Modèles semi-paramétriques appliqués à la prévision des séries temporelles. Cas de la consommation d électricité.

Transcription

1 Modèles semi-paramétriques appliqués à la prévision des séries temporelles. Cas de la consommation d électricité. Vincent Lefieux To cite this version: Vincent Lefieux. Modèles semi-paramétriques appliqués à la prévision des séries temporelles. Cas de la consommation d électricité.. Mathématiques [math]. Université Rennes 2, Français. HAL Id: tel Submitted on 16 Oct 2007 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 UNIVERSITÉ RENNES 2 HAUTE BRETAGNE Unité de Recherche Ecole Doctorale - Humanités et Sciences de l Homme Modèles semi-paramétriques appliqués à la prévision des séries temporelles Cas de la consommation d électricité Thèse de Doctorat Discipline : Statistiques Présentée par Vincent LEFIEUX Directeurs de thèse : Michel CARBON et Michel DELECROIX Soutenue le 12 octobre 2007 Jury : M. BIAU Gérard Rapporteur Université Pierre et Marie Curie Mme BONGRAIN Marie-Pierre RTE DMA M. BOSQ Denis Université Pierre et Marie Curie M. CARBON Michel Université Rennes 2 M. DELECROIX Michel Université Pierre et Marie Curie M. SIMAR Léopold Rapporteur Université Catholique de Louvain

3

4 ! " # $! %# $!! &' #( )!$!* +,!!-. / $ / * 0! (!!! ( 1 # '2!$!! +,!$!!! 3 ( # 1 '!-!!$ + 4!-!$ (!0!* # +& $5!* $5!*! 3#2 $!!*$ 3#2 $$!**. ( $*!- ( 1 # +& $-!- $-

5 ! "!# $%!#!-! + 4 $)!) & 1 $0!) %# $0!)! " &.6!7 $8!)$ " &.+&697 *!)* " :3(: *$!)- " :; (: *-!)) " :3: */!/ & 1 *8 & '' $ -- $!, -0 $! -0 $!! +, -8 $$, )5 $$ )5 $$! ( 6+&7 )$ $*, ( )- $- " )) $- " )) $-! " )8 $) 1 # +& /! $/ & 1 /$ ( ) " * +, * /8 *! 3, 0! *$ 3, 08 ** 3 # 8 -,+

6 . +# 2. *55<!!- <!! =, * $ 3 =, / * 3 # / - 3 / ) 3 6# / 8 0 > 5 8! 5 % # * % # -! ( 1 )! 3, +&? &.6!7 $8!! +&? &.6!7 *5!$ +& 67? &.6!7 *5!* 3, +&? &.+&697 *!- +&? &.+&697 *!!) +& 67? &.+&697 *!!/ 3,? 3( *$!0 +&? 3( **!8 +& 67? 3( **!5 3, +&? ; +( *-! +&? ; ( *)

7 ! "!# /01!#!! +& 67? ; ( *)!$ 3, +&? 3 */!* +&? 3 *0!- +& 67? 3 *0!) 3 +& 6( 7 67? 9, -!/ 3 +& 6( 7 67? 9 -!0 3 +& 6( 7 67?!9, -!!8 3 +& 6( 7 67?!9 -$ $ )/ $! 3,?@ )0 $$ /5 $* 3,?@ / $- 3 +&6( 7 67? 9, /- $) 3 +&6( 7 67? 9 /) $/ 3 +&6( 7 67?!9, /) $0 3 +&6( 7 67?!9 // * ' #? 5$A5*A5)58A5/A5) 8! *! ' #? -A5A5/50A5*A5/ 8!

8 ! :+&: :B':? &.6!7 $8!! :+&: :B':? &.+&697 *!$ :+&: :B':? 3( *$!* :+&: :B':? ; ( *-!- :+&: :B':? 3 */!)? -5!/ 3,? -5!0?! -!!8 3,?! -! $? /* $! 3,? /* $$?! /- $* 3,?! /-

9 #! "!#!12

10 +# % 2 # " 1 ( #, > 1 # C ( 2 ( 1 +# 3 #, >, 1 D E " 2 #, > ( % E =' > "F B"& ".!9 9 2 # # > ( 1 & & # 9, '# > #, %9 +G""9,( %+&.F >, = > 1, + E(9 >H.'< # 3## 3 #, ;9 1 2 ( 1 9 I

11

12 # 1 9 % 9.F #( ( F 1? J (.F K = 9 J ( L2.F 1 ;( # M # J +# K ', 9 4 ; 1.F9 ( 1

13 = N ( 1 9 <.F 1 M # 9 #.F, 1!) 9 & ( 9, = ;.F, 6# # ( 9 7 # ( # 6 ; 7, 9 ' 9.F O ; # N # = # P 3 # ( ( =? L, (# # 3 2, 2 9 = ; #, 1 1.FG N? 9 ' # # #, ( ( 2 = 9 ' E2 > <, ( ; 1 # ( Q ( G 1( ( 9 L

