国土技術政策総合研究所資料

Similar documents
国土技術政策総合研究所　研究資料

²�ËÜËܤǻþ·ÏÎó²òÀÏÊÙ¶¯²ñ - Â裱¾Ï¤ÈÂ裲¾ÏÁ°È¾

国土技術政策総合研究所　研究資料


N cos s s cos ψ e e e e 3 3 e e 3 e 3 e

Microsoft Word - 表紙.docx

橡表紙参照.PDF

医系の統計入門第 2 版 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 第 2 版 1 刷発行時のものです.

McCain & McCleary (1979) The Statistical Analysis of the Simple Interrupted Time-Series Quasi-Experiment

日本内科学会雑誌第102巻第4号

chap9.dvi

時系列データ解析による予測と最適化 ～エネルギー需要、発電、価格のモデリング～

Ł\”ƒ-2005

第90回日本感染症学会学術講演会抄録（I）

chap10.dvi

y = x x R = 0. 9, R = σ $ = y x w = x y x x w = x y α ε = + β + x x x y α ε = + β + γ x + x x x x' = / x y' = y/ x y' =

fiúŁÄ”s‘ê‡ÌŁª”U…−…X…N…v…„…~…A…•‡Ì ”s‘ê™´›ß…−…^†[…fiŠ‚ª›Âfl’«

LA-VAR Toda- Yamamoto(1995) VAR (Lag Augmented vector autoregressive model LA-VAR ) 2 2 Nordhaus(1975) 3 1 (D2)

研究シリーズ第40号

微分積分 サンプルページ この本の定価 判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです.

金融政策の波及経路と政策手段

untitled

.2 ρ dv dt = ρk grad p + 3 η grad (divv) + η 2 v.3 divh = 0, rote + c H t = 0 dive = ρ, H = 0, E = ρ, roth c E t = c ρv E + H c t = 0 H c E t = c ρv T

ii 3.,. 4. F. (), ,,. 8.,. 1. (75%) (25%) =7 20, =7 21 (. ). 1.,, (). 3.,. 1. ().,.,.,.,.,. () (12 )., (), 0. 2., 1., 0,.

Stata 11 Stata ts (ARMA) ARCH/GARCH whitepaper mwp 3 mwp-083 arch ARCH 11 mwp-051 arch postestimation 27 mwp-056 arima ARMA 35 mwp-003 arima postestim

基礎数学I

Lecture 12. Properties of Expanders

201711grade1ouyou.pdf

1 Tokyo Daily Rainfall (mm) Days (mm)

10

LCC LCC INOUE, Gaku TANSEI, Kiyoteru KIDO, Motohiro IMAMURA, Takahiro LCC 7 LCC Ryanair 1 Ryanair Number of Passengers 2,000,000 1,800,000 1,

日本内科学会雑誌第98巻第4号

日本内科学会雑誌第97巻第7号

D = [a, b] [c, d] D ij P ij (ξ ij, η ij ) f S(f,, {P ij }) S(f,, {P ij }) = = k m i=1 j=1 m n f(ξ ij, η ij )(x i x i 1 )(y j y j 1 ) = i=1 j

抄録／抄録１　　　　（１）Ｖ

時系列データ解析による予測と最適化 ～エネルギー需要、発電、価格のモデリング～

パーキンソン病治療ガイドライン2002

研修コーナー

Myers, Montgomery & Anderson-Cook (2009) Response Surface Methodology

seminar0220a.dvi

COE-RES Discussion Paper Series Center of Excellence Project The Normative Evaluation and Social Choice of Contemporary Economic Systems Graduate Scho

renshumondai-kaito.dvi

On model selection problems in terms of prediction mean squared error and interpretaion of AIC (slides)

II III II 1 III ( ) [2] [3] [1] 1 1:

,,,,., = (),, (1) (4) :,,,, (1),. (2),, =. (3),,. (4),,,,.. (1) (3), (4).,,., () : = , ( ) : = F 1 + F 2 + F 3 + ( ) : = i Fj j=1 2

ii 3.,. 4. F. ( ), ,,. 8.,. 1. (75% ) (25% ) =7 24, =7 25, =7 26 (. ). 1.,, ( ). 3.,...,.,.,.,.,. ( ) (1 2 )., ( ), 0., 1., 0,.

