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Modèles ARMA non linéaires

  • 1. h‚itL? _it h @ Aih4i _ @U@L i| L_ i*it + L?w?‚i@hit 5@_ N,}N| i| Ui* CjiiB5B# U|LMhi bbH QJUHTDP hw Xqlyhvlwh gh Shusljqdq +h0pdlo = erojrwChkhvv1fquv0puv1iu, ODPHWD +Xqlyhuvlwh gh Prqwshoolhu L, hw Xqlyhuvlwh gh Shusljqdq
  • 2. +‚it4‚i i| @h|U*i i @4?i *‚iL*|L? @ ULh| |ih4i _it ULht _ U@U@L th *i 4@hU‚i _i i vLh! Lt itt@)L?t _‚i|@M*h _it Th‚itL?t Lht ‚iU@?|**L? i? |*t@?| ?i 4L_‚i*t@|L? ?L? *?‚i@hi _i |)Ti h‚iti@ _i ?ihL?it Lt i @4?L?t @tt *4T@U| _it L*4it _i |h@?t@U|L?tc _i *@ L*@|*|‚i @?t ^i *it TLt|L?t Lih|it th *@ ^@*|‚i _it Th‚itL?t wit 4L_ i*it ThLTLt‚it tL?| UL4T@h‚it @ *@ 4@hUi @*‚i@|Lhi i| @ 4L_ i*it +W *?‚i@hit _i L ai?!?t Lt UL?t|@|L?t *@ tT‚ihLh|‚i _it 4L_ i*it ?L? *?‚i@hit @ Th‚iLh Ui |)Ti _i UhL?^it Mt|h@U| At T@Tih tLt |i tLh|h? ULUL@ ThUit iL*|L? L? |i ivLh! @h!i| `i @||i4T| |L M*_ L| Lu t@4T*i uLhiU@t|t M) t?} ?ih@* ?i|Lh!t 4L_i**?} *tLc i i@*@|i |h@?t @U|L?t L*4itc LTi? ?|ihit| @?_ L*@|*|it igiU|t L? uLhiU@t|t @UUh@U) Ai t}}it|i_ 4L_i*t @hi ML| UL4T@hi_ |L h@?_L4 @*! @?_ |L L ai?!?t +W 4L_i*t ih@* i|Lh! + hit*|t @hi tTihLh |L |i *?i@h + L?it *@tt€U@|L? a,w G 22c eDc D
  • 4. c Bec e . L|t *iut G @U@Lc +c B+Oc +c +‚iti@ _i ihL?itc h‚itL?
  • 5.  W?|hL_U|L? L44i *@ T*T@h| _it 4@hU‚it _i 4@| ihit Thi4 ihitc i? T@h|U*ih Ui _| |hLTU@ c *i 4@hU‚i _ U@U@L ti Th‚iti?|i tLt _i uLh4it EdDoc d2
  • 6. o G ? 4@hU‚i T)t^i L tTL| i| ? 4@hU‚i @ |ih4i #@?t Ui _ih?ihc *it UL?|h@|t t‚iU@?}i?| T@h *L|t _i f |L??it i| *@Ui|ih ?i _tTLti _@U?i ?uLh4@|L? ^@?_ @ *@ ^@*|‚i L @ *Lh}?i _i *@ |h@?t@U|L? @h UL?|hic *@Ui|ih RtTL| Ti| UL?|h L*ih T@hu@|i4i?| *it U@h@U|‚iht|^it _i t@ 4@hU@?_ti i _ih?ih TL?| t|€i i? T@h|i *@ _g‚ihi?Ui _i Th ^ ti _gti @ _i Th?UT@ 4@hU‚it ?tc @ wL?_hit *it |it|t _i ^@*|‚i ‚i|@?| T*t i }i@?|tc *it Th @U‚it th Ui||i T*@Ui tL?| tLi?| tT‚ihiht @ Ui U L|‚it @ ivLh! W* u@| ?L|ih ^i *i 4@hU‚i _ U@U@L it| tLi?| Lhi?|‚i @ *@ M@tti Lh tL|i?h *it Th i? U@t _i thThL_U|L?c *h}@?t@|L? W?|ih?@|L?@*i _ @U@L @U i|i i| t|LU!ic T@huLtc _i }h@?_it ^@?||‚it _i U@U@L @tc *Lht^* ) @ ‚iUiUc *it Th M@tti?| h@T_i4i?| UL44i Ui u | *i U@t i? bHH ^@?_ *t tL?