Reading input spec file from Rout.spc

Reading data from Rout.dat

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U. S. Department of Commerce, U. S. Census Bureau

X-13ARIMA-SEATS monthly seasonal adjustment Method,
Release Version 1.1 Build 39

 

This software application provides an enhanced version of
Statistics Canada's X-11-ARIMA extension (Dagum, 1980)
of the X-11 variant of the Census Method II of
Shiskin, Young and Musgrave (1967).

It also provides an ARIMA model-based method following
Hillmer and Tiao (1982) and Burman (1980) that is very similar
to the update of the method of SEATS (Gómez and Maravall, 1996)
produced at the Bank of Spain by G. Caporello and
A. Maravall for TSW (Caporello and Maravall, 2004).
The present application includes additional enhancements.

X-13ARIMA-SEATS includes an automatic ARIMA model selection procedure
based largely on the procedure of Gómez and Maravall (1998)
as implemented in TRAMO (1996) and subsequent revisions.

Primary Programmers: Brian Monsell, Mark Otto and,
for the ARIMA model-based signal extraction,
Gianluca Caporello and Víctor Gómez

Series Title- R Output for x12a
Series Name- Rout
Aug 5, 2021 03.07.21

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FILE SAVE REQUESTS (* indicates file exists and will be overwritten)

Rout.a1 time series data (for the span analyzed)
Rout.b1 original series (prior adjusted)
Rout.ftr point forecasts and standard errors for the transformed data
Rout.d10 final seasonal factors
Rout.d11 final seasonally adjusted data
Rout.d12 final trend cycle
Rout.html* program output file
Rout_err.html* program error file
Rout.udg seasonal adjustment and model diagnostics file
Rout.gmt graphics metafile

 

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LINKS TO OTHER HTML FILES

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Contents of spc file Rout.spc

 Line #
 ------
      1: series{
      2: save=(a1 b1)
      3: title="R Output for x12a"
      4: start=2004.1
      5: period=12
      6: DECIMALS=5
      7: file = "Rout.dat"
      8: }
      9: transform{
     10: function=auto
     11: }
     12: automdl{
     13: acceptdefault=no
     14: balanced=yes
     15: maxorder=(3,2)
     16: maxdiff=(1,1)
     17: savelog=(adf amd b5m mu)
     18: }
     19: forecast {
     20: save=ftr
     21: maxlead=12
     22: }
     23: x11{
     24: save=(d10 d11 d12)
     25: sigmalim=(1.5,2.5)
     26: final=(user)
     27: appendfcst=yes
     28: savelog=all
     29: }

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Likelihood statistics for model fit to untransformed series.

Likelihood Statistics
Number of observations (nobs) 182
Effective number of observations (nefobs) 169
Number of parameters estimated (np) 3
Log likelihood (L) 181.4587
AIC -356.9175
AICC (F-corrected-AIC) -356.7720
Hannan Quinn -353.1070
BIC -347.5278

 

Likelihood statistics for model fit to log transformed series.

Likelihood Statistics
Number of observations (nobs) 182
Effective number of observations (nefobs) 169
Number of parameters estimated (np) 3
Log likelihood 561.8948
Transformation Adjustment -381.3013
Adjusted Log likelihood (L) 180.5935
AIC -355.1870
AICC (F-corrected-AIC) -355.0416
Hannan Quinn -351.3765
BIC -345.7973

 

***** AICC (with aicdiff=-2.00) prefers log transformation *****

***** Multiplicative seasonal adjustment will be performed. ****

 

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A 1 Time series data (for the span analyzed)

From 2004.Jan to 2019.Feb
Observations 182

A 1 Time series data (for the span analyzed)
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTAL
2004 8.30500 8.27638 8.50826 8.43936 8.48784 8.48070 8.50011 8.54934 8.52512 8.56815 8.58128 8.66497 101.88651
2005 8.67987 8.64835 8.85946 8.77174 8.80259 8.78589 8.71676 8.81351 8.76370 8.64931 8.67314 8.72639 104.89071
2006 8.82230 8.76147 8.98844 8.83732 9.00018 8.89432 8.94382 9.01945 8.90435 8.95963 8.99416 8.96619 107.09163
2007 9.12564 9.04930 9.22503 9.13748 9.34486 9.18490 9.22699 9.27534 9.13175 9.30097 9.29360 9.24955 110.54541
2008 9.29754 9.24670 9.42923 9.37419 9.31325 9.27350 9.32553 9.18949 9.25250 9.14100 9.06158 9.00418 110.90869
2009 9.09885 9.10353 9.34143 9.44472 9.37564 9.41981 9.41822 9.38213 9.32515 9.36262 9.33849 9.31112 111.92171
2010 9.31998 9.35898 9.64014 9.50192 9.55990 9.53590 9.54589 9.63813 9.57358 9.48729 9.59035 9.54797 114.30003
2011 9.44000 9.57018 9.62245 9.54860 9.69091 9.69295 9.65034 9.75452 9.69363 9.59342 9.74724 9.62245 115.62669
2012 9.64147 9.62688 9.72448 9.74355 9.91398 9.83916 9.77064 9.84188 9.60319 9.82379 9.73430 9.62199 116.88531
2013 9.82828 9.79484 9.87349 9.96515 9.96599 9.88914 9.90504 9.96077 9.82698 9.88680 9.80405 9.76503 118.46556
2014 9.85666 10.00374 9.84044 9.90053 9.92945 9.90319 9.89212 9.81192 9.85713 10.11529 9.93101 9.86646 118.90794
2015 9.83489 9.77474 9.95385 9.85019 9.83092 9.85435 9.80978 9.79183 9.80565 9.59533 9.73026 9.69708 117.52887
2016 9.62371 9.69295 9.75719 9.71299 9.75754 9.80824 9.72119 9.79646 9.56437 9.68868 9.68949 9.63247 116.44528
2017 9.74285 9.74678 9.89651 9.76623 10.03998 9.98082 9.86287 9.95513 9.84055 9.92701 9.91936 9.89202 118.57011
2018 10.02942 9.90962 10.02637 10.04507 10.12479 10.10545 10.10932 10.18964 10.02615 10.20806 10.11168 10.11022 120.99579
2019 10.22325 10.19526                     20.41851
AVGE 9.42936 9.42248 9.51245 9.46927 9.54252 9.50989 9.49324 9.53130 9.44625 9.48716 9.48000 9.44521  

Table Total- 1725.38875     Mean- 9.48016     Standard Deviation- 0.46621
Minimum- 8.27638     Maximum- 10.22325

 

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Automatic ARIMA Model Selection

Procedure based closely on TRAMO ,method of Gomez and Maravall (2000)
"Automatic Modeling Methods for Univariate Series",
A Course in Time Series (Edited by D. Pena, G. C. Tiao, R. S. Tsay),
New York : J. Wiley and Sons

Maximum order for regular ARMA parameters : 3

Maximum order for seasonal ARMA parameters : 2

Maximum order for regular differencing : 1

Maximum order for seasonal differencing : 1

Results of Unit Root Test for identifying orders of differencing:

Regular difference order : 1 Seasonal difference order : 0

Mean is not significant.

Preliminary model choice : (3 1 2)(1 0 1)

 

Final Checks for Identified Model

 

Checking for Unit Roots.

Seasonal unit root found.

( 3, 1, 2) ( 0, 1, 1)

 

Checking for nonseasonal overdifferencing.

Nonseasonal MA not within 0.001 of 1.0 - model passes test.

 

Checking for insignificant ARMA coefficients.

Final automatic model choice : (3 1 2)(0 1 1)

End of automatic model selection procedure.

Average absolute percentage error in within-sample forecasts:

Last year: 0.92
Last-1 year: 1.04
Last-2 year: 0.64
Last three years: 0.87

Estimation converged in 84 ARMA iterations, 594 function evaluations.

 

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ARIMA Model

ARIMA Model: (3 1 2)(0 1 1)

Nonseasonal differences: 1
Seasonal differences: 1

ARIMA Model
  Estimate Standard Error
Nonseasonal AR
Lag 1 -1.57750 0.06636
Lag 2 -1.47777 0.07712
Lag 3 -0.40947 0.06627
Nonseasonal MA
Lag 1 -1.18430 0.03055
Lag 2 -1.00000 0.03465
Seasonal MA
Lag 12 0.86047 0.04400

 

Model Innovation Variance
Variance 0.55838E-04
Standard Error of Variance 0.60744E-05

 

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Likelihood Statistics
Number of observations (nobs) 182
Effective number of observations (nefobs) 169
Number of parameters estimated (np) 7
Log likelihood 576.5353
Transformation Adjustment -381.3013
Adjusted Log likelihood (L) 195.2340
AIC -376.4679
AICC (F-corrected-AIC) -375.7722
Hannan Quinn -367.5767
BIC -354.5586

 

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Durbin-Watson Statistic for regARIMA Model Residuals

dw = 2.169632

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Friedman Non-Parametric Test for regARIMA Model Residuals

ken = 2.274725 ( Asymptotically distributed as Chi-Square(11), P-Value = 0.997274 )

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QS Statistic for regARIMA Model Residuals

QS Statistic for regARIMA Model Residuals (full series): 0.00 (P-Value = 1.0000)

QS Statistic for regARIMA Model Residuals (starting 2011.Mar): 0.00 (P-Value = 1.0000)

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10*LOG(SPECTRUM) of the regARIMA model residuals

Spectrum estimated from 2011.Mar to 2019.Feb.

