• Keine Ergebnisse gefunden

Unit Root Tests for Time Series with Level Shifts

N/A
N/A
Protected

Academic year: 2022

Aktie "Unit Root Tests for Time Series with Level Shifts"

Copied!
11
0
0

Wird geladen.... (Jetzt Volltext ansehen)

Volltext

(1)

!#"%$&'$)(+*,!-/. " 0"%*1/"%$)23'4 56"87+"%9:0;4/(<$>=

? @ +. ACBD*E/$F+ (HG,IJ"%*'"%K3LM*'+AN+$FBO9P$

Q

RSUTTVSWXYYZ

[>Y\^]Z/U_`\^ab Kcd<e>Z/f^_`\gTV\

Yh

e>Z/fgiDa>WkjlamTZnocpYf

e>Yi Q cfghlaq[rY\s]Z`_`\sab tuZ/Ufg\^

vDwoxzy{|}~y

N€‚rƒY„z…‡†‰ˆ€VŠŒ‹o…††‰‹‹b„Žb‹ŽX‘E’Š”“U’%•‰“z“m†~‚–‚%†—•P‹b„E•k—˜„z‹b„z…‚™Š”€Š”Žb‹Šs“›šŒ„zœ‰„š˜Ž’ŠŒˆg‹•P‹&•Ÿž€˜†‘E€¡ Y†~Š”€¢‹Š”€8‹Š”‚–„

•P…„u“m†~‚% V•P…„—DŠ”€™•r£+†~€‹b„q¤<•P…šŒ†>Ž‹—˜¥‰¦§1’˜„¨‹b„Žb‹Ž›—VŠª©„z…FŠ”€%‹’˜„¨‘F•«¥–‹’˜„z¥%‹b…„•P‹F‹’˜„u—˜„z‹b„z…‚–Š”€VŠ”Žb‹Š”“<‹b„z…‚

†‰ˆ<‹’˜„­¬q®Ÿ¯¦o°±‹q‹…€Žk†~˜‹>‹’•P‹r¯›’Š”š”š”Š” VŽ³²´¯„z……†~€µ‹´¥ Y„–‹b„Žb‹Ž8’•œ‰„Dœ‰„z…¥K Y††‰…>Ž‚–•‰š”šXŽ•‰‚– VšŒ„% …†‰ Y„z…‹Š”„Ž

•‰€—;“z•‰€V€˜†‰‹qƒY„%…„“m†~‚–‚%„€V—˜„—ˆg†‰…>•P  Vš”Š”„—K‘›†‰…ž¦™£µ†‰…„z†«œ‰„z…«¶‹b„Ž‹Žq‘E’Šs“’„Žb‹Šs‚–•P‹b„–‹’˜„™—„z‹b„z…‚–Š”€ŠsŽb‹Š”“

‹b„z…‚·ƒ¥•;®Ÿ¸¹ …†“m„—˜…„­€—„z…r‹’˜„O€Š”‹>…††‰‹8€š”š›’¢¥ Y†‰‹’˜„ŽŠ”Ž8•P…„ºŽ˜ Y„z…Š”†‰…rŠ”€»‹b„z…‚–Ž8†‰ˆEŽŠ”¼z„D•‰€—

 Y†«‘F„z…1 …†‰ Y„z…‹Š”„Ž<…„š”•P‹ŠŒœ‰„q‹b†™‹b„Žb‹Ž1‘E’VŠ”“’O„Žb‹Šs‚–•P‹b„q‹’˜„>—„z‹b„z…‚–Š”€ŠsŽb‹Š”“¨‹b„z…‚½ƒ¥ ¾k¸¹­ …†“m„—˜…„Žz¦

¿~À&ÁNÂzÌÄ/ÅÅ`ÆÇFÂĉÈÉÆËÊPÌlÍ

¤'ΉζY¤ŸÏÎ

Ð%ÑmÒPÓ&ÊPÔbÕ/ÅzÍ<Ö €Š”œ/•P…Šs•P‹b„k‹Š”‚%„qŽb„z…Š”„Žz¶€ŠŒ‹<…††‰‹z¶VŽb‹b…U“m‹˜…•‰šŽ’VŠŒˆ^‹z¶˜•‰˜‹b†‰…„z׉…„ŽŽŠŒ†~€

Ø`Ùoګ۟۟ÜÝ/ÞàߛáPâ8ãVä~åªßFæFåèçêéËëXçªìíÝìqìîàÜ1ï«î³ìzÞàܐð”ä~çèçèâ8ìñ³ò/Ý¢ÚzóçôÜ`õ‰ï«Ü`õ˜ö‡÷­Ü¨Þ±ø¢ì«Ý~òrÞ±ø~Üuù&ÜUä‰Þàßàñ³ø~ܨú¢Ú«î³ß±ñ³øPä~Ý¢ïß±ï«Ü۟ÜUåô݉é

ßàñ³ø¢ìzðŒÞ`û/ü‰úYýÿþzþ¢û«ìÝõuÞ±ø~Üä~îàÚÜUìÝqÙoګ۟۟åªß±ß±åôÚݟä~Ý¢õ‰ÜUî Þ±ø¢ÜVî³ìåèÝ~åèÝ~ï'ìÝ¢õ–Ú«á~åèçôåôÞâEÚ«ð ÜUß±ÜUì«îàñ³ø~ÜUîàßî±Úï«î³ìÛŸÛŸÜ

ñÚ«Ý/Þ±î³ì«ñÞXÚö &ýú ›Ù`þð”Ú«î¢Ý¢ìÝñåªìçlß±äÚ«î±ÞUöìî±ÞXڏðÞ±ø¢åèߛî±Ü`ß´Ü`ìî³ñ³ø¡óìßXñì«î±îàåôÜ`õ¡Ú«ä‰Þ›óø~åôçèÜ1Þàø~Ü

¢î³ßÞXì«ä‰Þ±ø~Úîóìß! Påèß±åêÞàåôÝ¢ï¨Þàø~Ü#"Xä¢ÛEáÚ«çªõPÞ$XÝ~å% «ÜUîàß±åôÞ âqåôÝ%ýÜîàçèåôÝö

(2)

-&Z/_Ua`\g.Od cuYY\saŸUclca`_Ÿ\g_0//ci+i+cKnY`1/a`\2//Z8aŸa`pYZ Q Z.\^YY\g3.Ocd&˜ ÿfs l_U\g_ŸcdXZ//cYci+\2/ra`\gi+Z

_`Z`\^Z/_ Q Z/PY_UZ8ampZ>a``Z/hY\g.™nYUcnoZUa`\gZ/_Ecd‡a`pYZ>_`Z/U\gZ_¨hYZ«amZ`i+\gYZqamc™_`ci+Z>Z4VamZa¨ampYZriµcVhYZfg_1Yh

\gld Z/`Z//Zºn`c5//Z/hY`Z_–a`c Q ZºY_UZ/h \gfgamZ¡_Uam1.Z_™cdEa`pYZ f^ V_`\^_687lY\^am Q f^ZDYY\sa–`cVca8a`Z/_am_%dc

hY\:9Z`Z/˜aD_`\^a`a`\gcY_™pP]Z Q ZZ/JnYUcnoc_`Z/h6+;¡YZ<.`cYnNcdŸamZ_Ua`_ºfgf^c=q_™dcD»f^Z]Zfu_UpY\^dËa­\g ampYZ

ham>.Z/YZma`\gc nYUc?/Z/_`_A@CBDEGF6#7l`nYU\g_`\^.fs 6fg\sa`a`fgZK_UZ/Z/i+_ amc Q Z;TYc=q Q ca ampZUZ/fgam\s]Z

nZ/Ud c`iµ//Z­cd'_UciµZ­cd'ampZ­amZ_Ua`_%\g»a`pY\g_H//fg_`_6JIbSa`pY\g_r_Uamh K=¨ZO\^a`Z/YhCa`c</ciµnY`Z­_`ci+ZDcd

ampZ/_`Z–amZ_Ua`_8h;a`pYZ/UZ Q L=¨ZM=q\^fgf/fgc_UZ%ampY\^_.˜na>fgZ/_UaqnUamfs N6

-kpYZ/UZKUZÿ;Yi

Q

Z/™cdua`Z/_am_=qpY\2/zpNfgf^c= d c%]`\^cY_–T\gYh_­cdu_`pY\sdËam_–\g ampZµi+ZP cd¨ampYZ