14 B # # # +&9 : :9 2 & ; # ( 9 Q, #, 1 #( +& ( 1 2(, 6 7, 9, 1 &,, 9 9, # 2 #, ( #'#, ( M ( B ( (

15

16 -3 4 <9( N ( 1 F ; ', 3 M : : ( ', (, # Q 9 M M, 9 9.F 6. F 7 (1 M A 1 2 K 6 2 ;( 7 N 1 M #P? ' ( 6 7 1( 9.F ( 1 9

17 J. *55<!!- <

18 4 # 3 & 2 N Q ( 1 N 2 1' N ( 3 1 # 9 ; 2 Q K 1 = ;91 = 3# =9 9 ( # 9 1 ( = 3 ( # G ( # (.F 9 # Q 1 # '9 ;(!.F ( #' ( M 1 # ' % ( 2 ( K ', 2 1 ' 1 4 # Q # 9 ( N =, 2 #, 1 4 # 3 44 " 3 # 9 M # 9 ( ( 9 9

19 (! J =, ; ;9 N # %M 2 ; 9 9 ( 9# =N? 6 7; 6 7 G (? J # J # ( ;? 2 9 ( L 3 # ( ', 9 # = J #?,( ' ( 2 G, =2 # 9 2, ( # = 2 # ( 2( #'#, Q 1; &9

20 4 # 3 ' # 2 9 : O : 9 % 9 2 # 1 ( # = ' 2 =.F #2 = ' ;,, 1 3B" 63 B 2 "', 7 #( ; 9, ; # % 6.F7 1? J &' #( 9 ; 9 2(, J + #,? # 1 # ' G '? R ( 1 9 2(,, 9 9 : : 1 J : :,?, : 2:, 1 N 9 ( J M # ', 9 2 M J "?, 1, 6 7 J "? 1 ( #'#, ( 3 # ( N L ( 6 2 # '27 (, 1 (

21 5 J "? #,, 4 G 9 =1 ( # ', , A2 % 2 2? 2 ; 6 N 8889 ; G ; '? J ' = 9 8# 8# 63 ( $7@ J ' # 9 -= ( S < R 63 ( *7@ J ' 9 = 2 - K 63 ( -7 %, = 9 ' 6 2 # S < 7 3, ( 1. ( #( # (@ 2 9# 7 ( N

22 4 # 3 + $ J 3 =, * J 3 # - J 3

23 7 )J3 6#7 6 7 ; #M( # #M( 8/5 1 ( ( 1 # 2 9 ( O ( 1 (( ' ;( ) G ( : : 9 # 9 =, 9 2 ( 1 ( ( M 9 1 #6? # 7 1 # I 6 '? # 1 = ( 7 5 6, ((7 0 6

24 4 # 3, / J L #M(? (I 1 M 9 ; 1 I 9 #M( ;( / #, =2 2 #( =, 6= 9 7 M,, 9 1, 9 * 2 (;? > 6M > 7 1 2!! = % = 6= ( 79 ; ' K K ( 7 ;( 0 M? = R 9 ( > '9 : M:, 7 F # 9 (, B 9!) 9

25 8 0 J >

26 4 # 3 ', 9 44& 1.F 2 # (I 1 E2 > <, "&.+& ( # 9( ( P# 9, G 2 ( E2 68/)79 <P 680$7 3#"&.+& M #2 # % #2, "&.+& /5 G /)7 & 68/87+# 9,,( 2 (,! =(, ( 6 (2 27 G ( ; T & ;9 =, M 63 ( 87? J G( #( 29; 1 2 G 1 M, ( 9, : : J G, "&.+& :( :@ ' J G, ; = 1 :( : 2!, &.+& Q 1

27 8 J 44( $ $, (.F? = ' = > ' # # # # 67? J ( # 9 = 1 # 6 $ K 7 J ( ' = 69 9 # 7 J ( ' = >

28 4 # 3 & J? # 6 7 J? M > J ( 6 ( =? 1 $)-7? = #( # =, #( # J #? ( 6# 7@? ( 67 J 2 9 # #? # # J ( 9 #M( J # 2? # R ( M.F (? J #? = ' J M? = > '

29 ( 5 J % # J 1 #? # # # J 1? # G (# #? ;( 5 # 6 P ((# 7 & 9 N ( 61 ( 2 79 ( ( 9 63 ( 7

30 4 # 3 ' J % #, 63 (!7? J 2 J 1 ( 6 # 7 M J M 7 3 ( 91 2 = ' 6 $ K9 ; #(, 7 M,, # (# 6U< > 7, ( =$K & 19 2 ( 2 2,,, (

31 5!J ( 1 ; N M ( $ 9 ( '!) + #$, "&.+& ; 1.F,?!!! " #! #!, 9 # # 1 ; E2 > < 3, ;2 9 1 ', 6 # 9, 1# 7B 9, "&.+& M#, 2N 9 $ / ( 9 (