 ++++++++++I+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++I
     -34.71I                                             *               I    -34.71
           I                                             *               I
           I                                             *               I
           I                                             *               I
     -36.00I                                             *               I    -36.00
           I                                             *               I
           I                                             *               I
           I                                             *               I
     -37.28I                                             *               I    -37.28
           I                                             *               I
           I                             *               *               I
           I                         *   *               *               I
     -38.56I                        **   *               **              I    -38.56
           I                        **   *               **              I
           I                        **  **    *          **              I
           I                        **  **    *          **     T        I
     -39.84I                        **  **    *          **     T       SI    -39.84
           I                        **  **    **         **     T       SI
           I             *          **  **    **         **     T       SI
           I            **          **  **    **         **     T       SI
     -41.13I            **          *** **S   **        ***     T       SI    -41.13
           I            **          ******S   **        ***     T* *    SI
           I            **         *******S   **        ***     T* *    SI
           I  *         **         *******S  ***        ***    *T* *    SI
     -42.41I  *         **         *******S  ***        ****   *T***    SI    -42.41
           I **         **       *********S  ***        ****   *T****   SI
           I **         **   *   *********S  ***   *    ****   *T****  *SI
           I **         **   *  S*********S* ***   *    ****   *T****  *SI
     -43.69I **         **   *  S*********S******  *    ****   *T****  *SI    -43.69
           I **         **   ** S*********S******  *    ****   *T****  *SI
           I **         **   ***S*********S******  *S   ****  S*T****  *SI
           I***         **  ****S*********S****** **S   ***** S*T****  *SI
     -44.97I***         **  ****S*********S*********S   ***** S*T***** *SI    -44.97
           I***    **   **  ****S*********S*********S   ******S*T***** *SI
           I***    **   *** ****S*********S*********S   ******S*T*******SI
           I***    **   *** ****S*********S*********S* *******S*T*******SI
     -46.26I***    **   ********S*********S*********S* *******S*T*******SI    -46.26
           I***    **   ********S*********S*********S* *******S*T*******SI
           I***    **   ********S*********S*********S*T*******S*T*******SI
           I***    **   ********S*********S*********S*T*******S*T*******SI
     -47.54I****   **  *********S*********S*********S*T*******S*T*******SI    -47.54
           I****   **  *********S*********S*********S*T*******S*T*******SI
           I****   **  *********S*********S*********S*T*******S*T*******SI
           I****   **  *********S*********S*********S*T*******S*T*******SI
     -48.82I****   *** *********S*********S*********S*T*******S*T*******SI    -48.82
           I****   *** *********S*********S*********S*T*******S*T*******SI
           I****   *** *********S*********S*********S*T*******S*T*******SI
           I****  ****S*********S*********S*********S*T*******S*T*******SI
     -50.10I****  ****S*********S*********S*********S*T*******S*T*******SI    -50.10
           I****  ****S*********S*********S*********S*T*******S*T*******SI
           I***** ****S*********S*********S*********S*T*******S*T*******SI
           I***** ****S*********S*********S*********S*T*******S*T*******SI
     -51.39I**********S*********S*********S*********S*T*******S*T*******SI    -51.39
 ++++++++++I+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++I
            S=SEASONAL FREQUENCIES, T=TRADING DAY FREQUENCIES

 

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FORECASTING

Origin : 2019.Feb
Number : 12

Forecasts and Standard Errors of the Transformed Data
Date Forecast Standard
Error
2019.Mar 2.33430 0.747247E-02
2019.Apr 2.33543 0.874056E-02
2019.May 2.33715 0.103802E-01
2019.Jun 2.33769 0.116105E-01
2019.Jul 2.33749 0.128295E-01
2019.Aug 2.33556 0.138451E-01
2019.Sep 2.32997 0.148565E-01
2019.Oct 2.33719 0.157967E-01
2019.Nov 2.32980 0.166407E-01
2019.Dec 2.33167 0.174953E-01
2020.Jan 2.33744 0.182933E-01
2020.Feb 2.33192 0.190291E-01

 

Confidence intervals with coverage probability ( 0.95000)
On the Original Scale
Date Lower Forecast Upper
2019.Mar 10.1721 10.3222 10.4745
2019.Apr 10.1584 10.3339 10.5125
2019.May 10.1432 10.3517 10.5645
2019.Jun 10.1242 10.3573 10.5957
2019.Jul 10.0980 10.3552 10.6189
2019.Aug 10.0585 10.3352 10.6195
2019.Sep 9.98263 10.2776 10.5812
2019.Oct 10.0365 10.3521 10.6776
2019.Nov 9.94614 10.2759 10.6166
2019.Dec 9.94805 10.2951 10.6542
2020.Jan 9.99002 10.3547 10.7327
2020.Feb 9.92072 10.2977 10.6890

 

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B 1 Original series (prior adjusted)

From 2004.Jan to 2019.Feb
Observations 182

B 1 Original series (prior adjusted)
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTAL
2004 8.30500 8.27638 8.50826 8.43936 8.48784 8.48070 8.50011 8.54934 8.52512 8.56815 8.58128 8.66497 101.88651
2005 8.67987 8.64835 8.85946 8.77174 8.80259 8.78589 8.71676 8.81351 8.76370 8.64931 8.67314 8.72639 104.89071
2006 8.82230 8.76147 8.98844 8.83732 9.00018 8.89432 8.94382 9.01945 8.90435 8.95963 8.99416 8.96619 107.09163
2007 9.12564 9.04930 9.22503 9.13748 9.34486 9.18490 9.22699 9.27534 9.13175 9.30097 9.29360 9.24955 110.54541
2008 9.29754 9.24670 9.42923 9.37419 9.31325 9.27350 9.32553 9.18949 9.25250 9.14100 9.06158 9.00418 110.90869
2009 9.09885 9.10353 9.34143 9.44472 9.37564 9.41981 9.41822 9.38213 9.32515 9.36262 9.33849 9.31112 111.92171
2010 9.31998 9.35898 9.64014 9.50192 9.55990 9.53590 9.54589 9.63813 9.57358 9.48729 9.59035 9.54797 114.30003
2011 9.44000 9.57018 9.62245 9.54860 9.69091 9.69295 9.65034 9.75452 9.69363 9.59342 9.74724 9.62245 115.62669
2012 9.64147 9.62688 9.72448 9.74355 9.91398 9.83916 9.77064 9.84188 9.60319 9.82379 9.73430 9.62199 116.88531
2013 9.82828 9.79484 9.87349 9.96515 9.96599 9.88914 9.90504 9.96077 9.82698 9.88680 9.80405 9.76503 118.46556
2014 9.85666 10.00374 9.84044 9.90053 9.92945 9.90319 9.89212 9.81192 9.85713 10.11529 9.93101 9.86646 118.90794
2015 9.83489 9.77474 9.95385 9.85019 9.83092 9.85435 9.80978 9.79183 9.80565 9.59533 9.73026 9.69708 117.52887
2016 9.62371 9.69295 9.75719 9.71299 9.75754 9.80824 9.72119 9.79646 9.56437 9.68868 9.68949 9.63247 116.44528
2017 9.74285 9.74678 9.89651 9.76623 10.03998 9.98082 9.86287 9.95513 9.84055 9.92701 9.91936 9.89202 118.57011
2018 10.02942 9.90962 10.02637 10.04507 10.12479 10.10545 10.10932 10.18964 10.02615 10.20806 10.11168 10.11022 120.99579
2019 10.22325 10.19526                     20.41851
AVGE 9.42936 9.42248 9.51245 9.46927 9.54252 9.50989 9.49324 9.53130 9.44625 9.48716 9.48000 9.44521  

Table Total- 1725.38875     Mean- 9.48016     Standard Deviation- 0.46621
Minimum- 8.27638     Maximum- 10.22325

 

B 1.A Forecasts of (prior adjusted) original series

From 2019.Mar to 2020.Feb
Observations 12

B 1.A Forecasts of (prior adjusted) original series
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTAL
2019     10.32220 10.33391 10.35172 10.35727 10.35517 10.33522 10.27758 10.35210 10.27588 10.29508 103.25613
2020 10.35470 10.29771                     20.65241

 

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C 17 Final weights for irregular component

From 2004.Jan to 2019.Feb
Observations 182

Lower sigma limit : 1.50
Upper sigma limit : 2.50

C 17 Final weights for irregular component
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec S.D.
2004 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 92.69483 0.34774
2005 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 96.50137 3.81062 100.00000 100.00000 0.34774
2006 100.00000 100.00000 100.00000 91.97246 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 0.34774
2007 89.00596 100.00000 100.00000 100.00000 0.00000 100.00000 100.00000 100.00000 0.00000 100.00000 100.00000 100.00000 0.35263
2008 100.00000 100.00000 100.00000 99.35417 100.00000 100.00000 100.00000 34.49800 0.00000 100.00000 100.00000 100.00000 0.37252
2009 100.00000 100.00000 100.00000 0.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 0.40914
2010 100.00000 100.00000 0.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 0.46897
2011 30.34565 100.00000 100.00000 98.32396 100.00000 100.00000 100.00000 100.00000 100.00000 77.31288 100.00000 100.00000 0.43826
2012 100.00000 100.00000 100.00000 100.00000 97.63867 100.00000 100.00000 100.00000 0.00000 28.12856 100.00000 76.26060 0.44650
2013 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 0.50382
2014 100.00000 0.00000 100.00000 100.00000 100.00000 100.00000 100.00000 0.00000 100.00000 0.00000 100.00000 100.00000 0.47643
2015 100.00000 100.00000 73.94515 100.00000 100.00000 100.00000 100.00000 100.00000 0.00000 0.00000 100.00000 100.00000 0.41065
2016 82.51951 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 0.39917
2017 100.00000 100.00000 100.00000 0.00000 0.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 0.38589
2018 98.62672 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 100.00000 0.37971
2019 100.00000 100.00000                     0.37971

 

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D 8 Final unmodified SI ratios