BDEO@´_UZ/Z ZP6Q.6sWXYYZoWŸja`TZ/ncpYfRS7\gTTcYZ/T@U1UNUVF¨d c> m.Z™cd›a`Z/_Ua`_¡f^fgc=q\g3.Dd ck]ZU

.ZYZ/`fu_UpY\^dËa™d Y/«am\gcY_WFX6erc=¨Z]Z/'ampZKc`\Y.\gYf'nY`cnoc_`fg_–dc5//Y_OcNampYZ</P_UZ<=qpYZ/UZÿampZ/`Zÿ\g_

»cYZµa`\gi+Zµ_UpY\^dËaM=qpY\2/zpZ/P Q Z<//na`Y`Zh Q 6hYYi+iD ]`\É Q fgZK@´ZP6Q.36^[E&Z/U`c\@UN]NUluUNUVF^FX6

R»cUZ/c‰]Z/ nYUc?/Z/hYYUZ/_>UZ–‰]\^fÉ

Q

fgZqdc_/P_`Z/_`=qpYZ`Z%ampYZ¡a`\gi+Z8cd&ampZ%_`pY\sdËak\g_kYTVc=q60Ibamp\g_

_Ua`Yh a=¨Z`//ci+nUZ>Y\^a1UclcaFamZ/_am_1d c#BDE1_[=q\samp+%_`pY\sdËa1\g iµZ/a=qpY\2/zpb/P Q ZqhYZ/_c//`\Q Zh Q +

_`p\^dËa›hYYi+iD ™YhDd c=qpY\Y/zpDampZ

Q

UZPT–ha`Z¨\^_›TYc=q!6[-kpZu`Z/_`cO\g_Xamp¢a=¨ZŸZ4lnZ/«aFamZ_Ua`_d=qpY\2/zp

nZ/Ud c`ie=uZfgf¨YYhYZ­ampZ/_`ZUZ/fgam\s]Z/fs _`\^iµnYf^Zf/cYhY\sam\^cY_­`Zÿfg_UcSnYUZdZ/` Q f^Zÿ\gNiµcUZf/ci+nYfgZX4

_`\sam¢am\gcY_6gIbKa`Y`lamZ_Ua`__=qpY\2/zphYcºcaŸnZ/d c`ih=uZfgfo\gK_U\gi+nYfgZ>_`\sama`\gc_uUZ¡YcauZ4lnZ/a`Z/h;amc

hYc8=¨Z/f^fo\^ÿhY\:ib//Yfsa0/\gc//Yi+_Uam//Z_6#j8_U_`Yi+\g3.O­TYc=q;_`p\^dËa¨hamZr\g_¨fg_UcDcd‡nYm1/«am\Y/Pf `ZfgZ«]//Z

Q

Z/PY_`Zÿa`pYZ/UZKUZµiµ˜ am\^iµZ _UZ/`\^Z/_M=q\^ampk/zp.Z/_O\^ a`pYZ/\^l/cY_Ua``/«am\^c6c™hYZmYY\^a`\gcn=qpY\2/zp

c5///Oa­»TYc=qJnc\g˜a™\g am\^iµZP6Lod4YiµnYf^Z/_­`ZpD–Z`iµ iÿ1/`cVZ/cYci+\2/Oa`\gi+Z+_UZ/U\gZ/_M=qpY\2/zp

pP]Z» _`pY\sdËaÿ¢aºampYZ;am\^iµZKcd8ampZqD%Z/Uiÿ#Y\Ymr//am\^c c Z4?/zp3.Z»`amZ_+d cs=qpY\2/zpt//YU`Z/3/

hvuU_Uami+Z/˜a`_>pY‰]Z­c5//Y`UZ/h!6

Ib+a`pYZkYZX4laE_UZ/a`\gca=¨ZqnY`Z_`Z/˜aEampYZŸa`Z/_am_[=q\^a`pYca1ZX4nfg\2/\^a`f^ ™hYZ/_c//U\Q \^.¡ampYZwBDE6N;¡d/cY`_UZ

O_`nZ/\ÉfBDME \g_u_`_UYi+Z/h;\ghYZ`\s]l\^.Da`pYZ¡amZ_Uam_6#Ibnm1/«am\2/ZlpYc=uZ«]Z/dcks.\s]Z/Ka`\gi+Z8_UZ/`\^Z/_

ÿ_UnoZ//\ÉfXa`Z/_a%\g_>Y_`Yfgfs nYnYf^\gZ/h»YYhYZ8ampZO_U_`Yi+nam\^c»a`pa8\^ar\g_>_`Y\saz

Q

f^Z™dc>a`pYZ­a`\gi+Z­_UZ/`\^Z/_

a%pYYh!6I³a–\g_8KhY\Y9oZ/UZ/˜axYZ/_am\^cA=qpYZa`pYZ/%a`pYZDamUYZyBDE:pY_–1/a`f^f^ z.Z/Z/m¢amZ/ha`pYZs.\s]Z/

am\^iµZ_`Z`\^Z/_6|{uf^ZPUf^ ŸampYZam`Z+BDMES=q\^fgf

Q

ZSYYTYc=q

Q

Z/PY_UZcampZ/c=q\^_`Z amZ/_ap=¨cYfgh Q Z

YYZ//Z_`_`U 16

-kpYZO_amYh \^_rcc.˜Y\Y}/ZhS_>dcfgf^c=q_6_j Yi

Q

Z/8cd'YY\sarUclcara`Z/_Ua`_¡f^fgc=q\g3. dcr+fgZ«]Z/f&_`p\^dËa

UZD`Z«]V\gZ=¨Z/h\^»a`pYZDYZX4Va%_`Z/am\^c!6wIbn7lZ/am\^c+~µR»c˜amZa{Ÿ`f^cf/ciµnY`\^_`c»\g_>noZUdcUiµZhCYh

//c//f^Y_`\^cY_kd cfgf^c=:\gK7lZ/«am\^cK36

(3)

-kpYZOa`Z/_Ua`_™`ZOhZ/_^/`\ Q Zh d c8ampYZa//_`Zs=qpZ/`Z+Kf^\gYZ/>a`\gi+Z­a``Z/h \^_¡\g3//fghYZ/h\^CampYZOi+cVhYZ/fC6MI³d

Sam\^iµZ+amUZ/Yh \g_DYcaºUZxY\gUZ/hJdcºSa`\gi+Zÿ_UZ/`\^Z/_ºcd>\^a`Z/UZ/_Ua/1\^as// _`\^iµnYfs Q ZKh`cnYnZ/h6Z-kpYZ

hvuU_Uami+Z/˜a`_q`Z%c Q ]V\gcY_qYh_amm\2.p˜a`d cc=u`h!6#B¡\:9Z`Zauaz Q f^Z/_udcuampYZ/`\sam\2//fo]f^YZ/_upP]Z%amc

Q Z8Y_UZ/hK\^µampYa‚//_`ZpYc=¨Z]Z/6GI³a¨\g_¨fg_UcO_U_`Yi+Z/hÿa`paEampYZr_`pY\sdËa‚// Q Z8i+cVhYZ/f^Z/h Q ÿ­hYiµi­

]`\g Q f^Z

ƒz„…†

‡

ˆŠ‰

?‹ Œ‚Ž!

1‹ Œ‚‘’Ž!

