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Scope and purpose
Seasonal adjustment consists of estimating seasonal factors and
applying them to a time series to remove the seasonal variations.
These variations represent the composite effect of climatic and institutional
factors that repeat with a certain regularity within the year. The seasonally
adjusted series consists of the trend-cycle and the irregular components.
The trend is the underlying long-term movement lasting many years.
The cycle, usually called the business-cycle, is a quasi-periodic
oscillation lasting from three to four years. The irregular component
represents those random variations that are unforeseeable movements related
to events of all kinds.
Statistical agencies publish many of their series in seasonally adjusted
form to reveal the underlying trend-cyclical movements and to help data
analysis. Seasonally adjusted series comprise not only the trend-cycle
but also the irregular component; consequently, they only give an approximate
idea of the underlying trend-cyclical movements. Smoothing the seasonally
adjusted series further is often desirable to eliminate the irregular
component and to publish trend-cycle estimates as a complement
to the seasonally adjusted series.
This section is a transcript of the Agency’s Guidelines for Seasonal
Adjustment and Trend-Cycle Estimation (Statistics Canada, 2000b).
Principles
Seasonally adjust a time series only when there is evidence that the
series is influenced by seasonal forces, and when the series contains
identifiable seasonality. Identifiable seasonality is defined as a seasonal
pattern that is not obscured by a high degree of irregular fluctuations
and thus can be identified reliably (Lothian and Morry, 1978).
A good seasonal adjustment procedure does not leave any residual seasonality
in the series, and the resulting seasonally adjusted series is much smoother
than the original.
The revisions to the seasonally adjusted estimates should be minimal
as more data points are added to the end of the series. The X11ARIMA (Dagum,
1980) and the X11ARIMA/88 (Dagum, 1988) seasonal adjustment methods were
adopted by Statistics Canada with the exact purpose of reducing the size
of revisions (Dagum, 1975; Kuiper, 1976; Dagum, 1982).
The frequency of revisions should be minimized. Although revisions arise
with each new data point added, implement revisions only when they bring
about improvement in the estimates, that is, when the revised estimate
moves appreciably closer to the final estimate.
Wherever seasonally adjusted figures pertaining to the same economic
activity are published, coordinate the seasonal adjustment options applied
by the areas involved, and make every effort to treat related series in
a consistent manner.
When trend-cycle estimates are produced as a complement to the seasonally
adjusted series it is important to keep in mind that they are used for
providing a reading of the stage of the business cycle, and therefore
their accuracy is important with regard to the direction of movement,
the amplitude of the cycle and especially the timing of turning points.
The trend-cycle estimates should be consistent with the published seasonally
adjusted estimates. If the latter estimates are frozen in the database
after three months, apply the trend-cycle estimator to the seasonally
adjusted estimates as they appear on the base and in the publication.
Guidelines
- Before seasonally adjusting a series for the first time, and after
that every few years, conduct a thorough seasonal analysis to assess
if seasonality is identifiable and publish the series in seasonally
adjusted form only if it is identifiable.
- During seasonal adjustment it is recommended that ARIMA extrapolations
be used in the calculations of the seasonal factors to reduce the size
of the revisions. Use the automatic ARIMA extrapolation subroutine of
the X11ARIMA program whenever possible. If none of the built-in models
is selected, it is recommended that the user supply an ARIMA model.
- For the seasonal adjustment of recent observations, use a concurrent
seasonal factor (Dagum, 1987). This is a factor obtained using
all the available data points. An exception to this guideline may apply
when the most recent observations have been subjected to historically
large revisions. In this case year-ahead (forecast) seasonal factors
may be more appropriate (Morry, 1992). These seasonal factors are based
on data that ended at the end of the previous year.
- When a concurrent seasonal factor is used, it is not necessary to
revise the seasonally adjusted estimates more than one period back when
the next observation becomes available. An exception to this guideline
applies when preliminary observations are used: it is recommended to
revise the seasonal factors whenever the original figures are revised
significantly. On an annual basis, revise the seasonally adjusted values
for the last three years when the first month (quarter) of the next
year becomes available (Dagum, 1987). When seasonally adjusted values
are obtained with year-ahead (forecast) seasonal factors, the annual
revision applies to the last four years.
- For series with trading-day variations, use the daily weights that
are automatically estimated by the X11ARIMA program. During the current
year, keep them fixed by supplying them as prior daily weights. They
will be modified at the next annual revision. Exceptions to this guideline
may occur when a-priori daily weights can be provided by subject matter
experts based on better knowledge of the series in question.
