Section 2: Issues related to analysis and interpretation

  1. 1. How do I interpret period-to-period changes in seasonally adjusted data?

    Period-to-period changes in raw data and period-to-period changes in seasonally adjusted data provide different information. To illustrate this, consider hypothetical employment data from a monthly industry survey. Every month, these data are collected and processed to obtain an estimate of total industry employment. This estimate is raw (not seasonally adjusted)—it is a measure of the number of people working in the industry in the reference month, without distinguishing between (or disentangling) the various time series components that contribute to this estimate.

    Before publication, this estimate of industry employment is seasonally adjusted, to remove the influence of seasonal and calendar effects from the raw data (using current and past information on industry employment). This adjusted estimate is the official estimate of industry employment released in The Daily.

    An important note about comparisons over time—the difference between the seasonally adjusted employment estimates for two consecutive months cannot be interpreted as the raw difference in the number of people actually working in the industry in these months. The raw difference is the difference in the unadjusted employment estimates obtained directly from the survey.

    Rather, the difference in the month-to-month seasonally adjusted estimates is a direct measure of the change in the number of people working, after expected changes due to the variation in seasonal employment between these two months are taken into account. The resulting number may be less than the raw difference or it may be more, depending on how seasonal effects are changing from month to month.

    The example below illustrates the distinction between raw and seasonally adjusted data, using hypothetical employment data for an industry, collected over two consecutive months. In this example, it is assumed that there are no other calendar effects.

    Table 1
    Industry employment, raw and seasonally adjusted
    Table summary
    This table displays the results of Industry employment. The information is grouped by Time Period (appearing as row headers), Unadjusted data, Seasonally adjusted data, Trend cycle, Irregular component and Seasonal effects (appearing as column headers).
    Time Period Unadjusted data Seasonally adjusted data Trend cycle Irregular component Seasonal effects
    Source: Statistics Canada, authors' calculations.
    Month 1 6,200 7,200 6,650 550 -1,000
    Month 2 5,400 6,800 6,500 300 -1,400
    Change (month 2 minus month 1) -800 -400 -150 -250 -400

    In month 1, the unadjusted estimate of industry employment was 6,200; the seasonally adjusted employment estimate was larger, at 7,200. Accordingly, the employment attributed to seasonal effects in month 1 was -1,000. What does this mean?

    It means that about 1,000 fewer employees were expected to be working in month 1 when compared with a generic average level of industry employment throughout the year. These "expected" and "average" levels are based on historical patterns that reflect typical seasonal movements in these data.

    Accordingly, these 1,000 fewer employees are added back into the employment estimate for month 1, yielding a seasonally adjusted estimate that is larger than the unadjusted, or raw, estimate collected from the survey. Why is this done? This occurs because the objective of seasonal adjustment is to make the month-to-month data more comparable so that they provide better information about trends and cyclical movements. Seasonally adjusting the data puts month-to-month comparisons on equal footing.

    The estimate of industry employment for month 2 exhibits a similar pattern, with the final seasonally adjusted estimate exceeding the unadjusted estimate. In this month, 1,400 fewer employees would be expected to be working in the industry (compared with a generic average level of monthly employment throughout the year), based on regularly occurring seasonal movements. Adding this employment back into the unadjusted estimate from the survey data brings the published (seasonally adjusted) estimate to 6,800.

    Both months are examples of "adding back" – supplementing the survey data with additional employment – because the seasonal effects are negative. In these cases, less employment is expected in the reference month because of past seasonal patterns, so employment has to be added back in to make the data comparable from month to month. For other months, the reverse could apply—because the seasonal factors are positive. In these months, more employees are expected to be working than in the hypothetical average month, so seasonal adjustment removes some employment from the unadjusted data to put these months (in statistical terms) on an equal footing with other months during the year.

  2. 2. How do seasonal patterns affect the interpretation of month-to-month changes?

    The interpretation of month-to-month changes can be complex because it involves some of the more technical aspects of the data modelling used in seasonal adjustment routines. Seasonal patterns can be modelled "additively" or "multiplicatively". If seasonal patterns are modelled as additive, the extent to which month-to-month changes in employment are being influenced by changes in the seasonal effects can be examined in a fairly straightforward fashion.

    To see this, consider again the hypothetical employment data used in the example in question 11. Seasonally adjusted employment fell from 7,200 in month 1 to 6,800 in month 2, a net decline of 400 workers.

    This is different from the unadjusted change calculated directly from the survey data. The unadjusted estimate fell from 6,200 in month 1 to 5,400 in month 2, a net decline of 800 workers, or twice the decline in the seasonally adjusted data.

    What accounts for the large difference in these two estimates? As noted above, both months had negative seasonal effects. This means that, in view of past patterns of seasonality, lower industry employment is expected in each of the two months when compared with an annual generic monthly average. But the negative seasonal effect in the second month was larger in absolute terms, by some 400 workers. While about 1,000 workers were added to the raw survey data in month 1 to obtain the seasonally adjusted estimate, some 1,400 workers were added back in month 2.

    Numerically, about 40% of this reduction in the seasonally adjusted estimate can be attributed to changes in the trend-cycle. The remaining 60% is due to the irregular component.