32 4& + 44' * 1 M ;? G, 2 9 ( 1 #( ; 3 (?! G (, "&.+& G $ $ G, 2 ( ; G 1 ( 9 1 ; (? $ 4& ", 1.F 9 2 2? J #9 2 ; 2 # 9 N #, 2 #' 9 = 9 9, 1 2 J 3 ' = (, 9 = # ( 9 # N 3 M

33 7 J & 1 9 ( 2 M # >% 6 (;7 4(, 2, Q ; " ' 9 =2, (, "&.+& ; G = (, (. 9 9 % =1 # % 9 N 1 9 ; # N ( 2 2(, I# 2 2 1, H ( ; 9 N = 9 N, P 3, 2 9 ; G 2 ( ; # = # M, (, O 6 9, (, 7

34 4(, % 9 2 Q " 2 9, 9 ( # # ( &; ;, 9 1 ( # " ( # B # 1 2 # #, "&.+&, (, #, 2(, G 1 ( 6 7 2(,

35 8

36 -3 G # 1 ( 3 O 2 # # 1 2(, B9 # # 1 #, 2 9 ( &, 2 2 9, ( G # 9, ; Q # 9 1 :( : M 2 (, 4 =1 # 9 N # , (? " " " #'#,,

37 # #'#, 1? # 1, # 2 9, &. %? " " " " G, ;, 9, & &.7 B 1.F 2,? J, (? (, 2 # (; M, #, J, "&.+& &; ;2 ( 9 2 # 2 2 # #? J # : : 6::7 # ( 9 9 J # # '29 'H 29 % 9 =1 M 1 # G U ' 688$7 ; &(. N 5V 9 &;N = 9 N 1 9 (, # 6 # ' 7 =1 - = # #P 5 =

38 & 9 2( # &(( 688* $7, 9 "&.+&, ( B 2 # '29 #? 1 +P G # 1 # '2 1 ; # 44 $ G, ( 9 # ' $7, " " 9 ( " " & 1 " " 9? " & " " " G %< 9 #'#,? R" " "! " & " " " " " " " "! G (

39 ( 3 #'#, ' ( G % :(:9 " " " " " " # " " 9 R " ( "? " ' " G,? " " " R? ( ( " " ( G? ( ( ) " ( ) " " ( G ) ) R) :': ;? J ) ' J ( ) ( 6( 7 R ( ( $ J ( ) ((* " 9 2 "? " & " R? " ) " " ) " " $ " 9

40 ' # 688*7 E 688)7 # 1 ' ( G #, 3 4 " % " " " " "! " # ( ( +(+ ( + +(+ ( ( ( $ % ( ($ " & ' ) "( #) " ", * B 2 ( #, R 44& $ : '1, 1 #2 N M '9 N

41 #, ' 9 1? ( ( ) ( ( ) ( R) ' +N 2 #2')9 #< 68)879 ' ( &9 '2 9 ( #< -3 *; #2 N 6 7 = 9 #, G 1 M,? - &% " R 1, G N #P 9 ( N N #P G # " -3 #2 N M, ( 1 G 2?. % &% " 1. % N, &; 9 Q 1 9 N #!* 6!7 # "

42 < &; 9 M '? 6 & 7 G 2? J '?. " " " & J '?. & " " G +&, 9, M 1, N (, #.+"9, # 2 => 9 M 2, M " " && 1 " " 9? J M & : :? " &&& G 99 J M &,? " 9 " " " 9 G 2 # 2 M #2@ 4 =; # F# 9 # " A 9

43 7 9 2, M 9 = 2 ; " 9 4& E # 9,,? J ( 6 ( 1, 7 J 3 #2')9 #2 N Q J ;9, = 2 6 L 7 ' ( 3, # ( ( = &; 9, ( 2 22 ' 9 &2 J + # 9 & UW 688)7 / 1 2 " " " 0 2 9? / " " R 0 J + #!, #9 3# 688$7 G? " " " " " R % " " " 6 1 7

44 4&,. J, -&. & / U U # /7 G? / " " R 2 2, 6 7 J +! 6"+? "( UW 688$79 # 688$ /79 % % 2 6!55)7 G? / " " R, 6 7 J +! 9 6!5579 6!55!79 6!55*7 G? / "! " R!, 6 7 3, 1 N ' L 2 M # #? J :& ( % :6&%79 UW UW 688!79 USP USP 688)79 U# 6!557 J :". ( :6" "#688*79 X# 688)7 J :+( & ( 67 : 6+&79 6!55!7

45 &8 # &% = 2, 1 & # 79 O # ". 1 ( # ". ' ", " ;? " " " " G ' #'#, ( = 3 # +& 2 9 N 4 2 4( 3 $?! 4(4 # +& #, ( 1 6!55!7 G,, (? /! " 6!7 R? J / 1 2 J " 0 2 J J " J J! !! 3 ( 1 9, 9 2 G 2 9 L 9 '