| T@tt‚it _i cbD m T@h |L??i 4‚i|h^i i? @?ih @ cm T@h |L??i 4‚i|h^i i? LU|LMhi #?i 4@? ihi }‚i?‚ih@*ic *@ _)?@4^i _it Th _ U@U@L it| h‚i}i T@h *@ *L _i *Lghi i| _i *@ _i4@?_i hc *Lghi _‚iTi?_ _i T*tiht u@U|iht ?Uih|@?t _Lh_hi U*4@|^it2c ‚iUL?L4^it L 4 i4i TL*|^it w?t|@M*|‚i @UUhi _it Th ?it| ^i *i hii| _i *@ h‚i@U|L? _i *@ _i4@?_i u@Ui @ Ui||i ?Uih||_i ? Ti| @*Lht _t|?}ih |hLt U@|‚i}Lhit _i U|@ |L?t _i Th d2
  • 7. o wit U|@|L?t _i *L?} |ih4i ^ _‚iTi?_i?| _ *i? ‚i|hL| i?|hi *it ThLi|t _i ?Li**it T*@?|@|L?tc *@ ThL_U|L?c *it t|LU!t i| *it Th N?i U|i _it Th c UL44i Ui u | *i U@t _@?t *it @??‚iit
  • 8. fc _‚iULh@}i Uit T*@?tc *@ ThL_U|L? _4?i _?i @??‚ii th *@|hic ?i hT|hi _it t|LU!t ti?t| ,? 4 i4i |i4Tt *@ _i4@?_i Tt *it Th @}4i?|i?| w@ _h‚ii _i Ui U)U*i Ei?|hi H i| f @?t it| Ui**i ?‚iUitt@hi @ U@U@L)ih TLh @||i?_hi tL? 4@ 44 _i ThL_U|L? wit U|@|L?t _i 4L)i? |ih4i ^ hi i|i?| *it @h@|L?t @??i**it _i ThL_U|L? ,**it Tii?| i|hi ML*iiht‚iit T@h _it UL?_|L?t U*4@|^it L _it _‚iUtL?t TL*|UL ‚iUL?L4^it wit U|@|L?t _i ULh| |ih4i ^ tL?| }‚i?‚ih@*i4i?| _ 4 i4i |)Ti ^i Ui**it LM tih‚iit th *it @|hit 4@hU‚it €?@?Uiht ,**it Tii?| i|hi _Lh}?i Thi4i?| tT‚iU*@|it L ?uLh4@|L??i**it BABA+ i| 7|i|jitd.o L?| |it|‚ic _@?t Ui U@_hi * @c *) TL| iti _iUi?Ui u@M*iEdbocdfo i? ti M@t@?| th ?i @TThLUi i? |ih4i _i UL?|‚i}h@|L? it @|iht UL?U*i?| ^i *i 4@hU‚i _ U@U@L ?it| T@t iUi?|
  • 9. c * ?it| _L?U T@t 4 TLttM*i _i T*L|ih *it Th T@tt‚it TLh itt@)ih _i Th‚iLh *it Th _ U@U@L #@?t Ui| @h|U*ic ?Lt ?Lt M@tL?t th Ui _ih?ih h‚it*|@| TLh UL4T@hih *it TihuLh4@?Uit Th‚itL??i**it _i *@ 4@hUi @*‚i@|Lhi @iU ?i 4L_‚i*t@|L? _i |)Ti + *?‚i@hi EL ai?!?t i| ?L? *?‚i@hi Eh‚iti@ _i ?ihL?it Lt i T*LhL?t *4T@U| _i |hLt @h@M*it i L} i?it G *it L*4it _i |h@?t@U|L?c *@ L*@|*|‚i t|Lh^i i| *it TLt|L?t Lih|it i||i Wrxwhirlv/ ohv surgxlwv sdvvhqw sdu ghv whvwv gh txdolwh plqlpxp #Oh Ho Qlqr hvw fhuwdlqhphqw oh phloohxu h{hpsoh srxu looxvwuhu fhwwh lqxhqfh gudpdwltxh vxu od surgxf0 wlrq gx fdfdr1 $Ohv dxwhxuv rqw hwxglh o*hflhqfh ghv sul{ vsrw1 
  • 10. _ih? ihi @h@M*i Ti| i|hi i UL44i ‚i|@?| ? ?_Ui th *it UhL)@?Uit _it ?|ihi?@?|t th Ui 4@hU‚i Th it @Lh h@TTi*‚i *itti?|i* _i *@ 4L_‚i*t@|L? i? |ih4i _i h‚iti@ _i ?ihL?it EtiU|L? 2c ?Lt _‚iUhL?t EtiU|L?