Dirac 38 5 Dirac 4 4 γ µ p µ p µ + m 2 = ( p µ γ µ + m)(p ν γ ν + m) (5.1) γ = p µ p ν γ µ γ ν p µ γ µ m + mp ν γ ν + m 2 = 1 2 p µp ν {γ µ, γ ν } + m

% 10%, 35%( 1029 ) p (a) 1 p 95% (b) 1 Std. Err. (c) p 40% 5% (d) p 1: STATA (1). prtesti One-sample test of pr

untitled

本文／目次（裏白）

SO(3) 7 = = 1 ( r ) + 1 r r r r ( l ) (5.17) l = 1 ( sin θ ) + sin θ θ θ ϕ (5.18) χ(r)ψ(θ, ϕ) l ψ = αψ (5.19) l 1 = i(sin ϕ θ l = i( cos ϕ θ l 3 = i ϕ

6.1 (P (P (P (P (P (P (, P (, P.

..3. Ω, Ω F, P Ω, F, P ). ) F a) A, A,..., A i,... F A i F. b) A F A c F c) Ω F. ) A F A P A),. a) 0 P A) b) P Ω) c) [ ] A, A,..., A i,... F i j A i A

量子力学 問題

ii 3.,. 4. F. (), ,,. 8.,. 1. (75% ) (25% ) =9 7, =9 8 (. ). 1.,, (). 3.,. 1. ( ).,.,.,.,.,. ( ) (1 2 )., ( ), 0. 2., 1., 0,.

評論・社会科学　１２３号（Ｐ）☆／１．福田

Hi-Stat Discussion Paper Series No.248 東京圏における 1990 年代以降の住み替え行動 住宅需要実態調査 を用いた Mixed Logit 分析 小林庸平行武憲史 March 2008 Hitotsubashi University Research Unit

JFE.dvi

, 1), 2) (Markov-Switching Vector Autoregression, MSVAR), 3) 3, ,, , TOPIX, , explosive. 2,.,,,.,, 1

1. 1 A : l l : (1) l m (m 3) (2) m (3) n (n 3) (4) A α, β γ α β + γ = 2 m l lm n nα nα = lm. α = lm n. m lm 2β 2β = lm β = lm 2. γ l 2. 3

Auerbach and Kotlikoff(1987) (1987) (1988) 4 (2004) 5 Diamond(1965) Auerbach and Kotlikoff(1987) 1 ( ) ,

○松本委員

80 X 1, X 2,, X n ( λ ) λ P(X = x) = f (x; λ) = λx e λ, x = 0, 1, 2, x! l(λ) = n f (x i ; λ) = i=1 i=1 n λ x i e λ i=1 x i! = λ n i=1 x i e nλ n i=1 x


waseda2010a-jukaiki1-main.dvi

( ) Note (e ) (µ ) (τ ) ( (ν e,e ) e- (ν µ, µ ) µ- (ν τ,τ ) τ- ) ( ) ( ) (SU(2) ) (W +,Z 0,W ) * 1) 3 * 2) [ ] [ ] [ ] ν e ν µ ν τ e

AR(1) y t = φy t 1 + ɛ t, ɛ t N(0, σ 2 ) 1. Mean of y t given y t 1, y t 2, E(y t y t 1, y t 2, ) = φy t 1 2. Variance of y t given y t 1, y t

151021slide.dvi

総研大恒星進化概要.dvi

autocorrelataion cross-autocorrelataion Lo/MacKinlay [1988, 1990] (A)

財政赤字の経済分析：中長期的視点からの考察

6.1 (P (P (P (P (P (P (, P (, P.101

( ) s n (n = 0, 1,...) n n = δ nn n n = I n=0 ψ = n C n n (1) C n = n ψ α = e 1 2 α 2 n=0 α, β α n n! n (2) β α = e 1 2 α 2 1

カルマンフィルターによるベータ推定（ ）

( )/2 hara/lectures/lectures-j.html 2, {H} {T } S = {H, T } {(H, H), (H, T )} {(H, T ), (T, T )} {(H, H), (T, T )} {1


生活設計レジメ

44 4 I (1) ( ) (10 15 ) ( 17 ) ( 3 1 ) (2)

I II III 28 29


1 (Contents) (1) Beginning of the Universe, Dark Energy and Dark Matter Noboru NAKANISHI 2 2. Problem of Heat Exchanger (1) Kenji

オーストラリア研究紀要　３６号（Ｐ）☆／３．橋本

untitled

Autumn II III Zon and Muysken 2005 Zon and Muysken 2005 IV II 障害者への所得移転の経済効果 分析に用いるデータ