46 4( 3 $?! & # / #'#, =, 6!7? / " ( /! "! (! " 1 2 = " G "9 9 " G 29, "+ 2 9! 6!7? / /! " 6!!7 R! 20 # +& G, / 1! "?! " / /! "! " ' G? '! " / /! ", 6!!7 1? '! " 6!$7, 6!7, # +&? + & ( 67 "? + + / " + " + " / " # /" M /! " " &9? /! "! " "

47 & R?! " G '! ", ( 1# 'H )7 G? '! " /! " " 4 R 4 2 " " 9? J &4 J 4 G '! " '! " G!9 6!!79,? /! " " 4 6!*7 4(4-3 ' 2 #2 4? J 3#2 ; # 'H 2 #2? 4 )! " " )! " " G O 2 3 ;? 4 ) " " ) " "

48 4( 3 $?! && J 3#2 Q G,, J G ; = ;? 4 ) " " ) " " 2 9,!! J G =? )! " " 4 )! " "!!9! 6!*7 3, 1 ( # +& 6: ; +&:7 4(4& -3 #2 2 M, -? R? J / J 0 ) / ) J 0 1 ) ) " " " " 9 0 (9 ;2 2 1

49 &( 4(4( 2 2 #, # +&9 #2 2, 9! " #'#,? U+ / " (?!!! " R ' " / &1 U+! / * " * U+$ 9 N ( 5 U+* & U+- 6=1 $7 U+) ) ' # "'" ! & "'" *2 6 2 #!! #! #, #!! #!#, 7 #!! # #! ## ##!!! #!!! 2!

50 4' 9 3 $?! &' 4' 9 3 $?! 4'4 # +& 1, ( 9 & #'#, # +& # G #( 3 688$7 " & 1 " " 9? " & " " " G %<? " & " " " " " R" " "! " R! G 9! 9 #P & # 5 "'"+ + 49:; "! " " < + " = " #5 # " 8 "'"+ %! " 49:; > ( #!

51 &5 4'4 $ : G # +& : : " "! G # '2 3 # 63 (( 688*77 % 9 N? N Q# =, G? ( ( "! " ( G? R? " &! " " )! )! " " " " &;! Q 9 # +& G,, 62;2 7?! $ "! % 4 " " -3 6 G # ) ' (? ) ( ( "! (

52 4' 9 3 $?! &+ -3 *; G M,? J!? N # 2 J # ' -3 G =1 # +& # % N 9# % 9 => G " & " & 1 " " 9 # " & && G! M J M & : :? " &&& G &! # 9 # 2 9, K 2 G Q! #P N # #P J M &,? " 9 " " " 9 9 ; " & G 9 1 & 9 1# G 1 M #2 2

53 & " 3 G 3 688$7 ; # '2 # +& 1 # '2, "&.+& B N # # E2 > < B # Q # +& N ; Q # +& : : ; ( 1 # 9 &? J 1 # '2@ J 1 # +&?! #P M # #P& 3 9.+" +&, # +& 1 # ' 3 ( M 9 # 2(, 9 2

54 45 9 &, 454 G &.6!7? R? J J #9 J " " " $3 " $#! $!@BA B' -!** & 5!!$8 5-5! J :+&: :B':? &.6!7! J 3, +&? &.6!7

55 (8!! J +&? &.6!7!$ J +& 67? &.6!7

56 45 9 ( 454& # $@CA G &.+&697? R? J J 9# J " " # $3 " $#! $!@BA B'!5 *0 55/* +& 5! -$ 558!! J :+&: :B':? &.+&697!* J 3, +&? &.+&697

57 (!- J +&? &.+&697!) J +& 67? &.+&697

58 45 9 (& 454( # D-D :3(: <P 680$7 ( 8)8 1 8/) 3 1 M 6!7, (; $3 " $#! $!@BA B' -!$$8 $! +& 5! 8$5!))!$ J :+&: :B':? 3(!/ J 3,? 3(

59 ((!0 J +&? 3(!8 J +& 67? 3(

60 45 9 (' 454' # D. D :; +(: <P 680$7 ; ( V 8-$ 1 8/! $3 " $#! $!@BA B'!* 5*$! 8!! +&!! 5$08 0*!!* J :+&: :B':? ; (!5 J 3, +&? ; +(

61 (5! J +&? ; (!! J +& 67? ; (

62 45 9 ( # D-D :3: <P680$7 # 2 "& 8-! $3 " $#! $!@BA B' * $*! $9$- +& 5! )0 *8!!- J :+&: :B':? 3!$ J 3, +&? 3

63 (7!* J +&? 3!- J +& 67? 3

64 4+ 9 (, 4+ 9 G 2, 1.F M G, ( 2 =, :( :, (, "&.+& & 9 ( +& G? 9 " & " " 9 # " & 9 1 M =, 1 1 5# = 9 M 1.F 1 G : : 6BY 2 7 3? J? $!55) 8 =!55) J!? - =!55/ 0!55/ 3 9 #2 # % 1 % N 9! # #P B ' 9 1#! &;, "&.+& # +&9 2, M 1!* # B * = 6$$) # 7, 1 -, 9 / ;( 2 (# ; 9 '# 9 (, #

