Census Bureau Seasonal Adjustment Software and Research

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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

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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)
  

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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

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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)

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Economic and Statistical Programming
DivisionTime Series Methods BranchResearch and
SAS, Excel Programming

• Catherine.C.Hood
• Kathleen.M.McDonald.Johnson
• Golam.Farooque
• Roxanne.Feldpausch

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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)
  

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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)

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RegARIMA Models (Forecasts, Backcasts, and
Preadjustments)
Modeling and Model Comparison Diagnostics and
Graphs
X-11 Seasonal Adjustment
Seasonal Adjustment Diagnostics and Graphs
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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.
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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

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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.)

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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

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Diagnoses from X-12-ARIMA/SEATS

• 1. Spectrum diagnostic reveals source of Invalid
  Decomposition problem

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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
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Message from seats run

• NOTE Spectral plot for the seasonally adjusted
  series cannot be done when SEATS cannot perform a
  signal extraction.

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Parameter Estimate
Errors ------------------------------------------
----------- Nonseasonal MA
Lag 1
0.3846 0.12087 Seasonal MA
Lag 12
-0.3665 0.12612
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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
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series file"serie.txt" format"tramo" transfor
mfunctionlog outliercritical3.7 arimamodel
(0 1 1)(0 1 1) check x11 seats
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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.
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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
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series file"serie.txt" format"tramo" transfor
mfunctionlog outliercritical3.7 arimamodel
(0 1 1)(0 1 1) regressionvariablestd check s
eats
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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.
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Standard Parameter
Estimate Errors ------------------------
----------------------------- Nonseasonal MA
Lag 1
0.1995 0.12871 Seasonal
MA Lag
12 0.3843 0.15795
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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

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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)
  

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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)

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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

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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?

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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

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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.

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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

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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.

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Series

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

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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

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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.

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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

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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

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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

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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

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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?

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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

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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

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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

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Next Steps

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

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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

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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.)

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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)

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More Information

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

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