Transcript A Painless Introduction to Seasonal Adjustment

A Painless Introduction to
Seasonal Adjustment
Brian C. Monsell
U. S. Census Bureau
[email protected]
April 19, 2009
Outline
• Review some basic concepts
– Definitions of components
• Current methods and software
• Future Developments
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What is a time series?
• In economics, we usually define time series
as “a set of values of a variable collected
at a regular interval”
• Time series are correlated observations over
time
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Purpose of seasonal adjustment
• Bell and Hillmer (1984)
• “Seasonal adjustment is done to simplify the data so
that they may be more easily interpreted … without a
significant loss of information”
• Large seasonal movements can obscure other
movements of importance.
• Easier to see related movements in different
series
5
Background:
Components of a Time Series
• Y=CxSxI
(or C + S + I)
where
• Y = Original series
• C = Trend-cycle
• S = Seasonal effects (+ other effects)
• I = Irregular
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Trend-Cycle
• Level of the series
– Local level estimates for the purpose of estimating
seasonal factors
• Reasonably smooth, includes movements
and cycles that last longer than a year
– Find turning points in the trend
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Seasonal Effects
• Reasonably stable in terms of
– Annual timing
• Within same month or quarter
– Direction
– Magnitude
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Irregular Effects
• Unpredictable in terms of
– Timing
– Impact
– Duration
• Residual after removing seasonal and trend
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Types of Decompositions
Multiplicative
Yt = StCtIt
At = CtIt
Additive
Yt = St+Ct+It
At = Ct+It
Yt
Ct
St
It
Original series
Trend-Cycle component
Seasonal component
Irregular component
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Calendar Effects
• Trading or Working Day:
– Effects related to:
• Which weekdays (Mondays,…, Sundays) occur five
times in a month
• Effects of variable length of February.
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August 2007
Sun
Mon
Tue
5
12
19
26
6
13
20
27
7
14
21
28
Wed
1
8
15
22
29
Thu
2
9
16
23
30
Fri
3
10
17
24
31
Sat
4
11
18
25
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August 2008
Sun
Mon
Tue
Wed
Thu
3
10
17
24
31
4
11
18
25
5
12
19
26
6
13
20
27
7
14
21
28
Fri
1
8
15
22
29
Sat
2
9
16
23
30
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Calendar Effects (Continued)
• Moving Holidays:
– Effects of holidays
• With changing dates
• Which can impact more that one month in a way that
depends on the date.
– Examples : Easter, Chinese New Year, Ramadan,
etc
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Current methods (and software) for
seasonal adjustment
• Non-parametric methods
– The X-11 family (U. S. Census Bureau, Statistics
Canada)
– SABL (Bell Labs)
– STL (Seasonal-Trend Loess – Bell Labs)
• Parametric (model-based) methods
– TRAMO/SEATS (Bank of Spain)
– STAMP (Andrew Harvey)
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“X-11” Family
X-11
X-11-ARIMA
X-12-ARIMA
X-13-ARIMA-SEATS
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X-11 (US Census)
• Shiskin, Young, and Musgrave (1967)
– First computerized seasonal adjustment program
(X=eXperimental)
• Features include:
– Treatment of extreme values (robustness)
– Trading day effect estimation
– Variety of moving averages for estimating evolving seasonal
patterns and trends
– One-sided moving averages for the ends of the series
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Example : 3x3 Moving Average
( 13 Yt  2  13 Yt 1  13 Yt ) / 3 
( 13 Yt 1  13 Yt  13 Yt 1 ) / 3 
( 13 Yt  13 Yt 1  13 Yt  2 ) / 3 
1
9
Yt  2  92 Yt 1  13 Yt  92 Yt 1  19 Yt  2
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Problems with X-11?
• Low quality of the asymmetric filters at the
ends of the time series
• Limited filter choices
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X-11-ARIMA
• Developed by Estella Dagum and her team at
Statistics Canada (1980, 1988, 2000)
• Advances include:
– ARIMA Forecast extension
• Reduces Revisions
• Improves quality of the end adjustments
– Quality diagnostics for seasonal adjustment
– Comparison of Direct vrs. Indirect Adjustment of Aggregate
Series
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Main Limitations
• No user-defined regressors for special
situations
• ARIMA modeling not robust against outliers
• Seasonal adjustment not robust against level
shifts
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Level Shift
Level shift at t0
LS regressor
– 1 for t < t0
0 for t  t0
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X-12-ARIMA
• Developed at the Census Bureau – Findley,
Monsell, Bell and Otto (1990)
• Current method for statistical agencies in
United States, UK, Canada, New Zealand,
Japan, and other countries
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Features of X-12-ARIMA
• Wide variety of seasonal and trend filter options;
• Suite of modeling and seasonal adjustment
diagnostics, including
– Spectral diagnostics;
– Diagnostics of the quality and stability of the seasonal
adjustments;
– Out of sample forecast error model selection diagnostics.
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Features of X-12-ARIMA
• Extensive time series modeling and model
selection capabilities
– linear regression models with ARIMA errors
(regARIMA models);
– Automatic model selection options;
– User-defined regression variables.
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RegARIMA Model
 Yt
log 
 D
t

