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Census Bureau Seasonal Adjustment Software and Research

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Title: Census Bureau Seasonal Adjustment Software and Research


1
Census Bureau Seasonal Adjustment Software and
Research
  • David.F.Findley_at_census.gov
  • U S C E N S U S B U R E A
    U

2
Outline of Talk Software
  • X-12-ARIMA and its Evolution to
    X-12-ARIMA/SEATS
  • Windows version ( Jurgen Doornik GiveWin)
  • Supporting software
  • Genhol (holiday regressors)
  • SAS Software
  • X-12-Graph (14 types of diagnostic graphs)
  • Interface (simplifies analyses sets of series)
  • X-12-Write (easy prod./modif. of .spc files)
  • X-12-Review (1 page diagnostic summaries)

3
Outline of Talk Research
  • TRAMO/SEATS Evaluation Improvement for
    X-12-ARIMA\SEATS (also for short series)
  • Filters and Filter Diagnostics
  • Automatic modeling TRAMO vs. X-12s TRAMO
  • Revisions
  • State-Space Models using Sampling Error Data
  • Non-Gaussian Structural State-Space Models
    for More Stable Resistance to Outliers

4
Statistical Research Division Time Series Group
Research and X-12-ARIMA Programming
  • Brian.C.Monsell
  • Kellie.C.Wills
  • William.R.Bell (honorary)
  • David.F.Findley (honorary)
  • Donald.E.Martin (Part-time, Howard University)
  • Trang.Ta.Nguyen (1-year in-house visitor)
  • John.Alexander.Aston (2-year Post-Doc from
    Imperial College, London)
  • S.J.M. Koopman (Fellow, Free Univ. of Amsterdam)

5
Economic and Statistical Programming
DivisionTime Series Methods BranchResearch and
SAS, Excel Programming
  • Catherine.C.Hood
  • Kathleen.M.McDonald.Johnson
  • Golam.Farooque
  • Roxanne.Feldpausch

6
Outline of Talk Software
  • X-12-ARIMA and its Evolution to
    X-12-ARIMA/SEATS
  • Windows version ( Jurgen Doornik GiveWin)
  • Supporting software
  • Genhol (holiday regressors)
  • SAS Software
  • X-12-Graph (14 types of diagnostic graphs)
  • Interface (simplifies analyses sets of series)
  • X-12-Write (easy prod./modif. of .spc files)
  • X-12-Review (1 page diagnostic summaries)

7
X-12-ARIMA
  • Improvements over StatsCans X-11-ARIMA
  • regARIMA models (including outliers, user-defined
    regressors, etc.) vs. ARIMA models
  • Much more extensive automatic options for
    modeling, including trading day, holiday est.,
    additive vs. multiplicative adjustment
  • More diagnostics (e.g. spectra, revisions)
  • Specialized output files, e.g. log files for
    users favorite diagnostics, from many X-12-Graph
    (SAS, but for non-SAS-users)

8
RegARIMA Models (Forecasts, Backcasts, and
Preadjustments)
Modeling and Model Comparison Diagnostics and
Graphs
X-11 Seasonal Adjustment
Seasonal Adjustment Diagnostics and Graphs
9
REGARIMA Model
transformation
ARIMA Process
Regressors for trading day and holiday or
calendar effects, additive outliers, temporary
changes, level shifts, ramps user-defined effects
Leap-year adjustment, or subjective strike
adjustment, etc.
10
Types of Regression Variables Available in
X-12-ARIMA
  • Outlier and Trend-Change Effects
  • Additive (or Point) Outliers
  • Temporary Change Outliers
  • Level shifts, Ramps
  • Seasonal Effects
  • Calendar month indicators
  • Trigonometric Seasonal (Sines-Cosines)
  • Calendar Effects
  • Trading Day (Flows or Stocks)
  • Leap-year February, Length of Month
  • Shifting Holidays (e.g. Easter)
  • Constant Term
  • User-Defined Effects
  • Two-regime option available
  • Note Regression coefficients can be fixed

11
X-12-ARIMA Releases
  • Ver. 0.2.10 July (Statistics Canada options)
  • Ver. 0.3 Summer (TRAMO-type automatic ARIMA
    model selection)
  • -based on information gleaned from TRAMO code
    provided by Victor Gomez
  • Ver. 1.0 End of year (Better organized output
    and manual, more testing etc.)

