Introduction to Seasonal Adjustment

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Introduction to Seasonal Adjustment

• Based on the
• Australian Bureau of Statistics Information
  Paper An Introductory Course on Time Series
  Analysis
• Hungarian Central Statistical Office Seasonal
  Adjustment Methods and Practices
• Bundesbank, Robert Kirchner X-12 ARIMA Seasonal
  Adjustment of Economic Data Training Course
• Artur Andrysiak
• Economic Statistics Section, UNECE

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Overview

• What and why
• Basic concepts
• Methods
• Software
• Recommended practices
• Step by step
• Issues
• Useful references

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Seasonally adjusted and original series
Industrial Production Index
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IIP percentage change from November 2007 to
December 2007
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Why seasonally adjust?

• Seasonal adjustment has three main purposes
• to aid in short term forecasting
• to aid in relating time series to other series or
  extreme events
• including comparison of timeseries from different
  countries
• to allow series to be compared from month to
  month

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Seasonal adjustment

• Seasonal adjustment is an analysis technique that
  estimates and then removes from a series
  influences that are systematic and calendar
  related.
• A seasonally adjusted series can be formed by
  removing the systematic calendar related
  influences from the original series.
• A trend series is then derived by removing the
  remaining irregular influences from the
  seasonally adjusted series.

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Aim of seasonal adjustment

• The aim of seasonal adjustment is to eliminate
  seasonal and working day effects. Hence there are
  no seasonal and working-day effects in a
  perfectly seasonally adjusted series
• Source Bundesbank

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Aim of seasonal adjustment

• In other words seasonal adjustment transforms
  the world we live in into a world where no
  seasonal and working-day effects occur. In a
  seasonally adjusted world the temperature is
  exactly the same in winter as in the summer,
  there are no holidays, Christmas is abolished,
  people work every day in the week with the same
  intensity (no break over the weekend) etc.
• Source Bundesbank

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IPI - Kazakhstan
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Basic concepts - timeseries

• A time series is a collection of observations of
  well defined data items observed through time
  (measured at equally spaced intervals).
• Examples monthly Industrial Production Index
• Data collected irregularly or only once are not
  timeseries.

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Types of timeseries

• Stock series are measures of activity at a point
  in time and can be thought of as stocktakes.
• Example the Monthly Labour Force Survey it
  takes stock of whether a person was employed in
  the reference week.
• Flow series are series which are a measure of
  activity to a date.
• Examples of flow series include Retail, Current
  Account Deficit, Balance of Payments.

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Basic concepts - seasonality

• Seasonality can be thought of as factors that
  recur one or more times per year.
• A seasonal effect is reasonably stable with
  respect to timing, direction and magnitude.
• The seasonal component of a time series comprises
  three main types of systematic calendar related
  influences
• seasonal influences
• trading day influences
• moving holiday influences

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Seasonal influences

• Seasonal influences represent intra-year
  fluctuations in the series level, that are
  repeated more or less regularly year after year.
• warmth in Summer and cold in Winter BUT Weather
  conditions that are out of character for a
  particular season, such as snow in a summer
  month, would appear in irregular, not seasonal
  influences.
• reflect traditional behaviour associated with the
  calendar and the various social (Chinese New
  Year), business (quarterly provisional tax
  payments), administrative procedures (tax
  returns) and effects of Christmas and the holiday
  season

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Trading day

• Trading day influences refer to the impact on
  the series, of the number and type of days in a
  particular month. A calendar month typically
  comprises four weeks (28 days) plus an extra one,
  two or three days. The activity for the month
  overall will be influenced by those extra days
  whenever the level of activity on the days of the
  week are different.

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Moving holidays

• Moving holiday influences refer to the impact on
  the series level of holidays that occur once a
  year but whose exact timing shifts
  systematically. Examples of moving holidays
  include Easter and Chinese New Year where the
  exact date is determined by the cycles of the
  moon.

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Basic concepts - trend

• The trend component is defined as the long term
  movement in a series.
• The trend is a reflection of the underlying level
  of the series. This is typically due to
  influences such as population growth, price
  inflation and general economic development.
• The trend component is sometimes referred to as
  the trend cycle.

