Seasonal adjustment
Training Workshop on the Compilation of Quarterly National Accounts
for Economic Cooperation Organization Member Countries
8-11 March 2015
Tehran, Islamic Republic of Iran
United Nations Statistics Division
Outline
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What is time series?
Components of time series
What is seasonal adjustment?
Seasonal adjustment models
Seasonal adjustment methods
Issues in seasonal adjustment
Conclusions
Questions
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What is time series?
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Is a series of data obtained through repeated
measurement of the same concept over time
that allows different periods to be compared
Examples:
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QNA
Monthly index of industrial production
Monthly consumer price index
Monthly retail sales
Data which are collected only once or irregularly
are not considered as time series
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What is time series?
Example of time series data
Source: IMF QNA Manual (2001)
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Components of time series
Trend cycle component
 Captures long-term trend and business cycle
movements in the data
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Long-trend trend is associated with structural changes
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Population growth
Progress in technology and productivity
Business cycle movements are related to periodic
oscillations of different phases of the economy
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Recession
Recovery
Growth
Decline
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Components of time series
Seasonal component
 Stable seasonal effects in terms of annual
timing, direction and magnitude
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Could be due to climatic factors, administrative or
legal rules, social/cultural traditions and
conventions, and calendar effects that are stable in
annual timing
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Example: Public holidays such as Christmas
Calendar-related systematic effects that are
not stable in annual timing, and due to
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Trading-day or working-day effect
Moving holiday effect, for example, Ramadan,
Chinese New Year
Leap year effect
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Components of time series
Irregular component
 Captures effects that are unpredictable in
terms of timing, impact and duration unless
additional information is available
 Includes outlier effects which cause abrupt
changes in the series, sometimes related to
unexpected events such as
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Unseasonable weather
Natural disasters
Strikes
Economic and financial crisis
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What is seasonal adjustment?
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Seasonal adjustment means using analytical
techniques to break down a series into its
components
The purpose is to identify the different
components of the time series and thus
provide a better understanding of the
behaviour of the series to
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Aid in short-term forecasting and modelling
Remove regular within-a-year seasonal patterns to
highlight the underlying trends and short-run
movements in the series
Allow series to be compared from quarter to
quarter
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Seasonal adjustment models
Most common forms of decomposition
• Additive: Yt = Tt + St + It
• Multiplicative: Yt = Tt x St x It
where
Yt = Observed time series at time t
Tt = Trend-cycle component at time t
St = Seasonal component at time t
It = Irregular component at time t
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Seasonal adjustment models
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Additive model assumptions
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The components of the series are independent of
each other
The size of the seasonal oscillations is independent of
the level of the series
Multiplicative model assumptions
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The components of the series are dependent on each
other
The size of the seasonal oscillations increases and
decreases with the level of the series
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Seasonal adjustment methods
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Moving average-based methods
Model-based methods
Integrated methods
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Seasonal adjustment methods
Moving average-based methods
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Are based on the use of different kinds of moving
average filter
Best example is the X-11 family
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US Bureau of Census developed X-11 in the 1960s
Statistics Canada developed X-11-ARIMA
US Bureau of Censes developed X-12-ARIMA in the
1980s
All X-11 family involve repeated application of
suitable moving average filters to decompose the
time series into its trend-cycle, seasonal and
irregular components
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Seasonal adjustment methods
Moving average-based methods
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Main steps of X-12-ARIMA program:
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The series is pre-adjusted using the regARIMA model
to detect and remove outliers and other distorting
effects such as calendar effects and to extend the
series with backcasts and forecasts to be used in the
decomposition process
The pre-adjusted series is then decomposed through
three rounds of seasonal filtering and extreme value
adjustments to produce the trend-cycle, seasonal and
irregular components
Various diagnostics and quality control statistics are
computed, tabulated and graphed
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Seasonal adjustment methods
Moving average-based methods
Main elements of X-12-ARIMA seasonal adjustment
program
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Seasonal adjustment methods
Model-based methods
 Estimate the trend-cycle, seasonal and irregular
components with signal extraction techniques
applied to an ARIMA model fitted to the unadjusted
data
 TRAMO/SEATS is most widely used
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Developed at the Bank of Spain
Consists of two main programs
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Time series regression with ARIMA noise, missing
observations and outliers (TRAMO), a regARIMA modeling
package with automatic identification of ARIMA models,
outliers and other components
Signal extraction in ARIMA time series (SEATS), which takes
modeling results from TRAMO and performs a model-based
signal extraction
Both programs are structured to be used together
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TRAMO pre-adjusts the series before seasonal adjustment by
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SEATS
Seasonal adjustment methods
Integrated methods
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X-13-ARIMA-SEATS
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Was recently released by US Bureau of Census
Implements the X-11 method and SEATS method
Allows comparison of X-11 and SEATS seasonal
adjustment using a common set of diagnostics
DEMETRA+
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Was developed by Eurostat
Offers choice of X-12-ARIMA and TRAMO/SEATS
Provides user-friendly tools to check quality of results
Allows multi-processing
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Seasonal adjustment methods
Example of seasonally adjusted series,
trend-cycle and irregular components
Source: IMF QNA Manual (2001)