12
X-12-ARIMA/SEATS
  • Offers both x11 and seats commands to
    provide X-11 or SEATS type seasonal
    adjustments with X-12-ARIMA diagnostics as well
    as SEATS diagnostics
  • Is being updated from SEATS2000 to SEATS20012002
    (with support from Agustin Maravall and Gianluca
    Caporello)
  • Schizophenic (duplicate) output, currently
  • Distribution for research and testing to
    statistical agencies and central banks in 2003

13
Diagnoses from X-12-ARIMA/SEATS
  • 1. Spectrum diagnostic reveals source of Invalid
    Decomposition problem

14
X-12-A/SEATS COMMAND FILE series
file"serie.txt" format"tramo" transformfunct
ionlog outliercritical3.7 arimamodel(0 1
1)(0 1 1) check x11 seats
15
Message from seats run
  • NOTE Spectral plot for the seasonally adjusted
    series cannot be done when SEATS cannot perform a
    signal extraction.

16
Parameter Estimate
Errors ------------------------------------------
----------- Nonseasonal MA
Lag 1
0.3846 0.12087 Seasonal MA
Lag 12
-0.3665 0.12612
17
10LOG(SPECTRUM) of the regARIMA model
residuals Spectrum estimated from 1990.Jan
to 1995.Oct. I
-22.11I I
I I

-23.34I
I
I
T
I T
-24.57I
T
I
T I
T
I
T -25.81I
T
I
T
18
series file"serie.txt" format"tramo" transfor
mfunctionlog outliercritical3.7 arimamodel
(0 1 1)(0 1 1) check x11 seats
19
X-12-ARIMA/SEATS Seasonal Adjustment
Program Version Number 0.3s Build 24
WARNING At least one visually significant
trading day peak has been found in one or more of
the estimated spectra.
20
G.1 10LOG(SPECTRUM) of the differenced,
transformed seasonally adjusted data. Spectrum
estimated from 1990.Jan to 1995.Oct.
I
I
T I
T
I
T -20.10I
T
I
T I
T
I
T -22.01I
T
I
T I
T
21
series file"serie.txt" format"tramo" transfor
mfunctionlog outliercritical3.7 arimamodel
(0 1 1)(0 1 1) regressionvariablestd check s
eats
22
X-12-ARIMA/SEATS Seasonal Adjustment
Program Version Number 0.3s Build 24 Reading
input spec file from metalss.spc Storing any
program output into metalss.out Storing any
program error messages into metalss.err
WARNING At least one visually significant
seasonal peak has been found in one or more of
the estimated spectra.
23

Standard Parameter
Estimate Errors ------------------------
----------------------------- Nonseasonal MA
Lag 1
0.1995 0.12871 Seasonal
MA Lag
12 0.3843 0.15795
24
X-12-ARIMA Diagnoses for SEATS
  • 2. T/S Practice of adding outliers to improve
    kurtosis, etc. can substantially increase the
    size of revisions of the initial seasonal
    adjustments
  • Example (from Catherine Hood) US Exports of
    Passenger Cars History diagnostic shows cost to
    revisions of adding outlier regressors to reduce
    kurtosis

25
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26
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27
Outline of Talk Software
  • X-12-ARIMA and its Evolution to
    X-12-ARIMA/SEATS
  • Windows version ( Jurgen Doornik GiveWin)
  • Supporting software
  • Genhol (holiday regressors)
  • SAS Utilities
  • X-12-Graph (14 types of diagnostic graphs)
  • Interface (simplifies analyses of many series)
  • X-12-Write (easy prod./modif. of .spc files)
  • X-12-Review (1 page diagnostic summaries)

28
Genhol
  • From holiday date file Generates regressor
    matrices and associated command files to enable
    X-12-ARIMA estimation of complex moving holiday
    effects (e.g. for Easter, Ramadan, etc.).
  • Regressors for up to three intervals
  • before-the-holiday interval
  • surrounding-the-holiday interval
  • past-the-holiday interval (recovery interval)

29
Proportionality Regressors An Example
  • Assume
  • An effect interval is 10 days long, and this year
    2 of its days fall in January and 8 in February.
  • The interval regressors values for this year
    will be
  • 0.2 in January
  • 0.8 in February
  • 0.0 for the rest of the year

30
Interface Program (SAS) for seasonal adjustment
of sets of series
  • Example Seasonally Adjusted Total U.S. Imports
    sum of 140 component series, c. 80 of which
    are seasonally adjusted.
  • What is the effect on the month-to-month changes
    and quality diagnostics of the S. A. Total
    Imports if the seasonal adjustment options are
    changed for 5 of the component series?

31
Outline of Talk Research
  • TRAMO/SEATS Evaluation Improvement for
    X-12-ARIMA\SEATS (also for short series)
  • Filter Diagnostics
  • Automatic modeling TRAMO vs. X-12s TRAMO
  • Revisions

32
Filters and Filter Diagnostics
  • Filter (spectral) diagnostics needed
  • To understand limitations/issues with short
    series (finite filter diagnostics, also for
    concurrent adjustments, trends)
  • To decide between closely competitive models
  • Paper by David Findley and Donald Martin.

