季節調整法の比較研究 －センサス局法X-12-ARIMA の我が国経済統計への適用－
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1 17 12
2 ( )
3 X-12-ARIMA * X-12-ARIMA X-12- ARIMA
4
5 1979 X11 X12ARIMA 1 X12ARIMA 2 X12ARIMA REGARIMA X12ARIMA X12ARIMA
6 REGARIMA X12ARIMA
7 MITI X X - 11 MITI X-11 X - 11 X - 11
8 X - 11 X - 11 X-12-ARIMA
9 ARIMA X11 X - 11 X - 12-ARIMA
10 X-12-ARIM X ARIMA X X - 12-ARIMA X - 11 X - 12-ARIMA 2 X - 12-ARIMA X - 11 X ARIMA X - 12-ARIMA - 11X - 12-ARIMA MITI DECOMP
11 X - 11 X - 12-ARIMA REGARIMA ARIMA ARIMA AIC ARIMA AIC ARIMA X - 12-ARIMA X - 12-ARIMA X - 12-ARIMA X - 11
12 X - 12-ARIMA X - 11 M 2 +CD M 1 X-12-ARIMA X - 12-ARIMA X-12- ARIMA MITI X - 12-ARIMA MITI
13 X - 12-ARIMA MITI X - 11X - 12-ARIMA X X - 12-ARIMA X ARIMA X - 12-ARIMA
14
15 1979 MITI X X - 11 MITI - 11 X X - 11 X - 12-ARIMA X - 12-ARIMA 1998 X - 12-ARIMA X-11 X ARIMA X X - 12-ARIMA X - 12-ARIMA X - 11
16 X-12-ARIMA p X ARIMA X - 12-ARIMA X - 12-ARIMAfinal version 02 2 X - 12-ARIMA version 02 7 X ARIMA X ARIMA X - 11 X ARIMA X - 12-ARIMA
17 4 1 3
18 Y tt tc ts ti t Y tt tc ts ti t
19 22 12
20
21 W.M.Persons 1919 link relative method NBER, National Bureau of Economic Research F R Macaulay 1931 the ratio-to-movinng-average method) 1941 H. C. Barton
22 1954 NBER Julius Shiskin 1954 ( ) 1956 experimental X X X X X X X - 11 X- 10 all-or-nothing TC 15 X - 11 OECDIMF X - 11 J. Shiskin et al42 X - 11
23 MITI X
24 IIX X-11 X-4C X-8 III
25 IIX - 11 IIX- 11 II -11 X - 11 X-11
26 2 X D.F.FINDLEY et al.39
27 X X ( ) 2 2
28 X - 11 SNA X - 11 X - 11 X - 11
29 X-12-ARIMA X-12-ARIMA X - 11 X - 11 X ARIMA 1996 Beta version Final version X - 11 X - 12-ARIMA X-12-ARIMA X - 12-ARIMA 1 REGARIMA 4 REGARIMA REGression and ARIMA ARIMA(Autoregressive
30 REGARIMA X - 11 X ARIMA 1 REGARIMA X - 11 X - 12-ARIMA REGARIMA X - 11 Integrated Moving Average) 5 X - 12-ARIMA RegARIMA ARIMA X - 12-ARIMA X - 11 ARIMA 12.29
31 1 REGARIMA ARIMA ARIMA ARIMA 2 X - 11 REGARIMA
32 REGARIMA REGARIMA (1) REGARIMA (2) ARIMA 3 ARIMA s (p d q)(p D Q)S y t (2) Z t REGARIMA Z t (3) ARIMA X - 12-ARIMA (3)
33 y t jxit ARIMA i Z t 2 Z t X - 11 REGARIMA Iterative Generalized Least Squares AR( MA( REGARIMA ß i GLS REGARIMA AR MA 0.1 i Z t y t jx it i Z t ARIMA AR MA ARIMA ARIMA X - 12-ARIMA X - 12-ARIMA D.F.Findley etal 39 Bureau of the Census38 26
34
35 X-12-ARIMA X-12-ARIMA X ARIMA X - 12-ARIMA X-11 X - 12-ARIMA X X - 11 X - 12-ARIMA X-12-ARIMA 2 DECOMP X - 12-ARIMA X-11 X- 12-ARIMA