‹

=qpYZ`ZŽ! \g_ŸampZ™_UpY\^dËaqhYamZP6

Ib a`pYZºam\^iµZº_UZ/`\^Z/_–fg\samZma`Y`ZDa“=¨cz.Z/YZma`\g.;i+Z/zpY\g_Uiµ_–cd¨_`pY\sdËam_–UZ hY\g_am\g3.Y\g_UpYZ/hXh?”

hY\sam\^]Z­camf^\gZ/qi+clhZ/fg_rYh»\gYc~]a`\gcYfca`fg\gZqiµcVhYZ/f^_6`-kpYZ™d c`i+Z/>`Z_`Yfsa¡\gSC Q `Ynla¡_`p\^dËa

\ga`pYZ%fgZ«]Z/f±=qpYZ/UZP_ka`pYZ–fÉaUamZ/qfgfgc= d cqº_UiµcVcamp;_UpY\^dËakdUci a`pYZ–\gY\sam\Éff^Z]Z/f‡amc+ YZ= fgZ«]Z/fC6

• Z=q\^fgfam`Z/aqamZ_Uam_kdcŸa`pYZ%a“=ucµiµcVhYZfab VnoZ_r\^KamYU»_azam\g3.y=q\samphYh\^am\s]Z%clamfg\^Z/Ÿi+cVhYZ/f^_6

–L——˜š™˜š›œ+žbŸ™ ¡˜¡œ¢b–L£¤£¤Ÿ¥Z¦™˜¡§¨

R»c_a8cdFampZ™a`Z/_Ua`_rhZ/`\s]ZhS\g;ampZDhhY\^a`\^]Z%camf^\gZ/Ÿd`i+Z=¨c`TiµP Q Z%]V\gZ=uZh_>hvuU_Uam\^. ampYZ

cU\2.\^foa`\gi+Z¡_`Z`\^Z/_/ _`‰ )©ªX‹¤«¤««‹¬©­&\gam`_ar_amZn!60-kpZ/C.i+Z/˜amZhAB¡\2/zTZ V”¯®Yf^fgZ@¡jJB®[Fuc

E'pY\gf^fg\^nY_°”“E›Z/U`cT@CE#EGF>amZ_Ua`_–`ZºnYnYfg\^Z/hSa`cKampYZOhvuUY_amZ/h _UZ/`\^Z/_6MIb ca`pYZ/H=ucUhY_/hZ/Yca`\g.µampYZ

hvuU_UamZh»_UZ/U\gZ/_ Q ²±©5ªW‹¤«¤«¤«‹V±©v­XYa`pYZ%d cfgf^c=q\g.DdcYŸamZ_Uaq]Z`_`\^cY_r`Z/cY_U\ghYZ`Z/h6

³

–L´)µO™œ5£™£

{uc_`\ghZ/>º`Z.`Z/_U_`\^c

¶ ±©P…!†¸·‚±©v…º¹rª!» ¼

½¾^¿

ªÀ

¾ ¶ ƒz„…º¹

¾ » ¼

½¾c¿

ªÁ

¾ ¶ ±©v…º¹

¾

»t¤ÃvÃPÄvÅ @à?«sF

h»hYZYca`Z–a`pYZl;%W7KZ_Uam\^iÿ¢amckcdg·CYh\^a`__ŒÅ”b_aza`\g_Ua`\2/ Q ±

·ChzŒ1Æ

Ç

YUZ/_`nZ/«am\s]Z/fs N6¨[r_U\g.

a`pYZrcaza`\gc

±Á

@F[† dÈ

±Á

ªÈ>ÉÉÉXÈ

±Á ¼

5=qpYZ`Z

±Á ¾

\^_1a`pYZJ;–W7 Z/_Ua`\giµamc'cd

Á ¾

@YÊa†HN‹¤«¤««‹ÌËF

a`pYZjÍB®J_Uamam\^_Uam\Y//_qUZ͎

±

·Î

±Á

@FŸYh)Œ1Æ

Ç

@´_UZ/ZME›Z``cAR|Ï1c1.Z/f^_m.K@UNUN~VFcF6

³tÐMÐ

™œ5£™£

B¡ZYcamZ%a`pYZ–`Z/_U\ghYYfg_kcdFº`Z.`Z_`_`\^c±©P…!†ÒÑJ±©v…º¹rª»²Â… Q Z±Â…@ӌ[† N‹¤««¤«‹^ŽJFŸhhZmYZ

±

ÔÕ

Ö

†×Ž

¹rª

­

½…¿ ª ±Â Յ

(4)

±

ÔÕ

†×Ž

¹rª

­

½…¿ ª ±Â Յ » vŽ

¹rªÙØ

½¾^¿

ªÛÚ

Ø

@:Ê?F

­

½

…

¿V¾cÜ

ª

±Â…¬±Â…º¹

¾

=q\samp

Ú Ø

@:Ê?F#† È

¾

Ø Ü ª

@¡ÝrZ=¨Z V”Ì•NZ_Ua¡Z_Ua`\giµamc¬F6g-kpZ/»a“=¨c ]Z/U_`\^cY_>cdgE#E a`Z/_am_r`Z

Þs@v±ÑdFG†×Ž8@v±ÑAÈ FdÈ

Ô!Õ ÈO±

Ô!Õ

Ö

FÍßێ

¹ Õ ­

½…¿ Õ ±© Õ

…º¹rª¯à

¹rª

h

Þs@šŒ

Æ

á

F#†

±

Ô Ö

±

Ô Œ Æ á È

Ô!Õ ÈO±

Ô!Õ

Ö

Ffâãv±

Ô

ߝŽ

¹ Õ ­

½…¿ Õ ±© Õ

…º¹rª¯à ªCä

Õ^åæ

¹rª

@_`Z/ZlE'pY\gf^fg\^nY_RSE&Z/`Ucç@UN]N]NFŸd cqa`pYZ%amZ_Uam_8YhKE›Z``cARèÏ1cN.Z/fg_`.q@U1UN~VF¨d c`//U\^a`\2/Pf

]f^YZ/_¬F6

-kpYZDd cf^fgc=q\g3.ºnoc_U_`\Q \gf^\^am\^Z/_Ÿd crhvuU_Uam\^.b©P…'pP]Z Q ZZ/Cn`cnc_`ZhC\g;ampZDfg\samZma`Y`ZP6`E›Z/U`c

@¤UN]NU‡¤UNUVF¨n`cnc_`Z_>a`c `Y»º`Z.`Z/_U_`\^c

©v…†êé!뻲骓Œ»tìvƒz„…3»t¤ÃvÃ1ÄÅ @ӌ#†HN‹¤«¤««‹^ŽJF« @à?«èNF

-kpYZ™`Z.`Z_`_`\^cSUZ/_U\ghYfg_<±©?í

…

†î©P…È|±é!ëGÈè±éª“ŒdÈ

±

ìPƒz„…@ӌG†MN‹«¤«¤«‹^ŽJFq`Z–ampYZ™hvuU_UamZhA©P…Å6‚-kpYZ

jÍB®S]Z/U_`\gcY_GŽ

±

·Î

±Á

@F<YhbŒPÆ

Ç

cdampYZq`Z_`Yfsam\^.%YY\sa1`cVca<amZ_UaE_Uamam\^_Ua`\2//_=q\gfgf Q ZqhYZYca`Z/h Q aï

Ç

ðñ

YhZï

…

ð3ñ

FUZ/_`nZ/«am\s]Z/fs FYh a`pYZ<Þs@v±ÑF™YhçÞs@šŒ

Æ

á

F8]Z/U_`\^cY_O`Z+hYZ/YcamZ/hN_lïlï á

ðñ

YhTïMï

…

ð3ñ

`Z_`nZ/«am\^]Z/fs N6

tŸ_UZ/hc+YY\sa¡`cVcaqamZ_Ua%cdG7?/zpYi+\ghaÍRòE'pY\gf^fg\gn_8@UNU˜1F«Ûj8i+_`f^Z/HR WZZL@¤UNUVóNFkY_`ZOÿWXv”

.`.Z¨R»Yfsam\^nYfg\^Z/#@´W›RqF&nnY`c˜P/zpOYh­nY`cnoc_UZEa`crZ_Ua`\giµamZ#骇Yh8ìqYhYZ/XampZ¨Yf^f˜p VncampZ/_`\^_/

ampYaq\g_@à?6èNFu\g_kiDYf^a`\gnYf^\gZ/h Q ampYZ–hY\:9Z`Z/3//\g3.+cnoZma`c ¶ ha`pYZ/»q;–W7K`Z.`Z_`_U\gc