From 2004.Jan to 2019.Feb
Observations 182

D 8 Final unmodified SI ratios
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2004 99.87749 99.19881 101.59556 100.37415 100.56426 100.12028 99.98144 100.15725 99.44234 99.52087 99.28467 99.92488 100.00350
2005 99.81858 99.24238 101.50668 100.36835 100.59318 100.29922 99.45654 100.55194 99.98696 98.66147 98.88042 99.37494 99.89506
2006 100.27660 99.34395 101.62184 99.62467 101.20586 99.78340 100.11611 100.73537 99.19503 99.51260 99.57618 98.95427 99.99549
2007 100.44588 99.39108 101.15432 100.04682 102.12528 100.11525 100.22786 100.34743 98.40808 99.91207 99.60418 99.01227 100.06588
2008 99.52922 99.07911 101.18900 100.78717 100.34089 100.14782 100.99119 99.82919 100.83198 99.88316 99.17100 98.54504 100.02706
2009 99.38652 99.06941 101.18585 101.83496 100.71358 100.93209 100.75497 100.26940 99.58677 99.90002 99.51775 99.05155 100.18357
2010 98.94904 99.18821 102.01194 100.38344 100.81860 100.38923 100.28991 101.03437 100.12135 98.99430 99.90315 99.39278 100.12303
2011 98.28164 99.69902 100.31466 99.56222 100.97658 100.82147 100.13115 100.93975 100.07010 98.88286 100.40606 99.11109 99.93305
2012 99.29709 99.09033 99.97068 100.01055 101.60386 100.71699 99.99731 100.78093 98.38805 100.63710 99.59819 98.21789 99.85908
2013 100.04434 99.44068 100.03248 100.84516 100.81372 100.04990 100.24509 100.84555 99.52317 100.15464 99.34803 98.99990 100.02855
2014 99.97131 101.49469 99.86312 100.47382 100.72718 100.36552 100.08339 99.06691 99.36215 101.88340 100.03868 99.50633 100.23638
2015 99.39482 99.02924 101.09238 100.26628 100.27002 100.68795 100.37924 100.31770 100.54860 98.45643 99.91342 99.65168 100.00065
2016 98.97718 99.77085 100.48360 100.03514 100.48530 101.00415 100.13438 100.96244 98.60824 99.88101 99.78076 98.97819 99.92510
2017 99.80657 99.51485 100.74676 99.19329 101.79421 101.05474 99.73571 100.50792 99.15351 99.81582 99.56378 99.15866 100.00382
2018 100.45059 99.19166 100.27140 100.32299 100.91183 100.44132 100.16992 100.67489 98.82347 100.41021 99.27132 99.06838 100.00067
2019 99.98550 99.50626                     99.74588
AVGE 99.65577 99.45316 100.86935 100.27527 100.92962 100.46196 100.17961 100.46807 99.46999 99.76707 99.59051 99.12986  

Table Total- 18202.86236     Mean- 100.01573     Standard Deviation- 0.79330
Minimum- 98.21789     Maximum- 102.12528

 

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D 8.A F-tests for seasonality

 

Test for the presence of seasonality assuming stability.
  Sum of
Squares
Degrees of
Freedom
Mean
Square
F-value
Between months 57.9430 11 5.268 15.835**
Residual 56.55019 170 0.333  
Total 114.49320 181    

 

**Seasonality present at the 0.1 per cent level.

 

 

Nonparametric Test for the Presence of Seasonality Assuming Stability
Kruskal-Wallis statistic Degrees of Freedom Probability level
99.4969 11 0.000%

 

Seasonality present at the one percent level.

 

Moving Seasonality Test
  Sum of
Squares
Degrees of
Freedom
Mean
Square
F-value
Between Years 1.3064 14 0.093 0.446
Error 32.22171 154 0.209  

 

No evidence of moving seasonality at the five percent level.

 

COMBINED TEST FOR THE PRESENCE OF IDENTIFIABLE SEASONALITY

IDENTIFIABLE SEASONALITY PRESENT

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D 8.B Final unmodified SI ratios, with labels for outliers and extreme values

From 2004.Jan to 2019.Feb
Observations 182

D 8.B Final unmodified SI ratios, with labels for outliers and extreme values
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
2004 99.87749 99.19881 101.59556 100.37415 100.56426 100.12028 99.98144 100.15725 99.44234 99.52087 99.28467 99.92488   * Link to definition of *
2005 99.81858 99.24238 101.50668 100.36835 100.59318 100.29922 99.45654 100.55194 99.98696   * Link to definition of * 98.66147   * Link to definition of * 98.88042 99.37494
2006 100.27660 99.34395 101.62184 99.62467   * Link to definition of * 101.20586 99.78340 100.11611 100.73537 99.19503 99.51260 99.57618 98.95427
2007 100.44588   * Link to definition of * 99.39108 101.15432 100.04682 102.12528   * Link to definition of * 100.11525 100.22786 100.34743 98.40808   * Link to definition of * 99.91207 99.60418 99.01227
2008 99.52922 99.07911 101.18900 100.78717   * Link to definition of * 100.34089 100.14782 100.99119 99.82919   * Link to definition of * 100.83198   * Link to definition of * 99.88316 99.17100 98.54504
2009 99.38652 99.06941 101.18585 101.83496   * Link to definition of * 100.71358 100.93209 100.75497 100.26940 99.58677 99.90002 99.51775 99.05155
2010 98.94904 99.18821 102.01194   * Link to definition of * 100.38344 100.81860 100.38923 100.28991 101.03437 100.12135 98.99430 99.90315 99.39278
2011 98.28164   * Link to definition of * 99.69902 100.31466 99.56222   * Link to definition of * 100.97658 100.82147 100.13115 100.93975 100.07010 98.88286   * Link to definition of * 100.40606 99.11109
2012 99.29709 99.09033 99.97068 100.01055 101.60386   * Link to definition of * 100.71699 99.99731 100.78093 98.38805   * Link to definition of * 100.63710   * Link to definition of * 99.59819 98.21789   * Link to definition of *
2013 100.04434 99.44068 100.03248 100.84516 100.81372 100.04990 100.24509 100.84555 99.52317 100.15464 99.34803 98.99990
2014 99.97131 101.49469   * Link to definition of * 99.86312 100.47382 100.72718 100.36552 100.08339 99.06691   * Link to definition of * 99.36215 101.88340   * Link to definition of * 100.03868 99.50633
2015 99.39482 99.02924 101.09238   * Link to definition of * 100.26628 100.27002 100.68795 100.37924 100.31770 100.54860   * Link to definition of * 98.45643   * Link to definition of * 99.91342 99.65168
2016 98.97718   * Link to definition of * 99.77085 100.48360 100.03514 100.48530 101.00415 100.13438 100.96244 98.60824 99.88101 99.78076 98.97819
2017 99.80657 99.51485 100.74676 99.19329   * Link to definition of * 101.79421   * Link to definition of * 101.05474 99.73571 100.50792 99.15351 99.81582 99.56378 99.15866
2018 100.45059   * Link to definition of * 99.19166 100.27140 100.32299 100.91183 100.44132 100.16992 100.67489 98.82347 100.41021 99.27132 99.06838
2019 99.98550 99.50626                    

 

Key to symbols:
*extreme value as determined by X-11 extreme value procedure

 

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D 9 Final replacement values for SI ratios

From 2004.Jan to 2019.Feb
Observations 182

D 9 Final replacement values for SI ratios
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
2004                       99.88516
2005                 99.96839 99.48094    
2006       99.66886                
2007 100.38354       100.77640       99.56909      
2008       100.78353       100.35839 99.77346      
2009       100.30333                
2010     100.80414                  
2011 98.94705     99.57339           99.05393    
2012         101.58765       99.63820 99.92760   98.40018
2013                        
2014   99.59259           100.68172   99.93784    
2015     100.90333           99.15134 99.94714    
2016 99.09362                      
2017       100.28732 100.62202              
2018 100.44271                      
2019                        

 

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D 9.A Moving seasonality ratio

D 9.A Moving seasonality ratio
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
I 0.434 0.281 0.312 0.438 0.345 0.381 0.340 0.289 0.294 0.291 0.386 0.407
S 0.088 0.041 0.109 0.072 0.045 0.065 0.062 0.045 0.090 0.061 0.075 0.069
RATIO 4.956 6.780 2.851 6.055 7.723 5.835 5.497 6.405 3.246 4.803 5.159 5.933

 

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D 10 Final seasonal factors

From 2004.Jan to 2019.Feb
Observations 182

Seasonal filter : 3 x 5 moving average

D 10 Final seasonal factors
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2004 100.05478 99.28607 101.51670 100.12857 100.79109 100.07977 99.91282 100.46749 99.54833 99.57388 99.30821 99.35443 100.00184
2005 100.03669 99.27468 101.47319 100.16259 100.75290 100.08139 100.00109 100.45626 99.56827 99.61695 99.31907 99.28541 100.00237
2006 99.98326 99.25276 101.39988 100.19030 100.72328 100.13476 100.13908 100.45260 99.59793 99.68489 99.34442 99.16160 100.00540
2007 99.85575 99.22358 101.30235 100.22841 100.71598 100.19379 100.31155 100.48244 99.63055 99.69860 99.42107 99.05709 100.01010
2008 99.67725 99.23788 101.14136 100.21886 100.72548 100.31758 100.41325 100.53142 99.70708 99.66125 99.55862 99.01040 100.01670
2009 99.45880 99.24036 100.93030 100.21411 100.78403 100.43764 100.45472 100.60136 99.77563 99.59579 99.67747 98.97682 100.01225
2010 99.33251 99.27287 100.69314 100.21439 100.85957 100.54678 100.39041 100.67033 99.81549 99.57726 99.73570 98.97210 100.00671
2011 99.33502 99.31474 100.45440 100.23457 100.95273 100.54924 100.28207 100.75604 99.78137 99.58854 99.77544 98.99016 100.00119
2012 99.43624 99.36359 100.30229 100.24908 100.95280 100.52658 100.19384 100.77039 99.68432 99.66718 99.81870 99.06602 100.00259
2013 99.50982 99.38698 100.23092 100.28419 100.88585 100.52625 100.16241 100.75931 99.50931 99.78432 99.81081 99.10334 99.99613
2014 99.57824 99.40521 100.29887 100.32509 100.75358 100.58300 100.15256 100.69666 99.31653 99.89791 99.76924 99.16198 99.99490
2015 99.64840 99.42051 100.37433 100.33724 100.66289 100.64447 100.13189 100.67099 99.14147 99.96367 99.72146 99.20880 99.99384
2016 99.70978 99.42738 100.48702 100.32032 100.59258 100.70140 100.12744 100.59892 99.06706 99.98607 99.66479 99.25760 99.99503
2017 99.77639 99.42895 100.52111 100.28627 100.60932 100.74200 100.12617 100.56361 99.01500 100.01677 99.57629 99.22281 99.99039
2018 99.88128 99.42545 100.54441 100.30583 100.63218 100.73735 100.12266 100.50780 99.03207 100.04104 99.47424 99.19565 99.99166
2019 100.00150 99.41868                     99.71009
AVGE 99.70473 99.33623 100.77802 100.24665 100.75962 100.45347 100.19480 100.59904 99.47936 99.75694 99.59837 99.13495  

