Title 相互相関を考慮した非線形予測モデルに基づく札幌市気温と北海道大学構内電力需要の同時推定 Author(s) 岩山, 浩将 Issue Date 212-3-22 Doc URL http://hdl.handle.net/2115/52278 Type theses (bachelor) File Information Iwayama_BachelorThesis211.pdf Instructions for use Hokkaido University Collection of Scholarly and Aca
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1 1 1.1......................................... 1 1.2...................................... 2 2 2 2.1 24 -..................... 2 3 2 3.1.................................... 3 4 4 4.1 PUCK...................................... 4 4.2 PUCK............................ 5 4.3 AIC............................... 5 5 6 5.1......................................... 6 5.2......................................... 6 6 7 6.1........................................... 7 6.2........................... 7 7 12 A 13 2
1 1.1,.,.,, 211 3 11,,,,,.,,?.,,.,,.,,, ( ) Hokkaido University,, 11/8/11 11:7 3 (=.5 ) [4].,,, ( 大 力力 力力 用 月 日 木 力力 用 日 日 月 大 用 力力 日 用 力力 1: 8 11. 212 2. ), /.,,,,.,,,.,,.,., 1 http://www.facility.hokudai.ac.jp/denryoku/ 1/1
,.,,AR ARMA GRACH, [1],[2]., [3].,,., 211 8,,,. 1.2. 2,,. 3,. 4 PUCK,. 5,. 6 5. 7. 2 2.1 24 - D t T t, (211 8 1 ), 2.,., D t T t 2 (D t, T t ), t = 1,, 48, 3. TD [6] ( 8.,,, ( ), 3 8.,,,,, -,. 3. 2
26 25 temperature 24 T 23 22 21 2 19 4 8 12 16 2 24 hours D 19 demand 18 17 16 15 14 13 12 11 1 4 8 12 16 2 24 hours 2: 211 8 1 ( ) ( ).. 3.1, ( ).,, t T t, D t, 2 T t = log T t log T t 1, D t = log D t log D t 1., M,. T t 1 M T t D t 1 M t T l (1) l=t M+1 t l=t M+1, -. T l D l (2) T D = T t D t ( T t )( D t ) [( T t ) 2 ( T t ) 2 ][( D t ) 2 ( D t ) 2 ] ρ (t) (3),ρ (t) T D, 1 ρ(t) T D 1., 4 ρ T D D.,, 1., 4 7,, D >,,., 4 7 D <,, 3
19 T-D curve 18 17 16 D 15 14 13 12 11 1 19 2 21 22 23 24 25 26 T 3: (T ) (D). 8..,,,,. 4 4.1 PUCK PUCK(Potential of Unbalanced Complex Kinetics),. T t,puck. T t+1 = T t d dt U(T, t) T =T t T + f (M) t (4) t f(t), M T (M) t. T (M) t = 1 M M 1 l= T t l (5), U., U T t = T (M) t 2, T t T (M) t,(4) f t, T (M) t., U 3,T t = T (M) t., 4
,, 2, 3 U(p, t) U(T, t) = K k=1 b k (t) k + 1 T k+1 (6).,, A., PUCK,. 4.2 PUCK,., (4)., Q, T t,d t. T t+1 = T t d Q 1 dt U(T, t) T =T t + λ T (M) q ρ (t q) T D + f t (7) t q= D t+1 = D t d Q 1 dd U(D, t) D=D t D + λ (M) q ρ (t q) T D + g t (8) t, Q λ. g t f t., U(T, t),u(d, t) (6). U(D, t) = K k=1 q= b k (t) k + 1 Dk+1 (9), PUCK, PUCK PUCK. 4.3 AIC (6)(9) K, (AIC). AIC T = 2ln(l(b 1, b γ, γ, M, λ)) + 2K (1) (11) AIC D = 2ln(l(b 1, b γ, γ, M, Q, λ)) + 2K (12) (13) 5