  • 11. i| e *it _L??‚iit |*t‚iit i| 4L?|hL?t *it h‚it*|@|t _i ?Lt Th‚itL?t _it Th _ U@U@L @
  • 12. 4Lt 2 wit h‚iti@ ?ihL?@ *Lh}?ic *_‚ii _i 4L_‚i*tih *i UL4TLh|i4i?| _ ?ihL?ic TLh 4i UL4Thi?_hi *i uL?U|L??i4i?| _ t)t| i4i ?ihi 4@? hi4L?|i @ |h@@ _i W,,NW i| ||t dHo ,? t@TT)@?| th *it UL??@tt@?Uit ML*L}^it _i *‚iTL^ic Uit _i UihUiht uhi?| *it Thi4iht @ ‚i|@M*h *@ t|hU|hi _i M@ti _ ?ihL?i uLh4i* wit Thi4iht h‚iti@ Li?| @?t *i Lh i| ti Th4i?| T@h +| ' s E%|c ' )E% | E #@?t Ui h‚iti@ L? @ ?i ULUi _i?|h‚ii i| ?i ULUi _i tLh|i E6} w@ Thi4 ihi i?Li _it t}?@ %| ' Ec %Q|c c %R| ^ i? |ih4it ‚iUL?L4‚i|h^it ULhhitTL?_i?| @ @h@M*it i L} i?it @}4i?|‚iit _i *@ UL?t|@?|i @TTi*‚ii @tt M@t L |hitL*_ it @h@M*it tL?| i?t|i TL?_‚ih‚iit T@h _it TL_t _i UL??i L? i| |h@?tuLh4‚iit T@h _it uL?U|L?t _@U|@|L? ) w@ ULUi _i tLh|i it| uLh4‚ii T@h *@ @h@M*i +| ' s E%|c A ^ it| i T*^‚ii T@h R @h@M*it i L} i?it % +i4@h^L?t |L| _@MLh_ ^i *‚i^@|L? E it| @tti3 }‚i?‚ih@*i TLh UL?|i?h ^i*^it 4L_ i*it ti*t _i *‚iUL?L4‚i|hi |h@_|L??i**i 5 *@ uL?U|L? _@U|@|L? it| *@ uL?U|L? _i?||‚i )E5 ' 5 @*Lht *‚i^@|L? E it| *i 4L_ i*i _i h‚i}hittL? *?‚i@hi, 5 T@h UL?|hi ) it| *@ uL?U|L? *L}t|^i L *@ uL?U|L? _i _t|hM|L? U4*@|i _?i *L ?Lh4@*ic L? LM|i?| hitTiU|i4i?| *it 4L_ i*it ‚iUL?L4‚i|h^it wL}| i| hLM|5 dSo w@ tLh|i +| t?|ihTh i|i _@?t Uit U@t UL44i *@ ThLM@M*|‚i _LM|i?h ?i @U|L? T*| L| ^?i @|hi i? ^i *i h‚iti@ t4T*i }‚i?‚ih@*ti *i 4L_ i*i _i h‚i}hittL? *?‚i@hic * ?i Tih4i| T@t _i h‚itL_hi Uih|@?t ThLM* i4it ,? T@h|U*ihc Ui _|t ?L? *?‚i@hi4i?| t‚iT@h@M*it w?|hL _U|L? _i ULUit U@U‚iit i| _i uL?U|L?t _@U|@|L?t ?L? *?‚i@hi @ Tih4t h@T_i4i?| _i _‚iT@ttih Uit LMt|@U*it i| @ u@Lht‚i *ittLh _ UL??i L?t4i wit h‚iti@ 4*|ULUit tL?| 4@?|i?@?| |*t‚it _@?t _i ?L4Mhitit _tUT*?it i| _L??i?| tLi?| _it h‚it*|@|t |h it t@|tu@t@?|t N?i 4@? ihi ULh@?|i i| UL44L_i _i Th‚iti?