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1 CIRJE-J-58 X-12-ARIMA 2000 :
2 How to use X-12-ARIMA2000 when you must: A Case Study of Hojinkigyo-Tokei Naoto Kunitomo Faculty of Economics, The University of Tokyo Abstract: We illustrate how to use the X-12-ARIMA program developed by the U. S. Census Bureau when you have to make seasonal adjustment data at the statistical division of the central government. As an i llustration we use the Hojinkigyo -Toukei, which is one of the major statistics including sales and investments data by corporate firms in Japan. We shall discuss reasonable ways to use and/or not to use the procedures available in the X-12-ARIMA (2000) pr ogram.
3 X-12-ARIMA(2000) X-11 X-12-ARIMA DECOMP X-12-ARIMA(2000) X-11X-12-ARIMA(2000)DECOMP 1
4 1. X-11 X-12-ARIMA () X-12-ARIMA2000 X-12-ARIMA(2000) 2
5 X-12-ARIMA X-11, X-12-ARIMA, Decomp 3
6 2. X-12-ARIMA X-12-ARIMA 1 X-12-ARIMA(2000) X-12-ARIMA(2000) X-12 Experimental Version X-12-ARIMA(β Version) β Version 2 X-12-ARIMA X-12-ARIMA(1998) β Version X- 12-ARIMA Version X-12-ARIMA(2000) (2001) U.S.Census Bureau (2000) (2001) X-12-ARIMA X-12-ARIMA(β Version) (1997) (1997) 1 (2001) 2 X-12-ARIMA Corrections() 4
7 X-12-ARIMA Findley et.al. (1998) (Technical Report) X-12-ARIMA statistical time series analysis spectral analysis periodogram NBERNational Bureau of Economic ResearchJulius Shiskin (Bureau of Labor Statistics) (moving average method) MITI 5
8 -III experimental methods Shiskin et.al. (1967) X-11 3 FORTRAN X-11 X-11 X-11 (Box=Jenkins (1976)) ARMA E.Dagun X-11-ARIMA X-11 ARIMA 4 X-11-ARIMA 3 (1983) 4 Autoregressive Integrated Moving Average Model 6
9 David FindleyX-12 X-11 X-11-ARIMA X-12-ARIMA (A.Zellner) BAYSEA BAYSEA DECOMP (1993) DECOMP Web-decomp Web sato =12 7
10 X-11 X-12-ARIMA DECOMP X-12-ARIMA 5 X-12-ARIMA 1-1, 2-1, 3-1, () X-12-ARIMA 5 (2001) 8
11 (statistical time series analysis) DECOMP 1-2(a) 6 X-12-ARIMA ARIMA (d + D>1) Web-Decomp (b) X-11 X-12-ARIMA 7 X-12-ARIMA 6 http : // sato Web-Decomp Web-Decomp Web-Decomp Decomp AR() 0 7 9
12 ARIMA 8 Web-Decomp 2-2(a) 2-2(b) ARIMA (d + D>1) 8 X-12-ARIMA transform() (2001) 10
13 Web-Decomp 3-2(a) 3-2(b) Web-Decomp 4-2 X-12-ARIMA ARIMA 4. X-12-ARIMA X-12-ARIMA X-12-ARIMA 9 X-12-ARIMA 9 X-12-ARIMA (2001) 11
14 X-12-ARIMA X-12-ARIMA Findley et. al. (1998) ( 5-1 ) X-12-ARIMA () {Y t, 1 t T } {y t } RegARIMA (forecasts) (backcasts) (regression) {Yt, H +1 t T + H} H ( 1) RegARIMA () {Yt } X-11 {Yt, 1 t T } X-11 X-11 X-11 () MPD 10 X-12-ARIMA X-11 RegARIMA 1 ( ) {y t,t =1, 2, } {y t } r {x it } r (4.1) φ p (B)Φ P (B s )(1 B) d (1 B s ) D (y t β i x it )=θ q (B)Θ Q (B s )a t. i=1 10 X-12-ARIMA X-12-ARIMA (U.S.Census Bureau (2000)) (2001) 12
15 y t () B (By t = y t 1 ) 11 s =(4 12), p, d, q, P, D, Q z φ p (z) =1 φ 1 z φ p z p, Φ p (z) =1 Φ 1 z Φ p z P,θ q (z) =1 θ 1 z θ q z q, Θ Q (z) =1 Θ 1 z Θ Q z Q Φ(B s ), Θ(B s ) B s (B s y t = y t s ) β i (i =1,,r), φ i (i =1,,p), Φ i (i =1,,P), θ i (i =1,,q), Θ i (i =1,,Q) {a t }, σ 2 (σ) t RegARIMA (linear regression) ARIMA() ARIMA (seasonal)arima (4.1) D =0, Φ P (z) =Θ Q (z) =1 ARIMA ARIMA ARIMA ARIMA (p, d, q) (P, D, Q) s (p, d, q)(p, D, Q)s Box=Jenkins(1976) ARIMA RegARIMA RegARIMA X-12-ARIMA (i)arima RegARIMA (identification) (4.2) (1 B) d (1 B s ) D y t = w t w r w t (r<t) t r 11 () B 2 y t = B(By t )=B(y t 1 )=y t 2 (1 B s )y t = y t y t s 13