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Basic concepts - irregular

• The irregular component is the remaining
  component of the series after the seasonal and
  trend components have been removed from the
  original data.
• For this reason, it is also sometimes referred
  to as the residual component. It attempts to
  capture the remaining short term fluctuations in
  the series which are neither systematic nor
  predictable.
• The irregular component of a time series may or
  may not be random. It can contain both random
  effects (white noise) or artifacts of
  non-sampling error, which are not necessarily
  random.
• Most time series contain some degree of
  volatility, causing original and seasonally
  adjusted values to oscillate around the general
  trend level. However, on occasions when the
  degree of irregularity is unusually large, the
  values can deviate from the trend by a large
  margin, resulting in an extreme value. Some
  examples of the causes of extreme values are
  adverse natural events and industrial disputes.

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Models for decomposing a series

• Components of timeseries
• It irregular
• St seasonal
• Tt trend
• Ot original
• Additive Decomposition Model
• Ot St Tt It
• Multiplicative Decomposition Model
• Ot St x Tt x It

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Additive Decomposition Model

• The additive decomposition model assumes that the
  components of the series behave independently of
  each other. The trend of the series fluctuates
  yet the amplitude of the adjusted series
  (magnitude of the seasonal spikes) remain
  approximately the same, implying an additive
  model.
• Ot St Tt It

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Additive model
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Example of additive series - IPI for Serbia
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Multiplicative Decomposition Model

• As the trend of the series increases, the
  magnitude of the seasonal dips also increases,
  implying a multiplicative model.
• Ot St x Tt x It

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Multiplicative Model
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Example of multiplicative series IPI for
Kyrgyzstan
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Seasonal adjustment philosophies

• Model based method
• Filter based method.

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Model based methods

• The model based approach requires the components
  of an original time series, such as the trend,
  seasonal and irregular to be modelled separately.
  Alternatively, the original series could be
  modelled and from that model, the trend, seasonal
  and irregular component models can be derived.
• Model based methods assume the irregular
  component is .white noise. i.e. the irregular has
  no structure, zero mean and a constant variance.

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Model based methods

• TRAMO/SEATS
• X13-ARIMA/SEATS
• STAMP

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TRAMO/SEATS

• TRAMO (Time Series Regression with ARIMA Noise,
  Missing Observations and Outliers) and SEATS
  (Signal Extraction in ARIMA Time Series) are
  linked programs originally developed by Victor
  Gómez and Agustin Maravall at Bank of Spain.
• The two programs are structured to be used
  together, both for in-depth analysis of a few
  series or for routine applications to a large
  number of them, and can be run in an entirely
  automatic manner. When used for seasonal
  adjustment, TRAMO preadjusts the series to be
  adjusted by SEATS.
• The two programs are intensively used at present
  by data-producing and economic agencies,
  including Eurostat and the European Central Bank.
• Programs TRAMO and SEATS provide a fully
  model-based method for forecasting and signal
  extraction in univariate time series. Due to the
  model-based features, it becomes a powerful tool
  for a detailed analysis of series.

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TRAMO/SEATS

• www.bde.es

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Filter based methods

• This method applies a set of fixed filters
  (moving averages) to decompose the time series
  into a trend, seasonal and irregular component.
  Typically, symmetric linear filters are applied
  to the middle of the series, and asymmetric
  linear filters are applied to the ends of the
  series.

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Filter based methods

• X11
• X11-ARIMA
• X12-ARIMA (uses regARIMA Models for forecasts,
  backcasts and preadjustments)
• STL
• SABL
• SEASABS

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X12-ARIMA

• X12-ARIMA was developed by US Census Bureau as an
  extended and improved version of the X11- ARIMA
  method of Statistics Canada (Dagum (1980)).
• The program runs through the following steps.
• First the series is modified by any user-defined
  prior adjustments.
• Then the program fits a regARIMA model to the
  series in order to detect and adjust for outliers
  and other distorting effects for improving
  forecasts and seasonal adjustment.
• The program then uses a series of moving averages
  to decompose a time series into three components.
  In the last step a wider range of diagnostic
  statistics are produced, describing the final
  seasonal adjustment, and giving pointers to
  possible improvements which could be made.
• The X12-ARIMA method is best described by the
  following flowchart, as presented by David
  Findley and by Deutsche Bundesbank respectively.