36 MAPRMean Absolute Percent Revision X - 11 X ARIMA MAPR y t t=1,,t y 1,y2,,yn n T At n y1 yn t m 1 m T Am T final FINAL y 1 y T m Am m concurrent CONCURRENT y T ym y 1 y m m percent revisionrm Am T= FINALAm mconcurrent Rm Rm{(FINAL / CONCURRENT)-1}100 Rm Rm MAPRMean Absolute Percent Revision At n
37 y 1,y2,,yn [ ] Ct n Ct n RCm RCm X - 12-ARIMA Revision Histories X - 12-ARIMA Revision Histories Sliding Spans Rm RC MAPR MAPR Rm RCm X - 11 X - 12-ARIMA MAPR MAPR 12 X - 12-ARIMA MAPR
38 X - 11 X - 12-ARIMA X - 12-ARIMA REGARIMA MAPR 2 MAPR MAPR X-12-ARIMA M 1,M2 +CD X - 11 X-12-ARIMA X - 12-ARIMA X-11 X - 12-ARIMA X - 11 X - 12-ARIMA 1996 X - 12-ARIMA X - 11
39 X - 12-ARIMA 1997 X - 12-ARIMA X - 11 X - 12-ARIMAMITI DECOMP
40 X ARIMA X - 12-ARIMA
41 X - 12-ARIMA X - 12-ARIMAX - 11MITI DECOMP AIC BIC MPD MAPR MPDMaximum Percentage Difference) X - 12-ARIMA Sliding Spans
42
43 X - 11 X - 12-ARIMA REGARIMA ARIMA REGARIMA X - 12-ARIMA IDENTIFY ARIMA d=1,d=1 p,q,p,q ARIMA AR (p)ma (q) ARIMA AR (P)MA (Q) AUTOMDL 6 6 ARIMA ARIMA
44 AIC( ARIMA REGARIMA ARIMA ARIMA ARIMA REGARIMA ARIMA REGARIMA Ljung=Box ARIMA MA 0.9
45 ARIMA ARIMA ARIMA ARIMA ARIMA ARIMA X - 12-ARIMA OUTLIER REGRESSION ARIMA X-12-ARIMA AUTOMDL AIC ARIMA t ARIMA 1 REGARIMA ARIMA AIC X - 12-ARIMA
46 OUTLIER AIC X - 12-ARIMA Reference Manual 4.5 Use of model selection criteria Bureau of the Census[38],p.30 Users of the model selection criteria (consider AIC for concreteness) should also be careful when comparing models for which X- 12- ARIMA is used to perform outlier detection. Outlier detection looks for the most statistically significant outliers, which are also (approximately) the outliers with the largest effect on the likelihood, and consequently on AIC. The result of this is that models with more outliers are almost always better as far as AIC is concerned, often substantially better. Therefore, AIC is generally inappropriate for comparing models with different outlier terms. X - 12-ARIMA outlier AIC AIC AIC X- 12-ARIMA ARIMA (0 1 1)(0 1 1
47 OUTLIER REGRESSION ARIMA ARIMA AIC 1 ARIMA AIC AIC ARIMA ARIMA ARIM AIC 1998 X - 12-ARIMA ARIMA ZAIC ARIMA p d q P D Q AIC AIC AIC ZAIC X - 12-ARIMA AUTOMDL AIC
48 TDNOLPYEAR ARIMA AIC ARIMA (0 1 0)(0 1 0) (2 1 2)(2 1 2) (0 1 0)(0 1 0) (3 1 3)(3 1 3) 256 p,q,p,q ARIMA HISTORY (0 1 0)(0 1 0) (2 1 2)(2 1 2) X - 12-ARIMA IDENTIFY 26 p.1617 AIC ARIMA AIC Bureau of the Census[38], p.30 ARIMAp,d,q integrated process AIC 7 ARIMA TDNOLPYEAR 7