|ih ? h‚iti@ 4*|ULUi it| _i *i _‚iUhhi tLt uLh4i _i tU‚i4@ L _? }h@Ti %Oh sdvvdjh dx fdv pxowlydulh rx |M @ +|M===|ML,! qh srvh dxfxq sureohph1 Pdlv/ srxu od foduwh gh o*h{srvh qrxv qrxv uhvwuhljqrqv dx fdv xqlydulh1 Gdqv fh fdv sduwlfxolhu/ oruvtxh v @ 4/ f*hvw0d0gluh hq suhvhqfh g*xqh vhxoh yduldeoh hqgrjhqh/ fh uhvhdx vlpsoh iaxw dsshoh DGDOLQH +Dgdswlyh Olqhdu Qhwzrun, sdu baiN hw QNuu +493, hw PDGDOLQH +Pxowlsoh Dgdswlyh Olqhdu Qhwzrun, srxu v A 41 Gdqv oh fdv rx * hvw xqh irqfwlrq elqdluh txl suhqg ohv ydohxuv 3 rx 4/ rq rewlhqw o*dqfahwuh gh fhv uhvhdx{ = oh Shufhswurq gh -NtjAO,B|| +48;,1 'Srxu soxv gh ghwdlov vxu fhv prghohv yrlu Dphpl|d +4;4,1 2
  • 13. 1 )(xϕ 1x px 2x )(xF 10 =x αˆ βˆ)(xϕ 1h 2h qh q0ˆα s0 ˆβ )(xϕ ),ˆ(ˆ 11 xwfy = ),ˆ(ˆ xwfy ss =)(xF ]ˆ,ˆ[ˆ βα=w 6}  +‚iti@ @ ?i ULUi U@U‚ii N? h‚iti@ 4*|ULUit it| ? ihUiT|hL? @^i* L? @ h@L|‚i _it ?|‚itc tLt uLh4i _i ULUit tUUittitc i?|hi *@ ULUi _i?|h‚ii i| *@ ULUi _i tLh|i it ?|‚itc UL?|h@hi4i?| @ ihUiT|hL?c tL?| 4?it _i uL?U|L?t _@U|@|L? ?L? *?‚i@hit i? ^L? Tttic i? |‚iLhic |*tih T*tiht ULUit U@U‚iit( tLi?|c _@?t *@ Th@|^ic L? ?i hi|i?| ^?i L _i _i Uit ULUit *tiht h@tL?t t|€i?| Ui UL w@ Thi4 ihi it| _Lh_hi ?4‚ih^ic U@h *it ihhiht _i Th‚iUtL? i| _@hhL?_t _i *@ 4@U?i Tii?| t@UU4*ih h@T_i4i?| w@ _i i4i h@tL? UL?Uih?i *i |i4Tt _i U@*U* ^ Ti| _ii?h ThLM|u N?i _ih? ihi h@tL? it| _Lh_hi |‚iLh^i G *it Th?UT@ h‚it*|@|t L?| ‚i|‚i _‚i4L?|h‚it TLh ? h‚iti@ @ ?i ULUi U@U‚ii ?tc t@?t @U?i Tih|i _i }‚i?‚ih@*|‚ic ?Lt ?i ?Lt ?|‚ihittL?t ^@ h‚iti@ @ ?i ti*i ULUi U@U‚ii 5 ?Lt _‚it}?L?t T@h ' Ekcq *i?ti4M*i _it T@h@4 i|hit _ 4L_ i*ic T@h ^ *i ?L4Mhi _?|‚it _@?t *@ ULUi U@U‚iic T@h 8 *@ uL?U|L? _@U|@|L? _it ?|‚it _i *@ ULUi _i tLh|i i| T@h ) Ui**i _it ?|‚it _i *@ ULUi U@U‚iic @*Lht *@ ULUi _i tLh|i ThL_| G +| ' 8E qB n ^ [ Q q )E kB n R [ Q k %| E2 L +| ' 8E ^ [ B q )E R [ B k %| E
  • 14. wit qB i| kB hiTh‚iti?|i?| *it M@t _ 4L_ i*i E@TTi*‚it UL?t|@?|it i? ‚iUL?L4‚i|hi i? ^i? |‚iLhi *i UL _it uL?U|L?t ) i| 8 tL| @hM|h@hic *i T*t tLi?| L? |*ti _it uL?U|L?t t}4L_@*it _i uLh4i }‚i?‚ih@*i G )E5 ' @e5  e5 n  n K @cKc # W+ e| @c : f
  • 15.