Table Total- 18199.67362     Mean- 99.99821     Standard Deviation- 0.58652
Minimum- 98.97210     Maximum- 101.51670

 

D 10.A Final seasonal component forecasts

From 2019.Mar to 2020.Feb
Observations 12

D 10.A Final seasonal component forecasts
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2019     100.52053 100.32476 100.66595 100.72035 100.09910 100.49560 99.04576 100.05533 99.42385 99.17533 100.05266
2020 100.08135 99.38499                     99.73317

 

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D 11 Final seasonally adjusted data

From 2004.Jan to 2019.Feb
Observations 182

D 11 Final seasonally adjusted data
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTAL
2004 8.30045 8.33589 8.38114 8.42852 8.42122 8.47394 8.50753 8.50956 8.56380 8.60482 8.64106 8.72127 101.88921
2005 8.67669 8.71154 8.73084 8.75750 8.73681 8.77875 8.71667 8.77348 8.80170 8.68257 8.73260 8.78920 104.88833
2006 8.82378 8.82743 8.86435 8.82053 8.93555 8.88235 8.93140 8.97881 8.94030 8.98795 9.05351 9.04200 107.08797
2007 9.13882 9.12011 9.10643 9.11666 9.27843 9.16714 9.19833 9.23081 9.16561 9.32909 9.34772 9.33759 110.53674
2008 9.32764 9.31771 9.32282 9.35372 9.24617 9.24414 9.28715 9.14091 9.27968 9.17207 9.10175 9.09418 110.88796
2009 9.14836 9.17321 9.25533 9.42454 9.30270 9.37876 9.37559 9.32605 9.34612 9.40062 9.36871 9.40737 111.90736
2010 9.38261 9.42753 9.57378 9.48159 9.47843 9.48404 9.50877 9.57395 9.59128 9.52757 9.61576 9.64713 114.29244
2011 9.50319 9.63621 9.57892 9.52625 9.59945 9.64000 9.62320 9.68133 9.71487 9.63306 9.76918 9.72061 115.62628
2012 9.69613 9.68854 9.69517 9.71934 9.82041 9.78762 9.75174 9.76664 9.63360 9.85659 9.75198 9.71270 116.88047
2013 9.87669 9.85525 9.85074 9.93691 9.87848 9.83737 9.88898 9.88571 9.87544 9.90817 9.82263 9.85338 118.46976
2014 9.89841 10.06360 9.81112 9.86845 9.85518 9.84579 9.87705 9.74404 9.92496 10.12563 9.95398 9.94984 118.91805
2015 9.86959 9.83171 9.91673 9.81708 9.76618 9.79125 9.79686 9.72657 9.89056 9.59882 9.75744 9.77442 117.53720
2016 9.65172 9.74877 9.70990 9.68198 9.70006 9.73992 9.70882 9.73814 9.65444 9.69003 9.72208 9.70452 116.45037
2017 9.76468 9.80276 9.84521 9.73835 9.97917 9.90731 9.85044 9.89934 9.93844 9.92535 9.96157 9.96950 118.58212
2018 10.04134 9.96689 9.97208 10.01444 10.06119 10.03148 10.09694 10.13816 10.12414 10.20387 10.16512 10.19220 121.00785
2019 10.22310 10.25487                     20.47797
AVGE 9.45770 9.48513 9.44097 9.44573 9.47063 9.46599 9.47463 9.47423 9.49633 9.50975 9.51767 9.52773  

Table Total- 1725.44008     Mean- 9.48044     Standard Deviation- 0.46520
Minimum- 8.30045     Maximum- 10.25487

 

Test for the presence of residual seasonality.

No evidence of residual seasonality in the entire series at the 1 per cent level. F = 0.24

No evidence of residual seasonality in the last 3 years at the 1 per cent level. F = 0.51

No evidence of residual seasonality in the last 3 years at the 5 per cent level.

NOTE: sudden large changes in the level of the adjusted series will invalidate the results of this test for the last three year period.

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D 12 Final trend cycle

From 2004.Jan to 2019.Feb
Observations 182

Trend filter : 13-term Henderson moving average
I/C ratio : 2.18

D 12 Final trend cycle
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec TOTAL
2004 8.32034 8.34666 8.37618 8.40764 8.43848 8.46741 8.49719 8.53074 8.56821 8.60680 8.64342 8.67461 101.87768
2005 8.70060 8.71962 8.73182 8.74081 8.74910 8.75591 8.75939 8.75987 8.76082 8.76561 8.77388 8.78700 105.00442
2006 8.80497 8.82534 8.84830 8.87026 8.88925 8.90814 8.92766 8.94867 8.97348 9.00304 9.03483 9.06569 107.09962
2007 9.09055 9.10936 9.12235 9.13301 9.14803 9.17140 9.20374 9.24213 9.27883 9.30797 9.32863 9.33983 110.47583
2008 9.33999 9.33264 9.32072 9.30538 9.28736 9.26566 9.23871 9.20756 9.17483 9.14620 9.12866 9.12727 110.87497
2009 9.14668 9.18463 9.23237 9.27958 9.31724 9.34130 9.35514 9.36238 9.36636 9.37106 9.37934 9.39319 111.72928
2010 9.41107 9.42857 9.44535 9.46484 9.48513 9.50399 9.52429 9.54506 9.56657 9.58680 9.60058 9.60447 114.16671
2011 9.60071 9.59298 9.58567 9.58534 9.59460 9.61482 9.64131 9.66888 9.69265 9.70685 9.71067 9.70880 115.70328
2012 9.70705 9.71080 9.72273 9.73924 9.75664 9.77128 9.77434 9.76845 9.76174 9.76089 9.77176 9.79488 117.03982
2013 9.82303 9.85027 9.87151 9.88246 9.88542 9.88347 9.88006 9.87721 9.87495 9.87328 9.87067 9.86579 118.43812
2014 9.86080 9.85663 9.85278 9.85117 9.85378 9.86253 9.88054 9.90362 9.92235 9.93245 9.93275 9.92075 118.63014
2015 9.89851 9.87208 9.84539 9.82117 9.80016 9.78188 9.76833 9.75859 9.75285 9.74906 9.74320 9.73484 117.52605
2016 9.72528 9.71501 9.70858 9.70805 9.70982 9.71100 9.70829 9.70213 9.69720 9.69715 9.70782 9.73027 116.52062
2017 9.76214 9.79649 9.82672 9.84967 9.86656 9.87880 9.88871 9.90216 9.92063 9.94145 9.96000 9.97504 118.56838
2018 9.98533 9.99217 10.00137 10.01447 10.03430 10.06138 10.09170 10.12032 10.14421 10.16530 10.18553 10.20600 121.00208
2019 10.22605 10.24732                     20.47337
AVGE 9.46269 9.47379 9.43279 9.44354 9.45439 9.46526 9.47596 9.48652 9.49705 9.50760 9.51812 9.52856  

Table Total- 1725.13038     Mean- 9.47874     Standard Deviation- 0.46169
Minimum- 8.32034     Maximum- 10.24732

 

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D 13 Final irregular component

From 2004.Jan to 2019.Feb
Observations 182

D 13 Final irregular component
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec S.D.
2004 99.76103 99.87095 100.05924 100.24843 99.79552 100.07710 100.12162 99.75174 99.94849 99.97693 99.97265 100.53796 0.21535
2005 99.72518 99.90725 99.98880 100.19097 99.85957 100.26080 99.51219 100.15537 100.46661 99.05269 99.52958 100.02496 0.38811
2006 100.21359 100.02372 100.18144 99.43938 100.52092 99.71049 100.04183 100.33684 99.63025 99.83236 100.20684 99.73872 0.30817
2007 100.53099 100.11803 99.82554 99.82094 101.42538 99.95352 99.94129 99.87751 98.77981 100.22684 100.20465 99.97603 0.57688
2008 99.86786 99.84001 100.02256 100.51946 99.55649 99.76781 100.52434 99.27615 101.14284 100.28281 99.70529 99.63746 0.49726
2009 100.01838 99.87574 100.24867 101.56211 99.84400 100.40105 100.21852 99.61195 99.78391 100.31542 99.88662 100.15099 0.50688
2010 99.69756 99.98902 101.35969 100.17704 99.92936 99.79016 99.83700 100.30267 100.25828 99.38214 100.15819 100.44416 0.48388
2011 98.98427 100.45071 99.92966 99.38356 100.05060 100.26193 99.81207 100.12876 100.22920 99.23977 100.60246 100.12166 0.47881
2012 99.88750 99.77074 99.71653 99.79571 100.65366 100.16719 99.76876 99.98142 98.68729 100.98045 99.79757 99.16108 0.58634
2013 100.54630 100.05056 99.78964 100.55102 99.92978 99.53356 100.09031 100.08605 100.00491 100.35333 99.51337 99.87421 0.32461
2014 100.38135 102.09978 99.57711 100.17543 100.01421 99.83029 99.96475 98.38868 100.02637 101.94487 100.21375 100.29327 0.97064
2015 99.70789 99.59114 100.72459 99.95840 99.65323 100.09581 100.29203 99.67188 101.41206 98.45885 100.14613 100.40650 0.68661
2016 99.24367 100.34750 100.01355 99.73147 99.89943 100.29784 100.00545 100.37109 99.55904 99.92654 100.14684 99.73529 0.32827
2017 100.02603 100.06404 100.18806 98.86980 101.14133 100.28855 99.61306 99.97149 100.17954 99.83805 100.01572 99.94449 0.49293
2018 100.56097 99.74694 99.70714 99.99971 100.26795 99.70287 100.05184 100.17622 99.80217 100.37949 99.79969 99.86482 0.27384
2019 99.97110 100.07371                     0.05599
S.D. 0.43526 0.56512 0.44218 0.59404 0.54957 0.26218 0.25075 0.50848 0.69769 0.79733 0.28298 0.34520  

Table Total- 18203.17465     Mean- 100.01744     Standard Deviation- 0.50588
Minimum- 98.38868     Maximum- 102.09978

 

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D 16 Combined adjustment factors