49 2 p AIC AIC Revision Histories MAPR AIC MAPR MAPR OUTLIER ARIMA (0 1 1)(0 1 1) X - 12-ARIMA Mathematical Statistician Brian C. Monsell X - 12-ARIMA Monsell E Monsell One thing I would suggest is that you make sure you use the same outliers/regression for all the AIC calculations you do with this method.( this AIC ARIMA ) The inclusion of a single outlier can have a drastic effect on the likelihood. I would suggest doing outlier and AIC regression tests on the (0 1 1)(0 1 1) model first,
50 so as not to bias your testing procedure with different outlier choices. (Monsell E ) (0 1 1)0 1 1 ARIMA airline model X - 12-ARIMA AUTOMDL (0 1 1)(0 1 1),(0 1 2)(0 1 1),(2 1 0)(0 1 1), (0 2 2)(0 1 1),(2 1 2)(0 1 1) (0 1 1)(0 1 1) AUTOMDL default Monsell default very robust G mez, Vctor and Agustn Maravall [40],p , REGARIMA ARIMA AIC ARIMA ARIMA AR MA ARIMA 26 p.20
51 2 ARIMAp d q 14 MA(1) AR(2) ARMA(1,1) MA(1) AR(2) ARMA(1,1) [32]p.9798 Box=Jenkins Box=Jenkins
52 Box=Jenkins information criteria AIC AIC (Akaike's Information Criterion) AIC 2 ˆ (pq ARIMA AR MA T )) AIC 1 1 p q 2 AIC log ˆ AIC 2(p+q) AIC A IC ARIMA
53 AIC MAPR
54 (1) TDNOLPYEAR X - 12-ARIMA REGRESSION VARIABLES TDNOLPYEAR Bell and Hillmer[37 X - 12-ARIMA Bureau of the Census[38],p.17X ARIMA REGRESSION TDNOLPYEAR t 2 2 p 1 1 TDNOLPYEAR
55 p (2) X ARIMA TDNOLPYEAR Labor Day Thanksgiving Day( ) Easter( ) X - 12-ARIMA (A) (B) 2 17 (A)(B) Holiday1 Holiday p.210~
56 Holiday1 Holiday
57 (3) TD1NOLPYEAR X - 12-ARIMA REGRESSION WEEKDAY LPYEAR X - 12-ARIMA REGRESSION TRANFORM ADJUST=LPYEAR Y t m t Y t /mt
58 REGRESSION VARIABLES=TD TRANSFORM TDNOLPYEAR TRANSFORM TDNOLPYEAR LPYEAR TRANSFORM 1 REGRESSION VARIABLES=TD 1 (0 1 1)(0 1 1) X - 12-ARIMA OUTLIER (a) additive outlier AO (b) level shift LS (c) temporary change TC exponentially)
59 X- 12-ARIMA 1991 LS AIC AIC (1) AIC AIC MAPR 16 X- 12- ARIMA MAPR 18 MAPR MAPR X-12- ARIMA MAPR X- 11
60 (1) X - 12-ARIMA MAPR X - 11 X - 12-ARIMA X-12-ARIMA 2+ X - 12-ARIMA MAPR X-11 (1) 1 12 p t t AIC TDNOLPYEAR) LPYEAR AIC MAPR 0.48 MAPR 0.48 AIC MAPR
61 AIC MAPR AIC MAPR X X - 12-ARIMA 0.67 X - 12-ARIMA AIC (2 1 2)(2 1 2) 81 ARIMA AIC (1 1 2)(2 1 2) (2 1 2)(0 1 (2 1 2)(2 1 2 ARIMA (2) 2 12 AIC AIC MAPR AIC MAPR MAPR X X - 12-ARIMA 0.76 X - 12-ARIMA