65 '8 G # +& (,, "&.+&, 9 (,, 9 +& 0V # +&!V # E2 > < 2 ( # +& 9 +& V # +& $V "&.+& 2 +& 3 ( N ; (, "&.+& # +& 9 2 N 1 ; # B #2.F@ 9 ( 2(, 63 3# $7 +& "&.+& +' 5* 58 ' -) )50 +!-/5 00/ C -V /! $! 0- C 8-V )/ !*8)!50!) J? +& "&.+& +& 6V7 0!.+" -8 )/!/ J 3,?

66 4+ 9 '!) J 3 +& 6( 7 67? 9,!/ J 3 +& 6( 7 67? 9

67 ' +& "&.+& +' 58 $** ' )50 )*) + 50/ 05 C -V -88 ) $$* C 8-V 85- * !55/!0 J?! +& "&.+& +& 6V7 $.+" /$! //*!8 J 3,?!!0 J 3 +& 6( 7 67?!9,

68 4+ 9 '&!8 J 3 +& 6( 7 67?!9

69 '(

70 -3 & &4 ( 1 # +& ; G > M, " # +&9 N? J / J " % 9 1 % #2 M # 9 2 # G,,?! 6$7 #'#,, +&

71 '5! %%2 9, ( % % G, 9#, G 1 M #'#, 2 # 2 G ', % % G M =, # 9 L! = G *8!/ 2 G ' 1 + # 9 9 # # 2, M?, N, 9 9, & 9 ( G ( ( #2 2 Q! 9 ( # 9 M &3 ; 2 # ( 9 M &3 =1 M 9,9 1 Q 1 ( ( L ( G M M # 2 9 (, ;, M #,, ( ( (# 2 (# 1, ( #2 N

72 &4 '+ 9 N # +&, G ',9 # K ( 2 ( " ' 1 #2 N G, 1 # +&9 N G ; = 2, 9 3 ( =2, (, ( #( ( #, "&.+& 2(, M ( M K 2 2(, 2, " = ; 2, 9 = 2, N 2 M 9 R '? R G (, 2 9Q #, G, ' % 6!55-7 P?, ( # 2(, 9, &.U679 ( ) 2(, 3 = # # 9 N G ( 2 U 688$7, ( 1 Q? / " "

73 '7 G (, ( ( G 2 1 ' , 2 =? / " " & 9, &4 * &44, ( 6:' :7G , (? / " 6$!7 R? J / 1 2 J " 0 2 J 5 2 J J, 6 7 J " &;, 6$!79 1"? %R? / " " " / / " " &, / " ", 9 # 9,

74 &4 * ', = M, = M #'#, # " / 9 "# 688)79, 2(9,? " " $ 6$$7 R? J " (, J 2(, # " ( ( $ + 3 ', 9 9, (, 2(, 9 L 2 N 1 O 1 &44 $ G,, (? /! " 6$*7 R? J / 1 2 J " 0 2 J 5 2 J J " J J! !! J, % 9? J /

75 58 J " J 3, 3 688/79 6!55)7, D"+ 1! B O 2 # +& ( 9 2 9, ( M 9, 6$*7, ' +&? Q 9 1 B9 = 2 :: " 9 " 3 9,, ;, ( ( &4&! G 2 2, 6$*79, 6$*79 # +& &4&4! &;, 6$*79 2?,, &9, 6$*7 1"9? / " "! " G? / / " " &# " / 9 / " " 9, 1, ( G / " ",? /

76 &4&! 5 B'Z? / ) " " / ) " " G / / G? R?!" ) " " ) " " 6$-7 Q ; ) " " 1 5 % N 9, #9 : :, = (, 9! 1 " / # +& G M? 1/! " G, 9 2? /! " " 4 6$)7 3 (# ; / " " 1 # '2 G # " / " G, ; N

77 5! G # / / $! G # " / G 2, ; 9 N J 3#2 G, ;? 2 - J # 6 # # 79, ; N G ( ; 1 6# +&7 3 # N "? L 9 (? / " " 1 # '2! $! * / " " 1 # +&? / )! " " / )! " " )! " " )! " " - G,!9 $ * =1

78 &4&! 5& $?!A & ; 1 9 +&9,, ( G, (,! 6$*7 ;? / /! " 6$/7 # R! 20 G # +& 1 G, / 1! "?! " / /! "! " ' G? '! " / /! ", 6$/7 1? "? ' #! " 6$ / " + " + " / " # /" %, ( 1 # +&9 M /! " " &? G '! "? '! " /! "! " " /! " " 4

