! " # $ % & '()**),+
-/.
02143658791;:<72=>5@?BACD:>1;14EF5GHCJI6KFL8MN5O14365O1;PQARS:>1KF5T7U5VR
.
0WKFKF5O1X
Y[Z[\]_^a`cbede]_fhg
i
f6j
i
]kdF`cbldnm
iao fF`cbe\prq
iasltvu
`cbn`w]
setxyi f t
`wz
i
fn]_{
|~}j[`
o
fnd
slt
`}\
o
dFfFbe]_`
u;i
\{
q4b
iao
\
t4a
`cb>}\dnfn]_f
o f g
o
b6B`
slt
\
o
\]kbnfnd
set;i
fndnz
i f t
`wz
i
fn]_{}>
x
pj
i
]kdF`cbednm
iao fF`cbe\
(
14EFK>UAU<6
t ]kd
i
`cbN¡]kmkm
i
`
i b i d¢
t;i
fF`cb¤£h¥
aW¦@§v§¨ª©¬«n®>¯4°a±;²¬©³²´°a²¬©µ¶«y·Q©±;°a±¸l«
`w]_fF`w
uº¹
¼»8½2g
i
bemk`ap8¾»8jm_`w]k\
¡p¿U»OÀÁf
iat
m¬p¿Àrbe]k\Âa`cb
´Ã
`cbem
i
¤ÄÅaÅÆÄr» [\`wm_`
s
fFb
\;]
s
^a`cbede]
\
a
f t ]Çd
u º
{
sci
\ u `
au f i
]Ç\4`w
b z È4ɺÉvÊ>ËFÌrÌÍrͺÍ>ÎÏaÐѶÒ4ÉÓvÔvÉ@ÎÕÁÔ » mÇmz`w\ºfn]
\4`wb
Âab
i z
sÖ
4`]kd<¡be]_fFfF`w\×]k\Ø[;m
ÆÙ
` i ^ i ]km
iu mk`
b z ÈÁÉrÉÆÊ6ËF̺ÌaͺÍrÍ>ÎÛÚÆÊ;ÓºÜvÝÁÔÁÞ4߶ÉÑaÉ<ÎàÕÁÔ »
ì¾í îïÁîñð î¶òôórõö³÷¶î¶øúùUû¾ü~ýþÁò*ÿù2û¾ü~ýyþø î¶õ[þÁõ³õî¶òôõ³î ¤ö öôîTþ õórò
ó ó óôö"!´þÁò*órð órõ#;÷¶ö³ð ï$Öí î òôö&%(þ!(' ð órð)¶ö óºõNö³ðÁî*+,yî¶ð, -/.10 ó23 õ³î* óròôî4Öí î
î*+Ööó2ôöþÁð þ!5ºórõ6 î87nó2+7Fòlö6&%9;:óÁû þÁò(Öí î î80Bî*)<Öîñø9lí þÁò!àórõõ=!´òôþ ó>Öö¤î3ôîñòôöî
þ!UõþÁïòôî<, òlð?*-A@Fð9 òôó) ôö6)ñî~ó ÿù2û¾ü~ý/ òôþB)¶î &¤þ!Uþròôø îñòCD þ2!;Öî¶ð òlþE;ö³ø î*¤ó
òôî¶óôþrð ó õ³î2ø î*)¶òlö6ôöþÁð þ!Fôí îø ó2Öó-G@FðÖí îH!´þÁõõ³þEIö³ð ï?Iîòôî*+Öòlö6) ~þ ò&lî¶õJÁî*KôþLÖí óM
)ó2ôî-
N îO)¶órõõQPRMSUTóV+Öòôþrð ï¾ÿù2û¾ü~ýW+EX òôþB)¶î*WöJ!