62 0.59 (3) AIC MAPR AIC MAPR MAPR X X - 12-ARIMA 0.90 MAPR X - 12-ARIMA (4) 12 AIC MAPR MAPR MAPR 0 AIC MAPR AIC AIC
63 MAPR MAPR X X - 12-ARIMA 1.20 (5) 12 AIC 4 MAPR MAPR AIC MAPR MAPR X (6) AIC AIC MAPR 1.34 AIC MAPR MAPR X
64 (7) t 12 AIC 0 MAPR AIC MAPR MAPR X X ARIMA 0.95 X - 12-ARIMA AIC 10 MAPR 1.04 AIC 10 MAPR MAPR MAPR
65 MAPR MAPR MAPR MAPR (8) 1 M 1 AIC AIC MAPR
66 (9) AIC AIC MAPR X X - 12-ARIMA AIC MAPR MAPR (10) 7 2 t 4.95 AIC 12 7 MAPR 1 t AIC AIC
67 AIC 1 (11)
68 AIC MAPR 0.04 X - 12-ARIMA ARIMA (0 1 1)(0 1 1) ARIMA AIC TC AO (2 1 2)(1 1 2) AIC MAPR X - 11 MAPR 0.05 X - 12-ARIMA 2 X - 12-ARIMA MAPR X-11 (12) 1 12 t AIC
69 MAPR 2.16 MAPR 6 AIC MAPR X-11 MAPR 1.83 X-12-ARIMA MAPR 1.9 MAPR X- 12-ARIMA X- 12- ARIMA X- 11 (13) AIC MAPR 0.01 MAPR AIC (1) MAPR X- 11 MAPR X-12- ARIMA X-12-
70 ARIMA X - 12-ARIMA 1 1 (14) t p MAPR ARIMA ARIMA AIC 10 LS 10 MAPR MAPR 1.01 X - 11 MAPR 1.14 (15)
71 6 AIC MAPR 0.02 X - 12-ARIMA X- 11 MAPR 4.04 X - 12-ARIMA (16) AIC MAPR X - 12-ARIMA X- 11
72 MAPR A X ARIMA MAPRB A C X - 12-ARIMA MAPRD B E A F AIC MAPR X-11 X ARIMA MAPR MAPR X - 12-ARIMA MAPR X - 11 MAPR A B C D E B A MAPR A B X - 12-ARIMA ARIMA MAPR 1 X - 11 MAPRA X - 12-ARIMA MAPR D 15 41
73 MAPR X - 11 X - 12-ARIMA X - 12-ARIMA MAPR X - 12-ARIMA MAPR 0.01 X - 12-ARIMA MAPR B D B D B D 2 X ARIMA MAPR X ( ) D B A 18 B A 30 X - 12-ARIMA MAPR X - 11 X - 12-ARIMA X - 11 X - 12-ARIMA
74 X - 12-ARIMA X-12-ARIMA X - 12-ARIMA X- 12-ARIMA X - 12-ARIMA X - 12-ARIMA X - 11 MAPRA X - 12-ARIMA MAPRB 14 B A X X - 12-ARIMA X - 11 X - 12-ARIMA
75 19 19 X - 11 MAPR X - 12-ARIMA MAPR 1 MAPR X -11 X - 12-ARIMA MAPR
76 X - 12-ARIMA X-12- ARIMA MAPR X X - 12-ARIMA X X - 12-ARIMA X - 12-ARIMA X - 12-ARIMA X - 11 MAPRA ) D )) X - 12-ARIMA MAPRB ) E )) C D
77 X - 11 X - 12-ARIMA 11 X - 11 MAPR 0.05 X - 12-ARIMA MAPR X - 11 X - 12-ARIMA MAPR 12 MAPR X - 11 MAPR A 1.83 X - 12-ARIMA MAPR B D 3.42 E X - 12-ARIMA MAPR X - 11 X ARIMA
78 MAPR X - 11 X - 12-ARIMA 14 X - 11 MAPR X - 12-ARIMA MAPR X - 12-ARIMA 15 X - 11 MAPR 4.04 X - 12-ARIMA MAPR MAPR X - 11 X - 12-ARIMA X - 11 X-12-ARIMA 16 2 A X X
79 11 MAPR X - 11 X - 12-ARIMA X - 11 X - 12-ARIMA MAPR 2 X X-12-ARIMA 13 X - 11 X - 12-ARIMA MAPR X - 11 X - 12-ARIMA MAPR MAPR X - 12-ARIMA 11 X - 11 X - 12-ARIMA MAPR X - 11 X - 12-ARIMA MAPR 16 14
80 2 model1 model 2 1 model2 ( ) model3 model4 model1 X - 12-ARIMA TRANSFORM adjust=lom
81 model1 model AIC TDNOLPYEAR model ) )