陦ｨ邏・2

I II III IV V


02.„o“φiflì„㙃fic†j

デフォルト相関係数のインプライド推計（ ）

1 (Berry,1975) 2-6 p (S πr 2 )p πr 2 p 2πRγ p p = 2γ R (2.5).1-1 : : : : ( ).2 α, β α, β () X S = X X α X β (.1) 1 2

ファイナンスのための数学基礎 第1回　オリエンテーション、ベクトル

# GDP 1 GDP 1992 GDP Hamilton and Flavin (1986) Doi and Ihori(2003) (2007) 2 Bohn(1998) /GDP Bohn # 1 2 Broda

t χ 2 F Q t χ 2 F 1 2 µ, σ 2 N(µ, σ 2 ) f(x µ, σ 2 ) = 1 ( exp (x ) µ)2 2πσ 2 2σ 2 0, N(0, 1) (100 α) z(α) t χ 2 *1 2.1 t (i)x N(µ, σ 2 ) x µ σ N(0, 1

22 / ( ) OD (Origin-Destination)

Milnor 1 ( ), IX,. [KN].,. 2 : (1),. (2). 1 ; 1950, Milnor[M1, M2]. Milnor,,. ([Hil, HM, IO, St] ).,.,,, ( 2 5 )., Milnor ( 4.1)..,,., [CEGS],. Ω m, P

1990年代以降の日本の経済変動


untitled

* n x 11,, x 1n N(µ 1, σ 2 ) x 21,, x 2n N(µ 2, σ 2 ) H 0 µ 1 = µ 2 (= µ ) H 1 µ 1 µ 2 H 0, H 1 *2 σ 2 σ 2 0, σ 2 1 *1 *2 H 0 H

q π =0 Ez,t =ε σ {e ikz ωt e ikz ωt } i/ = ε σ sinkz ωt 5.6 x σ σ *105 q π =1 Ez,t = 1 ε σ + ε π {e ikz ωt e ikz ωt } i/ = 1 ε σ + ε π sinkz ωt 5.7 σ

Transcription:

ISSN 1346-7328 国総研資料第 652 号平成 23 年 9 月 国土技術政策総合研究所資料 TECHNICAL NOTE of Naional Insiue for Land and Infrasrucure Managemen No.652 Sepember 2011 航空需要予測における計量時系列分析手法の適用性に関する基礎的研究 ~ 季節変動自己回帰移動平均モデル及びベクトル誤差修正モデルの適用性 ~ 井上岳 丹生清輝 Sudy on Applicaion of Time-series Analysis o Air Transpor Demand Esimaion Gaku INOUE, Kiyoeru TANSEI 国土交通省国土技術政策総合研究所 Naional Insiue for Land and Infrasrucure Managemen Minisry of Land, Infrasrucure, Transpor and Tourism, Japan

No.652 2011 9 (YSK-N-238) * ** (ARIMA) 5-10 (VECM) GDP GDP GDP GDP : (ARIMA) (VECM) * ** 239-0826 3-1-1 :046-844-5032 Fax: 046-844-5080 e-mail: inoue-g23i@ysk.nilim.go.jp i

Technical Noe of NILIM No.652 Sepember 2011 (YSK-N-238) Sudy on Applicaion of Time-series Analysis o Air Transpor Demand Esimaion Gaku INOUE* Kiyoeru TANSEI** Synopsis Time-series analysis echniques have been applied o he various fields, including economic and financial analyses. This sudy examined he general applicabiliy of Auoregressive Inegraed Moving Average model(arima), one of ime-series analysis echniques, o air ranspor demand esimaion. Furhermore, his sudy also analyzed long-erm equilibrium beween air ranspor demand and GDP by using Vecor Error Correcion Model (VECM). These analysis comes o be basic daa for fuure research on air ranspor demand esimaion. Key Words: Air Transpor Demand Esimaion, Time-series Analysis, Auoregressive Inegraed Moving Average model(arima), Vecor Error Correcion Model (VECM) * Senior Researcher, Airpor Deparmen ** Direcor of Airpor Planning Division, Airpor Deparmen 3-1-1 Nagase, Yokosuka 239-0826 Japan Phone: +81-46-844-5032 Fax: +81-46-844-5080 e-mail: inoue-g23i@ysk.nilim.go.jp ii

