components of time series, seasonality and pre-conditions for seasonal adjustment anu peltola...
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Components of Time Series, Seasonality and Pre-conditions
for Seasonal Adjustment
Anu PeltolaEconomic Statistics Section, UNECE
UNECE Workshop on Short-Term Statistics (STS) UNECE Workshop on Short-Term Statistics (STS) and Seasonal Adjustmentand Seasonal Adjustment14 – 17 March 2011, Astana, Kazakhstan
March 2011 UNECE Statistical Division Slide 2
Overview
Basic Concepts Components of Time Series Seasonality Pre-conditions for Seasonal Adjustment
March 2011 UNECE Statistical Division Slide 3
Basic Concepts
Index comes from Latin and means a pointer, sign, indicator, list or register• A ratio that measures change• As per cent of a base value (base always 100)• Each observation is compared to the base value
Time series are a collection of observations, measured at equally spaced intervals• Stock series = at a point in time (discrete)• Flow series = period in time (continuous)
new observation
old observation
x 100
March 2011 UNECE Statistical Division Slide 4
Components of Time Series
Seasonal adjustment is based on the idea that time series can be decomposed
The components are:SeasonalIrregularTrend
March 2011 UNECE Statistical Division Slide 5
Trend-Cycle Component
50
60
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Relation of ComponentsComponents of the Industrial Production Index of Kazakhstan
Ind
ex
20
05
=1
00
Original component
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140
Jan-
00
Jan-
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Jan-
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Jan-
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Jan-
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Jan-
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Jan-
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Jan-
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Jan-
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Jan-
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Jan-
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Seasonal component
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Jan-0
0
Jan-0
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Jan-0
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Jan-0
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Jan-0
4
Jan-0
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Jan-0
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Jan-0
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Jan-0
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Jan-0
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Jan-1
0
Irregular component
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Jan-
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Jan-
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March 2011 UNECE Statistical Division Slide 6
Seasonal Component
= Depicts systematic, calendar-related movements
has a similar pattern from year to yearrefers to the periodic fluctuations within a
year that re-occur in approximately the same way annually
Is removed in seasonal adjustment
March 2011 UNECE Statistical Division Slide 7
Irregular Component
= Depicts unsystematic, short term fluctuations The remaining component after the seasonal
and trend components have been removed Certain specific outliers, such as those caused
by strikes, also belong to this component Sometimes called the residual component May or may not be random with random
effects (white noise) or artifacts of non-sampling error (not necessarily random)
March 2011 UNECE Statistical Division Slide 8
Trend Component
= Depicts the long-term movement in a series A trend series is derived by removing the
irregular influences from the seasonally adjusted series
A reflection of the underlying development Typically due to influences such as population
growth, technological development, inflation and general economic development
Sometimes referred to as the trend-cycle
March 2011 UNECE Statistical Division Slide 9
IPI – KazakhstanAn Example of the Components of Time Series
Ind
ex
20
05
=1
00
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Jan-
00
Jul-0
0
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Jul-0
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Jul-0
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Jul-0
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Jul-0
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Jan-
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Jul-0
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Jul-0
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Jan-
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Jul-0
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Jan-
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Jul-0
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Jan-
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Jul-1
0
Original Seasonally adjusted Trend
March 2011 UNECE Statistical Division Slide 10
Causes of Seasonality
= seasons e.g. holidays and consumption habits, which are related to the rhythm of the year• Warmth in summer and cold in winter BUT not
extreme weather conditions (irregular component) Seasonality reflects traditional behavior
associated with: The calendar Christmas and New Year Social habits (the holiday season), Business (quarterly provisional tax payments) and Administrative procedures (tax returns)
March 2011 UNECE Statistical Division Slide 11
Seasonality
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1 2 3 4 5 6 7 8 9 10 11 12
2000
2001
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2008
Industrial production in Moldova, original series 2000-2008
months
Ind
ex
20
05
=1
00
March 2011 UNECE Statistical Division Slide 12
Seasonal Effect
= Intra-year fluctuations in the series that repeat A seasonal effect is reasonably stable with
respect to timing, direction and magnitude The seasonal component of a time series is
comprised of three main types of systematic calendar-related influences: • Seasonal influences• Trading day influences • Moving holiday influences
March 2011 UNECE Statistical Division Slide 13
Trading Day Effect
= The impact on the series, of the number and type of days in a particular month
Different days may have a different weight A calendar month comprises four weeks (28
days) plus extra one, two or three days Rarely an issue in quarterly data, since
quarters have 90, 91 or 92 days
March 2011 UNECE Statistical Division Slide 14
Trading DaysSaturday
Source: Analysis of Daily Sales Data during the Financial Panic of 2008, John B. Taylor (Target Corporation’s sales)
March 2011 UNECE Statistical Division Slide 15
Moving Holidays
= The impact on the series of holidays whose exact timing shifts from year to year
Examples of moving holidays:• Easter • Chinese New Year - where the exact date is
determined by the cycles of the moon• Ramadan
March 2011 UNECE Statistical Division Slide 16
0
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10
15
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25
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
avera
ge w
ork
ing
days
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2010
2011
Moving HolidaysImpact of moving holidays to the number of working days
Ascension day Christmas moves between weekdays and weekend
March 2011 UNECE Statistical Division Slide 17
Working Days and Seasonality
Example of average working days in 2009 - 2011
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Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
aver
age
wo
rkin
g d
ays
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2011
March 2011 UNECE Statistical Division Slide 18
Sudden Changes Outliers
• Extreme values with identifiable causes (strikes or extreme weather conditions)
• Part of irregular component Trend breaks (level shifts)
• The trend component suddenly increases or decreases in value
• Often caused by changes in definitions (tax rate, reclassification)
Seasonal breaks• The seasonal pattern changes, e.g. due to a structural
change caused by a crisis or administrative issues such as timing of invoicing
March 2011 UNECE Statistical Division Slide 19
Pre-conditions for Seasonal Adjustment
1. Good quality of raw data• Strange values to be checked (zeros or outliers)• Revision of errors with new acquired data
2. Length of time series 36/12 or 16/4• At least 36 observations for monthly series and
16 observations for quarterly series needed
3. Consistent time series• To provide data according to a base year• Use of comparable definitions and classifications• Remove non-comparable changes
4. Solid structure• Presence of seasonality, moderate volatility• No major breaks in seasonal behaviour