79 5( R??! " " " 9? J &4 J 4 G!9 6$/79,? # /! " " 4 6$87 G 6$87,? G (#!G 2! (? / 7! G! ;2 $ G! ;2 * G,! $ =1 B #2 1 # +& G # Q # G # +& 6' +&7

80 &4( 5' &4( 6!55)7 ( 6! 7 " #'#,? U / " ( ( U! 2 2 "2 " " ( (7 ( ( $7 U$ 7 ( ( *7 ( ( U* 6=1 $7 " (9 " ( 9 6 " ( 6 6 " ( 9 R6 " 9 / " ( 9 " ( 9 " ( " ( " ( " ( 9 $9 (( ( 9 U- 9 1 ) ' # 9 1 ( U) " ( " ( ; 3 & !?&<@4 5 " "'"+ 3&53& $ * *8* 9 > = / = 5

81 55 B 1 (, 6$*79 1 # +&Q # ( #, # ( B #!! # ##!! 1 ' # = ( &4' # G # +& 2 = 2 9 1, ( 9 1 G = 2 6!55!7 6!55)7 2; ;, 1 &4'4 # G,? / " " " " R? J J J J J J 9" G 1 +&G

82 &4' # 5+ $ J 3,?@

83 57 $! J 3,?@

84 &4' # 5, G ;( $, % N 9 ;( $!, O G (, P 2 9 M ;, ( 9 N? & %#% #!! #!# &4'4 # G,? R? J J J / "! " " J R J " R? R- J 9" G 1 +& G ;( $$ $* 2 N B, 2

85 +8 $$ J 3,?@

86 &4' # + $* J 3,?@

87 + ;, 9 N? ' () (* % #!! #!## & $?! G " & 1 / 9, ;? "! " 6$57 R 2(, G 2(, 61 2, 7 G! # +&1 " % 6 " 9! 9? %&6! " G 6 1 # '29 " 1? " & 6 & R % 9, 2(, + ( ; : ; 1 G $7

88 &4+ 9 +& &4+ 9 B # +& 1 G? J / J " C 1 2(, 9 (? J M #,.F 63 3# 7@ J J J (!) 9 B # ( 2.F 3 ( : : =, B 1 3# 688$7 & 2, 9 =, # 1 # B M M!*; =, G 2 #? J? $!55) 8 =!55) J!? - =!55/ 0!55/ G # +&, 2 +&!V +& 58V,.F9, " 9 N +& 0V +&!V.F B 2(, 6 ( 7 =; = 6; #!55)!55/79 = 6!55)7, +& 2

89 +( N 9 2(,, 1 ( 1, +&, ; # 6( "&.+&79N K, =, 9, D( 9 ;, ; +&.F +'!8*!/$ ' )0) *0! +!58) 5*$ C -V 0** -* + $55!*8 C 8-V *$$ 5/ +2!5$$!!$ $ J? +&.F +& 6V7 58!.+" --* /$0 $! J 3,?

90 &4+ 9 +' +&.F +' *! *0 ' $ *0!!)-/ C -V!5!0 -$* + 0$!0/ C 8-V!!0 $/8 +2 *$5!!/08 $$ J?! +&.F +& 6V7 0!.+" $-) 88 $* J 3,?! $-J3 +&6( 7 67? 9,

91 +5 $)J3 +&6( 7 67? 9 $/J3 +&6( 7 67?!9,

92 & $0J3 +&6( 7 67?!9

93 +7

94 -3 ( ) " * (4 G, &.+& E2 > < 3, ; N 'H ( ' +# 9 9 : : A :: B 1 M 9 N, 9 N 2 ", : :9 =, &.+& " " &.+& 6&. ( +( & ( ? " " # R 9 9 # # 9 # '

95 78 ) " * "?!.!! #! R! 9?!".! B 9.9 ; G " 'H M 6 # 7, &.+& K, ( #( P 1, ( F( # G 1, (? J 59 2? R J 59 2? " " " "! " " R! 6 7 ;, G ( ( # 680)7 ( ( 9 ( ( ( B ( 9 R N = ( ( G ; ( (

96 (4 7, ( 9, ( 9 #'#, Q ; ; N 1 = Q ( (, ( 9 3 ( ( &; ( (, ( 9, #O +< B 2 FS ' 68/-7 = (

97 7 ) " * (4 - G,,? " " " R? J J " % ; ;% J G " " 6*7, 6*7, (, $7 1 # '2 G, 6*7? " " " " " R? J " " " J " " " " J 6*!7 " #O +< #(, G M? ( ; " " ( " % " % ( "? ( ( " " ( 2 2 ( ( 2 & 688)79 & 688/7 F( "#O +< " ; 6*!7 ( ( " N ( ( G ; 1

