国土技術政策総合研究所資料
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1 ISSN 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
2 No (YSK-N-238) * ** (ARIMA) 5-10 (VECM) GDP GDP GDP GDP : (ARIMA) (VECM) * ** : Fax: inoue-g23i@ysk.nilim.go.jp i
3 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 Nagase, Yokosuka Japan Phone: Fax: inoue-g23i@ysk.nilim.go.jp ii
4 (ARIMA) (VECM) GDP (VECM) A iii
5 iv
6 No ) 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 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 -
7 / 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) (3) - 2 -
8 No.652 domesic d_domesic Auocorrelaions of d_domesic Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of d_domesic Lag 95% Confidence bands [se = 1/sqr(n)] - 3 m m E(y ) = µ % 5% ρ k 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 -
9 / y predicion, one sep domesic - 1 ARIMA(1, 1, 1) (0, 1, 1) 12 p AR(1) MA(1) MA(12) AIC Q p (0.4185) - 5 Auocorrelaions of e Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of e Lag 95% Confidence bands [se = 1/sqr(n)] ARIMA(1, 1, 1) (0, 1, 1) 12-1 ϕ 1 = AR(1) θ 1 = MA(1) Θ 1 = MA(12) -5 ARIMA % -1 (Pormaneau es) Q χ 2 (m) 95% P 0.42 (1) ( ) (2) ( ) -2-3 (1) (2) ARIMA(0, 1, 1) (0, 1, 1) ARIMA(1, 1, 1) (0, 1, 1) Q - 4 -
10 No m1 2000m1 2005m1 2010m1 prediced(1994m12) domesic prediced(1999m12) m1 2000m1 2005m1 2010m1 observaion upper(95%) lower(68%) predicion upper(68%) lower(95%) % p MA(1) MA(12) AIC Q p (0.4583) p MA(1) MA(12) AIC Q p (0.2589) χ 2 (m) 95% P (1) (2) (3) % % 40% (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 -
11 / N y (k), k = 1, 2,, N +h MSE y (k), k = 1, 2,, N +h N = 1, 000 MSE h 95% (±1.96σ) h 68% (±σ) % 68% 68% 95% 95% % 5 100% 68% E(y ) = µ % 5% 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
12 No.652 inl d_inl d_ln_inl Auocorrelaions of d_inl Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of d_inl Lag 95% Confidence bands [se = 1/sqr(n)] % (Pormaneau es) Q χ 2 (m) 95% P 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 SARS 10% % 40-50% % 68% 68% 95% (MSE) 95% 68% 95% 95% 5 50% % 95% SARS - 7 -
13 / observaion y predicion, one sep ARIMA(1, 1, 2) (0, 1, 1) 12 p AR(1) MA(1) MA(2) MA(12) AIC Q p ( ) Auocorrelaions of e Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of e Lag 95% Confidence bands [se = 1/sqr(n)] SARS SARS SARS SARS SARS SARS SARS SARS 3 (150) SARS 3 0.3% SARS : SARS :
14 No observaion predicion p AR(1) MA(1) AR(12) AR(13) MA(12) MA(13) AIC Q p ( ) m1 2002m1 2004m1 2006m1 2008m1 2010m1 observaion upper(95%) lower(68%) predicion upper(68%) lower(95%) residual, one sep m1 2002m1 2004m1 2006m1 2008m1 2010m % SARS SARS SARS SARS 2000m1 2002m1 2004m1 2006m1 2008m1 2010m1 observaion errorism predicion errorism&sars - 21 SARS - 9 -