©v…†\éª!»tì

ƒ)„…»t¤ÃvÃPÄvÅ @ӌ[† ?‹«¤«¤«‹cŽÍF @à?«Q~VF

\g_8noZUd cUiµZh!68B¡ZYca`\g.ÿa`pYZº`Z_`Yfsam\^.n`iµZ«amZ¡Z/_am\giµa`c`_ Q Ò±éª8Yh

±

ìKhhYZm\g.t±éôa†

©5ª‚Èõ±éª'ampZ;hvuUY_amZ/h _UZ/`\^Z/_º\^_>±© ð?ö

…

†÷©v…gÈø±éôlÈø±éª“Œ_È

±

ìvƒz„…¯6k-kpZ`Z/_UYf^a`\g.Ca`Z/_a _Uaz¢am\g_am\Y//_

//c``Z_`ncYhY\^.Sa`cqŽ

±

·Î

±Á

@F«dŒ1Æ

Ç

#Þs@±ÑgF™YhùÞs@šŒ

Æ

á

F=q\^fgf Q ZµhYZ/camZh _súÍû

Ç

ð3ü!ý gúÍû

…

ð3ü!ý gúÍû á

írí

YhzúÍû

…

írí

`Z/_UnoZ/a`\^]Zf^ 16

od4la`Z/Yh\g.ampYZ+\ghYZ/_–cd`7l\gTTcYZ/ZR WkjlamTZnocpYfw@U1UNUVF«&WXYZ›Wkja`TZnocpf0Rõ7\gTTcYZ/

@¤UNUNUVFa@pYZ//ZdcampNW&W7F¡nYUcnc_`ZºamcZ/_am\^iÿa`ZOampYZ+n`i+ZamZ`_–cd¨iµcVhYZf`@à?6èNF

Q

qD–W7n?”

nYUc˜1/zp YYhYZºfgc5/Pf¨fsamZ/Ua`\^]Z_OcDa`pYZKY\^aºUclcaDYfgf¨p VncampZ/_`\^_+_O\gê@±?6Q~VF6+• Zÿdc?/Y_ºc

(5)

amcl=ucUT Q ZaUamZuampKZ/_am\giµa`\gc+YYhYZkfgc5/PffsamZ`a`\^]Z/_@ _`ZZ%WXW73F65j8_`_UYi+\g.Da`pa¨ampYZ¡Z`Uc`_

\g×@à?6Q~VF™pY‰]Z;TjJþ8@ÿËF™_UZ/`\gf‚/c`UZ/fgam\^c _amU/a`Y`Z1a`pYZ NnY`cnoc_UZÿamcSZ/_Ua`\giµamZ+ampYZÿ`Z/f^Z]˜a

n`i+ZamZ`_†S@Óé!뤋¬éªW‹Wì1F Q i+\g\gi+\2}/\^.

¼

@?‹

Á

F#† @OÈùÞNF

¼ @ Á F

¹rª

@¸ÈùÞ1F‹ @à?«F

=qpYZ`Z

¼ @Á F‚†

Ô ¹ Õ

{uc‰]@“„ÍFw=q\sampn„ Q Z/\^.µa`pYZDZ`Ucr]Z/a`c¡cd`@à?6F«h†Š©ª@Ó©

Õ

Èù©ªcFÉÉÉ

@¡©­gȁ©­Û¹rªcF

YhsÞê†Þ‚ª5Þ

Õ

5ÞV=q\samp8Þ_ª[†ŒN‹z3‹«¤«¤«‹z

Õ

†ŒN‹PN‹¤««¤«‹/

hsÞ_†ƒ)„Gª

@Cƒ)„

Õ

ÈMƒz„#ª^FrÉÉÉ@Cƒz„­#ÈMƒz„­Û¹rªcF

6dj8fsampYc.p–ampYZ¨hvuUY_amZhDham<±© ö1ö

…

†\©P…¬ÈK±é!ëPÈq±éª¯ŒÈ

±

ìPƒ)„…

//cYfgh Q Z+_`Z/h \gampZfjJB® YhZE#E nYnY`c1/zpYZ/_<WXW7 n`cnc_`Z+_`f^\2.p˜a`f^ Ch\Y9oZ/`Z˜a­n`c5//Z/hY`Z

=qpY\Y/zp»hvuUY_Ua`_Ÿd cua`pYZ%Z/_am\giµa`\gcµZ/`Uc`_k\^KampYZ%Y\^_m3//Z%n`i+ZamZ`_kYhL=ucUTZhKxY\samZÍ=¨Z/fgfo\g

_`iµf^f_miµnYf^Z¡_`\^iOYfgam\^cY_6dB¡Z/Ycam\g3.OampYZjJþ nocf^ VYci+\Éf Q Á

@CûGF#† È

Á

ªcû>ȒÉÉÉ1È

Á ¼ û ¼ Yh

\^a`_¡Z/_am\^iÿa`cqd `ci @à?6F Q ±Á

@¡û0FWXW7ShYZmZO±

!

…[†

±Á

@CûGF1±© ö1ö

…

Yh Q _UZOampYZºY\^a%UclcaramZ_Ua–c

ampZ­?4l\gfg\gU +UZ.UZ/_`_U\gci+clhYZf

¶ ±

!

…†#"»t·b±

!

…º¹rª»%$

±Á

@CûGF ¶ ƒ)„…» ¼

½¾c¿

ª Ñ ¾ ¶ ±©

ö1ö

…º¹

¾

»²Â¤ÃPÃPÄvÅ @šŒ#†²Ë8» ?‹¤«¤«¤«‹^ŽJF« @à?«%óNF

-kpYZµYY\^a™Uclca–a`Z/_UaD_Uamam\^_Uam\Y/ \g_™1.˜\^ c Q az\gYZh6_–ampYZ+Y_Uf#ŒÅ”b_Uamam\^_Ua`\2/ºcdŸa`pYZ+Z/_Ua`\giµamc%cdw·

Q _UZ/h»cK;–W7Z/_am\giµa`\gcKcd›a`pY\g_ki+clhZ/fÌ6dI³aw=q\^fgf Q Z–hYZYcamZh Q zû#û'&

ðñ

6

( ¨¨§?›*)3™˜Ó§¨+)r wžyŸ™ ¡˜Óœ5¢b–L£¤£Ÿ¥Z¦™˜Ó§¨

[rhYZ/8a`pYZº_U_`Yi+na`\gcCcdEC\gYc‰]¢am\gcfca`fg\^Z/qampYZOnYmi+Za`Z/U_8cd'a`pYZOhYZ«amZ/Uiµ\^Y\g_am\Y/™a`Z/`i+_

/P Q Z–Z/_Ua`\giµamZhauUc\g˜amfs f=q\samp;ampYZ–n`i+ZamZkc)=qpY\2/zpampYZ–YY\saq`cVcakamZ_Uar\g_ Q _`Z/h6‚-kpY\^_`=u_

nYUcnoc_`Z/h Q zE›Z``cT@UN]NUVFX6'erZ–_U.N.Z_Uam_>Y_U\g. ampYZ–UZ.UZ/_`_U\gci+clhYZf

¶ ©P…!†¸·©v…º¹rª»Té!ë»Z骯Œ»çìPƒz„…5»çì-, ¶ ƒz„…?» ¼

½¾^¿

ª Á ¾ ¶ ©P…º¹

¾

»T¤ÃPÃPÄÅ @šŒ#†çËM»J?‹¤«¤««‹^ŽJF>@à?«ôVF

=q\^a`pYca–n`\gc–hvuUY_ami+Z/˜a™cd¨a`pYZ ham;_UZ/U\gZ/_6fjH.˜\^CampYZaŒÅ”b_aza`\g_am\2/ºcd·N\^_–a`pYZ `ZfgZ]˜a–Y\^a

`cVca–_aza`\g_Ua`\2/P6aj8_–iµZ˜am\gcYZ/h ZPUfg\^Z//oampYZµh]˜azP.Z cdui+cVhYZ/f`@±?6ôVF8\g_%ampYa%ampYZ f^Z]Zf1_`pY\sdËa–\g_

.`hYfma`pYZ/'ampYÿ Q `Ynla¤6g-kpYZ>`Z_`Yfsam\^.jÍB®Cab VnoZqYY\saE`cVca<amZ_Ua¨_Uamam\^_Uam\Y//_g=q\^fgf Q ZqhYZ/YcamZ/h

Q )ï

Ç

. ñ YhKï

…

. ñ 6

tŸ_UZ/h#cJ\ghYZ/_OcdrWkjamTZ/ncpYf±ER jYfgf^Z/sR÷7\^TTcYZÒ@UNU1UVF«1WXW7Jfg_UcA//c_`\ghZ/ C_`Z//ch

nc_`_U\Q \^fg\^ab ºdcŸZ/_am\giµa`\g.™ampYZ%Y\^_m/Z–nmiµZ«amZ/U_ŸYYhZ/ŸampZ%YY\^aŸ`cVcaŸYf^fp˜ Vnoca`pYZ/_U\g_qY_U\g.