, Q Q = 1., K, l( ) w[f t ],w[g t ]., n l(b 1, b γ, γ, M, λ) = w[f(t)] (14) t=n+n 1. n l(b 1, b γ, γ, M, Q, λ) = w[g(t)] (15) t=n+n 1 5, 211 8 23 18 [ ],, 211 8. 5.1 24 t T t, D t ˆT t, ˆD t, 23 ε (T ) 1 (t) = E[(T t ˆT t ) 2 ] (16) ε (D) 1 (t) = E[(D t ˆD t ) 2 ] (17)., E[ ] 23.,,,,., : T t sgn(t t+1 T t ), (18) ˆT t sgn( ˆT t+1 ˆT t ), (19) D t sgn(d t+1 D t ), (2) ˆD t sgn( ˆD t+1 ˆD t ) (21) ε (T ) 2 (t) = 1 2 (1 E[T t ˆT t ]), ε (D) 2 (t) = 1 2 (1 E[D t ˆD t ]) (22) 2.,. 5.2 211 8,. 23, ε 1, ε 2 5,6, - T-D 7. 6
6 6.1,, PUCK.,, ε 1, ε 2,,,.,. 3,., PUCK,., 211 8 1, 31 31 23.,.,,. 6.2,., + + t(i) + s(i) + f(i) [7],,. 7
D 4 2-2 :-3:3-4 -1 -.5.5 1 ρ TD D 4 2-2 4:-7:3-4 -1 -.5.5 1 ρ TD D 4 2-2 8:-11:3-4 -1 -.5.5 1 ρ TD D 4 2-2 12:-15:3-4 -1 -.5.5 1 ρ TD D 4 2-2 16:-19:3-4 -1 -.5.5 1 ρ TD D 4 2-2 2:-23:3-4 -1 -.5.5 1 ρ TD 4: ρ T D D. 8
.9.85 PUCK PUCK + correlation.8 T.75.7.65.6.55 5 1 15 2 hours.8.6 PUCK PUCK + correlation.4 ε 1.2 -.2 -.4 5 1 15 2 hours 2.5 2 PUCK PUCK + correlation 1.5 ε 2 1.5 -.5 5 1 15 2 hours 5:, ε (T ) 1, ε (T ) 2. 23. 9
D ε 1 1.5 1.95.9.85.8.75.7.65.6.55 5 1 15 2.12.1.8.6.4.2 -.2 -.4 hours PUCK PUCK + correlation -.6 5 1 15 2 hours PUCK PUCK + correlation 2.5 2 PUCK PUCK + correlation 1.5 ε 2 1.5 -.5 5 1 15 2 hours 6:, ε (D) 1, ε (D) 2. 23. 1
1.95.9.85 D.8.75.7.65 PUCK PUCK + correlation.6.55.62.64.66.68.7.72.74.76.78.8.82 T 7: (T ) (D). 8. 8: (R ) 11
7 8,,., 211 6, 8.,,.,., [8, 9],, ( ),.,, (1 ).,, First-passage process [1, 11, 12]...,,,.,,,. [1] T. Kaizoji, Physica A 287, 493 (2). [2] J.-P Bouchaud and R.Cont, The European Physics Journal B 6, 543 (1998). [3] W.Watanabe, H. Takayasu and M. Takayasu, Phys. Rev. E 8, 5611 (29). [4] http://www.facility.hokudai.ac.jp/denryoku/ [5] http://www.data.jma.go.jp/obd/stats/etrn/index.php [6],,, 1-A-7 (1995). [7],, (25). [8],, SIG-FIN-8-4, pp. 18-25 (212). [9], NC211-18, pp. 65-7 (212). [1] J. Inoue and N. Sazuka, Physical Review E 76, 21111 (27). [11] N. Sazuka, J. Inoue and E. Scalas, Physica A 388, pp. 2389-2853 (29). [12] J. Inoue and N. Sazuka, Quantitative Finance 1, pp. 121-13 (21). 12
A, P (t + 1) P (t), P (t) P M (t) : P (t + 1) P (t) P (t) P M (t)., : p d U(p, t) (23) dp d U(p, t)dp = U(p, t) + U(, t) (24) dp. (23) (24), p P (t) P M (t) ( ) U(P (t) P M (t), t) + U(P () P M (), t) U(P (t) P M (t)) + U(P () P M ()) P (t) PM (t) { P (l + 1) P (l) = P () P M () P (l) P M (l) t { P (l + 1) P (l) = P (l) P M (l) = l= t l= (P (l + 1) P (l)) 2 P (l) P M (l) } {P (l) P M (l)} } [P (l + 1) P (l) {P M (l + 1) P M (l)}] t l= (P (l + 1) P (l))(p M (l + 1) P M (l)) P (l) P M (l) (25). d{p (l) P M (l)} = {P (l) P M (l)} = P (l + 1) P (l) {P M (l + 1) P M (l)} (26)., U(P (t) P M (t)). U(P (t) P M (t)) = U(P () P M ()) + t (P (l + 1) P (l))(p M (l + 1) P M (l)) P (l) P M (l) l= t l= (P (l + 1) P (l)) 2 P (l) P M (l) (27), t P (t ) P M (t ) ( ), (27) t l l = l = t t P (t ) P M (t ),, ( l = ). 13