From 2004.Jan to 2019.Feb
Observations 182

D 16 Combined adjustment factors
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2004 100.05478 99.28607 101.51670 100.12857 100.79109 100.07977 99.91282 100.46749 99.54833 99.57388 99.30821 99.35443 100.00184
2005 100.03669 99.27468 101.47319 100.16259 100.75290 100.08139 100.00109 100.45626 99.56827 99.61695 99.31907 99.28541 100.00237
2006 99.98326 99.25276 101.39988 100.19030 100.72328 100.13476 100.13908 100.45260 99.59793 99.68489 99.34442 99.16160 100.00540
2007 99.85575 99.22358 101.30235 100.22841 100.71598 100.19379 100.31155 100.48244 99.63055 99.69860 99.42107 99.05709 100.01010
2008 99.67725 99.23788 101.14136 100.21886 100.72548 100.31758 100.41325 100.53142 99.70708 99.66125 99.55862 99.01040 100.01670
2009 99.45880 99.24036 100.93030 100.21411 100.78403 100.43764 100.45472 100.60136 99.77563 99.59579 99.67747 98.97682 100.01225
2010 99.33251 99.27287 100.69314 100.21439 100.85957 100.54678 100.39041 100.67033 99.81549 99.57726 99.73570 98.97210 100.00671
2011 99.33502 99.31474 100.45440 100.23457 100.95273 100.54924 100.28207 100.75604 99.78137 99.58854 99.77544 98.99016 100.00119
2012 99.43624 99.36359 100.30229 100.24908 100.95280 100.52658 100.19384 100.77039 99.68432 99.66718 99.81870 99.06602 100.00259
2013 99.50982 99.38698 100.23092 100.28419 100.88585 100.52625 100.16241 100.75931 99.50931 99.78432 99.81081 99.10334 99.99613
2014 99.57824 99.40521 100.29887 100.32509 100.75358 100.58300 100.15256 100.69666 99.31653 99.89791 99.76924 99.16198 99.99490
2015 99.64840 99.42051 100.37433 100.33724 100.66289 100.64447 100.13189 100.67099 99.14147 99.96367 99.72146 99.20880 99.99384
2016 99.70978 99.42738 100.48702 100.32032 100.59258 100.70140 100.12744 100.59892 99.06706 99.98607 99.66479 99.25760 99.99503
2017 99.77639 99.42895 100.52111 100.28627 100.60932 100.74200 100.12617 100.56361 99.01500 100.01677 99.57629 99.22281 99.99039
2018 99.88128 99.42545 100.54441 100.30583 100.63218 100.73735 100.12266 100.50780 99.03207 100.04104 99.47424 99.19565 99.99166
2019 100.00150 99.41868                     99.71009
AVGE 99.70473 99.33623 100.77802 100.24665 100.75962 100.45347 100.19480 100.59904 99.47936 99.75694 99.59837 99.13495  

Table Total- 18199.67362     Mean- 99.99821     Standard Deviation- 0.58652
Minimum- 98.97210     Maximum- 101.51670

 

D 16.A Combined adjustment component forecasts

From 2019.Mar to 2020.Feb
Observations 12

D 16.A Combined adjustment component forecasts
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2019     100.52053 100.32476 100.66595 100.72035 100.09910 100.49560 99.04576 100.05533 99.42385 99.17533 100.05266
2020 100.08135 99.38499                     99.73317

 

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E 4 Ratios of annual totals

From 2004 to 2018
Observations 15

E 4 Ratios of annual totals
  Unmodified
(D11)
Modified
(E3)
2004 99.99735 99.99735
2005 100.00227 100.00227
2006 100.00342 100.00342
2007 100.00785 100.00662
2008 100.01870 100.01899
2009 100.01282 100.01256
2010 100.00664 100.00587
2011 100.00036 100.00036
2012 100.00414 100.00379
2013 99.99645 99.99645
2014 99.99150 99.99362
2015 99.99291 99.99387
2016 99.99562 99.99562
2017 99.98987 99.98956
2018 99.99003 99.99003

 

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E 5 Month-to-month percent change in the original series

From 2004.Feb to 2019.Feb
Observations 181

E 5 Month-to-month percent change in the original series
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2004   -0.34461 2.80171 -0.80980 0.57445 -0.08412 0.22887 0.57917 -0.28330 0.50474 0.15324 0.97526 0.39051
2005 0.17196 -0.36314 2.44104 -0.99013 0.35170 -0.18972 -0.78683 1.10993 -0.56516 -1.30527 0.27551 0.61396 0.06366
2006 1.09908 -0.68950 2.59055 -1.68127 1.84287 -1.17620 0.55653 0.84561 -1.27613 0.62082 0.38540 -0.31098 0.23390
2007 1.77835 -0.83654 1.94192 -0.94905 2.26955 -1.71174 0.45825 0.52401 -1.54808 1.85309 -0.07924 -0.47398 0.26888
2008 0.51884 -0.54681 1.97400 -0.58372 -0.65008 -0.42681 0.56106 -1.45879 0.68567 -1.20508 -0.86883 -0.63344 -0.21950
2009 1.05140 0.05144 2.61327 1.10572 -0.73141 0.47111 -0.01688 -0.38319 -0.60732 0.40182 -0.25773 -0.29309 0.28376
2010 0.09516 0.41846 3.00417 -1.43380 0.61019 -0.25105 0.10476 0.96628 -0.66974 -0.90133 1.08630 -0.44190 0.21562
2011 -1.13082 1.37903 0.54618 -0.76748 1.49038 0.02105 -0.43960 1.07955 -0.62422 -1.03377 1.60339 -1.28026 0.07029
2012 0.19766 -0.15133 1.01383 0.19610 1.74916 -0.75469 -0.69640 0.72912 -2.42525 2.29715 -0.91095 -1.15376 0.00755
2013 2.14394 -0.34024 0.80297 0.92834 0.00843 -0.77112 0.16078 0.56264 -1.34317 0.60873 -0.83697 -0.39800 0.12720
2014 0.93835 1.49219 -1.63239 0.61064 0.29211 -0.26447 -0.11178 -0.81075 0.46077 2.61902 -1.82180 -0.64998 0.09349
2015 -0.31997 -0.61160 1.83238 -1.04141 -0.19563 0.23833 -0.45229 -0.18298 0.14114 -2.14489 1.40620 -0.34100 -0.13931
2016 -0.75662 0.71947 0.66275 -0.45300 0.45866 0.51960 -0.88752 0.77429 -2.36912 1.29972 0.00836 -0.58847 -0.05099
2017 1.14592 0.04034 1.53620 -1.31642 2.80303 -0.58924 -1.18177 0.93543 -1.15096 0.87861 -0.07706 -0.27562 0.22904
2018 1.38900 -1.19449 1.17815 0.18651 0.79362 -0.19102 0.03830 0.79451 -1.60447 1.81436 -0.94416 -0.01444 0.18716
2019 1.11798 -0.27379                     0.42209
AVGE 0.62935 -0.07820 1.55378 -0.46658 0.77780 -0.34401 -0.16430 0.40432 -0.87862 0.42051 -0.05856 -0.35105  

Table Total- 21.58865     Mean- 0.11927     Standard Deviation- 1.09613
Minimum- -2.42525     Maximum- 3.00417

 

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E 6 Month-to-month percent change in seasonally adjusted series (D11)

From 2004.Feb to 2019.Feb
Observations 181

E 6 Month-to-month percent change in seasonally adjusted series (D11)
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2004   0.42695 0.54284 0.56532 -0.08665 0.62604 0.39635 0.02389 0.63742 0.47896 0.42117 0.92828 0.45096
2005 -0.51123 0.40165 0.22157 0.30539 -0.23626 0.47998 -0.70716 0.65180 0.32164 -1.35349 0.57625 0.64808 0.06652
2006 0.39344 0.04142 0.41822 -0.49429 1.30396 -0.59538 0.55220 0.53086 -0.42896 0.53304 0.72944 -0.12718 0.23806
2007 1.07083 -0.20476 -0.14998 0.11228 1.77446 -1.19949 0.34032 0.35304 -0.70627 1.78357 0.19968 -0.10828 0.27212
2008 -0.10656 -0.10649 0.05486 0.33139 -1.14978 -0.02193 0.46524 -1.57462 1.51810 -1.15965 -0.76664 -0.08325 -0.21661
2009 0.59583 0.27166 0.89515 1.82828 -1.29276 0.81762 -0.03388 -0.52839 0.21524 0.58311 -0.33946 0.41273 0.28543
2010 -0.26327 0.47878 1.55131 -0.96293 -0.03339 0.05927 0.26068 0.68554 0.18095 -0.66426 0.92571 0.32622 0.21205
2011 -1.49203 1.39973 -0.59453 -0.54984 0.76839 0.42242 -0.17435 0.60406 0.34648 -0.84215 1.41308 -0.49713 0.06701
2012 -0.25183 -0.07832 0.06847 0.24929 1.03988 -0.33390 -0.36662 0.15281 -1.36217 2.31475 -1.06136 -0.40275 -0.00265
2013 1.68839 -0.21707 -0.04578 0.87473 -0.58799 -0.41616 0.52461 -0.03309 -0.10388 0.33145 -0.86330 0.31303 0.12208
2014 0.45697 1.66885 -2.50884 0.58435 -0.13442 -0.09532 0.31752 -1.34670 1.85679 2.02181 -1.69518 -0.04157 0.09035
2015 -0.80655 -0.38378 0.86470 -1.00482 -0.51851 0.25667 0.05730 -0.71750 1.68608 -2.94975 1.65251 0.17399 -0.14080
2016 -1.25525 1.00554 -0.39875 -0.28758 0.18677 0.41098 -0.31938 0.30199 -0.85947 0.36863 0.33074 -0.18065 -0.05804
2017 0.62000 0.38992 0.43300 -1.08533 2.47293 -0.72016 -0.57398 0.49637 0.39505 -0.13179 0.36495 0.07965 0.22838
2018 0.72058 -0.74149 0.05213 0.42481 0.46675 -0.29522 0.65247 0.40827 -0.13823 0.78750 -0.37973 0.26637 0.18535
2019 0.30313 0.31083                     0.30698
AVGE 0.07750 0.29147 0.09362 0.05940 0.26489 -0.04031 0.09275 0.00055 0.23725 0.14012 0.10052 0.11384  

