Download Introduction to the International Family of Classification

UNECE Workshop on Short-Term Statistics (STS)
and Seasonal Adjustment
14 – 17 March 2011, Astana, Kazakhstan
Components of Time Series,
Seasonality and Pre-conditions
for Seasonal Adjustment
Anu Peltola
Economic Statistics Section, UNECE
Overview




Basic Concepts
Components of Time Series
Seasonality
Pre-conditions for Seasonal Adjustment
March 2011
UNECE Statistical Division
Slide 2
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
new observation
old observation

x 100
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)
March 2011
UNECE Statistical Division
Slide 3
Components of Time Series
Seasonal adjustment is based on the
idea that time series can be
decomposed
 The components are:

Seasonal
 Irregular
 Trend

March 2011
UNECE Statistical Division
Slide 4
March 2011
UNECE Statistical Division
Jul- 10
Jan-10
Jul- 09
Jan-09
Jul- 08
50
Jan-08
50
Jul- 07
60
Jan-07
60
Jul- 06
70
Jan-06
80
Jul- 05
100
Jan-05
110
Jul- 04
130
Jan-04
Irregular component
Jul- 03
Jan-10
Jan-09
Jan-08
Jan-07
Jan-06
Jan-05
Jan-04
Jan-03
50
Jan-03
60
Jan-02
80
Jul- 02
120
Jan-02
90
Jan-01
90
Jul- 01
100
Jan-01
80
Jan-00
130
Jul- 00
Jan-10
Jan-09
Jan-08
Jan-07
Jan-06
Jan-05
Jan-04
Jan-03
Original component
Jan-00
Jan-10
Jan-09
Jan-08
Jan-07
Jan-06
Jan-05
Jan-04
Jan-03
120
Jan-02
Jan-01
Jan-00
140
Jan-02
Jan-01
Jan-00
Index 2005=100
Relation of Components
Components of the Industrial Production Index of Kazakhstan
Seasonal component
120
110
110
100
70
70
60
50
Trend-Cycle Component
120
110
90
100
90
80
70
Slide 5
Seasonal Component
= Depicts systematic, calendar-related
movements
 has a similar pattern from year to year
 refers 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 6
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 nonsampling error (not necessarily random)
March 2011
UNECE Statistical Division
Slide 7
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 8
IPI – Kazakhstan
An Example of the Components of Time Series
140
120
110
100
90
80
70
60
Original
March 2011
Seasonally adjusted
UNECE Statistical Division
Jul-10
Jan-10
Jul-09
Jan-09
Jul-08
Jan-08
Jul-07
Jan-07
Jul-06
Jan-06
Jul-05
Jan-05
Jul-04
Jan-04
Jul-03
Jan-03
Jul-02
Jan-02
Jul-01
Jan-01
Jul-00
50
Jan-00
Index 2005=100
130
Trend
Slide 9
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:





March 2011
The calendar
Christmas and New Year
Social habits (the holiday season),
Business (quarterly provisional tax payments) and
Administrative procedures (tax returns)
UNECE Statistical Division
Slide 10
Seasonality
Industrial production in Moldova, original series 2000-2008
150
140
130
2000
2001
Index 2005=100
120
2002
2003
110
2004
100
2005
2006
90
2007
2008
80
70
60
1
March 2011
2
3
4
5
6
months
7
8
9
UNECE Statistical Division
10
11
12
Slide 11
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 12
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 13
Trading Days
Saturday
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 14
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 15
Moving Holidays
Impact of moving holidays to the number of working days
Ascension day
Christmas moves between
weekdays and weekend
25
average working days
20
15
2009
2010
2011
10
5
0
Jan
March 2011
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
UNECE Statistical Division
Oct
Nov
Dec
Slide 16
Working Days and Seasonality
Example of average working days in 2009 - 2011
25
average working days
20
15
2009
2010
2011
10
5
0
Jan
March 2011
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
UNECE Statistical Division
Nov
Dec
Slide 17
Sudden Changes

Outliers
•
•

Trend breaks (level shifts)
•
•

Extreme values with identifiable causes (strikes or
extreme weather conditions)
Part of irregular component
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 18
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
•
•
March 2011
Presence of seasonality, moderate volatility
No major breaks in seasonal behaviour
UNECE Statistical Division
Slide 19