1. 1 2. (ARIMA) 1 2.1........................................................... 1 2.2............................................. 3 2.3............................................. 6 2.4............................................. 10 3. (VECM) GDP 12 3.1....................................................... 12 3.2 (VECM)....................... 13 3.3......................................................... 14 3.4........................................................... 14 4. 16 17 A 3.1 18 iii

iv

No.652 1. 1) 1 2) GDP GDP (ARIMA) (VECM) GDP 2 (ARIMA) 3 (VECM) GDP 4 2. (ARIMA) 2.1 (1) (ARIMA) (ARIMA) 2) (2010) 3) Hamilon(1994) 4) y ϕ(l)φ(l s ) D s d y = θ(l)θ(l s )ε (1) ϕ(l) = 1 ϕ 1L ϕ 2L 2 ϕ pl p Φ(L s ) = 1 Φ 1 L s Φ 2 L 2s Φ P L sp θ(l) = 1 + θ 1 L + θ 2 L 2 + + θ q L q Θ(L s ) = 1 + Θ 1 L s + Θ 2 L 2s + + Θ Q L sq ϕ i, Φ i, θ i, Θ i (1) L : Ly = y 1 : y = y y 1. s : s y = y y s ε E(ε ) = 0 { σ 2 (k = 0) E(ε ε k ) = 0 (k 0) (1) ARIMA(p, d, q) (P, D, Q) s (2) p, d, q p : d : y q : P : D : Q : s : ARIMA - 1 -

/ k E(y ) = µ Var(y ) = E[(y µ) 2 ] = γ 0 (3) Cov(y, y k ) = E[(y µ)(y k µ)] = γ k (4) (5) (1) ϵ ρ k = Corr(y, y k ) = Cov(y, y k ) Var(y )Var(y k ). (5) ρ k = Corr(y, y k ) = γ k γ 0 (6) k y y k k y y k y 1, y 2,, y k+1 5) k 0 95% ϵ ε (Pormaneau es) H 0 : ρ 1 = ρ 2 = = ρ m = 0 H 1 : 1 k [1, m] ρ k 0 Ljung and Box Q Q Ljung and Box Q(m) = T (T + 2) m k=1 ˆρ k 2 T k χ2 (m) (7) χ 2 (m) m T Q(m) χ 2 (m) 95% 5% ε p, d, q (AIC) (BIC) AIC AIC = 2 L(ˆθ) + 2n (8) L(ˆθ) n 2 BIC BIC = 2 L(ˆθ) + log(t )n (9) (2) 1975 50 2009 21 (3) - 2 -

No.652 domesic 2000 4000 6000 8000 10000 d_domesic 2000 1000 0 1000 2000-1 - 2 Auocorrelaions of d_domesic 0.50 0.00 0.50 1.00 0 10 20 30 40 Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of d_domesic 1.00 0.50 0.00 0.50 1.00 0 10 20 30 40 Lag 95% Confidence bands [se = 1/sqr(n)] - 3 m1 1 1990m1 1990 1 2.2-1 -2 E(y ) = µ -3 0 95% 5% 12 24 36-4 ρ k -4 12-3 1 2 3-4 1 2 3 ARIMA(p, d, q) (P, D, Q) s d = D = 1 s = 12 0 p, q, P, Q 2 81 (p, q, P, Q) ϕ, Φ, θ, Θ 2.1 AIC ϕ, Φ, θ, Θ - 3 -

/ 2000 4000 6000 8000 10000 y predicion, one sep domesic - 1 ARIMA(1, 1, 1) (0, 1, 1) 12 p -1.805 2.210-0.82 0.414 AR(1) 0.186 0.089 2.09 0.037 MA(1) -0.667 0.063-10.65 0.000 MA(12) -0.434 0.039-11.22 0.000 189.4963 AIC 5436.876-2713.4379 Q p 41.1854 (0.4185) - 5 Auocorrelaions of e 0.10 0.05 0.00 0.05 0.10 0 10 20 30 40 Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of e 0.15 0.10 0.05 0.00 0.05 0.10 0 10 20 30 40 Lag 95% Confidence bands [se = 1/sqr(n)] - 6-7 ARIMA(1, 1, 1) (0, 1, 1) 12-1 ϕ 1 = AR(1) θ 1 = MA(1) Θ 1 = MA(12) -5 ARIMA -6-7 0 95% -1 (Pormaneau es) Q χ 2 (m) 95% P 0.42 (1)1975 1994 20 1995 2009 ( 1994 12 ) (2)1975 1999 25 ( 1999 12 ) -2-3 (1)1994 12 (2)1999 12 ARIMA(0, 1, 1) (0, 1, 1) 12 1975 2009 ARIMA(1, 1, 1) (0, 1, 1) 12 40 Q - 4 -

