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

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1 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 Doc URL Type theses (bachelor) File Information Iwayama_BachelorThesis211.pdf Instructions for use Hokkaido University Collection of Scholarly and Aca

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3 PUCK PUCK AIC A 13 2

1 1.1,.,.,, 211 3 11,,,,,.,,?.,,.,,.,,, ( ) Hokkaido University,, 11/8/11 11:7 3 (=.5 ) [4].

4 1 1.1,.,.,, ,,,,,.,,?.,,.,,.,,, ( ) 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: ), /.,,,,.,,,.,,.,., 1 1/1

5 ,.,,AR ARMA GRACH, [1],[2]., [3].,,., 211 8,,, ,,. 3,. 4 PUCK,. 5, D t T t, ( ), 2.,., D t T t 2 (D t, T t ), t = 1,, 48, 3. TD [6] ( 8.,,, ( ), 3 8.,,,,, -,. 3. 2

6 26 25 temperature 24 T hours D 19 demand hours 2: ( ) ( ).. 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

7 19 T-D curve D T 3: (T ) (D). 8..,,,, 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

8 ,, 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

9 , 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, [ ],, 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., ,. 23, ε 1, ε 2 5,6, - T-D 7. 6

10 6 6.1,, PUCK.,, ε 1, ε 2,,,.,. 3,., PUCK,., , ,.,,. 6.2,., + + t(i) + s(i) + f(i) [7],,. 7

11 D :-3: ρ TD D :-7: ρ TD D :-11: ρ TD D :-15: ρ TD D :-19: ρ TD D :-23: ρ TD 4: ρ T D D. 8

12 .9.85 PUCK PUCK + correlation.8 T hours.8.6 PUCK PUCK + correlation.4 ε hours PUCK PUCK + correlation 1.5 ε hours 5:, ε (T ) 1, ε (T )

13 D ε hours PUCK PUCK + correlation hours PUCK PUCK + correlation PUCK PUCK + correlation 1.5 ε hours 6:, ε (D) 1, ε (D)

14 D PUCK PUCK + correlation T 7: (T ) (D). 8. 8: (R ) 11

15 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] [5] [6],,, 1-A-7 (1995). [7],, (25). [8],, SIG-FIN-8-4, pp (212). [9], NC211-18, pp (212). [1] J. Inoue and N. Sazuka, Physical Review E 76, (27). [11] N. Sazuka, J. Inoue and E. Scalas, Physica A 388, pp (29). [12] J. Inoue and N. Sazuka, Quantitative Finance 1, pp (21). 12

16 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

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-99- Title 総合討議 : 1 日目を通して Author(s) Citation Issue Date 2016-03-31 DOI Doc URLhttp://hdl.handle.net/2115/61143 Right Type bulletin (other) Additional Information File Information CATS8_5tougi_1.pdf

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

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