(6)

©v…†êé!ëWƒs…r»ùéª!»tì

ƒz„…r» ¼

½¾c¿

ª Á ¾ ¶

©P…º¹

¾

»²Â¤ÃPÃPÄÅ @šŒ#†HN‹¤«¤«¤«‹^ŽJF‹ @à?«0/NF

=qpYZ`Zzƒs…M†d csŒb†h²}Z/Uc Zfg_`Z=qpYZ/UZYhù©P…† d c8Œ21N6ç®Uci,a`pY\g_ºi+cVhYZ/fEampYZ

n`i+ZamZ`_›`ZEZ/_am\^iÿa`Z/h Q 8;%W76-kpYZuY\^a›`cVcaXamZ_Ua<\^_ Q _`ZhOcz±

3

…†

±Á

@¡ûGF°©P…¬È+±é!ëVÈ+±éª“ŒÈ

±

ì1ƒ)„…

Y_U\g.ºampZ­?4l\gfg\gU µ`Z.`Z_`_U\gc

¶ ±

3

…†4"M»t·#±

3

…º¹rª» ¶ ƒz„…5$!ª» ±

6 … $ Õ

»t¤ÃvÃ1ÄÅ @ӌ[† ?‹¤«¤««!‹^ŽJF‹ @à?«Q]VF

=qpYZ`Z>±

6

…

†7¶ ©P…º¹rª#ÈS±é ,

ÉÉÉ8 ¶ ©P…º¹

¼ Ü ª[È é± ,

FYhê±é , † éªcα

±Á

@FX6JjH.˜\g»ampYZ8ŒÅ”³_Uamam\^_Uam\Y/­cd'ampYZ

Z/_am\^iÿa`Z/h<·K\g_1Y_`Zh_'ampZrY\^aE`cVca1amZ_Ua¨_Uaz¢am\g_am\Y/16dI³aG=q\gf^f Q ZrhYZYca`Z/h Q bû#û'&

. ñ

6dj8fgfYa`pYZkamZ_Uam_

UZ¡fg\^_UamZhK\g<-F Q fgZON6[IbKa`pYZ%YZX4laq_UZ/«am\gcp=uZÍ=q\^fgf Z4lnYf^c`Z¡a`pYZ/\^u_`iµf^fo_`iµnfgZ8n`cnZ/am\gZ_ŸY_U\g.

+R»c˜amZ8{ŸUfgcºZ4lnZ/U\gi+Z/˜a¤6

9 ): ¡œ<;>= [>Y\^aþ>cVca`-&Z/_Ua`_

-›Z_Uar_Uamam\^_Uam\Y/ o'_am\giµa`\gcKcd þqZd Z`Z//Z_

hZamZ`i+\gY\^_Ua`\2/8a`Z/`i+_

ï Ç

ð3ñ

;%W7 E&Z/U`cZ@U1]NU‡U1UVF

ï …

ð3ñ

;%W7 E&Z/U`cKR|Ï1cN.Z/fg_`.K@¤UNUN~VF

ïlï á

ðñ

;%W7

ïlï

…

ðñ

;%W7

úÍû

Ç

ðü!ý

;%W7KYYhYZ?aë jriµ_UfgZ`RMWZ/Zf@¤UNUVóNF

úÍû

…

ðü!ý

;%W7KYYhYZ?aë 75/zpYiµ\^hawR E'pY\^fgf^\gnY_Í@UNUNF

úÍû

á

írí

;%W7KYYhYZ?aë

úÍû

…

írí

;%W7KYYhYZ?aë

û#û@&

ð3ñ

D–W7KYYhYZ?aë WXYZ WkjamTZ/ncpYfRS7\gTTcYZ/Z@¤UNUNUVF

ï Ç

. ñ

;%W7Kcd&dYfgf‡i+cVhYZ/f E&Z/U`cZ@U1]NU‡U1UVF

ï …

. ñ

;%W7Kcd&dYfgf‡i+cVhYZ/f

û#û@&

. ñ

D–W7KYYhYZ?aë>\gdYf^f‡iµcVhYZf WXYZ WkjamTZ/ncpYfRS7\gTTcYZ/Z@¤UNUNUVF

(7)

A B +K<" BD*19/ +. ACBO*1P$›µ

• Z™pY‰]Zl/ci+n`ZhampYZ–YY\saq`cVcakamZ_Ua`_rY_U\g.ºa`pYZ%d cfgf^c=q\^.Da“=¨c<BDE'_

©P…!†Òƒz„…»%Cr…¯‹ @`È

Á

ªcû0F@`ÈEDûGFCr…†GF… @ӌ[† N‹¤«¤««‹^ŽJF @C~3«sF

Yh

@`È

Á

ªcûGF°©P…†Òƒz„…»

3

…¯‹

3

…†HD

3

…º¹rª»%F… @ӌ[† N‹¤««¤«‹cŽÍF @C~3«èNF

=q\^a`p2Fv…JI4KLKLMNT@´3‹PFODa† 1‹z3«QU3‹z3«Q]ºYh)Žê† ‰3‹?6[E'`c5//Z/_U_`Z_8cd&ampY\^_kab lnZ=uZ`ZDfg_UcºY_`Zh

\g6R»c˜amZL{Ÿ`f^cS_Ua`Yh Q NWXW76Ib hYhY\^a`\gc amcSa`pYZÿ_`i+nYfgZ+]fgYZ_l=¨ZKpP]ZL.ZYZ/`amZh ‰

nYUZ/_miµnYf^Zr]f^YZ/_‚=qp\2/zpp=¨Z/`Z%h\g_^//`hZ/hZ4?/Z/naqampYaŸ_UciµZ8cdampYZi·`Z¡Y_UZ/h;\gµampYZ¡Z_Ua`\giµam\^c

nYUc?/Z/hYYUZ/_'d cg=qpY\Y/zp nY`Z_mi+nYfgZ¨]fgYZ_1`ZkUZxY\gUZ/h!6d-kpYZqnY`c5//Z_`_H@C~36sF›UZ/nYUZ/_UZ/˜am_¨+hYhY\sam\s]Z

ca`fg\^Z/%i+clhYZfg=q\^a`p6 Q UYna­_`pY\sdËaD¢a­a`\gi+ZsŽ!’=qpYZ`Z/_­a`pYZµi+cVhYZ/fw@¡~36ª1F/c`UZ/_UnochY_­a`cC

\gYc‰]¢am\gcf1ca`fg\gZ­n`c5//Z/_U_º\^d

Á

ªQP† ?6q•NZKnYnYfs 6f^f'amZ/_am_Oa`cCampYZÿa`\gi+Zµ_UZ/U\gZ/_8.Z/YZma`Z/h Q

ampZOa“=uc;hY\:9Z`Z/˜aBDE'_%fsampYc3.p‡_amU\2/a`f^ »_`nZPT\^.Ya`pYZDamZ_Ua`_™hZ/_`\Y.YZh dc¡hYh\^am\s]ZOcamf^\gZ/U_

UZ8Yca‚//c_UamU/a`Z/hKa`cOnoZUd cUiò=uZfgf d cEa`\gi+Zr_UZ/U\gZ/_0=q\^ampµ\gYc~]a`\gcYfca`fg\gZ`_¨Yhÿ]V\Y//Zr]Z/U_m36

Ib nm1/«am\2/ZŸpc=¨Z]Z/qa`pYZ»ab VnZScdÍBDME|=q\gfgf Q ZYYTYc=q \g².Z/Z/mfrYh‡ŸpYZ//Zq\^ay=ucYfgh