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X12-ARIMA
The X12-ARIMA method is best described by the
following flowchart, as presented by David
Findley and by Deutsche Bundesbank respectively.
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X12-ARIMA

• http//www.census.gov/srd/www/x12a/

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Software

• TRAMO/SEATS
• http//www.bde.es
• X12-ARIMA
• http//www.census.gov/srd/www/x12a/
• DEMETRA
• http//circa.europa.eu/irc/dsis/eurosam/info/data/
  demetra.htm
• http//circa.europa.eu/irc/dsis/eurosam/info/data/
  

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The criteria of a good seasonal adjustment
process

• series which does not show the presence of
  seasonality should not be seasonally adjusted
• it should not leave any residual seasonality and
  effects that have been corrected (trading day,
  Easter effect, ) in the seasonally adjusted data
• there should not be over-smoothing
• it should not lead to abnormal revisions in the
  seasonal adjustment figure with respect to the
  characteristics of the series
• the adjustment process should prefer the
  parsimonious (simpler) ARIMA models
• the underlying choices should be documented

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Recommended practices for Seasonal Adjustment
(Eurostat)

• Aggregation Approach
• Preserving relationships between data - indirect
  approach
• Series that have very similar seasonal components
  (summing up the series together will first
  reinforce the seasonal pattern while allowing the
  cancellation of some noise in the series) -
  direct adjustment
• Revisions
• Concurrent adjustment vs forward factors
• Take into account the revision pattern of the
  raw data, the main use of the data, the stability
  of the seasonal component
• Publication Policy
• When seasonality is present and can be
  identified, series should be made available in
  seasonally adjusted form.
• The method and software used should be explicitly
  mentioned in the metadata accompanying the
  series.
• Calendar adjusted series and/or the trend-cycle
  estimates (in graph format) could be also
  disseminated in case of user demand.

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Recommended practices for Seasonal Adjustment
(Eurostat)

• Additional information to be published
• The decision rules for the choice of different
  options in the program
• The aggregation policy
• The outlier detection and correction methods with
  explanation
• The decision rules for transformation
• The revision policy
• The description of the working/trading day
  adjustment
• The contact address.
• Calendar Effects
• Proportional approach vs regression approach
• model based methods - regression approach should
  be used
• Outliers Detection
• Expert information is especially important about
  outliers
• Outliers should be removed before seasonal
  adjustment is carried out

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Recommended practices for Seasonal Adjustment
(Eurostat)

• Transformation Analysis
• Most popular software packages provide automatic
  test for log-transformation
• Automatic choice should be confirmed by looking
  at graphs of the series
• If the diagnostics are inconclusive - visually
  inspect the graph of the series
• If the series has zero and negative values it
  must be additively adjusted
• If the series has a decreasing level with
  positive values close to zero and the series do
  not have negative values - multiplicative
  adjustment has to be used
• Time Consistency
• Time consistency of adjusted data should be
  maintained in case of strong user interest, but
  not if the seasonality is rapidly changing

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Forward Factors versus Concurrent Adjustment

• Forward factors rely on an annual analysis of the
  latest available data to determine seasonal and
  trading day factors that will be applied in the
  forthcoming 4 quarters or 12 months (depending if
  the series is quarterly or monthly).
• Concurrent adjustment uses the data available at
  each reference period to re-estimate seasonal and
  trading day factors. Under this method data for
  the current month are used in estimating seasonal
  and trading day factors for the current and
  previous months. This method continually fine
  tunes the estimates whenever new data becomes
  available.

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Seasonal Adjustment Step by Step

• STEP 0 Length of series
• Series has to be at least 3 year-long (36
  observations) for monthly series and 4 year-long
  (16 observations) for quarterly series
• For an adequate seasonal adjustment data of more
  than five years are needed.
• For series under 10 years the instability of
  seasonally adjusted data could arise,
• If the series is too long information regarding
  seasonality, many years ago could be irrelevant
  today, especially if changes in concepts,
  definitions and methodology occurred.
• STEP 1 Preconditions, test for seasonality
• Have a look at the data and graph of the original
  time series
• Possible outlier values should be identified
• Series with too many outliers (more than 10)
  will cause estimation problems
• The spectral graph of the original series should
  be examined
• If seasonality is not consistent enough for a
  seasonal adjustment series should not be
  seasonally adjusted.

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Seasonal Adjustment Step by Step

• STEP 2 Transformation type
• Automatic test for log-transformation is
  recommended
• The results should be confirmed by looking at
  graphs of the series
• STEP 3 Calendar effect
• It should be determined which regression effects,
  such as trading/working day, leap year, moving
  holidays (e.g. Easter) and national holidays, are
  plausible for the series
• If the effects are not plausible for the series
  the regressors for the effects should not be
  applied
• STEP 4 Outlier correction
• Series with high number of outliers relative to
  the length of the series should be identified -
  attempts can be made to re-model these series
• STEP 5 The order of the ARIMA model
• Automatic procedure should be used
• Not significant high-order ARIMA model
  coefficients should be identified.