98 (4-7& ". (4 > " ( (!!! * ' " % ;!' " % ; > " ( ( =<!!!< ; #O +< ". (4 > "A 4 " B 1 * < $ ( = ($ ". (4& "A 4 " B 1 > ' ( 5. 1( ( & ( ( & < "A 4 " "A 4 " ". (4( "A 4 " B 1 >! = = (! ($= ( ( ;

99 7( ) " * ". (4' > "A 4 " B 1 ( ( = < ( < # # ( # # " 6*$7 * " (4 &! & < " (4 # B C < "A 4 " B 1 ( 6 U7 2 M ( (, 6*79 1? (4 8" DE # + B < "A 4 " B 1 5 (4 F 2 "A 4 " B 1 5 # + B = # < 6 ( > " " ( < (7 6 ( " " ( 7 < "A 4 " 9 :# :9 ( #O +<9 1 2 #O

100 (4-7' (4& F.G" 2 " "A 4 = " " (4( " "A 4 = " "'"+ B 1 " " " 8 B 1 B C 2#, Q (, 6*79, 3 (4 9 "A 4 " B 1 # + B ( (?( ( 7 *? 7 < " G & 688)7 # % 9, 9 ( ;2 = " > # ( ( ( (

101 75 ) " * > " " " " "?" " 7? " 7 " " " " "?" " " 7??" " 7 " " 7? " " " " 7 7?" " 7 7? " 7 > > H* "? " %7 " " "? " %7 " " ( " " (? " %7 " (? " " (%7 " ( " (? (%7? (7 * 7 %7 6 < *?*<* > " " (< ( <? (7 ; = 8 ( (8 (

102 (4-7+ * ( < %. <?.7 7 $ + 8 ( ( *., 8 > ( > " " ( < ( <? (7 < ( <?8 ( 7 < ( <?.7 < (7 6 = 7 ( " " (? (7 7 <! B B % 3 (4 "A 4 " B 1 # + B * ( ( ( ( 7 * 7 < " + F.G" 2 > # ( ( ( ( * > > " " ( " " (

103 77 ) " * " " " " " " " " " " " " " " 7 " " " " " 7 ' () (* +? > H* " " " 7 * 1%* * * * "? " " 7? " 7 " " (? ( 7? (7 * 7 7 <! "+ B " (4& < "+ B 1 "+ B

104 (4& - 7, (4& - G,, ( 61 7? "! " " 6**7 R? J J " % ; ;% J J! 9 2*%9!! (4( <! " " 49:; 0 # " "'"+ 2 # # # # % G, 2 #, Q ( (, 6**7 3 (4& " + B B # ( (? % ( ( 7 6*-7 *? 7 "

105 ,8 ) " * " >! ( ( ( ( ( (? % ( ( ( ( 7 + B E? % ( ( ( ( 7? % ( ( 7? ( ( 7 % %? ( ( 7 ; % 8"' 2 % <! "+ B 3 (4( " + B B # ( ( % ( ( 7 6*)7 * * 7 "

106 (4( - 3, " >! ( ( ( ( ( ( % ( ( ( ( 7 + B ( ( 7 % % ( ( 7 > % % * % <! "+ B 1 (4' < "+ B B "+ B C (4( - 3 G =1 # 9 #'#, &9 # 63(*[*!7 N 1 ; 1

107 , ) " * * J ' #? 5$A5*A5)58A5/A5) *! J ' #? -A5A5/50A5*A5/

108 (4( - 3,& G,,? " " " ' " " 6*/7 R? J J " % ; ;% J J ' G, 6*/7? " " " " " ' " 6*07 R? J " " " J " " " " J ' " ' " J J ( 3# 6!5557, ( (, 6*/7 #, 3 (4' 8" 1222 "A 4 " B D # + B I ( ( ( ( 7 * 7 # ' + B I ' ( ( ( ( 7 * 7 * "

109 ,( ) " * G ( 61 7 # 3 (45 " + "! " " ' " " 6*87 * 6 # 6 " % ; ;% 6 # 6 ' # 6! 2*%!! # ' ( ( % ( ( 7 ' ( ( ( ( 7 6*57 6*7 * 7 7 * < " " >! ( ( ( % % ( 7 ( ( 7

110 (4( - 3,' > % % * % <! "+ B E

111 ,5 ) " *

112 - 2 #, = # 1, =#9, 9, = 2, 2 G 1 # 1 : : #( ( 1 ( # 2 7% # 9 N =.F9 #( M A # ( 1 # 6+&79 Q 1 ", Q ( N (? #2 N 9( = Q M, ; ; B ;,, # 2 6 (, 2(, 7 1, B 1 ( #( (, 9, :H : 9.F