RMSZY [?S\GS
[^]
S Y _`9a(RM]
Scbd
`fe([^]
Scbd
+
Iöôí öð ø î*Bî¶ð ø îñðWö³ø î¶ðôö6)óºõõ#yø öôòôö6Öîñø*ö³ð ð þºó2Öö³þÁð?K\GSQí óg;öð ïhyîórðji×órð øjºóròlöJ7
órð?)ñîk-Qù$&Bî*)¶öórõ)¶óôî>ölÖí î6ö³ðôî¶ïÁòôó2ÖîñøNÿùUû¾ü~ýmyþø îñõrþ!;þÁòlø î¶ò=DJE8þÁò^@eÿù2û¾ü~ýn+JE
yþø îñõIí î¶òlînaj`$e4YoNórð øl?!´òôî* îñðÖõ#?_fYpi×öó&?¤îñø^ öU-î-
[^]S YqanRM]Scbd `rD5sfat[^]Scbd u
ì¾í övyþø î¶õ^!´þÁò3Kôí î( óôöw!´þÁòkôí îLx-zyQ-|{ þròôï4órð ûö6&%}{ î<Öòlö6)*5:óÁûórð órõ#Bôö5?ôö³ð ï
î<0}BþÁð îñðôö órõyþö³ð ïógÁî¶òôórïÁî 5~ òÖóºð?%rî2rýnóròôø õ³î[óºð ø/ýWó2!´ð îñò*2iiÁü[í ó2ÖîñòE<-Qì¾í î
ïÁîñð î¶òôórõOÿù2û~ü~ýL+EG òlþ})ñî*&[í ó' ð öôîwºóròlöórð?)ñîv[
]
Y_X ?+Gs>a3sVe1>ö!^aL`Ce$r
órð ø öJ ö6+Öòôö) ôõ#cóMÖöþrð órò# ö!v.KPÆõþrïa\
]S
`qe18Ti-fîñîj~ òÖórð?%ºîýLóròlø õîóºð ø
ýUóM!´ð î¶òUiiü[í óôî¶òvEt!´þÁòGÖí î ôîórð ø3! ò+Öí îñòX òlþTîñòôöî*þ! ÿùUû¾ü~ýq òlþ})ñî*ôî* -
@Fð4& öJÖî þ!ö&HBþ? õóròôöJ#lôí îyÿùUû¾ü~ýyþø îñõ<í óþrð î ø òÖógI5 ó2)%@&O+#B3yî ôòôö6)
ø î Tîñð ø î¶ð)¶îþÁð óQòlî , òôð?¿ø þ;î* ð þ2Qórõõ³þEI4!´þÁò8öð?)ñõ6 ø ö³ð ïXôí î6õî rî¶òôórïÁî>î Tî*)<QöðÖþkÖí î
yþø îñõU ö-î2-5ôí î(!´òlî* îñðôõ#Vóºø îêþ?ôîñòºó2Öö³þÁðVôí ó2WõóròlïÁîNð î¶ï4óMÖörîêòlî & òôð?Uþ!Gôþ})%
òlö6)¶î í ógÁîNó ïÁòôî¶ó2Öîñò¾ö6 ó) ~þÁðÁþÁõó2Öö³õö#hôí órðõóròlïÁîHBþôöJÖöJÁî2òlî , òôð? -ì¾í îñòôî<!´þÁòôî2
ºóròôö³þ?3 óròÖó2¤î<Öòôö)Vyþ;ø ö')¶ó2Öö³þÁð?yõö%rîVôí îî80BþÁð îñðÖö óºõÿù2û¾ü~ý.ÿùUû¾ü~ýH¤þrò
Öí îhôí òôî ôí þrõøJÿù2û~ü~ý´ìÿùUû¾ü~ýHyþø îñõ í ógÁîTîñî¶ð òôþBþlî¶øôþ ó2)*)¶þ ðO!´þrò
Bþ&lö6 õ³î/ó+#B3yî ôòôö6)Nø î Tîñð ø î¶ð)¶î þ!trþÁõóMÖöõ³ö#þÁðòôî<, òlð?*-ì¾í îìÿù2û~ü~ýoyþø îñõU
!´þÁòWî<0 ó õî2OöðÖòlþø?)¶î órðórø ø öÖö³þÁð órõFôî¶ò& öðÖþ3Öí înrþÁõóMÖöõ³ö#î B ó2Öö³þÁð órõ³õþIöð ï
!´þÁòórð*öð)¶òôî¶óôîñø î<8î ) þ!ð î¶ïÁó2ÖöJÁîREScbdþÁð"[
]S
RESFYq[?S\tSB [
]S
Y_`9aOR
]Scbd
`9a b R
]ScbdG
;REScbd5AiF`fe([
]Scbd
u
ìQþø î rî¶õþ×órðî<0} õ³þÁòÖóMÖþÁò+#OôþþrõBIí ö)cí×órõõ³þI5QÖþ, ø#(ôí î~ð þrð õö³ð îóròø î*Bî¶ð ø î¶ð?)ñî¾þ!