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  • 17. L L_ i*i |Lhi}hittu L)i??i LM*i ?L? *?‚i@hi G +ETc^ @h @?@*L}i @ 4L_ i*it + *?‚i@hic L? Ti| _‚i€?h ?i ?Li**i U*@tti _i 4L_ i*i +ETc^ ?L? *?‚i@hi |i**i ^i G +| ' sE+|3cc+|3R(0|3cc0|3^(kcq n 0| Eb i?ULhi i? ?|hL_t@?| _it @h@M*it i L} i?it ‚ii?|i**i4i?| hi|@h_‚iit G +| ' sE+|3cc+|3R(0|3cc0|3^(%|c%|3cc%|3(kcq n 0| Ef ' Ekcq it| *i?ti4M*i _it T@h@4 i|hit _ 4L_ i*i @ it|4ih T@h ? @*}Lh|4i _i |)Ti +‚i|hLThLT@}@|L? _ }h@_i?|c B@tti|L?c wii?Mih}@h^@h_| L |L| @|hi @*}L h|4i ^ UL?i?| _@?t Ui U@t L|hi M| it| _i UL?t|hhic @ T@h|h _? ‚iU@?|**L? ~ c ? it|4@|ih s _i *@ uL?U|L? s 5@U@?| _i ?Li**it @*iht %|nc ?Lt TLL?t igiU|ih _it Th‚itL?t UL?Uih?@?| ?L|hi @h@M*i _?|‚ih i| +c Uit| @ _hi +|n Lh Ui*@ c L? it|4i *i?ti4M*i _it T@h@4 i|hit _i 4@? ihi @ 4?4tih ?i uL?U|L? LMiU|u M@t‚iic T@h i i4T*ic th *@ tL44i _it U@hh‚it _it h‚it_ t ' @h} 4? M` 3 [ |' d+| s E%|co2 QNiAc 7|AWN6Oj i| b|jdeoc DB,,BA| i| b|jd2o _‚i4L?|hi?| _@?t *itT@Ui _i 5LML*i EitT@Ui _it uL?U|L?t UL?|?it i| _‚ih@M*it ^i *‚i^@|L? Ee |h it }‚i?‚ih@*i Tih4i| _ @TThL 4ih ?i |h it }h@?_i U*@tti _i uL?U|L?t @?t ^i *iht _‚ih‚iit @iU @|@?| _i Th‚iUtL? ^L? *i tL@|i tLt *@ _LM*i UL?_|L? _@Lh tt@44i?| _?|‚it _@?t *@ ULUi U@U‚ii i| ^i *it ULiUi?|t tLi?| RThLThi4i?| it|4‚it ? Ti| |hLih _it h‚it*|@|t t4*@hit _@?t +OjANdeoc 8ABBtdo i| QjW|j,tjAd
  • 18. o Lh ‚i|ih Uih|@?t ThLM* i4it _i th@TThi?|tt@}i *‚itc i?|hi @|hitc @ *|*t@|L? _i T@h@4 i|hit tTiht E ^ }h@?_c @|hi4i?| _|c TLh ^i *@ ULhMi it|4‚ii tL| *ttic L? 4?4ti *@ tL44i _it U@hh‚it _it h‚it_t T‚i?@*t‚ii EL h‚i}*@ht‚ii 3 [ |' d+| s E%|co2 n b[ wi _i i4i |ih4i _i Ui||i i ThittL? Tih4i|c @ |h@iht *i ULiUi?|t bc _i UL?|h L*ih *i _i}h‚i _i *tt@}i _i *@ uL?U|L? s [ it| ? t|@M*t@|ih EL h‚i}*@|ih ^ T‚i?@*ti *i _i}h‚i _i ULhMhi _i *@ uL?U|L? hiUihU‚ii ,? }‚i?‚ih@* [ ' Uis E|j2_| @t * Ti| Thi?_hi Mi? _@|hit uLh4it _L?| *@ T*t t4T*i it| [ ' S2 E`i}| #iU@) b Ti| i|hi LT|4t‚i @ *@_i _i *@ 4‚i|L_i _i @*_@|L? UhLt‚ii wit T@h@4 i|hit _?|ih i| Tii?| i|hi it|4‚it _i _g‚ihi?|it 4@? ihic *@ T*t TLT*@hi ‚i|@?| Ui**i _i *@ _itUi?|i _ }h@_i?| n ' n #~E+| sE%|c D