Q Zÿhl]am1.ZcY_­d cD;amZ/_aDa`c Q ZµUc Q Y_a8=q\^a`pNUZ/_`nZ/«aOamcampYZfBDE6-kpY\g_™\g_™cYZµ\g_U_`YZ amc Q Z

hYh`Z/_U_`ZhS\ga`pYZ–_`\giDYfÉa`\gcÿ_Uamh N6

j8fsampYc3.pampYZfBDME'_%hYcYca™pP]ZµhYZ«amZ`i+\gY\^_Uam\Y/Ofg\^YZP8amUZ/Yh amZ`i+_/=uZ pP]ZµnYnfg\gZhampYZ

amZ_Ua`_Í=qpY\2/zp f^fgc=½d c8_U/zp ÿamZ/Ui hnY`Z_`Z/˜a™_`ciµZOUZ/_UYf^a`_¡d c8_`iµnfgZO_U\2}/ZlŽè† ‰ Q `Z/T

nc\g˜aMŽ!\†õVU»Yh6hY\:9Z`Za­]fgYZ_Dcd

Á

ª%\gZ-› Q f^Z/_OSYhZ~36K-kpZ<mr.YUZ/_­\g a`pYZµam Q f^Z/_O`Z

`Z“uUZ/«am\gc­d `ZxYZ//\gZ_FdcXamZ/_am_=q\^amp­Yci+\gf˜_`\2.Y\Ymr///Z¨f^Z]ZflcdÛóSR Q _UZ/hOcÿ‰>UZ/nYf^\2/P¢am\gcY_

cdqampZZ4lnoZ`\^iµZa6T-kpY_/1ampZSRc˜amZz{ŸUfgc_UamYh`h Z/U`cº\^_UT ï<@Èùï8FcÎl‰»d cºSa``YZ

`Z“uUZ/«am\gcn`c Q Q \gf^\^ab <ïb6#®ck\^Y_Uam//ZYd c`ïO† 3«èNós=¨ZM.Za> _UamYhUh»Z`UckcdF36èV/?6

j _am`\^T\g.™c Q _UZ/U]a`\gc+d `ciò-› Q f^Z/_Ÿ­Yh<~­\^_Ea`pYZr]Z/U µnclcEnZ/Udc`iµ//Z>cdoampYZJEGE6a`Z/_Ua`_6

-kpYZ« `Z–Z4Va``Z/i+Z/fs L//cY_`ZU]am\s]Z­Yh‡ _rºUZ/_`f^aPpY‰]Z™]Z/ ;fg\^aUamf^Z¡noc=¨Z/kdc

Á

ª‘ =qpYZ/UZP_

ampZ ;c‰]Z``Z“uUZ/«a¡hY`iÿ¢am\2//fgfs +YYhYZW?aë>d c

Á

ªX1:K@´_UZ/Z–ampYZYDy†MM//cf^Yi+Y_WFX6_7l\Y}/Z–nYUc Q fgZiµ_qcd

E#E amZ_Ua`_#=¨Z/UZ>fg_Uc%c Q _`ZU]Z/h Q b75/zp=¨Z/a@UN]NUNF&d c#BDE1_=q\^ampca1_Ua``/«amY`f_`p\^dËam_6djrf^ampc.p

ampZwm\^amZq_`iµnfgZknYUcnoZUa`\gZ/_1cdoampYZ_`Z>amZ/_am_E\gi+nY`c‰]Z>_Ufg\Y.p˜amf^ ­d cgŽê† ˜ampZ/\g1P/amYf `Z¯uUZ/a`\gc

d `ZxYZ//\gZ_O\g ampYZKn`Z/_UZ//ZcdqSY\^a­`cVcaD`Zµ_Uam\^fgf<d´–d `ci a`pYZÿciµ\^f0óSR3Z«]Z/Jd c™_`3/zp

`ZfÉa`\^]Z/f^ ÿfÉc.Z–_mi+nYf^Z/_6GIbq-› Q f^Z/_8+Yhq~loºamUY//am\^c;fÉ1.+cd[Zp†½ pY_ Q Z/ZSY_UZ/hd ckampYZ

amZ_Ua`_6J-kpZDnYUc Q fgZiµ_>nZ/`_U\g_aPpc=¨Z]Z/dc>campYZra``Y//am\^cSfg1._>_`/zp _\ZL†O‹z3‹W]?6w{ufgZP`f^

(8)

-kpYZLï

Ç

ðñ

a`Z/_UaOfg_UcSp_D_`\Y}/Z+nY`c Q fgZiµ_6zI³aDc‰]Z/U`Z“uUZ/a`_ Q \sa­a`clciO/zpN\gN_Uci+Zÿ_`\sam¢am\gcY_

@´_UZ/ZVZP6Q.36^

Á

ª[† 3«Q]VF=qpY\^fgZu\sam_<nc=uZ'\g_<cdËamZ/ºc Q ZaUamZFamp a`pa'cdû#û'&

ðñ

hyûGû'&

. ñ

6gÝ>cam\Y//Z

ampYa–ampYZ nc=¨Z/mr.`Z/_™UZ Yca™_`\Y}/Z”bhvuUY_amZh!6+erZ/3//Zdï

Ç

ð3ñ

\^_//fgZ/`fs C\^d Z/U\gc8a`czûGû'&

ð3ñ Yh

û#û'&

. ñ

Yh‡3//cY_UZxYZa`f^ o\sa`/PYca Q Z–UZ//ciµi+Z/YhZ/h;dckZ/i+nY\gU\2//f=¨c`TÿZ/\^a`pYZ/6

7l\g3//Zµfgf'ca`pYZ/–amZ_Ua`_OUZf/cY_`ZU]a`\^]Zµ\g _`ci+Z _`\sama`\gc_/&\^a–iµ‰ ca Q Z+_`YUnY`\^_`\g3.a`pa

ampZ `Zf^_`c6\^dZ/U\gc+\g amZ/Uiµ_ÿcd–noc=¨Z/Ka`cùûGû'&

ð3ñ

Yh\û#û@&

. ñ

=qpY\Y/zp:a`Z/Yh a`cJc‰]Z/U`Z“uUZ/a

_`f^\2.p˜a`f^ \^ _UciµZb/P_`Z/_6)-kpYZKiµ1.Y\samYhYZºcdŸampYZf.˜\^Y_–\g noc=¨Z/Oc Q az\^YZ/h Q _`\g3.»ampZÿfÉ¢a`amZ

amZ_Ua`_E\^_<`Ziÿ`T¢ Q f^ZpYc=¨Z]Z/6[I³a1\^_'f^_`c%Yca`Z=¨cUa`p˜ Oamp¢a'ampYZŸa`Z/_Ua`_1`Zk_UYnZ/`\^c<Z«]Z/µ\^da`pYZ `Z

nYnfg\gZhO\gº_U\^a`am\^cY_=qpYZ/UZqa`pYZ/\^<YYhZ/`fs V\g.–_U_`Yi+na`\gcY_F`Z.`hY\^.8a`pYZ`BDME UZu]V\gcfgamZh!6Ib

ca`pYZ/_=¨c`h_/û#û@&

ð3ñ

nZ/dc`i+_ŸUZ/fÉ¢am\^]Z/fs f=¨Z/f^f‡d cBDE¸@C~?6ªNF¨YhampYZ–_`iµZ%\^_uamUYZ%dcû#û'&

. ñ

=q\^a`pJ`Z_`nZ/a a`cCampYZLBDE @C~36sFDfsampYc.pNa`pYZ/_UZn`c5//Z/_U_`Z_µ`ZKYcaºampYZKcYZ/_+_U_`Yi+Z/h \g ampYZ

hYZ`\^]a`\gccdEa`pYZºamZ_Uam_X`Z/_UnoZ/a`\^]Zf^ 16a-kpV_/&c~]Z/`fgf#û#û'&

ðñ

Yh>û#û'&

. ñ

`Za/fgZ/`fs »a`pYZOamZ_Uam_

=q\^a`pampYZ Q Z/_Ua>nZ/dc`iµ/Z™\^cYq_`\^iOYfgam\^cY_6

] @ ++,>9¤*$</+$

• ZDpP]Zl//ci+nUZ/hSµm.Z™cd'YY\sa8Uclca>a`Z/_am_¡fgfgc=q\^.ºdc8+_Ua``/«amY`f Q `ZPT\^a`pYZ/\^ri+ZP!6