16 d D (autocorrelation function acf) 12 (partial autocorrelation function pacf) acf pacf (stationary stochastic processes) d + D 1 d = D =1 I(2) I(2) overdifferencing 13 (ii) ARIMA (p) (q) (P) (Q) X-12-ARIMA automodel() ARIMA X-12-ARIMA 14 (Akaike s Information Criterion AIC) AIC AIC AIC 12 s γ(s) =E[(y t µ)(y t s µ)] s E( ) µ = E(y t ) 13 (1985) 14 Akaike(1973) (1989) 14
17 1ARIMA 1 (0,1,1) (0,1,1)4 2 (1,1,0) (0,1,1)4 3 (1,1,1) (0,1,1)4 4 (2,1,0) (0,1,1)4 5 (0,1,2) (0,1,1)4 6 (2,1,1) (0,1,1)4 7 (1,1,2) (0,1,1)4 8 (2,1,2) (0,1,1)4 (1) AIC AIC case case case case case case case case () AIC (common factor) ARIMA (AR) (MA) 15
18 (2) AIC AIC case case case case case case case case (3) AIC AIC case case case case case case case case (4) AIC AIC case case case case case case case case () 16
19 (iii) X-12-ARIMA X-11 X-12-ARIMA X-12-ARIMA regression() outlier() regression() X- 12-ARIMA (AO) (LS) AIC regression() arima( ) ARIMA AIC 17
20 AIC ARIMA RegARIMA X-12-ARIMA X-12-ARIMA outlier() X-12-ARIMA RegARIMA (non-stationary time series) (change point) 16 Findley et.al. (1998) (iv) X-12-ARIMA RegARIMA RegARIMA 17 X-12-ARIMA 1-3(a) 1-3(b) (v) X-12-ARIMA (2000) 18
21 X-12-ARIMA slidingspans() history() (vi) X-12-ARIMA X-11, X-12, DECOMP X-11, X-12-ARIMA, DECOMP X-11 X-12-ARIMA X-11 X-11 X-11 X-11 X-12-ARIMA RegARIMA 19 X-12-ARIMA X-11 X-11 X-11 X-12-ARIMA X-11 X-12-ARIMA DECOMP 18 (2000) 19 X-11 (1983) 19
22 Web-decomp 20 X-12-ARIMA 1-3(a) 1-3(b) X-11 Decomp 1-3(c) 1-3(d) 1-4(a) 1-4(b) X-12-ARIMA X-11 X-12-ARIMA X-11 RegARIMA X-12-ARIMA DECOMP X-11 X X-12-ARIMA ARIMA d=d=1 DECOMP AIC X-12-ARIMA 20
23 X-12-ARIMA 2-3 X-12-ARIMA 2-4(a) 2-4(b) X-11 X-12-ARIMA DECOMP X-12-ARIMA DECOMP 3-3(a) 3-3(b) 3-4(a) 3-4(b) X-11 X-12-ARIMA DECOMP X-11 X-12-ARIMA X-12-ARIMA DECOMP 4-3(a) 4-3(b) 21
24 X-12-ARIMA X (c) 4-3(c) X-12-ARIMA RegARIMA DECOMP X-11 X-12-ARIMA X-12-ARIMA DECOMP X-12-ARIMA RegARIMA ARIMA AIC X-12-ARIMA composite() RegARIMA (direct method) (indirect method) 22
25 6. X-12-ARIMA(2000) X-11, X-12-ARIMA, DECOMP X-11 X-12-ARIMA X-11 X-12-ARIMA DECOMP X-11 X-11 X-11 X-12-ARIMA DECOMP X-11 X-12-ARIMA RegARIMA X-12-ARIMA 23
26 X-12-ARIMA X-12-ARIMA X-12-ARIMA X-12-ARIMA RegARIMA DECOMP X-12-ARIMA composite() 21 X-12-ARIMA RegARIMA 22 X-12-ARIMA X-12-ARIMA RegARIMA X-12-ARIMA DECOMP
27 7. Akaike, H. (1973), Information Theory and an Extension of the Likelihood Principle, in the Second International Symposium on Information Theory, eds. B.N. Petrov and F. Czaki, Budapest: Akademia Kiado, Box, G.E.P., and G.M. Jenkins (1976), Time Series Analysis: Forecasting and Control, San Francisco: Holden Day. Findley, D.F., B.C. Monsell, W.R. Bell, M.C. Otto, B.C. Chen (1998), New Capabilities and Methods of the X-12-ARIMA Seasonal Adjustment Program, Journal of Business and Economic Statistics, 16, (with Discussion). U.S. Bureau of Census (2000), X-12-ARIMA Reference Manual Version 0.2.7, Statistical Research Division, http : // (1989), (), A.C. (1985) (1993) (1997) X-12-ARIMA, Discussion Paper No. J-97-1 Vol.25-1 http : // tokyo.ac.jp (2001) X-12-ARIMA2000 Discussion Paper No. CIRJE-J-47, http : // tokyo.ac.jp/cirje/research/03research02dp j/html (1983)() (2000) (1997) 25
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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－
17 12 100-8970 3-1-1 03-3581-9747( ) X-12-ARIMA * 2000 4 13 1999 3 X-12-ARIMA X-12- ARIMA 1979 X11 X12ARIMA 1 X12ARIMA 2 X12ARIMA REGARIMA X12ARIMA X12ARIMA REGARIMA X12ARIMA 1979 54 MITI X - 11 1979
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