  • 19. L # it| *i T@t _it|4@|L? ^ Ti| i|hi UL?t|@?| L @h@M*i i| ~ ' Ys*Y E@ULMi? Ui| @*}Lh|4i ?Lt @L?t Th‚iu‚ih‚i Ui* _i wii?Mih}@h^@h_| T*t h@T_i i| T*t hL Mt|i( * ti Th4i ti*L? G n ' E~ ~ n U! ~ E+| sE%|c wi T@h@4 i|hi Tih4i| _i hi?_hi *@ 4@|hUi ~ ~ ?ihtM*i *Lht^i Ui**iU it| 4@* UL?_ |L??‚ii i| @*}Lh|4i UL?t||i ? UL4ThL4t i?|hi Ui* _i B@tti|L? E f i| Ui* _i *@ _itUi?|i _ }h@_i?| E
  • 20. #L??‚iit i| U@h@U|‚iht|^it t|@|t|^it wit _L??‚iit tL?| uLh?it }h@||i4i?| T@h *i 5,. @ W?|ih?i| Lt @L?t hi|i? TLh Ui||i ‚i|_i *it ULht _i U* L|hi _ UL?|h@| u|h @
  • 21. 4Lt E?i@hM)c *it L*4it _i |h@?t@U|L?c *it TLt|L?t Lih|it i| *@ L*@|*|‚i t|Lh^i U@*U*‚ii th *it
  • 22. f _ih?iht Th _ UL?|h@| ULhhitTL?_@?| @
  • 23. 4Lt L|hi ‚iU@?|**L? t‚i|i?_ _ 2 @?ih bbf @ 2b 4@ bbHc tL| 2be TL?|t _L?| HH 4@?^@?|t it _ih?iht tL?| hi4T*@U‚it T@h *it UL|@|L?t _i *@ i**i w@ €}hi 2 U@Th it **t|hi Uit _L??‚iit G Prix journaliers à 3 mois du cacao 1990 1991 1992 1993 1994 1995 1996 1997 1998 720 840 960 1080 1200 1320 1440 1560 1680 1800 Volatilité historique 1990 1991 1992 1993 1994 1995 1996 1997 1998 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 Volumes de transactions 1990 1991 1992 1993 1994 1995 1996 1997 1998 0 2500 5000 7500 10000 12500 15000 17500 20000 Positions ouvertes 1990 1991 1992 1993 1994 1995 1996 1997 1998 0 10000 20000 30000 40000 50000 6}2 G #L??‚iit _ U@U@L :Oh _Frhh Vxjdu dqg Frfrd H{fkdqjh% gh Qhz0run hvw od suhplhuh sodfh gdqv oh prqgh rx v*hfkdqjhqw ohv frqwudwv vxu oh fdfdr1 Fhwwh sodfh q*lqwhuylhqw sdv gdqv od ghwhuplqdwlrq ghv sul{1 kwws =22zzz1fvfh1frp2 S
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  • 26. U _ittLt échéance fin base début 3 mois 6 mois réelle théorique 6}