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Seasonal Adjustment Step by Step

• STEP 6 for family X Filter choices
• It should be verified that the seasonal filters
  are generally in agreement with the global moving
  seasonality ratio.
• STEP 7 Monitoring of the results
• There should not be any residual seasonal and
  calendar effects in the published seasonally
  adjusted series or in the irregular component.
• If there is residual seasonality or calendar
  effect, as indicated by the spectral peaks, the
  model and regressor options should be checked in
  order to remove seasonality.
• STEP 8 Stability diagnostics
• Even if no residual effects are detected, the
  adjustment will be unsatisfactory if the adjusted
  values undergo large revisions when they are
  recalculated as new data become available. In any
  case instabilities should be measured and
  checked.

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Forward Factors versus Concurrent Adjustment

• Concurrent adjustment uses the data available at
  each reference period to re-estimate seasonal and
  trading day factors. Under this method data for
  the current month are used in estimating seasonal
  and trading day factors for the current and
  previous months. This method continually fine
  tunes the estimates whenever new data becomes
  available

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Issues that can complicate the seasonal
adjustment process

• Outliers (unusual estimates)
• The focus is on unusual estimates, not unusual
  observations as in the sampling sense. Outliers
  can cause blips in an original series, seasonally
  adjusted series and trend series unless they are
  modified or corrected during the seasonal
  adjustment process
• Revisions
• The seasonal adjustment process leads to
  revisions to the seasonally adjusted and trend
  series. Revisions are not desirable, either for
  the ABS or the users of the series. The analysis
  technique chosen aims to strike a balance between
  revisions and quality of the seasonally adjusted
  and trend series. This issue is commonly referred
  to as the .end point problem.
• Aggregation and Disaggregation
• Regular and irregular influences are often
  estimated and removed from series at fine levels
  of disaggregation, such as at the State by
  Industry level. Higher level seasonally adjusted
  series, such as at the Australia level, can be
  constructed by adding up component series to a
  higher level (to form an indirectly adjusted
  series) or by directly seasonally adjusting the
  higher level series (to form a directly adjusted
  series). The resulting series will not be
  identical. A common issue faced by time series
  analysts is explaining why the two approaches do
  not result in the same series.

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Outliers
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Outliers

• Outliers are data which do not fit in the
  tendency of the time series observed, which fall
  outside the range expected on the basis of the
  typical pattern of the trend and seasonal
  components.
• Additive outlier the value of only one
  observation is affected. AO may either be caused
  by random effects or due to an identifiable cause
  as a strike, bad weather or war.
• Temporary change the value of one observation is
  extremely high or low, then the size of the
  deviation reduces gradually (exponentially) in
  the course of the subsequent observations until
  the time series returns to the initial level. For
  example in the construction sector the production
  would be higher if in a winter the weather was
  better than usually (i.e. higher temperature,
  without snow). When the weather is regular, the
  production returns to the normal level.
• Level shift starting from a given time period,
  the level of the time series undergoes a
  permanent change. Causes could include change in
  concepts and definitions of the survey
  population, in the collection method, in the
  economic behavior, in the legislation or in the
  social traditions. For example a permanent
  increase in salaries.

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Useful references

• Eurostat. ESS Guidelines on Seasonal Adjustment
• http//epp.eurostat.ec.europa.eu/pls/portal/docs/
  PAGE/PGP_RESEARCH/PGE_RESEARCH_04/ESS20GUIDELINES
  20ON20SA.PDF
• Eurostat. Eurostat Seasonal Adjustment Project.
  http//circa.europa.eu/irc/dsis/eurosam/info/data/
  
• Hungarian Central Statistical Office (2007).
  Seasonal Adjustment Methods and Practices.
  www.ksh.hu/hosa
• US Census Bureau. The X-12-ARIMA Seasonal
  Adjustment Program. http//www.census.gov/srd/www/
  x12a/
• Bank of Spain. Statistics and Econometrics
  Software. http//www.bde.es/servicio/software/econ
  ome.htm
• Australian Bureau of Statistics (2005).
  Information Paper, An Introduction Course on Time
  Series Analysis Electronic Delivery.
  1346.0.55.001. http//www.abs.gov.au/ausstats/abs_at_
  .NSF/papersbycatalogue/7A71E7935D23BB17CA2570B1002
  A31DB?OpenDocument

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• Questions?
• THANK YOU