Table Total- 21.76563     Mean- 0.12025     Standard Deviation- 0.82913
Minimum- -2.94975     Maximum- 2.47293

 

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E 7 Month-to-month percent change in final trend cycle (D12)

From 2004.Feb to 2019.Feb
Observations 181

E 7 Month-to-month percent change in final trend cycle (D12)
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2004   0.31643 0.35363 0.37553 0.36681 0.34291 0.35171 0.39478 0.43931 0.45037 0.42548 0.36077 0.37979
2005 0.29963 0.21868 0.13983 0.10299 0.09482 0.07787 0.03979 0.00543 0.01086 0.05463 0.09434 0.14962 0.10737
2006 0.20447 0.23132 0.26013 0.24828 0.21400 0.21256 0.21917 0.23529 0.27721 0.32951 0.35300 0.34157 0.26054
2007 0.27430 0.20687 0.14259 0.11689 0.16450 0.25540 0.35259 0.41713 0.39714 0.31407 0.22188 0.12015 0.24863
2008 0.00163 -0.07862 -0.12776 -0.16458 -0.19364 -0.23370 -0.29084 -0.33713 -0.35551 -0.31200 -0.19186 -0.01523 -0.19160
2009 0.21270 0.41487 0.51981 0.51140 0.40578 0.25826 0.14818 0.07732 0.04253 0.05019 0.08837 0.14767 0.23976
2010 0.19034 0.18590 0.17805 0.20626 0.21438 0.19884 0.21364 0.21810 0.22531 0.21147 0.14372 0.04058 0.18555
2011 -0.03916 -0.08057 -0.07622 -0.00337 0.09657 0.21076 0.27557 0.28586 0.24593 0.14646 0.03940 -0.01930 0.09016
2012 -0.01800 0.03862 0.12287 0.16975 0.17863 0.15013 0.03128 -0.06021 -0.06869 -0.00871 0.11133 0.23654 0.07363
2013 0.28744 0.27735 0.21557 0.11089 0.03003 -0.01974 -0.03455 -0.02884 -0.02282 -0.01690 -0.02652 -0.04939 0.06021
2014 -0.05056 -0.04232 -0.03902 -0.01641 0.02656 0.08873 0.18259 0.23360 0.18913 0.10186 0.00296 -0.12083 0.04636
2015 -0.22418 -0.26701 -0.27032 -0.24601 -0.21387 -0.18662 -0.13846 -0.09978 -0.05880 -0.03879 -0.06015 -0.08578 -0.15748
2016 -0.09827 -0.10553 -0.06618 -0.00556 0.01832 0.01212 -0.02794 -0.06340 -0.05083 -0.00049 0.11003 0.23125 -0.00387
2017 0.32754 0.35178 0.30868 0.23353 0.17149 0.12405 0.10023 0.13606 0.18655 0.20980 0.18666 0.15098 0.20728
2018 0.10312 0.06856 0.09207 0.13099 0.19797 0.26986 0.30141 0.28361 0.23605 0.20783 0.19903 0.20097 0.19096
2019 0.19651 0.20798                     0.20224
AVGE 0.11117 0.12152 0.11692 0.11804 0.11816 0.11743 0.11496 0.11319 0.11289 0.11329 0.11318 0.11264  

Table Total- 20.87203     Mean- 0.11532     Standard Deviation- 0.21217
Minimum- -0.35551     Maximum- 0.51981

 

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E 8 Month-to-month percent change in original series adjusted for calendar factors (A18)

From 2004.Feb to 2019.Feb
Observations 181

E 8 Month-to-month percent change in original series adjusted for calendar factors (A18)
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2004   -0.34461 2.80171 -0.80980 0.57445 -0.08412 0.22887 0.57917 -0.28330 0.50474 0.15324 0.97526 0.39051
2005 0.17196 -0.36314 2.44104 -0.99013 0.35170 -0.18972 -0.78683 1.10993 -0.56516 -1.30527 0.27551 0.61396 0.06366
2006 1.09908 -0.68950 2.59055 -1.68127 1.84287 -1.17620 0.55653 0.84561 -1.27613 0.62082 0.38540 -0.31098 0.23390
2007 1.77835 -0.83654 1.94192 -0.94905 2.26955 -1.71174 0.45825 0.52401 -1.54808 1.85309 -0.07924 -0.47398 0.26888
2008 0.51884 -0.54681 1.97400 -0.58372 -0.65008 -0.42681 0.56106 -1.45879 0.68567 -1.20508 -0.86883 -0.63344 -0.21950
2009 1.05140 0.05144 2.61327 1.10572 -0.73141 0.47111 -0.01688 -0.38319 -0.60732 0.40182 -0.25773 -0.29309 0.28376
2010 0.09516 0.41846 3.00417 -1.43380 0.61019 -0.25105 0.10476 0.96628 -0.66974 -0.90133 1.08630 -0.44190 0.21562
2011 -1.13082 1.37903 0.54618 -0.76748 1.49038 0.02105 -0.43960 1.07955 -0.62422 -1.03377 1.60339 -1.28026 0.07029
2012 0.19766 -0.15133 1.01383 0.19610 1.74916 -0.75469 -0.69640 0.72912 -2.42525 2.29715 -0.91095 -1.15376 0.00755
2013 2.14394 -0.34024 0.80297 0.92834 0.00843 -0.77112 0.16078 0.56264 -1.34317 0.60873 -0.83697 -0.39800 0.12720
2014 0.93835 1.49219 -1.63239 0.61064 0.29211 -0.26447 -0.11178 -0.81075 0.46077 2.61902 -1.82180 -0.64998 0.09349
2015 -0.31997 -0.61160 1.83238 -1.04141 -0.19563 0.23833 -0.45229 -0.18298 0.14114 -2.14489 1.40620 -0.34100 -0.13931
2016 -0.75662 0.71947 0.66275 -0.45300 0.45866 0.51960 -0.88752 0.77429 -2.36912 1.29972 0.00836 -0.58847 -0.05099
2017 1.14592 0.04034 1.53620 -1.31642 2.80303 -0.58924 -1.18177 0.93543 -1.15096 0.87861 -0.07706 -0.27562 0.22904
2018 1.38900 -1.19449 1.17815 0.18651 0.79362 -0.19102 0.03830 0.79451 -1.60447 1.81436 -0.94416 -0.01444 0.18716
2019 1.11798 -0.27379                     0.42209
AVGE 0.62935 -0.07820 1.55378 -0.46658 0.77780 -0.34401 -0.16430 0.40432 -0.87862 0.42051 -0.05856 -0.35105  

Table Total- 21.58865     Mean- 0.11927     Standard Deviation- 1.09613
Minimum- -2.42525     Maximum- 3.00417

 

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E 18 Final adjustment ratios

From 2004.Jan to 2019.Feb
Observations 182

E 18 Final adjustment ratios
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2004 100.05478 99.28607 101.51670 100.12857 100.79109 100.07977 99.91282 100.46749 99.54833 99.57388 99.30821 99.35443 100.00184
2005 100.03669 99.27468 101.47319 100.16259 100.75290 100.08139 100.00109 100.45626 99.56827 99.61695 99.31907 99.28541 100.00237
2006 99.98326 99.25276 101.39988 100.19030 100.72328 100.13476 100.13908 100.45260 99.59793 99.68489 99.34442 99.16160 100.00540
2007 99.85575 99.22358 101.30235 100.22841 100.71598 100.19379 100.31155 100.48244 99.63055 99.69860 99.42107 99.05709 100.01010
2008 99.67725 99.23788 101.14136 100.21886 100.72548 100.31758 100.41325 100.53142 99.70708 99.66125 99.55862 99.01040 100.01670
2009 99.45880 99.24036 100.93030 100.21411 100.78403 100.43764 100.45472 100.60136 99.77563 99.59579 99.67747 98.97682 100.01225
2010 99.33251 99.27287 100.69314 100.21439 100.85957 100.54678 100.39041 100.67033 99.81549 99.57726 99.73570 98.97210 100.00671
2011 99.33502 99.31474 100.45440 100.23457 100.95273 100.54924 100.28207 100.75604 99.78137 99.58854 99.77544 98.99016 100.00119
2012 99.43624 99.36359 100.30229 100.24908 100.95280 100.52658 100.19384 100.77039 99.68432 99.66718 99.81870 99.06602 100.00259
2013 99.50982 99.38698 100.23092 100.28419 100.88585 100.52625 100.16241 100.75931 99.50931 99.78432 99.81081 99.10334 99.99613
2014 99.57824 99.40521 100.29887 100.32509 100.75358 100.58300 100.15256 100.69666 99.31653 99.89791 99.76924 99.16198 99.99490
2015 99.64840 99.42051 100.37433 100.33724 100.66289 100.64447 100.13189 100.67099 99.14147 99.96367 99.72146 99.20880 99.99384
2016 99.70978 99.42738 100.48702 100.32032 100.59258 100.70140 100.12744 100.59892 99.06706 99.98607 99.66479 99.25760 99.99503
2017 99.77639 99.42895 100.52111 100.28627 100.60932 100.74200 100.12617 100.56361 99.01500 100.01677 99.57629 99.22281 99.99039
2018 99.88128 99.42545 100.54441 100.30583 100.63218 100.73735 100.12266 100.50780 99.03207 100.04104 99.47424 99.19565 99.99166
2019 100.00150 99.41868                     99.71009
AVGE 99.70473 99.33623 100.77802 100.24665 100.75962 100.45347 100.19480 100.59904 99.47936 99.75694 99.59837 99.13495  

Table Total- 18199.67362     Mean- 99.99821     Standard Deviation- 0.58652
Minimum- 98.97210     Maximum- 101.51670

 

E 18.A Final adjustment ratio forecasts

From 2019.Mar to 2020.Feb
Observations 12

E 18.A Final adjustment ratio forecasts
  Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec AVGE
2019     100.52053 100.32476 100.66595 100.72035 100.09910 100.49560 99.04576 100.05533 99.42385 99.17533 100.05266
2020 100.08135 99.38499                     99.73317

 