  • 27. G L?ih}i?Ui _i *@ M@ti wit Th @ |ih4i UL?|i??i?| @*Lht ?i UL4TLt@?|i t@tL?? ihic Uit| @ _hi G | ' Bc| n | L Bc| hiTh‚iti?|i *i Th UL4T|@?| i| | *@ M@ti ^i* U@tc * tih@| tL@|@M*i _i? *iih Ui||i UL4TLt@?|i @@?| |L|i 4L_‚i*t@|L? @t _@?t *@ h‚i@*|‚ic *@ M@ti ti UL4TLh|i _?i 4@? ihi |h it ihh@|^i ^?i _g‚ihi?U@|L? Thi4 ihic T@h i i4T*ic ?i t| T@t @ t|@|L?@htih *it Th @ |ih4i ,? igi|c *i t|i?Ui _i *@ M@ti ?i ti T*^i T@t T@h *it UL |t _i t|LU!@}i i| _i €?@?Ui4i?| ti*i4i?|c 4@t @tt T@h *?|ihi?|L? _it tT‚iU*@|iht ^ ?i?Ui?| T@h *iht @?|UT@|L?t *it |i?_@?Uit _it Th tTL| d22o
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  • 37. i| tL?| |it|‚it th *it ff LMtih@|L?t ^ ti?| Ui||i T‚ihL_i wi |@M*i@ 2 t)?|‚i|ti *it _g‚ihi?|t h‚it*|@|t |hL‚it L_ i*it W 5 5, 5, OLht ‚iU @u eHSeSe eHSeSe e.H2e D22
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  • 65. €? _@TTh‚iUih *4T@U| _it @h@M*it i T*U@|it L*4it _i |h@?t@U|L?tc TLt|L?t Lih|it i| L*@|*|‚i th *i 4L_ i*i +Eec ?Lt @L?t it|4‚i tiT| 4L_ i*it W*t ULhhitTL?_i?| @ *@L | tUUittu _i Uit @h@M*it ^ tL?| hi|@h_‚iit D uLt E ' D Lt @L?t hi|i? *i 4L_ i*i +Ee @iU *it L*4itc +jEecL*4itcD ^ 4?4ti ?Lt Uh| ihit @h4 *it t‚i*iU|L?t h‚i@*t‚iit *i 4i**ih 4L_ i*i it| *i +Ee w@ €}hiD **t|hi tit TihuLh4@?Uit i? |ih4it _i Th‚itL?t _@?t *‚iU@?|**L? i| Lht ‚iU@?|**L? @ Q 6(J ? UL?t|@|i ?i _‚i|‚ihLh@|L? _it Th‚itL?t t|@|^it Lht ‚iU@?|**L? _ it ^L? t‚i*L}?i _i *@ T‚ihL_i _it|4@|L? 0 10 20 30 40 50 60 70 80 90 1450 1500 1550 1600 1650 1700 1750 Prévisions hors échantillon 300 310 320 330 340 1600 1650 1700 Région élargie 0 50 100 150 200 250 300 350 400 1200 1300 1400 1500 1600 1700 1800 Prévisions dans l`échantillon 6}D G h‚itL? _ L_ i*i ihL?@* +Ee D L?U*tL? wit 4L_ i*it ?ihL?@ Th‚iti?|i?|c i?ULhi ?i uLtc _it TihuLh4@?Uit Th‚itL??i**it ?i||i 4i?| tT‚ihihit @ Ui**it h‚i@*t‚iit @iU _it uLh4it *?‚i@hit _i |)Ti L ai?!?t iU tit ^@|Lh3i hi|@h_t t‚i*iU|L??‚it @ 4L)i? _it Uh| ihit W i| 5c *i 4L_ i*i |Lh‚i}hittu ?L? *?‚i@hi }‚i? ihi _it ihhiht _i Th‚itL? Lht ‚iU@?|**L? ?u‚ihihitc _i *Lh_hi _i
  • 66. @ e TL?|t i? @*ih @MtL*i 4L)i??i W* UL?_| _@?t SSI _it U@t @ *@ _hiU|L? ULhhiU|i _i *@ Th‚itL?c Ui ^ *i hi?_ T@h|U* ihi4i?| @||h@)@?| TLh *it ?|ihi?@?|t th *i 4@hU‚i _it LT|L?t f
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