& óºòôî¶øOÁþÁõó2Öö³õöJ#[
]S
þÁðO ó+òlî & òôð?órð øÁþrõ ó2ôöõöJÖö³î*|IîöðÖòlþø?)¶î6óð þÁð? óºòÖóyî ôòôö6)
ÿù2û¾ü~ýn+JEXyþø îñõ
RESZY [?S\GS
[ ]
S Y lREScbd ,[ ] Scbd
U
¡*©+£,¤³´¨2£&¦¢¶µ¦¢X£, ¡µ·?¥?¬<£,¤6¦¥´¸¨©&¡ ±j¦¥j¨n²¨¢+£,¤¬*·?¹6¨¢=µ¦¢&³W¦µº¹6¦B¬g¨¹©&³¦B¦£, ?¤¥?»?®t¼}·?¬
¨¥"¡*©+£,¤6³3¨2£&¡³´¨g½¡·?©&¡ ±V£,¦±?¡ ¬*¤6±¡(¤Jµ1¨h²¨¢+£,¤¬*·?¹6¨¢K²¨¢&¨³¡ £,¢¤6¬¥?¦¥?¹6¤¥?¡g¨¢w¾¿HÀKÁKÂ
³¦}±?¡ ¹^¹6¤Ã¡H£& ?¡Äw¾¿ÀkÁK°¤6©5¨²?²¢&¦²?¢¤c¨2£&¡®
¯¡¢&¡*³3¨¢Ã£& ¨2£K£& ?¡H§¦¹6¨2£,¤¹6¤J£½Lµ·?¥?¬<£,¤6¦¥¸3¬*¨¥?¥?¦2£5|¡H¡ ©£&¤6³3¨2£,¡ ±½´¬*¦³³¦¥Ã¡ ¢&¥?¡ ¹
¦¢3¹6¦B¬g¨¹w²|¦¹½B¥?¦³¤c¨¹k©³3¦B¦£& ?¡*¢©¨©´£& ?¡>§¦¹c¨2£&¤6¹6¤J£,¤¡*©Å?«(¨¢&¡>¥?¦£¦©&¡*¢+§¡ ±q±?¤¢&¡ ¬ £,¹J½®
Æ(Ç
·? ?¹³´¨2¥?¥h¨¥?±´ÈV¬gÉw¡*¤¹1ÊDËÌÌÌÍ1 ¨g§¡w¬*¦¥?©¤6±?¡ ¢&¡ ±¨¥¤£&¡*¢,¨M£,¤§¡5¨¹6»¦¢&¤J£, ?³"®ÏÎ1¤6¢©£gУ& ?¡ ½
Ñ
£n¨V¬ ¦³3³¦¥4²¨¢&¨³¡ £,¢¤6¬3¾¿HÀkÁKÂnÊ+ËÐJËEͳ3¦B±?¡*¹t£&¦V£& ?¡3±?¨2£¨jµ¢&¦³5 ?¤¬ £& ?¡ ½Ò»¡<£
©,¨2³3²?¹¡´§¦¹c¨2£&¤6¹6¤J£,¤¡*©OÓÅ?«v£&¦Ò¢¡*²?¹6¨¬*¡£& ?¡·?¥?¦©&¡*¢+§2¨?¹6¡£&¢&·?¡§¦¹c¨2£&¤6¹6¤J£,¤¡*©*®4Äk ?¡ ¥^У& ?¡ ½
·?©¡¨n¬*¦³³¦¥?¤J§¨2¢&¤c¨M£,¡wá*¢¥?¡*¹l¡*©£&¤6³3¨2£,¡w£,¦¡ ©£,¤³´¨M£,¡v¸hµ¢¦³ÕÔM«Q¨¥±Ó Å^Ö
«
®¶×v©¤6¥?»(£, ?¤©
²?¢¡*¹6¤³3¤¥¨¢+½¡*©+£,¤6³3¨2£&¡wµ¦¢=¸£, ?¡<½´¦£¨¤¥¥?¡<q©&¨³²?¹6¡5§¦¹6¨2£,¤¹6¤J£,¤6¡ ©t5 ?¤6¬ j¨2¢&¡·©&¡*±µ¦¢
¨µ·?¢£& ?¡*¢vá*¢¥?¡*¹Ï¡*©+£,¤³´¨2£&¡¦µ1¸®XÄk ¤6©w²?¢&¦B¬*¡ ±?·?¢&¡(¤6©5¤£&¡*¢&¨2£,¡ ±>©&¡<§¡ ¢,¨¹º£,¤³3¡ ©w·¥£&¤6¹F£, ¡
¡*©+£,¤³´¨2£&¡©£,¨?¤6¹¤6Ø ¡*©*®
¿¹J£,¡ ¢&¥¨2£&¤§¡*¹½ÐQ¦¥?¡3¬ ¦·?¹±Ò£&¢½£,¦
Ñ