113 ,7 - ; ;,, ;, C 9 ( M.F

114 3 \] & >9+ 9:, &.+& 1 ( =, :9.&.G. # # A. #9 $9 B \!] & 9 & &9 % 9 :% ( S# :9 3 " % &'9!55)9-59 B 8 \$] &U93# +9U(9:F# ( (' 2 :9 " [ ' 9 88/9 $ \*] & U9 U( 9 :F# ( (' ( :9 " "9 88)9 ) \-] & E9 F=^# &9 :" # (; ( :9 E <9 88)9 0$9 B $ \)] E Z &9 S >9 F# D9 :B # :9 3 ( ' 9!55* \/] E +9 % :" ( 2 (? #:9 3 "9 88$9 09 B $ \0] E %9 :B # :9 "( 9 B " ) \8] E2 D 9 > < D +9 :F " &'? ( 3:9 U %'9 8/) \5] 3 X9 >9 _ C9 : Q ( :9 > # & " &9! B *- \] 3( 39 :+, ( ( :9 F#, F 9!555

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

116 E0=! 8 \!)] >9 D= 9: ' ( :9 3# [ U9 88) \!/] >9 X#( Z9 :" '( Q :9 F# & "9 88/9!/9 B - \!0] U 9 :G = ( :9 F# & " /9 B! \!8] UW Z9 :& ( :9 " ' + (#9 88!9 8 \$5] UW Z9 U 9 # U9 :G #( ( 2 :9 F# & 9 88$9!9 B \$] UW Z9U>9+>"9F' <&E9:ES## ( :9 > # & " &9 88!9 0/9 B */ \$!] UW Z9 T &9 :" # (; ( :9 E <9 88)9 0$9 B $ \$$] U ' &9 T " >9 : ( #' ' ( '( :9 > # & " &9 88$9 009 B *!* \$*] UW Z9 ( U9 D >9 :' :9 #' (9!555 \$-] UW Z9 + 9 :3( ( ;:9 F# & "9 88$9!9 B * \$)] UW Z9 +` +9 " # "9 Z SP &9 :B :9 "( 9!55* \$/] UW Z9 "< F +9 : (( # ( ' # # ( :9># & "& *9 B *50 \$0] UW Z9 9 :T ( #( :9 > F " &'9 88!9 $9 B $ \$8] U F9 F #.9 :'( Q :9 > #.' " " '9 88$9 --9 B * \*5] USP >9 :" # :9 "( 9 B "9 $9 880 \*] USP >9 UW Z9 :% ( 2 S# :9 > # & " &9 88)9 89 B *$)9 F# ' #

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

119

120

121 Résumé Une prévision correcte de la consommation d électricité est fondamentale pour le bon fonctionnement du réseau électrique français, dont Réseau de Transport d Electricité a la charge. Les prévisions utilisées quotidiennement par RTE sont issues d un modèle alliant une régression paramétrique non linéaire et un modèle SARIMA. Dans l idée d obtenir un modèle de prévision adaptatif, des méthodes de prévision non-paramétriques ont déjà été testées sans succès véritable. On sait notamment que la qualité d un prédicteur nonparamétrique résiste mal à un grand nombre de variables explicatives, ce qu on appelle communémentlefléaudeladimension. On a proposé récemment des méthodes semi-paramétriques d estimation d une régression qui améliorent l approche non-paramétrique pure. L une d elles, basée sur la notion de directions révélatrices appellée MAVE (Moving Average -conditional- Variance Estimation), peut s appliquer aux séries temporelles. Nous étudions empiriquement son efficacité pour prédire les valeurs futures d une série temporelle autorégressive. Nous adaptons ensuite cette méthode, d un point de vue pratique, pour prédire la consommation électrique. Nous proposons un modèle semi-paramétrique semi-linéaire, basé partiellement sur la méthode MAVE, qui permet de prendre en compte simultanément l aspect autorégressif du problème, et l introduction de variables exogènes. La procédure d estimation proposée se révèle efficace en pratique. Mots-clefs Prédictions non-paramétriques. Prédictions semi-paramétriques. Modèles à directions révélatrices multiples. Modèles semi-linéaires. Réduction de la dimension. Séries temporelles. Consommation d électricité. Abstract Réseau de Transport d Electricité(RTE), in charge of operating the French electric transportation grid, needs an accurate forecast of the power consumption in order to operate it correctly. The forecasts used everyday result from a model combining a nonlinear parametric regression and a SARIMA model. In order to obtain an adaptive forecasting model, nonparametric forecasting methods have already been tested without real success. In particular, it is known that a nonparametric predictor behaves badly with a great number of explanatory variables, what is commonly called the curse of dimensionality. Recently, semiparametric methods which improve the pure nonparametric approach have been proposed to estimate a regression function. Based on the concept of dimension reduction, one those methods(called MAVE: Moving Average-conditional- Variance Estimate) can apply to time series. We study empirically its effectiveness to predict the future values of an autoregressive time series. We then adapt this method, from a practical point of view, to forecast power consumption. We propose a partially linear semiparametric model, based on the MAVE method, which allows to take into account simultaneously the autoregressive aspect of the problem and the exogenous variables. The proposed estimation procedure is practicaly efficient.