33
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34
Outline of Talk Research
  • TRAMO/SEATS Evaluation Improvement for
    X-12-ARIMA\SEATS (also for short series)
  • Automatic modeling TRAMO vs. X-12s TRAMO
  • Accuracy
  • Results from simulated series
  • Revisions
  • Results from Census Bureau series

35
ESMPDs Automatic Modeling Study
  • First presented at the International Forecasters
    Symposium, June 2001
  • Continuation of this work to appear at the ASA
    meetings, August 2002, in a paper by Kathleen
    McDonald-Johnson, et al.

36
Series
  • 306 time series from the US Census Bureaus
    Import/Export series and Retail Sales

37
Results
  • 88 series (29) with same regARIMA model
  • 27 series (9) with same differencing and same
    regressors but different ARMA choices
  • 123 series (40) with same differencing, but
    different regressors
  • 32 series (10) with different nonseasonal
    differencing order (but sometimes offset by a
    constant)
  • 36 series (12) with different seasonal
    differencing order

38
Conclusions
  • TRAMOs weakness is the procedure for deciding
    about trading day modeling
  • TRAMO developers are aware of our results
  • X-12-ARIMA has a problem with choosing
    nonparsimonious models
  • Monsell has already implemented some changes,
    including a unit root test.

39
Why Are Different Models Chosen?
  • Model estimation method is different
  • TRAMO Hannan-Rissanen and m.l.e conditional on
    AR part of model
  • X-12-ARIMA Exact MLE
  • Model residuals are different, which can lead to
    different choices of outliers
  • Outlier procedure itself is different
  • TRAMO removes insignificant outliers after each
    iteration
  • TRAMO uses approximate BIC

40
Accuracy X-12-ARIMA vs T/S (ESMPD)
  • Results from 54 simulated series were first
    presented at the ASA meetings, August 2000
  • Continuation of the first SEATS studies,
    beginning in 1997

41
The Simulated Series
  • Fifty-four series
  • Six different trends three from SEATS and three
    from X-12
  • Six different seasonal factors three from SEATS
    and three from X-12
  • Irregular sampled from three sets of irregular
    factors combined from SEATS and X-12

42
Results of Accuracy Study
  • SEATS performed better on the majority of series
    with large irregulars if the series are 9 years
    long, but most adjustments were not acceptable.
  • Both programs did better than expected on the
    short series, but X-12-ARIMA adjustments were
    usually better than SEATS adjustments on series
    4-7 years long

43
Revisions X-12-ARIMA vs T\S
  • New ESMPD study using X-12-SEATS on Census
    series. Final results will be presented at
    the ASA meetings, August 2002.
  • Can we identify characteristics in the series
    that will indicate if its linearized series
    will be a better candidate for a model-based
    adjustment than for an X-11 filter adjustment or
    vice versa?

44
Methods
  • Use X-12-SEATS to get revision diagnostics from
    both an X-11/X-12-type adjustment and a SEATS
    adjustment
  • Used TRAMO to get the ARIMA model, and then used
    either an x11 or a seats spec

45
Very Preliminary Results
  • 260 US Import/Export series
  • Only a very small subset (18 series) where we can
    see definite differences in the revision
    diagnostics for the seasonal adjustment

46
An Observation Series with
  • Large revisions in X-12 and smaller revisions in
    SEATS had generally large values for ?12 (most
    greater than 0.95) and values for X-12s I/S
    ratio lt 5.
  • Large revisions in SEATS and smaller revisions in
    X-12 had generally 0.4 lt ?12 lt 0.6 and values
    for I/S gt 6.
  • In both cases, smaller revisions are associated
    with more constant seasonal factor estimates

47
Next Steps
  • Look at more series
  • Look at more diagnostics/characteristics of the
    series to try to find patterns, not just revisions

48
Outline of Talk Research
  • Projects almost ready to yield results
  • State-Space Models using Sampling Error Data
  • Non-Gaussian Structural State-Space Models
    for More Stable Resistance to Outliers

49
State-Space Models with Sampling Error
Statistics Bell and Nguyen
  • 100 Disaggregate Construction series with high
    sampling error variances
  • Consider model-based adjustment with
  • regARIMAobservation error
  • models that incorporate sampling error variance
    and autocovariance estimates to achieve
    acceptable or better seasonal adjs.
  • (Need state-space for model est. seas adj.)

50
Non-Gaussian Structural State-Space Models for
More Stable Resistance to Outliers Koopman
and Aston
  • X-12-ARIMA and T\S use outlier regressors
    identified by t-statistics and critical values.
    Identifications can change as new data arrive,
    causing seasonal adjustment revisions.
  • Use heavy tailed non-Gaussian models instead of
    critical values. (Hard to estimate such models,
    simplest for Harveys structural models)

51
More Information
  • WWW site for X-12-ARIMA (papers and software)
  • www.census.gov/srd/www/x12a

52
  • Thanks to Catherine Hood for supplying some of
    these slides.
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