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

• Period covered- 1st month,2004 to 2nd month,2019
• Type of run - auto-mode seasonal adjustment
• Sigma limits for graduating extreme values are 1.5 and 2.5 .
• 3x3 moving average used in section 1 of each iteration, 3x5 moving average in section 2 of iterations B and C, moving average for final seasonal factors chosen by Global MSR.
• Spectral plots generated for selected series
• Spectral plots generated for series starting in 2011.Mar

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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

• Error file for Rout
• Log entry for Rout

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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 for model fit to log transformed series.

 

***** 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

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

 

 

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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

 

 

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B 1 Original series (prior adjusted)

From 2004.Jan to 2019.Feb
Observations 182

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

 

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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

 

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D 8 Final unmodified SI ratios

From 2004.Jan to 2019.Feb
Observations 182

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

 

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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

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

 

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D 11 Final seasonally adjusted data

From 2004.Jan to 2019.Feb
Observations 182

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

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

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

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

 

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E 4 Ratios of annual totals

From 2004 to 2018
Observations 15

 

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

From 2004.Feb to 2019.Feb
Observations 181

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

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

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

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

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

 

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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	0.00	100.00	87.74
Span 2	28.94	20.96	50.10	0.00	0.00	100.00	92.56
Span 3	12.14	34.14	53.72	0.00	0.00	100.00	95.39
Span 4	10.09	34.48	55.44	0.00	0.00	100.00	103.70
Span 5	8.61	43.81	47.58	0.00	0.00	100.00	108.77
Span 6	5.02	45.54	49.45	0.00	0.00	100.00	112.13
Span 7	6.93	57.78	35.29	0.00	0.00	100.00	106.14
Span 8	5.22	64.00	30.78	0.00	0.00	100.00	109.66
Span 9	4.40	77.35	18.25	0.00	0.00	100.00	101.70
Span 10	5.66	83.08	11.27	0.00	0.00	100.00	105.41
Span 11	3.75	85.90	10.35	0.00	0.00	100.00	103.85
Span 12	4.47	95.42	0.11	0.00	0.00	100.00	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%

 

  Previous Table | Index | Next Table

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

 

  Previous Table | Index | Next Table

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:

• differenced, transformed original series (Table A1 or B1) (1 Trading Day peak(s))
• differenced, transformed seasonally adjusted series (Table E2) (1 Trading Day peak(s))
• Modified irregular component (Table E3) (1 Trading Day peak(s))

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.

  Previous Table | Index | Next Table

 

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

• Program Header
• File Save Requests
• Links to other HTML files
• Content of input specification file
• AIC test for transformation
• A 1 Time series data (for the span analyzed)
• Automatic ARIMA model selection
• ARIMA model
• Maximized log-likelihood and model selection criteria
• Durbin-Watson statistic for model residuals
• Friedman non-parametric test for residual seasonality
• QS Statistic for regARIMA Model Residuals
• Plot of Spectrum of the regARIMA model residuals
• Forecasting
• B 1 Original series (prior adjusted)
• C 17 Final weights for irregular component
• D 8 Final unmodified SI ratios
• D 8.A F-tests for seasonality
• D 8.B Final unmodified SI ratios, with labels for outliers and extreme values
• D 9 Final replacement values for SI ratios
• D 9.A Moving seasonality ratio
• D 10 Final seasonal factors
• D 11 Final seasonally adjusted data
• D 12 Final trend cycle
• D 13 Final irregular component
• D 16 Combined adjustment factors
• E 4 Ratios of annual totals
• E 5 Month-to-month percent change in the original series
• E 6 Month-to-month percent change in seasonally adjusted series (D11)
• E 7 Month-to-month percent change in final trend cycle (D12)
• E 8 Month-to-month percent change in original series adjusted for calendar factors (A18)
• E 18 Final adjustment ratios
• F 2 Summary measures
• F 3 Monitoring and quality assessment statistics
• QS diagnostic to detect seasonality
• Plot of Spectrum of the original series
• Plot of Spectrum of differenced seasonally adjusted series
• Plot of Spectrum of modified irregular series
• Peak probabilties for the Tukey spectrum

 

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• Error Messages
• Log Entry