-kpYZ+amZ/_am_D`Z Q _UZ/hJc hY\Y9oZ/UZ/˜aDi+Za`pYcVhY_™d c™Z_Ua`\giµam\^.ampYZµhYZa`Z/`i+\g\g_Ua`\2/Oa`Z/`i+_™\g/fgYhY\^.

ampZµf^Z]Zf1_`pY\sdËa¤6y-kpYZ f^_`c;hY\:9Z™\^ a`pYZa=ŸP ampZ 1///cY˜a™dc–_`pYcUac”àamZ`i h Viµ\Y//_6<7lnZ/\^dº”

\2//fgfs GjÍB®½ab VnoZamZ/_am_b=qpY\2/zp amTZK/PUZ»cd%_`pYcUac”àamZ`i h Vi+\2/_µ\^ n`iµZ«amU\2/L=ŸP Yh

E'pY\gf^fg\^nY_°”“E›Z/U`c]Z/`_U\gc_J=qpY\2/zp»Y_`ZDYcYnmi+Za``\2/™huUY_Ua`iµZa`_rdc>_`pcUa°”³amZ`i)h Viµ\Y//_¡`Z

//cY_`\^hYZ/UZ/h!6#I³aqamYUY_qcaka`pawE'pY\gf^fg\^nY_°”“E›Z/U`cKab VnZ%amZ/_am_>noZUd cUi ]Z/U ;ncVc`fs ÿYhYZ/qcYk_U\gia”

Yfgam\^c6_`Z«amYn6²-kpZ #UZK]Z/ ù//c_`Z/]am\s]ZYhù//cY_`ZxVZ/˜amfs fg_`cpY‰]Z]Z/ Jfgc= noc=¨Z/ \g

_`ciµZq_`\sam¢am\gcY_/N=qpYZ`Z/_u\^µca`pYZ/#//_`Z_¨ampZ +c‰]Z/U`Z“uUZ/auhYmiÿa`\2//fgfs N6j8i+c.%ampZrca`pYZ/'a`Z/_Ua`_/

ampc_`ZJ=qp\2/zpZ/_am\^iÿa`Z>a`pYZ¡hYZ«amZ`i+\gY\^_Uam\Y/rnYUaucdampYZÍBDME Q KsD™W7µnYUc?/Z/hY`Z¡YhYZ/ua`pYZ¡Y\^a

`cVca1Yf^fp VncampZ/_`\^_¨pY‰]Z Q ºd´'ampZ Q Z/_au_UiÿfgfY_`iµnfgZknYUcnoZUa`\gZ/_1c‰]Zmf^fÌ6-kpYZ +pP]Z>`c.pYfs

//c``Z/a>_`\Y}/Z–fsampYc.pKampZ _UciµZ«am\^iµZ_kc~]Z/U`Z¯uUZ/ar_`f^\2.p˜amfs N6<R»c`Zc‰]Z/ampYZ\gknc=¨Z/q\^_Ÿd´ Q Za`a`Z/

ampYa`paqcd&ampc_`Z//ciµnZa`\^amc`__=qpY\Y/zpSf^_`cºUZ/_`nZ/«ara`pYZ–Yci+\gf_`\Y.Y\:mr/P3//Z–fgZ«]Z/fC6

(9)

jriµ_UfgZ/G{J6[R 36<WXZZ>@U1UVóNF«[jr#W›R a`Z/_Uaºd cºYY\^aO`cVcaO\^6ampYZnYUZ/_UZ//Z»cdr_Ua``/«amY`f

/zp.Z_^X`ba-c_a-dfehgikjL`2l8mOeba-iknr~Vó1U8”0~N]?6

WXYZ'R>6^'eM6&Wkja`TZnocpf0R E6d7l\gTTcYZ/\@UNUNUNF«d{uciµnY`\^_`c cdkY\^a­`cVca–amZ/_am_™d c™a`\gi+Z

_UZ/`\^Z/_g=q\sampOf^Z]ZfY_`p\^dËam_B¡\g_c//Y_U_`\gcaEFnZ/#]1]73®<tç~S/1~˜e>Yi

Q

cfgha°”[>Y\^]Z/`_U\^a‰jad}+tuZ/Ufg\g6

WkjamTZ/ncpYf±ueM6^_{J6uR#jfgfgZyR E6G7l\gTTcYZ/¸@UNU1UVF«u[rY\sa `cVca amZ/_am_ d cºam\^iµZ_UZ/`\^Z/_y=q\^a`p

_am`3/ammf Q UZPTw=qpYZ/–ampZ Q `ZPT¡noc\g˜a\g_TVc=qNB¡\g_c//Y_U_`\^cEFnZ/N7?®<tn~V/1~~e>Yi Q cfgha°”

[>Y\^]Z/`_U\^a‰ja`}/»tuZ/Ufg\^!6

E&Z/`Uc‡?E6@UN]NUVFV-kpYZw.`Z/aG//m_`p‡ampYZqc\^fYnYU\2//Zq_UpYc?/zT+h+a`pYZqYY\^aEUclca1p˜ VncampYZ_`\^_/O^`ba-c_a-o

dfehgikjL`pÛóS/l‡¤~͔>¤˜16

E&Z/`Uc‡E6#@U1UVF«-›Z_Ua`\g.Kd c¡KYY\^a¡`cVca¡\^ ÿam\gi+ZD_UZ/U\gZ/_Í=q\samp p/zp.\g3.iµZ/‡rqOa-stihcp u

avwxszyhj5c_ebyby|{#^X`ba-c_a-d|jL`\}>gLp gj~yhgjL`by«r]ló1~l”>‰˜56

E&Z/`Uc‡ÛE6ÛRè-6è36ÛÏ1c1.Z/f^_m.K@UNUN~VFo'``ami»^X`ba-c_a-dfehgikjL`p vV]8”uPVU36

E'pY\^fgfg\^nY_/JE6%{J6ètH6ÍR E6HE›Z``ch@U1]N]VF«-&Z/_am\^. dc» YY\saSUclcaS\^ a`\gi+Z _UZ/`\^Z/_»`Z.`Z/_U_`\^c‡

wXjLa-dfehgikj~ pO/NóVr~N~Vól”0~1˜?6

7\gTTcZ/‡3E6?R eM6WŸja`TZ/ncpYfg@U1UNUVF«-&Z/_am\g3.Dd cuY\^a¨`cVcam_¨\g+am\gi+Z>_`Z/U\gZ_0=q\^a`pKfgZ«]Zf_`p\^dËam_

B¡\^_^//_`_`\^czEFnZ/73®<tê~V/1~YerYi Q cf^hac”b[rY\s]Z/U_`\sa~ja‚}/»tuZ/Ufg\g6

7?/zpiµ\^haP?E63R|E6{J6ôtJ63E1p\gfgf^\gnY_H@UNU˜NFW&Ra`Z/_Ua`_udcuDYY\saŸ`cVca¨\gÿa`pYZ8n`Z/_UZ//Z–cdXhYZa`Z/Uiµ\^?”