transformation
Xt 


 

 X t  Z t
ARIMA Process
Regressor for trading day and holiday
or calendar effects, additive outliers,
temporary changes, level shifts, ramps,
user-defined effects
Dt  Leap-year adjustment, or
“subjective” strike adjustment, etc.
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Uses of RegARIMA Models in
X-12-ARIMA
• Forecast (and Backcast) extension of series
before applying X-11 filters
• Detect and adjust for outliers and other
distorting effects to improve the forecasts and
seasonal adjustments (automatic option)
• Detect and estimate additional components
(e.g. calendar effects)
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Model Based (Parametric) Seasonal
Adjustment Methods
• TRAMO/SEATS
– Developed at the Bank of Spain by Victor Gomez
and Agustin Maravall (1996)
– Uses ARIMA model as basis for seasonal
decomposition
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Airline Model –
ARIMA(0 1 1)(0 1 1)
(1 - B)(1 – B12) zt = (1 - B)(1 - 12B12) at
• Can infer
– A model for the seasonality from seasonal MA term
– A model for the trend from the nonseasonal MA term
• Hillmer and Tiao (1978)
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TRAMO/SEATS (Bank of Spain)
• Consists of two linked programs
– TRAMO is a complete regARIMA modeling
package, with automatic identification of ARIMA
models, outliers and other components
– SEATS takes modeling results from TRAMO and
performs a model-based signal extraction
• Used by European statistical agencies
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Advantages of SEATS
• The adjustment filter is determined by a
model, not a finite set of moving average
filters.
• In practice, SEATS sometimes gives
smoother adjustments with smaller revisions
for some irregular Census Bureau series
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What’s Next?
X-13ARIMA-SEATS =
X-13A-S =
X-12-ARIMA + SEATS
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What is X-13A-S?
• Users can choose between model-based seasonal
adjustments from SEATS and non-parametric
adjustments with X-11.
• Collaboration between the U. S. Census Bureau and
the current developers of SEATS, Agustin Maravall
of the Bank of Spain and Gianluca Caporello.
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Why X-13A-S?
• Allows users to
– generate X-11 and SEATS seasonal adjustments
using the same interface
– compare X-11 and SEATS seasonal adjustments
using a common set of diagnostics
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Contact Information
[email protected]
Brian Monsell
U.S. Census Bureau
SRD, Room 5K018
Washington DC 20233
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For more information about X-11
“Seasonal Adjustment with the X-11 Method”,
by Dominique Ladiray and Benoît
Quenneville (2001), Springer
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TRAMO/SEATS
• Bank of Spain website
www.bde.es/servicio/software/econome.htm
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X-12-ARIMA Web Site
X-12 Download Site
www.census.gov/srd/www/x12a
OR
–
–
–
–
Access www.census.gov
Choose “A to Z Index”
Choose “X”
Link to X-12-ARIMA Website
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