£n¨V¥?¦¥²¨¢,¨2³3¡<£,¢&¤¬¿HÀkÁKÂW³3¦B±?¡ ¹G¦µk ?¤» ¦¢&±?¡ ¢
£,¦L£& ?¡±¨2£,¨n£,¦»¡<£5©&¦³¡
Ñ
¢©£w¨²²?¢&¦gÙ}¤6³3¨2£,¤¦¥?©ÓÅ^Ö
«
£,¦Å^Ö« ¨¥?±£& ?¡*¥"·?©¡¨L¹6¦B¬g¨¹|¹6¤6¥¡g¨¢
¡*©+£,¤³´¨2£&¡¨©¡*±"¦¥"£& ?¡O¨²?²?¢¦gÙ¤³´¨M£,¡H¢¡*¹c¨M£,¤6¦¥
ÓÅ Ö
«Ú
¸^Ê;ÔE«cÛÜ<Ý&Ó Å
Ö
«cÛÜ Í8Þ
Âv¦¡ §¡*¢*ÐQ¨¬*¦³3²?¹¡ £&¡L¥?¦¥?²?¨¢,¨³¡ £&¢&¤¬L¨²?²¢&¦¨¬ 4¤©H¥?¦£Hµ¡*¨©&¤?¹6¡n¨© ?¤» }ߦ¢&±?¡ ¢¥?¦¥Bß
²¨¢&¨³¡ £,¢¤6¬C¿ÀkÁK³¦}±?¡ ¹6©?¨©&¡ ±q¦¥àÅ^Ö
«Aá
¸lÊÔE«cÛÜ8ÝgÞgÞgÞ Ý&ÔE«cÛMâEÍ´¬g¨¥¥?¦£"|¡¢¡*¹¤c¨?¹J½
¡*©+£,¤³´¨2£&¡*±Ò½¹¦}¬*¨¹t©³3¦B¦£, ¡*¢&©O±?·?¡h£,¦"£, ?¡©&²?¨¢&©¡*¥?¡ ©&©L¦µX£, ?¡±¨2£,¨"¤¥ ?¤» Ò±?¤6³¡*¥}ß
©&¤¦¥?© ®AÄk ?¡ ¢&¡ µ¦¢&¡Ðk¦¥?¡X¦·¹6±A ?¨§¡V£&¦¡ ³3²?¹¦½$¢&¡ ©£,¢¤6¬<£,¤6¦¥?©h¹6¤6Ã2¡j¨±?±?¤J£,¤J§}¤J£½£&¦£, ¡
¿HÀKÁKÂq³¦}±?¡ ¹UФ®z¡2®tÅ Ö
«á
¸Ü*ÊÔE«cÛÜÍãmÞgÞgÞ&ã>¸*âBÊ;ÔE«cÛMâMÍ<ݦ¢=¡ §¡ ¥·?©&¡¨(²¨2¢,¨³¡ £&¢&¤6¬5¿ÀkÁKÂ
³¦}±?¡ ¹?Å Ö
« áä
ãVå1Ü+Ô Ö
«cÛÜ
ãÞgÞgÞã>åâFÔ Ö
«cÛMâ
ÞÄk ?¡v¨¹£&¡*¢¥¨2£,¤J§¡K¡¬ ¦¥?©&¤±?¡*¢¶ ?¡ ¢&¡w¤6©¶¨±?¤6¢¡*¬<£
¨²?²¢&¦¨¬ £&¦O¡ ©£&¤6³3¨2£,¤¥?»v¸(¨©¡*±¦¥h±?¡*¬ ¦¥§¦¹·£,¤¦¥há*¢¥?¡*¹¡ ©£&¤6³3¨2£,¡ ©t5 ?¤6¬ h±?¦B¡*©G¥?¦2£
¢&¡ æ·?¤6¢¡O²¢&¤6¦¢K¡*©+£,¤6³3¨2£&¡*©KÓÅ^Ö
« Þ
ç è°éHêKë´ìOíwë´î+ïOðÏñë3ì òéOì(ótñðôöõLìnò ÷éwø÷évóÏótñUë´ì évóFðQñùúõHð^éó
û
¡*¬ ¦¥§¦¹·£,¤¦¥Ã2¡*¢&¥¡*¹^¡ ©£,¤³´¨M£,¡*© ¨g§¡¡*¡ ¥±?¡*©¬*¢&¤|¡ ±"¨¥?±¡8Ù}£&¡*¥?©¤§¡*¹½´±?¤6©¬*·?©©&¡ ±V¤¥
£, ¡¬*¦¥£,¡8ÙB£v¦2µº¡*©£&¤6³3¨2£,¤¥?»¨L²?¢¦¨¤6¹6¤J£½h±?¡*¥©&¤£½´µ¢&¦³W¤6¥?±¡*²¡*¥?±?¡ ¥£w¨¥?±j¤6±?¡ ¥£,¤6¬*¨¹6¹J½
