. “Seasonality in employment.” Perspectives on Labour and Income. Statistics Canada Catalogue no. 75-001-XPE, Spring 1999.
This shifting seasonality occurred in various construction-related series such as residential construction, building permits, and housing starts.
During the Toronto municipal strike in 2009, the stoppage in the approval of building permits led to a large decline in the number of permits issued in July and a subsequent recovery in the autumn as the city caught up with the backlog of applications.
The variability in January and February as measured by the standard deviation of growth in these months, was 1.8 and 1.3, respectively, compared with a standard deviation of 1.1 for the entire series.
On average, between 2004 and 2007, retail sales were 13% higher in December than in May.
Some data are not adjusted for seasonality, either because the irregular pattern is so large that it overwhelms the seasonal pattern, which consequently cannot be identified, or because there is no seasonal pattern to that particular economic activity. For example, for the Industrial Product Price Index (IPPI), many industries raise prices once a year and leave them unchanged for the rest of the year. Seasonally adjusting the series would only pro-rate this once-a-year price increase over the twelve months, which is analytically meaningless and therefore is not undertaken.
See Benoit Quenneville, “Gain and phase shift of the Annual Difference Operator,” Statistics Canada, Working Paper of the Methodology Branch (forthcoming) which demonstrates that the trend of the year-over-year calculation is dominated by what happened, on average, six months earlier rather than what is taking place in the current month.
When using unadjusted data, it is more useful to analyze the change in the year-over-year calculation (that is, the difference in the growth between January 2008 and January 2009 and the growth between February 2008 and February 2009) than to focus only on the same-month year-ago percentage change calculation in isolation.
The ‘cash for clunkers’ program in the US, which allowed households with older cars to receive money toward a new vehicle purchased in July and August 2009, is one example of how the issue of an outlier month is partially addressed by using seasonally adjusted data. Some analysts speculated that sales would spike during the ‘cash for clunkers’ program and then sharply retreat as demand dried up. However, after a small dip in September, sales followed their pre-clunkers trajectory and by late in 2009 had grown above the pre-‘clunkers’ level. Ignoring July, August, and September therefore reveals the underlying trend of the seasonally adjusted series.