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Issues in seasonal adjustment
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Direct vs indirect seasonal adjustment
Relationship among price, volume and value
Temporal consistency with annual accounts
Length of series for seasonal adjustment
Seasonal adjustment of indicators or QNA series
Organizing seasonal adjustment in the QNA
Presentation of seasonally-adjusted estimates
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Issues in seasonal adjustment
Direct vs indirect seasonal adjustment
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Seasonally adjusted series of aggregates can be
derived by
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Directly adjusting the aggregates, or
Indirectly by aggregating seasonally adjusted data of the
components
Both approaches have merits
Direct approach
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May result in improved quality of seasonally adjusted
series
May give best results if the component series show similar
seasonal patterns and trend cycles are highly correlated
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Issues in seasonal adjustment
Direct vs indirect seasonal adjustment
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Indirect approach
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May give best results when the component series show
different seasonal patterns
May make it easier to identify breaks, outliers, calendar
effects, etc, in detailed series
May give better results for balancing items (for example,
value added) if component series are available
May, however, leave residual seasonality in the aggregates
Country practices vary
Choice may be guided by expected uses of the
seasonally adjusted data
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Issues in seasonal adjustment
Relationship among price, volume and value
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Seasonally adjusted price indices, volume
measures and current price data can be derived
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Independently, or
By seasonally adjusting 2 of them and deriving the
third residually
Either approach will give different results
Choosing which series to derive residually should
be determined on a case-by-case basis,
depending on which approach produces the most
reasonable results
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Issues in seasonal adjustment
Temporal consistency with annual accounts
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Annual totals based on seasonally adjusted data
and unadjusted data will not be automatically
equal due mainly to calendar effects and moving
seasonality
If effects are strong, seasonally adjusted data
should be benchmarked to the calendar adjusted
annual data
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Issues in seasonal adjustment
Length of series for seasonal adjustment
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Seasonal adjustment requires sufficiently long
time series to ensure results with sufficient
quality
For QNA variables, at least 5 years (20 quarters)
of data should be used
When starting a new QNA system, unadjusted
data should be reconstructed as far back as
possible before doing seasonal adjustment
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Issues in seasonal adjustment
Length of series for seasonal adjustment
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Sometimes, seasonal adjustment may return
questionable results for very long time series
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Reasons
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Discontinuities and structural breaks due to different
economic conditions over a long period of time
Solution
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Divide the series into 2 or more contiguous relatively
stable periods
Apply seasonal adjustment to each sub-period separately
Link the resulting seasonally-adjusted series
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Issues in seasonal adjustment
Seasonal adjustment of indicators or QNA series
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Seasonally adjusted QNA can be obtained by
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Using seasonally adjusted indicators, or
Applying the chosen seasonal adjustment method to the
unadjusted QNA
Both approaches have merits
Applying seasonal adjustment directly to indicators
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Means correcting seasonal effects at the actual data
sources
May avoid artificial seasonality due to use of QNA
techniques such as benchmarking
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Issues in seasonal adjustment
Seasonal adjustment of indicators or QNA series
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Seasonally adjusting the QNA
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Has the advantage of ensuring the unadjusted QNA is
consistent with other variables
Ensures high degree of consistency in the seasonality of
production, expenditure and income components of GDP
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Issues in seasonal adjustment
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Organizing seasonal adjustment in the QNA
Seasonal adjustment programs offer automatic
selection procedures that produce satisfactory
results for most time series, with little intervention
from users
Some series may be problematic with substantial
experience and expertise is needed to check
whether seasonal adjustment is done properly or
fine tune options
General recommendation is for statisticians who
compile the statistics to seasonally adjust the series,
either solely or together with specialists
A small unit of seasonal adjustment experts should
also be set up to handle problematic series
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Issues in seasonal adjustment
Presentation of seasonally-adjusted estimates
 Seasonally-adjusted QNA estimates can be used to
calculate
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Quarter-to-quarter rates of change
Annualized quarterly rates of change
Whatever growth rates that are published should be
clearly indicated
The levels of seasonally-adjusted QNA estimates can
be annualized
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Not recommended as presentation
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Seems artificial
Is not easy to interpret
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Conclusions
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Seasonally adjusted QNA estimates should be
calculated to facilitate the analysis of current
economic developments without the influence of
seasonal and calendar effects
Seasonally adjusted data should, however, not
replace the unadjusted QNA data
There are a number of methods to do seasonal
adjustment
The choice of which seasonal adjustment method to
use can be based on past experience, subjective
appreciation and characteristics of the time series
A minimum of 5 years (20 quarters) data is needed
to seasonally adjust QNA data.
Metadata and methodological notes on seasonal
adjustment methods should be made available for
transparency
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Questions
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Is your country compiling and publishing
seasonally-adjusted QNA?
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If yes, what method and software are you using to do
seasonal adjustment?
If not, do you have plans to do so?
Is there a specific unit doing seasonal
adjustment or is it done by the unit compiling
QNA?
Is the method to do seasonal adjustment
published in your national accounts
methodological notes?
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Thank you
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