No.652 0 3000 6000 9000 12000 15000 1995m1 2000m1 2005m1 2010m1 prediced(1994m12) domesic prediced(1999m12) 0 10000 20000 30000 1995m1 2000m1 2005m1 2010m1 observaion upper(95%) lower(68%) predicion upper(68%) lower(95%) - 8 1994 12 1999 12-9 95% 1994 12-2 1994 12 p 0.596 5.150 0.12 0.908 MA(1) -0.349 0.051-6.84 0.000 MA(12) -0.171 0.058-2.95 0.003 137.1608 AIC 2886.888-1439.444 Q p 40.2695 (0.4583) - 3 1999 12 p -0.015 3.854 0.00 0.997 MA(1) -0.440 0.033-13.37 0.000 MA(12) -0.310 0.042-7.30 0.000 162.4464 AIC 3745.766-1868.883 Q p 45.3457 (0.2589) χ 2 (m) 95% P 0.45 0.25 40-8 (1)1994 12 (2)1999 12 (3) 2002 1999 12 2005 10% 2005 20% 40% 1994 12 1999 12 1995-1999 (MSE) MSE MSE (2010) 3) MSE h ŷ +1,, ŷ +h 1 y ˆε 2 1 y ˆε h ε ε 0 0 ε ˆε ε +h 0 ε (k) +1,, ε(k) +h N(0, σ2 ) y, y 1,, ε, ε 1, ε y (k) +h - 5 -

/ N y (k), k = 1, 2,, N +h MSE y (k), k = 1, 2,, N +h 1994 12 N = 1, 000 MSE h 95% (±1.96σ) h 68% (±σ) -9 5 95% 68% 68% 95% 95% 2000 100% 5 100% 68% 1994 12 1999 12 2002 5 10 15 90 2.3-10 -11 E(y ) = µ -12-11 -11-13 0 95% 5% -14 12 ARIMA(p, d, q) (P, D, Q) s d = D = 1 s = 12 0 p, q, P, Q 2 81 (p, q, P, Q) ϕ, Φ, θ, Θ 2.1 AIC ϕ, Φ, θ, Θ ARIMA(1, 1, 2) (0, 1, 1) 12-4 ϕ 1 = AR(1) θ 1 = MA(1) θ 2 = MA(2) Θ 1 = MA(12) -15 ARIMA -16-17 - 6 -

No.652 inl 0 500 1000 1500 2000 d_inl 600 400 200 0 200 400 d_ln_inl.4.2 0.2.4.6-10 - 11-12 Auocorrelaions of d_inl 0.20 0.00 0.20 0.40 0.60 0.80 0 10 20 30 40 Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of d_inl 0.40 0.20 0.00 0.20 0.40 0.60 0 10 20 30 40 Lag 95% Confidence bands [se = 1/sqr(n)] - 13 0 95% -4 40 (Pormaneau es) Q χ 2 (m) 95% P 0.06 1999 12-5 1999 12 ARIMA(1, 1, 1) (2, 1, 2) 12 ARIMA(1, 1, 2) (0, 1, 1) 12 ϕ 1 = AR(1) θ 1 = MA(1) Φ 1 = AR(12) Φ 2 = AR(13) Θ 1 = MA(12) Θ 2 = MA(13) Φ 1 Φ 2 Θ 1 40 Q χ 2 (m) 95% - 14 P 0.45 0.25 40-18 1999 12 2001 9 2003 3 SARS 10% 2005 25% 40-50% -19 5 95% 68% 68% 95% (MSE) 95% 68% 95% 95% 5 50% 2009 95% 95% SARS - 7 -

/ 0 500 1000 1500 2000 observaion y predicion, one sep - 15-4 ARIMA(1, 1, 2) (0, 1, 1) 12 p -0.165 0.218-0.75 0.451 AR(1) 0.820 0.036 22.90 0.000 MA(1) -0.819 0.044-18.50 0.000 MA(2) -0.222 0.045-4.88 0.000 MA(12) -0.719 0.030-24.28 0.000 53.00414 AIC 4436.357-2212.178 Q p 54.7446 ( 0.0602) Auocorrelaions of e 0.15 0.10 0.05 0.00 0.05 0.10 0 10 20 30 40 Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of e 0.20 0.10 0.00 0.10 0.20 0 10 20 30 40 Lag 95% Confidence bands [se = 1/sqr(n)] - 16-17 1999 12 SARS SARS SARS SARS SARS SARS 1999 12 SARS -20-4 -4 53 6-318 2001 9 2003 4 SARS 3 (150) SARS 3 0.3% 2001 9 12 SARS 2003 3 2003 5 :2001 8 2001 12 SARS :2003 2 2003 5-8 -