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F 2. Summary Measures

F 2.A: Average percent change without regard to sign over the indicated span

Table F 2.A
  B1
O
D11
CI
D13
I
D12
C
D10
S
A2
P
D18
TD&H
F1
mcd
E1
Mod.O
E2
Mod.CI
E3
Mod.I
Span 1 0.87 0.63 0.58 0.18 0.55 0.00 0.00 0.25 0.75 0.45 0.39
Span 2 0.90 0.71 0.59 0.35 0.54 0.00 0.00 0.43 0.79 0.57 0.41
Span 3 0.98 0.75 0.48 0.51 0.64 0.00 0.00 0.59 0.90 0.63 0.31
Span 4 1.23 0.93 0.56 0.67 0.85 0.00 0.00 0.73 1.12 0.79 0.36
Span 5 1.26 1.02 0.53 0.82 0.86 0.00 0.00 0.86 1.19 0.93 0.36
Span 6 1.41 1.10 0.49 0.97 1.01 0.00 0.00 0.98 1.35 1.04 0.32
Span 7 1.50 1.27 0.58 1.10 0.86 0.00 0.00 1.10 1.41 1.20 0.38
Span 8 1.50 1.33 0.52 1.24 0.86 0.00 0.00 1.22 1.47 1.29 0.35
Span 9 1.56 1.43 0.47 1.36 0.66 0.00 0.00 1.33 1.53 1.39 0.32
Span 10 1.64 1.59 0.58 1.47 0.54 0.00 0.00 1.44 1.57 1.53 0.38
Span 11 1.66 1.65 0.47 1.58 0.55 0.00 0.00 1.55 1.67 1.62 0.33
Span 12 1.78 1.77 0.55 1.68 0.06 0.00 0.00 1.66 1.73 1.73 0.36

 

F 2.B: Relative contributions to the variance of the percent change in the components of the original series

Table F 2.B
  E3
I
D12
C
D10
S
A2
P
D18
TD&H
TOTAL Ratio
(X100)
Span 1 31.40 6.26 62.34 0.00 0.00100.00 87.74
Span 2 28.94 20.96 50.10 0.00 0.00100.00 92.56
Span 3 12.14 34.14 53.72 0.00 0.00100.00 95.39
Span 4 10.09 34.48 55.44 0.00 0.00100.00 103.70
Span 5 8.61 43.81 47.58 0.00 0.00100.00 108.77
Span 6 5.02 45.54 49.45 0.00 0.00100.00 112.13
Span 7 6.93 57.78 35.29 0.00 0.00100.00 106.14
Span 8 5.22 64.00 30.78 0.00 0.00100.00 109.66
Span 9 4.40 77.35 18.25 0.00 0.00100.00 101.70
Span 10 5.66 83.08 11.27 0.00 0.00100.00 105.41
Span 11 3.75 85.90 10.35 0.00 0.00100.00 103.85
Span 12 4.47 95.42 0.11 0.00 0.00100.00 99.05

 

F 2.C: Average percent change with regard to sign and standard deviation over indicated span

Table F 2.C
  B1
O
D13
I
D12
C
D10
S
D11
CI
F1
mcd
Avg. S.D. Avg. S.D. Avg. S.D. Avg. S.D. Avg. S.D. Avg. S.D.
Span 1 0.12 1.09 0.00 0.80 0.12 0.18 -0.00 0.72 0.12 0.82 0.11 0.29
Span 2 0.24 1.10 0.01 0.78 0.23 0.35 0.00 0.64 0.23 0.87 0.23 0.48
Span 3 0.34 1.24 0.00 0.68 0.34 0.51 -0.01 0.84 0.35 0.88 0.34 0.64
Span 4 0.44 1.46 0.00 0.79 0.45 0.67 -0.01 0.97 0.46 1.06 0.45 0.76
Span 5 0.55 1.49 0.00 0.70 0.56 0.80 -0.02 0.95 0.57 1.09 0.55 0.86
Span 6 0.65 1.62 0.00 0.68 0.67 0.92 -0.02 1.10 0.67 1.16 0.66 0.97
Span 7 0.76 1.66 0.00 0.80 0.78 1.04 -0.02 0.96 0.78 1.32 0.76 1.07
Span 8 0.86 1.67 0.01 0.71 0.88 1.14 -0.02 0.98 0.88 1.34 0.86 1.15
Span 9 0.97 1.63 0.00 0.64 0.98 1.23 -0.02 0.85 0.98 1.38 0.96 1.23
Span 10 1.07 1.67 0.01 0.79 1.08 1.31 -0.01 0.65 1.08 1.53 1.05 1.31
Span 11 1.17 1.69 0.01 0.66 1.17 1.39 -0.00 0.71 1.17 1.54 1.14 1.38
Span 12 1.26 1.64 0.00 0.75 1.26 1.46 0.00 0.08 1.26 1.64 1.23 1.46

 

F 2.D: Average duration of run

Table F 2.D
CI I C mcd
1.69 1.55 12.07 2.84

 

F 2.E: I/C Ratio for months span

Table F 2.E
  Span 1 Span 2 Span 3 Span 4 Span 5 Span 6 Span 7 Span 8 Span 9 Span 10 Span 11 Span 12
I/C 3.31 1.68 0.94 0.83 0.65 0.50 0.52 0.42 0.35 0.40 0.30 0.33

 

months for cyclical dominance: 3

 

Relative contribution of the components to the stationary portion of the variance in the original series

Table F 2.F
I C S P TD&H Total
2.58 88.13 8.96 0.00 0.00 99.67

 

F 2.G: The autocorrelation of the irregulars for spans 1 to 14

Table F 2.G
  Span 1 Span 2 Span 3 Span 4 Span 5 Span 6 Span 7 Span 8 Span 9 Span 10 Span 11 Span 12 Span 13 Span 14
ACF -0.24 -0.17 0.12 -0.20 0.07 0.13 -0.23 0.05 0.23 -0.18 0.21 -0.06 -0.19 0.17

 

F 2.H:
   The final I/C Ratio from Table D12: 2.18
   The final I/S Ratio from Table D10: 5.11

 

F 2.I: Seasonality tests

Table F 2.I
  Statistic Probability
level
F-test for stable seasonality from Table B 1. 11.479 0.00%
F-test for stable seasonality from Table D 8. 15.835 0.00%
Kruskal-Wallis Chi Squared test for stable seasonality from Table D 8. 99.497 0.00%
F-test for moving seasonality from Table D 8. 0.446 95.67%

 

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F 3. Monitoring and Quality Assessment Statistics

All the measures below are in the range from 0 to 3 with an acceptance region from 0 to 1.

Monitoring and Quality Assessment Statistics
1. The relative contribution of the irregular over threemonths span (from Table F 2.B). M1 = 1.214
2. The relative contribution of the irregular component to the stationary portion of the variance (from Table F 2.F). M2 = 0.258
3. The amount of month to month change in the irregular component as compared to the amount of month to monthchange in the trend-cycle (from Table F2.H). M3 = 0.591
4. The amount of autocorrelation in the irregular as described by the average duration of run (Table F 2.D). M4 = 0.274
5. The number of months it takes the change in the trend-cycleto surpass the amount of change in the irregular (from Table F 2.E). M5 = 0.483
6. The amount of year to year change in the irregular as compared to the amount of year to year change in the seasonal (from Table F 2.H). M6 = 0.444
7. The amount of moving seasonality present relative to the amount of stable seasonality (from Table F 2.I). M7 = 0.513
8. The size of the fluctuations in the seasonal component throughout the whole series. M8 = 0.988
9. The average linear movement in the seasonal component throughout the whole series. M9 = 0.375
10. Same as 8, calculated for recent years only. M10 = 1.021
11. Same as 9, calculated for recent years only. M11 = 1.005

 

ACCEPTED at the level 0.60

Check the 3 above measures which failed.

Q (without M2) = 0.64 ACCEPTED

 

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QS Statistics for seasonality

QS statistic for seasonality (Full series)
  QS p-value
Original Series 30.30 0.0000
Original Series (extreme value adjusted) 30.30 0.0000
Residuals 0.00 1.0000
Seasonally Adjusted Series 0.00 1.0000
Seasonally Adjusted Series (extreme value adjusted) 0.00 1.0000
Irregular Series 0.00 1.0000
Irregular Series (extreme value adjusted) 0.00 1.0000

 

QS statistic for seasonality (Series start in 2011.Mar)
  QS p-value
Original Series 5.58 0.0613
Original Series (extreme value adjusted) 5.58 0.0613
Residuals 0.00 1.0000
Seasonally Adjusted Series 0.00 1.0000
Seasonally Adjusted Series (extreme value adjusted) 0.00 1.0000
Irregular Series 0.00 1.0000
Irregular Series (extreme value adjusted) 0.00 1.0000

 

Visually significant residual trading day peaks have been found in the spectral plots of the following series starting in 2011.Mar:

WARNING:   Series should not be a candidate for seasonal adjustment because the spectrum of the original series (Table A1 or B1) has no visually significant seasonal peaks.

If this is a component series of an indirectly adjusted composite series, consider using type = trend or type = summary in the x11 spec.

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G 0 10*LOG(SPECTRUM) of the differenced, transformed Original Series (Table A1 or B1)

Spectrum estimated from 2011.Mar to 2019.Feb.