15 / inlcargo d_inlcargo d_ln_inlcargo Auocorrelaions of d_ln_inlcargo Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of d_ln_inlcargo Lag 95% Confidence bands [se = 1/sqr(n)] - 25 SARS E(y ) = µ % 5% ARIMA(p, d, q)
16 No observaion predicion - 6 ARIMA(0, 1, 1) (0, 1, 1) 12 p MA(1) MA(12) AIC Q p (0.9964) - 27 Auocorrelaions of e Lag Barle s formula for MA(q) 95% confidence bands Parial auocorrelaions of e 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 % (Pormaneau es) Q χ 2 (m) 95% P ARIMA(0, 1, 1) (0, 1, 1) θ 1 = MA(1) Θ 1 = MA(12) 40 Q
17 / observaion predicion p MA(1) MA(12) AIC Q p ( ) χ 2 (m) 95% P (MSE) 95% 68% 68% 95% % % m1 2002m1 2004m1 2006m1 2008m1 2010m1 observaion upper(95%) lower(68%) predicion upper(68%) lower(95%) % (VECM) GDP 3.1 1) (1) (2) (3) (4) ( ) (5) GDP
18 No random1 random2 random3 random4 random5 α (152.67) (240.50) (91.99) (228.14) (226.37) β (15.79) (16.62) (8.74) (13.92) (18.87) R random1 random2 random3 random4 random5 α (86.64) (141.89) (59.13) (127.53) (137.00) β (15.11) (16.23) (9.86) (12.63) (19.15) R random1 random2 random3 random4 random5 α (89.00) (162.32) (61.99) (138.05) (176.93) β (16.78) (20.16) (11.47) (14.91) (26.95) R 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 x = x ε, ε N(0, 2 2 ) (10) -A.1-32 R GDP GDP (VECM) 3.2 (VECM) (VECM) (2010) 3) Hamilon(1994) 4) GDP Chang 6)
19 / - 11 Phillips-Perron uni roo ess Variables Wih a ime rend DP IP IC Y DP ** IP ** IC ** Y ** ** : 1% - 12 Maximum likelihood coinegraion ess Saiics Saiics * 14.28* * 15.31* * 95% ** 99% 2 x y ψ y ψx 2 2 x y 2 2 x y y = α 1 + λ 11 y λ 1p y p + β 11 x β 1p x p + η 1 (y ψx ) + ε 1 x = α 1 + λ 21 y λ 2p y p + β 21 x 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 ) 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
20 No VECM ( - 14 VECM ( - 15 VECM ( ) DP Y ( 0.00) (-0.04) DP(-1) ( 2.42)* ( 1.55) Y(-1) (-0.67) ( 2.08)* ECT(-1) (-3.18)** (-1.84) R F DP-0.992Y(-6.07) ) IP Y ( 0.00) (-0.18) IP(-1) ( 0.46) ( 1.41) Y(-1) (-0.96) ( 2.87)** ECT(-1) (-3.78)** (-1.12) R F IP-1.591Y(-9.16) ) IC Y ( 0.01) (-0.68) IC(-1) ( 0.19) ( 2.31)* Y(-1) (-0.99) ( 3.61)** ECT(-1) (-3.74)** (-0.46) R F IC-2.052Y(-8.89) F T ( DP Y ECT 1 DP ** Y ** 1% F T ( IP Y ECT 1 IP ** Y ** 1% F T ( IC Y ECT 1 IC ** Y 5.33 * ** 1% *5% (AIC) (BIC) AIC AIC BIC 2 BIC 2 AIC BIC 2 2 (3) VECM VECM ECT (11) η i ( ) ( ) GDP GDP GDP GDP GDP Y OLS GDP 5% GDP GDP GDP DP Y GDP GDP GDP GDP GDP Y OLS GDP 5% GDP
21 / GDP GDP IP Y GDP GDP GDP GDP GDP Y OLS 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 VECM GDP GDP GDP GDP GDP GDP GDP
22 No.652 ( ) 1) (2007): hp:// juyou1.hml (2011/8/31 ) 2) (2003): No ) (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
23 / A A year random1 random2 random3 random4 random x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x = x x
24 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 神奈川県横須賀市長瀬 管理調整部企画調整課電話 :
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