No.652 0 500 1000 1500 2000 2500 observaion predicion - 18 2000 1-5 2000 1 p 0.140 0.421 0.33 0.741 AR(1) 0.588 0.087 6.79 0.000 MA(1) -0.824 0.065-12.68 0.000 AR(12) -0.454 0.354-1.28 0.199 AR(13) 0.192 0.152 1.26 0.207 MA(12) -0.159 0.354-0.45 0.652 MA(13) -0.315 0.154-2.04 0.041 35.63412 AIC 2887.723-1435.861 Q p 34.3137 ( 0.7234) 0 1000 2000 3000 4000 2000m1 2002m1 2004m1 2006m1 2008m1 2010m1 observaion upper(95%) lower(68%) predicion upper(68%) lower(95%) residual, one sep 400 200 0 200 2000m1 2002m1 2004m1 2006m1 2008m1 2010m1-19 95% 2000 1-21 1999 12 SARS SARS 1999 12 2001 9 2003 4 SARS 0 1000 2000 3000 4000-20 SARS 2000m1 2002m1 2004m1 2006m1 2008m1 2010m1 observaion errorism predicion errorism&sars - 21 SARS - 9 -

/ inlcargo 0 50000 100000 150000 d_inlcargo 20000 0 20000 40000 d_ln_inlcargo.2 0.2.4-22 - 23-24 Auocorrelaions of d_ln_inlcargo 0.50 0.00 0.50 1.00 0 10 20 30 40 Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of d_ln_inlcargo 0.40 0.20 0.00 0.20 0.40 0.60 0 10 20 30 40 Lag 95% Confidence bands [se = 1/sqr(n)] - 25 SARS 5 10 2.4-22 - 26-23 E(y ) = µ -24-11 -24-25 0 95% 5% 12 24 36-26 2 10 12 ARIMA(p, d, q) - 10 -

No.652 0 50000 100000 150000 observaion predicion - 6 ARIMA(0, 1, 1) (0, 1, 1) 12 p -4.969 10 4 4.174 10 4-1.19 0.234 MA(1) -0.242 0.038-6.37 0.000 MA(12) -0.803 0.036-22.24 0.000 0.0467088 AIC -1318.483 663.2413 Q p 20.0920 (0.9964) - 27 Auocorrelaions of e 0.10 0.05 0.00 0.05 0.10 0 10 20 30 40 Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of e 0.10 0.05 0.00 0.05 0.10 0 10 20 30 40 Lag 95% Confidence bands [se = 1/sqr(n)] - 28 (P, D, Q) s d = D = 1 s = 12 0 p, q, P, Q 2 81 (p, q, P, Q) ϕ, Φ, θ, Θ 2.1 AIC ϕ, Φ, θ, Θ ARIMA(0, 1, 1) (0, 1, 1) 12-6 θ 1 = MA(1) Θ 1 = MA(12) -27 ARIMA -28-29 0-29 95% -6 40 (Pormaneau es) Q χ 2 (m) 95% P 0.99 1999 12-7 1999 12 ARIMA(0, 1, 1) (0, 1, 1) 12 1975 2009 θ 1 = MA(1) Θ 1 = MA(12) 40 Q - 11 -

/ 0 50000 100000 150000 observaion predicion - 7 2000 1 p -4.983 10 4 4.971 10 4-1.00 0.316 MA(1) -0.353 0.046-7.67 0.000 MA(12) -0.773 0.048-16.05 0.000 0.0446181 AIC -951.4157 479.7078 Q p 23.5174 ( 0.9823) - 30 2000 1 χ 2 (m) 95% P 0.98 40-30 1999 12 2001 9 1999 12-31 1999 12 (MSE) 95% 68% 68% 95% 2003 100% 2007 200% 5 50000 100000 150000 200000 250000 2000m1 2002m1 2004m1 2006m1 2008m1 2010m1 observaion upper(95%) lower(68%) predicion upper(68%) lower(95%) - 31 95% 2000 1 5 3. (VECM) GDP 3.1 1) (1) (2) (3) (4) ( ) (5) GDP - 12 -