 ++++++++++I+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++I
     -30.09I                                                  S          I    -30.09
           I                                          T       S          I
           I                                          T       S          I
           I                                          T       S          I
     -32.08I                                          T       S          I    -32.08
           I                                          T       S          I
           I                                          T       S*         I
           I                                          T       S*         I
     -34.06I                                          T       S*         I    -34.06
           I                                         *T       S*         I
           I                                         *T       S*         I
           I                                         *T* *    S*         I
     -36.05I                                         *T* *   *S*         I    -36.05
           I                                         *T***   *S*         I
           I                                         *T****  *S*T        I
           I                                         *T****  *S*T        I
     -38.04I                                         *T****  *S*T*       I    -38.04
           I                                         *T****  *S*T*       I
           I                                        S*T***** *S*T** **   I
           I                                  *     S*T*******S*T*****   I
     -40.03I           *                      **    S*T*******S*T*****   I    -40.03
           I           *            **        **    S*T*******S*T*****   I
           I          S*            **  *     **    S*T*******S*T*****   I
           I          S**           **  **    **    S*T*******S*T*****   I
     -42.02I          S**           **  **    ***  *S*T*******S*T******  I    -42.02
           I         *S**           ******    ***  *S*T*******S*T******  I
           I         *S**           ******   *******S*T*******S*T******  I
           I         *S**          *******   *******S*T*******S*T******  I
     -44.01I         *S**          *******   *******S*T*******S*T******  I    -44.01
           I         *S**          *******S  *******S*T*******S*T******  I
           I  *      *S**          *******S  *******S*T*******S*T******* I
           I  *      *S***        ********S ********S*T*******S*T******* I
     -46.00I  *      *S***      S*********S*********S*T*******S*T*******SI    -46.00
           I  *      *S***    **S*********S*********S*T*******S*T*******SI
           I  *      *S***   ***S*********S*********S*T*******S*T*******SI
           I  *      *S**** ****S*********S*********S*T*******S*T*******SI
     -47.99I  *     **S*********S*********S*********S*T*******S*T*******SI    -47.99
           I **     **S*********S*********S*********S*T*******S*T*******SI
           I **     **S*********S*********S*********S*T*******S*T*******SI
           I **     **S*********S*********S*********S*T*******S*T*******SI
     -49.98I **     **S*********S*********S*********S*T*******S*T*******SI    -49.98
           I***     **S*********S*********S*********S*T*******S*T*******SI
           I****    **S*********S*********S*********S*T*******S*T*******SI
           I****    **S*********S*********S*********S*T*******S*T*******SI
     -51.97I****    **S*********S*********S*********S*T*******S*T*******SI    -51.97
           I****    **S*********S*********S*********S*T*******S*T*******SI
           I****   ***S*********S*********S*********S*T*******S*T*******SI
           I****   ***S*********S*********S*********S*T*******S*T*******SI
     -53.96I****   ***S*********S*********S*********S*T*******S*T*******SI    -53.96
           I****   ***S*********S*********S*********S*T*******S*T*******SI
           I*****  ***S*********S*********S*********S*T*******S*T*******SI
           I***** ****S*********S*********S*********S*T*******S*T*******SI
     -55.95I**********S*********S*********S*********S*T*******S*T*******SI    -55.95
 ++++++++++I+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++I
            S=SEASONAL FREQUENCIES, T=TRADING DAY FREQUENCIES

  Previous Table | Index | Next Table

 

G 1 10*LOG(SPECTRUM) of the differenced, transformed Seasonally Adjusted Data (Table E2).

Spectrum estimated from 2011.Mar to 2019.Feb.

 ++++++++++I+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++I
     -34.27I                                          T                  I    -34.27
           I                                          T                  I
           I                                          T                  I
           I                                          T                  I
     -36.06I                                          T                  I    -36.06
           I                                          T                  I
           I                                          T                  I
           I                                          T                  I
     -37.85I                                          T                  I    -37.85
           I                                          T                  I
           I                                          T                  I
           I                                *    *    T                  I
     -39.64I                                *    *    T                  I    -39.64
           I                                *    *    T                  I
           I                                *    *    T*                 I
           I                                *    *    T*                 I
     -41.43I                                *    *    T*                 I    -41.43
           I                                *    *    T* *               I
           I                                *    *    T* *               I
           I                                *    *    T* *           *   I
     -43.22I                                *    *    T***           *   I    -43.22
           I                        *       *    *    T***          **   I
           I                        *       **   *    T****     T*  **   I
           I                        *       **  **    T****     T*  **   I
     -45.01I  *                     *       **  **   *T****     T*  **   I    -45.01
           I  *                     *       **  **   *T****     T*  **   I
           I  *          *          *       **  **   *T****     T*  **   I
           I  *          *         **       **  **   *T****     T*  **   I
     -46.80I  *    *     *         **   *  ***  **   *T****     T******  I    -46.80
           I **    *     *         **   ** ***  ***  *T****     T******  I
           I **    *     *         **   ** ***  ***  *T****    *T******  I
           I **    *     *         **   ** ***  ***  *T*****   *T******  I
     -48.59I **    *     *         ***  **S***  *** S*T*****   *T******  I    -48.59
           I **    *     *         ***  **S******** S*T*****   *T******  I
           I **    *     *         *** ***S******** S*T*****   *T******  I
           I***    *     **        *** ***S*********S*T*****  S*T******* I
     -50.38I***    *     **        *******S*********S*T****** S*T*******SI    -50.38
           I***    *     **       ********S*********S*T****** S*T*******SI
           I***    *    ***       ********S*********S*T*******S*T*******SI
           I***    *    ****      ********S*********S*T*******S*T*******SI
     -52.17I****   *    ****      ********S*********S*T*******S*T*******SI    -52.17
           I****  ***   *****     ********S*********S*T*******S*T*******SI
           I****  ***   *****     ********S*********S*T*******S*T*******SI
           I****  ***   *****     ********S*********S*T*******S*T*******SI
     -53.96I****  ***   *****    *********S*********S*T*******S*T*******SI    -53.96
           I****  ***   ******   *********S*********S*T*******S*T*******SI
           I****  ***   ******   *********S*********S*T*******S*T*******SI
           I***** ***   ******  S*********S*********S*T*******S*T*******SI
     -55.75I*********   ******* S*********S*********S*T*******S*T*******SI    -55.75
           I*********  *********S*********S*********S*T*******S*T*******SI
           I*********  *********S*********S*********S*T*******S*T*******SI
           I********** *********S*********S*********S*T*******S*T*******SI
     -57.53I**********S*********S*********S*********S*T*******S*T*******SI    -57.53
 ++++++++++I+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++I
            S=SEASONAL FREQUENCIES, T=TRADING DAY FREQUENCIES

  Previous Table | Index | Next Table

 

G 2 10*LOG(SPECTRUM) of the Modified Irregular (Table E3).

Spectrum estimated from 2011.Mar to 2019.Feb.

 ++++++++++I+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++I
     -39.00I                                          T                  I    -39.00
           I                                          T                  I
           I                                          T                  I
           I                                          T                  I
     -41.21I                                          T                  I    -41.21
           I                                          T                  I
           I                                          T                  I
           I                                *         T                  I
     -43.41I                                *         T                  I    -43.41
           I                                *    *    T                  I
           I                                *    *    T                  I
           I                                *    *    T                  I
     -45.62I                        *       *    *    T*                 I    -45.62
           I                        *       *    *    T*                 I
           I                       **       *    *    T*                 I
           I                       **       *    *    T* *               I
     -47.83I                       **       **   *    T* *               I    -47.83
           I                       **       **   *    T***               I
           I                       **    *  **  **    T***           *   I
           I                       **   **  **  **    T***          **   I
     -50.03I                       ***  ** ***  **   *T****     T*  **   I    -50.03
           I                      ****  ** ***  **   *T****     T*  **   I
           I                      ****  **S***  **   *T****     T*  **   I
           I                      ****  **S***  **   *T****     T*  **   I
     -52.24I                      **** ***S***  ***  *T****     T*  **   I    -52.24
           I                      ********S***  ***  *T****     T* ***   I
           I              *       ********S********  *T****     T******  I
           I             **      *********S******** S*T*****   *T******  I
     -54.45I             **      *********S******** S*T*****   *T******  I    -54.45
           I             **      *********S*********S*T*****   *T******  I
           I             **      *********S*********S*T*****   *T******  I
           I             **      *********S*********S*T****** S*T******* I
     -56.66I    *        **  ** S*********S*********S*T****** S*T*******SI    -56.66
           I    *     S  *** ***S*********S*********S*T*******S*T*******SI
           I    *     S  *******S*********S*********S*T*******S*T*******SI
           I    *     S ********S*********S*********S*T*******S*T*******SI
     -58.86I    *     S*********S*********S*********S*T*******S*T*******SI    -58.86
           I   **     S*********S*********S*********S*T*******S*T*******SI
           I   **    *S*********S*********S*********S*T*******S*T*******SI
           I   **    *S*********S*********S*********S*T*******S*T*******SI
     -61.07I   **    *S*********S*********S*********S*T*******S*T*******SI    -61.07
           I   **    *S*********S*********S*********S*T*******S*T*******SI
           I   **    *S*********S*********S*********S*T*******S*T*******SI
           I   **    *S*********S*********S*********S*T*******S*T*******SI
     -63.28I   **    *S*********S*********S*********S*T*******S*T*******SI    -63.28
           I   **    *S*********S*********S*********S*T*******S*T*******SI
           I   ***   *S*********S*********S*********S*T*******S*T*******SI
           I   ***  **S*********S*********S*********S*T*******S*T*******SI
     -65.48I  ****  **S*********S*********S*********S*T*******S*T*******SI    -65.48
           I  ****  **S*********S*********S*********S*T*******S*T*******SI
           I  ****  **S*********S*********S*********S*T*******S*T*******SI
           I ****** **S*********S*********S*********S*T*******S*T*******SI
     -67.69I**********S*********S*********S*********S*T*******S*T*******SI    -67.69
 ++++++++++I+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++I
            S=SEASONAL FREQUENCIES, T=TRADING DAY FREQUENCIES

  Previous Table | Index | Next Table

Peak probabilities for Tukey spectrum estimator

Tukey spectrum estimated from 2011.Mar to 2019.Feb.

Peak probabilities for Tukey spectrum estimator
  S1 S2 S3 S4 S5 S6 TD
Model Residuals 0.022 0.077 0.515 0.302 0.694 0.810 0.027
Original Series (Table A1 or B1) 0.799 0.504 0.538 0.323 0.931 Link to definition of * * 0.219 0.855
Seasonally adjusted series (E2) 0.009 0.023 0.026 0.000 0.166 0.376 0.942 Link to definition of * *
Modified Irregular (E3) 0.235 0.028 0.029 0.001 0.169 0.366 0.941 Link to definition of * *

 

  ----------
  ** - Peak Probability > 0.99,
  * - 0.90 < Peak Probability < 0.99

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Extreme value as determined by X-11 extreme value procedure.

Back to Table D 8.B

Definition of *

Tukey spectral peak probability greater than 0.99

Back to Tukey Spectral Peaks Table

Definition of *

Tukey spectral peak probability greater than 0.99

Back to Tukey Spectral Peaks Table

Definition of *

Tukey spectral peak probability greater than 0.99

Back to Tukey Spectral Peaks Table

Index for Rout.html