82
83 [6][ 2]
84 (1) (2) (3) (1) ) (2) (2) 4.4 (3) 4.4 X - 11 X - 12-ARIMA X - 11 (2)
85 S 4.4 X - 11 X - 12-ARIMA (2)(3) (2) 13 (3) X - 11 X - 12-ARIMA MAPR X - 12-ARIMA (2)(3) 4.4 (2)X (3)X - 12-ARIMA 17.5 (2) X ARIMA
86 X - 12-ARIMA X-11 X - 12-ARIMA X B A X - 11 X - 12-ARIMA 1999 [25]p X-12-ARIMA B X - 12-ARIMA X - 11 A B X - 12-ARIMA X - 11 MAPR X - 12-ARIMA X - 11 X ARIMA X - 12-ARIMA X - 11 X - 12-ARIMA
87 X - 11 X - 12-ARIMA X X - 11 X - 12-ARIMA X - 11 X X - 11 X ARIMA X- 12- ARIMA X X - 12-ARIMA X - 11 X - 12-ARIMA X - 12-ARIMA X
88 1997 2,000cc 10 2,000cc ) X- 12-ARIMA ) (1) X - 11 (2) AIC X - 12-ARIMA X - 11 (3) X - 12-ARIMA (4) X - 12-ARIMA X - 11 X - 12-ARIMA X (3)X- 12-ARIMA (2) X - 12-ARIMA MAPR X - 11 X- 12-ARIMA X - 11
89 1997 X - 12-ARIMA X X - 12-ARIMA X - 11 X ARIMA X - 12-ARIMA MAPR X - 11 X - 12-ARIMA X - 11 X - 12-ARIMA REGARIMA ARIMA airline model (0 1 1)(0 1 1)ARIMA X - 12-ARIMA OUTLIER AIC ARIMA (0 1 0)(0 1 0) (2 1 2)(2 1 2) 81
90 AIC AIC ARIMA REGARIMA ARIMA ARIMA AIC airline model REGARIMA ARIMA ARIMA AR MA ARIMA AIC ARIMA ARIMA ARIMA X - 12-ARIMA IDENTIFY
91 1 ARIMA(p d q) ARIMA(P D Q)p,q,P,Q(p,q ARIMA AR MA P Q ARIMA AR MA 26 p.19) P Q P 12 Q 12 ARIMA (4 1 1)(2 1 1) (3 1 1)(1 1 1) (2 1 1)(2 1 1) (3 1 3)(2 1 2) (1 1 1)(1 1 1) (2 1 1)(1 1 1) (2 1 1)(1 1 1 ARIMA
92 (4 1 1)(3 1 1) X - 12-ARIMA ARIMA LINE 111 ARIMAMODEL=(4 1 1)(3 1 1 ERROR ORDER OF THE AR OPERATOR IS TOO LARGE ARIMA AR P ) (4 1 1)(2 1 1) ARIMA 1 ARIMA AIC AIC MAPR AIC MAPR
93 ATIMA ARIMA AIC ARIMA (2 1 1)(2 1 2) ARIMA (4 1 1)(2 1 1) REGARIMA AIC AIC AIC SRIMA REGARIMA MAPR REGARIMA (3 1 1)(1 1 1) AIC ARIMA
94 AO AIC MAPR [ ] AIC MAPR MAPR p X - 12-ARIMA MAPR ( REARIMA MAPR MAPR MAPR 0.05 MAPR
95 MAPR MAPR MAPR MAPR p ARIMA AIC ARIMA 10 MAPR ARIMA (0 1 1)(0 1 1) MAPR ARIMA MAPR
96 A B A B X - 12-ARIMA AIC MAPR A B AO AIC AIC MAPR 0.59 B AIC MAPR 0.62 A B AIC A MAPR A AIC A B A AIC MAPR B AIC
97 AO MAPR 1.20 AIC AIC MAPR AIC MAPR A AIC MAPR 0.29 B AIC MAPR 0.31 B AIC A MAPR 0.32 B A AIC A LS1989.4, LS1997.4, AO B AIC B A AIC MAPR A B LS1989.1,
98 LS1989.4, LS1997.4, AO ) AIC MAPR AIC AO , AO1990.4, LS ) AIC MAPR 0.23 AIC MAPR 0.22 AIC MAPR 0.01 AIC MAPR B AIC MAPR 0.22 AIC MAPR AIC AIC ARIMA A MAPR 0.01 B A B
99 AIC MAPR ARIMA REGARIMA ARIMA AIC MAPR AIC ARIMA X - 12-ARIMA
100 AIC ARIMA p 0.00 t (1) (2) (3) X-12-ARIMA
101 2000 X - 12-ARIMA X - 12-ARIMA X - 12-ARIMA ARIMA X - 12-ARIMA MITI X - 12-ARIMA MITI X- 12-ARIMA