No.652-8 random1 random2 random3 random4 random5 α 16.292 16.835 16.411 16.969 16.605 (152.67) (240.50) (91.99) (228.14) (226.37) β 0.0385 0.0254 0.0605 0.0237 0.0299 (15.79) (16.62) (8.74) (13.92) (18.87) R 2 0.880 0.890 0.689 0.850 0.913-9 random1 random2 random3 random4 random5 α 13.752 14.521 13.840 14.729 14.185 (86.64) (141.89) (59.13) (127.53) (137.00) β 0.0549 0.0362 0.0895 0.0334 0.0429 (15.11) (16.23) (9.86) (12.63) (19.15) R 2 0.870 0.885 0.739 0.823 0.915-10 random1 random2 random3 random4 random5 α 17.025 18.037 17.070 18.309 17.582 (89.00) (162.32) (61.99) (138.05) (176.93) β 0.0734 0.0489 0.1225 0.0453 0.0579 (16.78) (20.16) (11.47) (14.91) (26.95) R 2 0.892 0.923 0.793 0.867 0.955 0 10 20 30 40 50 60 70 1975 1980 1985 1990 1995 2000 2005 2010 year random1 random2 random3 random4 random5-32 GDP (OLS) y y = y y 1 y x x y GDP (y ) 5 (x ) y = α + βx -8-9 -10 x = x 1 + 1 + ε, ε N(0, 2 2 ) (10) -A.1-32 R 2 0.8 GDP GDP (VECM) 3.2 (VECM) (VECM) (2010) 3) Hamilon(1994) 4) GDP Chang 6) - 13 -

/ - 11 Phillips-Perron uni roo ess Variables Wih a ime rend DP 0.101 IP -0.506 IC -0.313 Y -0.254 DP -4.232 ** IP -6.625 ** IC -6.509 ** Y -5.128 ** ** : 1% - 12 Maximum likelihood coinegraion ess Saiics Saiics 0 13.28 10.26 0 18.63* 14.28* 0 20.36* 15.31* * 95% ** 99% 2 x y ψ y ψx 2 2 x y 2 2 x y y = α 1 + λ 11 y 1 + + λ 1p y p + β 11 x 1 + + β 1p x p + η 1 (y ψx ) + ε 1 x = α 1 + λ 21 y 1 + + λ 2p y p + β 21 x 1 + + β 2p x p + η 2(y ψx ) + ε 2 (11) (Vecor Error Correcion Model) y ψx (x, y ) 2 x x x, y x (MSE) y x (11) λ 2i = 0 i p VECM F ( (11) η i ) 3.3 2 1975 2009 GDP 2000( 12) GDP 1979 GDP 68SNA 93SNA 3.4 (1) GDP Phillips and Perron PP -11 DP IP IC Y GDP 1 PP GDP (2) GDP H 0 : 5% 95% VECM GDP - 14 -

No.652-13 VECM ( - 14 VECM ( - 15 VECM ( ) DP Y 0.0001( 0.00) -0.0002(-0.04) DP(-1) 0.4134( 2.42)* 0.1153( 1.55) Y(-1) -0.3458(-0.67) 0.4664( 2.08)* ECT(-1) -0.1966(-3.18)**-0.0495(-1.84) R 2 0.6129 0.7506 F 47.49785 90.26574 DP-0.992Y(-6.07)-5.264 ) IP Y 0.0001( 0.00) -0.0011(-0.18) IP(-1) 0.0792( 0.46) 0.0634( 1.41) Y(-1) -0.7838(-0.96) 0.6021( 2.87)** ECT(-1) -0.3248(-3.78)**-0.0248(-1.12) R 2 0.5220 0.7335 F 32.75935 82.58806 IP-1.591Y(-9.16)+4.250 ) IC Y 0.0001( 0.01) -0.0042(-0.68) IC(-1) 0.0319( 0.19) 0.0972( 2.31)* Y(-1) -0.7297(-0.99) 0.6635( 3.61)** ECT(-1) -0.2498(-3.74)**-0.0078(-0.46) R 2 0.6129 0.7568 F 47.49253 93.33706 IC-2.052Y(-8.89)+6.011-16 - 17-18 F T ( DP Y ECT 1 DP - 0.45-3.18 ** Y 2.39 - -1.84 ** 1% F T ( IP Y ECT 1 IP - 0.93-3.78 ** Y 2.00 - -1.12 ** 1% F T ( IC Y ECT 1 IC - 0.99-3.74 ** Y 5.33 * - -0.49 ** 1% *5% (AIC) (BIC) AIC AIC BIC 2 BIC 2 AIC BIC 2 2 (3) VECM -13-14 -15 VECM ECT (11) η i ( ) -16-17 -18 ( ) GDP GDP GDP GDP GDP Y OLS 1.458 GDP 5% GDP GDP GDP DP Y GDP GDP GDP GDP GDP Y OLS 2.102 GDP 5% GDP - 15 -