\^_Uam\Y/8amUZ/Yh_/'€v‚a-i„ƒwXstu5u~ehgj5c<av^X`ba-c_a-d|jL`by…p cƒ}>g†p gj~yhgjL`by«óvY NóS/l”u1]S/?6

7?/zpV=¨Z/aPDy6Š•Ù6@¤UN]NUVF3-&Z/_Ua`_>dcŸYY\saq`cVcam_‡[j R»c˜amZl{ŸUfgcº\g˜]Z/_Ua`\2.˜¢am\gc‡qOa-stihcp uravwXszyhj5o

c_ebyby|{#^X`ba-c_a-d|jL`}>g†p gj~yhgjL`by«/V‡¤z/l”>ó1U?6

(10)

R»c˜amZl{ŸUfgcbþ>ZnYfg\Y/Pa`\gc_/37i+nYfgZM7l\Y}/Z͎ê†H‰ Yh»tuUZPTLE&c\g˜aŽ+†êNU

-›Z_Ua BDE¸@¡~36^F BDMEî@C~36èNF

Ds† N«ô Da† 3«%U Ds† 3«Q] Da† N«è Ds† 3«QU Da† 3«%]

Á

ªG† 3«%ó

ï Ç

ð3ñ

36ôNU1 ?6ªNó 36˜V/ 36è1U1 36sU 36QVó

ï …

ð3ñ

36ôVól ?6^~S/ 36Q~˜l 36èNól 36s~V/ 36%~l‰

ïlï á

ðñ

36ô ?6èl 36ô¤ 36è 36ô˜ 36èl¤

ïlï

…

ðñ

36ôN~ ?6èS/ 36ô˜1] 36èN~ 36ôNU 36è1]

úÍû

Ç

ðü!ý

36ô˜l ?6^P 36Q~] 36èl 36s 36%~l¤

úÍû

…

ðü!ý

36ô‰/ ?6èNU1~ 36èV/ 36èlU 36ôN]Vó 36ª1ó1]

úÍû á

írí

36ô ?6èNó 36ôVóS/ 36è 36ô1 36èNóP

úÍû

…

írí

36ô ?6èNó 36ô1˜ 36è 36ôN~ 36èPV~

û#û@&

ð3ñ

36ôN] ?6ª1~1~ 36%ó 36èS/Nó 36èl‰ 36QNUNU

ï Ç

. ñ

36ôN~ ?6^~1] 36Q~N~V/ 36è1~˜ 36s~V/ 36%~1~N]

ï …

. ñ

36ôVó1~ ?6^~l 36Q~‰ 36èNó 36s~NU 36%~l‰

û#û@&

. ñ

36ôN] ?6ªlŠ/ 36óNó 36èS/1U 36èl‰ 36QN]

Á

ªG†ÙÈ83«%ó

ï Ç

ð3ñ

36ô1ó ?6^‰S/ 36%ó 36èPó 36s‰N] 36ó1

ï …

ð3ñ

36ôVó1U ?6^ó 36%óN] 36èNó1] 36só1~ 36óN~

ïlï á

ðñ

36Q~N]V/ ?6‹/S/1ó 36QUNU 36%~1]1 360/S/1U 36%U1U

ïlï

…

ðñ

36VUVó ?6%]Nó 36QUNU 36ó 36Q]V/ 36%U1U

úÍû

Ç

ðü!ý

36ô˜P ?6èNUP 36Q~N~Vó 36è1~ 36ôNUN~ 36%~1~

úÍû

…

ðü!ý

36ô] ?6èV/ 36èS/ 36èl] 36ôV/1] 36ªP]

úÍû á

írí

36s] ?6óNó 360/1UVó 36^Š/Nó 36%ó˜ 36‹/PUNU

úÍû

…

írí

36sUNU ?6óP 36Q]˜P 36^¤U 36%óNóS/ 36%]

û#û@&

ð3ñ

36ôV/1] ?6ª1]P 36ôN] 36èS/1U 36è1]1 36è1UNU

ï Ç

. ñ

36ô] ?6^P 36NVU 36èl] 36s‰NU 36QN~Vó

ï …

. ñ

36ô ?6^óP] 36V]1 36èNóS/ 36s¤˜ 36Q

û#û@&

. ñ

36ôV/ ?6ªP] 36%óS/1] 36èS/Nó 36èNó 36èl‰

(11)

R»c˜amZl{ŸUfgcbþ>ZnYfg\Y/Pa`\gc_/37i+nYfgZM7l\Y}/Z͎ê†H‰ Yh»tuUZPTLE&c\g˜aŽ+†êNU

-›Z_Ua BDE¸@¡~36^F BDMEî@C~36èNF

Ds† N«ô Da† 3«%U Ds† 3«Q] Da† N«è Ds† 3«QU Da† 3«%]

Á

ªG† 3«Q]

ï Ç

ð3ñ

36s‰ ?6ª / 36èNU 36^ó1] 36èl] 36ª

ï …

ð3ñ

36ôN~˜ ?6èV/ / 36s‰/ 36è1~ 36ôV/P 36^z/

ïlï á

ðñ

36ô ?6è 36ô 36è 36ô 36è

ïlï

…

ðñ

36ô ?6èNó 36ô 36è 36ôVó 36è1

úÍû

Ç

ðü!ý

36ô˜P ?6èN]Nó 36s‰/ 36èNó 36ôV/1U 36^ó

úÍû

…

ðü!ý

36ôó ?6èV/V 36s~ 36èl] 36ô 36^‰l

úÍû á

írí

36ô ?6è 36ô 36è 36ô 36è

úÍû

…

írí

36ô ?6è 36ô 36è 36ô 36è

û#û@&

ð3ñ

36ôVó ?6^‰S/ 36è1] 36èN~ 36s¤VU 36ª˜

ï Ç

. ñ

36ôN~Vó ?6èNUS/ 36s‰/1] 36èP˜ 36ôNU 36^¤]Vó

ï …

. ñ

36ôVó ?6^P 36s] 36èNóP 36s~ 36^¤]1

û#û@&

. ñ

36ôV/S/ ?6^óPU 36èN] 36èS/1U 36s‰ 36ªNU

Á

ªG†ÙÈ83«Q]

ï Ç

ð3ñ

36ô1ó ?6^‰P 36%ó1]N~ 36èP˜ 36s‰V/ 36óP]N]

ï …

ð3ñ

36ôVó ?6^óP~ 36%ól‰/ 36èNó 36sól 36óV~

ïlï á

ðñ

36Q]N]N~ ?6%UNU1] N6ô 36%]1]V/ 36QUNUN] N6è

ïlï

…

ðñ

36QU˜S/ ?6%UNU1U N6ô 36%U 36QUNUNU N6è

úÍû

Ç

ðü!ý

36ô˜ ?6èl 36èl‰ 36èl 36ôN] 36ªV~

úÍû

…

ðü!ý

36ô˜ ?6èVó 36s] 36èl] 36ôVó 36^Š/Nó

úÍû á

írí

36%ó1]1 ?6%]N] 36QUV/ 36óP]N] 36Q]N]Vó 36%UNU

úÍû

…

írí

36ô˜S/ ?6%US/ 36QUN] 36èS/ 36QUVó 36%U1]

û#û@&

ð3ñ

36ôN] ?6ª1UP 36ôNU 36è1] 36è1U˜ 36‹/VU

ï Ç

. ñ

36ô ?6ª1~1] 36ôNU 36è 36è1~ 36è1]

ï …

. ñ

36ô ?6^‰ 36%ó 36èNól 36só 36ó

û#û@&

. ñ

36ôNU ?6ª / 36%óS/1U 36èS/1~ 36èNó 36èl¤

Referenzen

ÄHNLICHE DOKUMENTE

Pour l’étude des faits stylisés sur les politiques fiscales en zone CEMAC, nous développerons l’approche non paramétrique employée pour le test de convergence des niveaux de

The various simplified models derived from unobserved components model in a state-space form can be called quasifilters due to their resemblance to the corresponding proper

The asymptotic local power of least squares based …xed-T panel unit root tests allowing for a structural break in their individual e¤ects and/or incidental trends of the AR(1)

It is also shown that incorporating an intercept in the regressions allows the standard jackknife estimator to be used and it is able also to produce substantial bias reduction

ҎaXÍa·TÂÃd N6ÃPW@[YX ·TÂÍQ]N@RaX[ËNLŽ\VQVRRTÂ^XÆÅÆaX1RaXHTÂËWËWNXW@Q]ËQ]@[ÃPPQ]Ã?ËT$N..

Then, according to what was said above about parameter estimation in this context it is clear that the counterpart of the residual series ^ x t obtained in this case still satises (

The Monte Carlo analysis reveals that ignoring level shifts reduces the tests’ sizes to zero and causes an important drop in the small sample power for increasing shift

These preliminaries indicate that when structural breaks are not accounted for, the fiscal budgets in BRICS countries largely contain a unit root whilst when