102 MITI MITI X - 11X - 12-ARIMA X X - 12-ARIMA X - 11 X - 12-ARIMA X - 12-ARIMA X- 12-ARIMA X p.4647 X - 12-ARIMA X - 11 X - 12-ARIMA 9 16
103 X - 12-ARIMA (1) (2) (1) ARIMA X - 12-ARIMA REGARIMA ARIMA ARIMA (0 1 1)(0 1 1) AIC ARIMA AIC ARIMA (2) X ARIMA
104 1 2 X - 12-ARIMA X - 12-ARIMA X - 11 X - 12-ARIMA X - 11 TDNOLPYEAR LPYEAR AIC MAPR 1 X - 12-ARIMA X - 11 M 2CD
105 X - 12-ARIMA X - 12-ARIMA X - 11 X - 12-ARIMA X - 11 X - 12-ARIMA X - 12-ARIMA X - 11 ARIMA X-12-ARIMA
106 X ARIMA DECOMP
107 p.2126 X - 12-ARIMA p.144 X - 12-ARIMA p p IMES Discussion Paper 96-J X - 12-ARIMA p p p p X - 12-ARIMA
108 25 p II 1999 p p p.1016 X - 12-ARIMA 25 I 1997 p II 1997 p p
109 X - 12-ARIMA 27 III p p.7596 X - 12-ARIMA X - 12-ARIMA X - 12-ARIMA No.3, 1998 p II 1997 p p p.1520 X - 12-ARIMA p.1419
110 p.814 Bell, W.R., and S.C.Hillmer, Modelling Time Series with Calendar Variation. Journal of the American Statistical Association, 78, 1983, pp Bureau of the Census, X - 12-ARIMA Reference Manual, version 0.2.6, March 23, Findley, David F. Brian C. Monsell, William R. Bell, Mark C. Otto, New Capabilities and Methods of the X- 12- ARIMA Seasonal- Adjustment Program. Journal of Business and Economic Statistics, Vol.16, No.2, April 1998, p Gomez, Victor and Agustin Maravall, Programs Tramo and Seats Instructions for the User (Beta Version: November 1997) Hylleberg,S. ed., Modelling Seasonality, Oxford Univer- sity Press, Shiskin, J., Young, A. H., and Musgrave, J. C., The X- 11 Variant of the Census Method II Seasonal Adjustment Program, Technival Paper 15, Bureau of the Census, U.S. Department of Commerce, Vandaele, Walter, Applied Time Series and Box-Jenkins Models, Academic Press, New York, 1983.W. 1988
111 X-12-ARIMA X - 12-ARIMA ARIMA X - 11 REGARIMA data generating process ARIMA GDP ARIMA Box=Jenkins ARIMA ARIMA
112 AR MA ) ARIMA ARIMA ARIMA X - 12-ARIMA ARIMA ARIMA ARIMA X - 12-ARIMA
113 X ARIMA MAPR X ARIMA X - 11 X - 12-ARIMA MAPR 19 X - 11 MAPR X - 11 X - 12-ARIMA MAPR
114 MAPR MAPR MAPR AIC BIC MAPR MAPR crucial MAPR ATM 500
115 time variant time invariant ATM time variant X-12-ARIMA data generating process X - 12-ARIMA ARIMA AR MA X - 12-ARIMA ARIMA X-12- ARIMA X - 12-ARIMA
116 X - 11 X - 12-ARIMA 13
117 REGARIMA X- 12-ARIMA X - 11 X - 12-ARIMA REGARIMA X- 12-ARIMA AIC MAPR
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