/ GDP GDP IP Y GDP GDP GDP GDP GDP Y OLS 2.798 GDP 5% GDP GDP GDP GDP IP Y GDP GDP GDP GDP GDP GDP GDP GDP GDP VECM GDP GDP Y OLS GDP 4. ARIMA 5 5 5-10 VECM GDP GDP GDP GDP GDP GDP GDP - 16 -

No.652 (2011 8 31 ) 1) (2007): hp://www.ysk.nilim.go.jp/kakubu/kukou/keikaku/ juyou1.hml (2011/8/31 ) 2) (2003): No.129 2003 3) (2010): 4) Hamilon,J.(1994), Time Series Analysis, Princeon Universiy Press. 5) A.C.(1985): 6) Chang,Y. and Chang,Y.(2009), Air cargo expansion and economic growh: Finding he empirical link, Journal of Air Transpor Managemen Vol.15, pp.264-265. - 17 -

/ A 3.1 3.1 A- 1 3.1 year random1 random2 random3 random4 random5 21.5152 20.0636 13.0901 16.6605 21.0571 x 1976-1.6269-0.7967-1.1156-1.8277 0.6846 x 1977 5.0865 0.0949 3.0174 1.1157 1.5968 x 1978 1.7356-1.1746-0.1697 2.2110-1.1048 x 1979-0.8327-1.9595-2.4691-0.0004-2.8855 x 1980 1.6659 2.9494 0.6135 1.2181 4.4391 x 1981 0.3240 0.9719-1.2078-2.1342 0.4409 x 1982 0.0884-0.6171-1.4606 0.6273-0.7412 x 1983 0.7361 1.3164 4.4721 0.6575-0.2992 x 1984 3.0261 0.2213 0.1105 2.5305-2.3176 x 1985-2.1516 0.3682 2.2527-1.5426 4.7845 x 1986-1.0144 3.6194 1.6065 2.7520 2.3140 x 1987-2.6689 1.6978-1.6592-0.9706 2.3758 x 1988-1.1406-1.4605-2.2163 2.4616-0.1269 x 1989-1.1954 0.9723-1.6835-2.4891 0.5397 x 1990 0.6647-0.1996-5.0440-0.5176-0.2042 x 1991 3.2423-0.5797 0.9462 2.0420 0.3803 x 1992 0.1225 0.0141-2.2360-4.9964-1.7739 x 1993-2.7237 3.0149-2.6006-0.0447-0.2916 x 1994-1.2686 1.9111-0.0473 1.7434 0.9801 x 1995 0.7250-1.7719 1.6053 1.4929-1.5770 x 1996 3.0404 1.6208 1.6039 3.3505 0.0935 x 1997 2.7687-0.4832-0.6633 1.4992 1.1292 x 1998-5.0720 1.3180-0.1754 1.1476-1.3473 x 1999-0.1684 0.1940-2.0454 0.4588-0.4381 x 2000-1.2422-3.6518-0.0994-0.4484 1.2728 x 2001-0.2571 1.3158-1.8019 0.6595-0.5286 x 2002-0.7625 0.2044 0.9966 2.2123 1.6951 x 2003-1.9928 0.1593-0.2768 5.0052-0.3260 x 2004 3.7934 1.3830-4.3017 2.1538 2.0064 x 2005 2.1311 2.2317-0.7544-2.4308-2.5891 x 2006-0.4466-1.1799-0.0655-3.1324-1.0023 x 2007-0.9095 0.1037 2.6574-0.0367 2.2986 x 2008 0.4347 1.2048-0.5445 0.3762-0.3973 x 2009-2.4000 4.8594-2.0381 2.1228 0.9300 0.1154 0.4472-0.4786 0.4562 0.4168 2.1729 1.7504 2.0091 2.0691 1.8836 x = x x 1 1-18 -

国土技術政策総合研究所資料 TECHNICAL NOTE of N I L I M No. 652 Sepember 2011 編集 発行 国土技術政策総合研究所 本資料の転載 複写のお問い合わせは 239-0826 神奈川県横須賀市長瀬 3-1-1 管理調整部企画調整課電話 :046-844-5019

2024 © docsplayer.net プライバシー | 利用規約 | フィードバック