  3. 3. Which estimate—seasonally adjusted or raw—is "correct"?

    Both estimates are correct, as both derive from legitimate statistical processes. The choice of one over the other depends on the purpose of the analysis.

    If users are interested in estimates of the actual level of industry employment in a particular period (the number of people working), or in the period-to-period changes in these actual employment levels, these estimates can be obtained directly from surveys without any seasonal adjustment.

    A problem arises when trying to use these unadjusted data to interpret changes in economic conditions. The raw data reflect the combined effect of all components that contributed to the observed level of employment in a monthly or quarterly period. This includes the trend-cycle, the seasonal effects, the other calendar effects and the irregular component. In the example in question 11, it is correct to say that industry employment declined by 800 workers from month 1 to month 2— the decline tabulated directly from the raw data. But it is less appropriate to attribute this decline to specific factors, such cyclical downturns, while ignoring the potential influence of other components, such as routine changes in seasonal hiring patterns, which also contribute to changes in the raw data.

    The key point is that the choice between seasonally adjusted and raw data is context-driven. It depends on the issue that the data are attempting to inform, and whether period-to-period movements in these data that derive from seasonal influences are relevant to that issue.

  4. 4. How do I interpret seasonally adjusted data when an industry is undergoing structural change?

    This question relates to the reliability of seasonally adjusted data. Two points warrant emphasis:

    • Seasonal effects reflect typical movements in time series data due to established seasonal patterns;
    • Seasonally adjusted data (which remove the seasonal component and the other calendar effects) are influenced by more than changes in the trend-cycle. They are also influenced by irregular events that, in many cases, have a large impact on the resulting estimate.

    Structural change can refer to situations in which some fundamental aspect of an economy or industry is changing, resulting in new conditions that differ from past norms. These could involve major technological innovations that alter the nature of production. They could also involve more routine changes in hiring patterns in response to new administrative practices.

    Both of these examples could bring about new seasonal patterns in an industry that contrast with traditional seasonal patterns. How are these reflected in the seasonally adjusted data?

    In the short run, these shifts would be regarded as irregular movements in the data, to the extent that they deviate suddenly from expected patterns. Over time, these new patterns would become seasonal and gradually incorporated into the historical record, as new time series information on these changes becomes available. This assumes that these changes are becoming a regular feature of the data—and not the result of irregular events or shocks.

    Accordingly, it can be more difficult to interpret movements in seasonally adjusted data when underlying seasonal patterns are evolving or changing rapidly. In such cases, irregular factors can exert a large impact on seasonally adjusted estimates.

  5. 5. How does seasonal adjustment account for "unseasonable" weather?

    This is a question that relates to a common misconception about seasonally adjusted data—namely, that it is a technique whose sole purpose is to remove the effect of changes in weather or climate from the data. Seasonal adjustment removes the average or anticipated effect of seasonal factors from monthly or quarterly data, many of which have to do with changes in weather or climate. But it is more accurate to state that these seasonal factors relate to all things seasonal—weather and climate-related or otherwise—that have the potential to affect the analysis of trend or cyclical patterns in the data.

    The idea of the "average" effect noted earlier is important, as the magnitude of these period-specific seasonal adjustments are again based on historical patterns. If weather or climate conditions are generally reflective of these past patterns, the seasonal adjustment routines can be expected to do a fairly complete job of factoring out movements in the unadjusted data that are attributable to these weather or climate changes. But unseasonable weather, such as the very warm spring in eastern Canada in 2012, is, by definition, not indicative of the average pattern, and will influence seasonally adjusted estimates.

  6. 6. What method does Statistics Canada use to produce seasonally adjusted data?

    Statistics Canada seasonally adjusts sub-annual time series data using the X-12-ARIMA method, which uses well-established statistical techniques to remove the effect of regular, calendar-related patterns from unadjusted data. Although less complex alternatives may be used, such as comparing the original data in the same period in each year, these techniques have limitations when it comes to removing calendar effects. Accordingly, Statistics Canada recommends the use of formal, established methods for dealing with seasonality. In practice, seasonal adjustment is performed following Statistics Canada Quality Guidelines.

  7. 7. Where can I find more information on selected issues?

    As mentioned at the start, this document is intended as a practical guide that provides users with additional perspective on issues related to the use and interpretation of seasonally adjusted data. It is designed to complement a paper by Wyman (2010), who illustrated many of these points with Statistics Canada data. In addition, the extensive literature on seasonal adjustment can provide readers with a fuller examination of the issues discussed in this document.

  8. References

    Ladiray, D. and Quenneville B. (2001) Seasonal Adjustment with the X-11 Method, Springer-Verlag, Lecture Notes in Statistics, vol 158.

    Statistics Canada (2009) Seasonal adjustment and trend-cycle estimation, Statistics Canada Quality Guideline, 5th edition, Catalogue no. 12-539-X

    Wyman, D. (2010), Seasonal adjustment and identifying economic trends, Statistics Canada. Canadian Economic Observer, March 2010, Catalogue no. 11-010-X

    Readers are also invited to consult the various papers

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