- For series with Easter variations, use the Easter effect factors calculated
automatically by the X11ARIMA program.
- For aggregate series resulting from the combination of component series,
seasonally adjust only those component series that contain identifiable
seasonality, and leave the others unadjusted. Seasonally adjust the
aggregate series by the indirect or direct method. In the indirect method,
combine the seasonally adjusted components and the unadjusted ones to
obtain the seasonally adjusted aggregate. In the direct method, seasonally
adjust the aggregate, and restore additivity (if required) by raking
the components, if possible without modifying the unadjusted ones. When
choosing between the indirect and the direct approach the following
factors need to be considered: the aggregate should not contain residual
seasonality and it should be relatively smooth (Lothian and Morry, 1977).
Choose the raked direct approach only if the raking does not distort
too much the month-to-month (quarter-to-quarter) movements of the component
series.
- Wherever seasonally adjusted figures pertaining to the same economic
activity are published, coordinate the seasonal adjustment options applied
by the areas involved. For example, when possible, make consistent choices
between direct and indirect adjustment of composite series, and ensure
that extreme occurrences in the time series brought about by events
such as plant closures, strikes, natural disasters, etc. are treated
in a consistent fashion by the different areas.
- Use the Henderson moving averages, available in the X11ARIMA program,
to produce the trend-cycle estimates. To ensure that the trend-line
lies within the scatter plot of the seasonally adjusted series, apply
the Henderson moving averages to the published seasonally adjusted series.
- Before applying the trend-cycle estimator, extend the seasonally adjusted
series with one year of forecasted values from an ARIMA model fitted
to the seasonally adjusted series.
- Apply the Henderson moving averages to the extended seasonally adjusted
series from which the extremes have been previously corrected.
- Use the Henderson moving average automatically selected by the X11ARIMA
program: the selection is based on the value of the I/C (irregular to
trend-cycle) ratio, which measures the relative importance of the irregular
variations in the seasonally adjusted series (Shiskin, et al., 1967).
- Inform the users that the last few trend-cycle estimates (and especially
the very last estimate) are subject to large revisions, and often to
a reversal of movement when one more data point is added to the series
(Dagum and Laniel, 1987). This high uncertainty associated with the
estimates around the end can be indicated, for example, by a dashed
line on the trend graph or by a written caveat to users.
References
Dagum, E.B. (1975). Seasonal factor forecasts from ARIMA models. Proceedings
of the International Institute of Statistics, 40th Session, Contributed
Papers, 3, Warsaw, 206-219.
Dagum, E.B. (1980). The X11ARIMA seasonal adjustment method. Catalogue
No. 12-564E, Statistics Canada.
Dagum, E.B. (1982). The effects of asymmetric filters on seasonal factor
revisions. Journal of the American Statistical Association,
77, 732-738.
Dagum, E.B. (1987). Current issues on seasonal adjustment. Survey
Methodology, 13, 63-74.
Dagum, E.B. (1988). The X11ARIMA/88 seasonal adjustment method - foundations
and user’s manual. Time Series Research and Analysis Division, Statistics
Canada technical report.
Dagum, E.B. and Laniel, N. (1987). Revisions of trend-cycle estimators
of moving average seasonal adjustment methods. Journal of Business
and Economic Statistics, 5, 177-189.
Kuiper, J. (1976). A survey and comparative analysis of various methods
of seasonal adjustment. Proceedings of the NBER/Bureau of the
Census Conference on Seasonal Analysis of Economic Time Series,
Arnold Zellner (ed.), Washington, D.C. 59-76.
Lothian, J. and Morry, M. (1977). The problem of aggregation: direct
or indirect seasonal adjustment. Research paper 77-08-001E, Seasonal Adjustment
and Time Series Staff, Statistics Canada.
Lothian, J. and Morry, M. (1978). A test for the presence of identifiable
seasonality when using the X-11 program. Research paper 78-10-002E, Seasonal
Adjustment and Time Series Staff, Statistics Canada.
Morry, M. (1992). Comparison of revisions in seasonally adjusted external
trade series obtained through the use of concurrent versus forecast factors.
Statistics Canada Working Paper, TSRA-92-004E.
Shiskin, J., Young, A.H. and Musgrave, J.C. (1967). The X-11 variant
of the census method II seasonal adjustment. Technical Paper No. 15, Bureau
of the Census, U.S. Department of Commerce.
Statistics Canada (2000b). Guidelines for Seasonal Adjustment and Trend-Cycle
Estimation. Issued by the Methods and Standards Committee, March, 2000.
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