±?¤©£,¢¤6?·}£,¡*±±¨2£,¨mÊUÁK¨2¢&¢&¦¹6¹¶¨¥?±Â¨¹¹UÐtËgÌüüýQ¼B£&¡ µ¨¥?©Ã½¨2¥?±fÁK¨¢¢&¦¹¹UÐtËÌÌþÍ<®´ÄQ¦C¡8Ùß
²?¹6¨¤6¥£& ?¡(?¨©&¤¬O¤±?¡g¨¡* ?¤¥?±j£, ?¤©5£½B²¡(¦2µ1¡ ©£,¤³´¨M£,¡*©k¡(¬ ¦¥?©¤6±?¡ ¢w£& ?¡±?¡*¬ ¦¥§¦¹·£,¤¦¥
²?¢¦?¹6¡ ³
Ñ
¢©£g®tÿº¡<£Ü ÝgÞgÞ*Þ^Ým¡5¤6¥?±¡*²¡*¥?±?¡ ¥£K¨¥±´¤6±¡*¥£,¤¬g¨¹¹½(±?¤6©+£,¢&¤?·£&¡*±h¢&¡*¨¹¢,¨¥}ß
±?¦³°§2¨¢¤c¨?¹¡*©º5¤£& L±?¡*¥©&¤£½gÊ |ÍF5 ?¤6¬ L¡XX¨¥£t£,¦H¡ ©£&¤6³3¨2£,¡2®Ï¯¡X±?¦¥?¦£gÐ2 ?¦X¡<§¡ ¢*Ð
¦?©¡*¢+§¡£, ?¡n±?¤¢&¡ ¬ £,¹J½>·£¦¥?¹J½V5¤J£, 4¨±?±¤£,¤J§¡(¡*¢&¢¦¢&©Ü*ÝgÞgÞgÞlÝ5®nÿF¡<£·?©¨©©&·?³¡
£, ?¨2£¶£, ?¡5¨2©¶¡*¹¹¨¢&¡k¤¥?±?¡*²¡*¥±?¡*¥£X¨¥?±¤6±?¡ ¥£&¤6¬*¨¹6¹J½n±?¤©£&¢&¤6·£,¡ ±5¤J£, h±?¡*¥©&¤£½Ê |Í
¨¥?±"¤6¥±?¡*²¡*¥?±¡*¥£w¦µ1£& ?¡MÞÂv¡ ¥?¬*¡2У& ?¡O¨g§¨2¤6¹c¨2?¹6¡v±¨2£¨¨¢¡
á
¶ãÝ á
ËÝgÞgÞgÞ^ÝVÞ
(G$4<47=8"8(2H$(IJKL#M)+4ONP,D,9QRS2"T*",4<)'(U0V.(2"8!4<"6<F$()+,4XWY;Y)+4AZ<74<([(2"
\
,PF&+7]()+,^.#I_SD)/(2YIJa`
IbPKL#MdceI_KL#MfAIJKL#Mhg
ij"
\
$,T(2"k6"l.6"(6<0Y("45()+=m$("dIbnKL#Md!P0T$
\
=8=m,8N"k6,"k&9"45()'=T$("$,*o"qp](6$
\ (
$,Y"45()'=T$("A.69I_KL#Mr7(d.#)'(QsS2)'4dNn)',*Y.#*"
\
,-F&'7()',mt#"k6$()+,1)'4ut6"l."6$!&'0
tv"6<.6=8"*w)',x(2"X.6"yP7"k,
\
0x*=m$)+,hB#)CQz"QE$.("6$tt&'0n)+,{o$o|H76<)+"k6(6$,45.6=^Q%}34
(2"84<7!4<"yP7",-(~)+,-F"k64"m|H76<)+"63(6$,4<.6<=)',
\
&'7*"4O$&+6"$*0w$4<=mn(2)+,{Rt$6<(D"
\
$,4<($6<([D)'(2(2"m"=8t)+6<)
\
$&r*)'4<(6<)+!7]()+,j.AWTggg9W8 )+,4<("$*.S$G4=8n(2"k*
F"k64<)+,. )'(QrU,*"k($)+&CBnD"
\
$&
\
7&$("3(2"O|76)'"6(6$,4<.6<=6
\
2$6$
\
("k6)+45()
\
.7,
\q
()',. (2"O"=8t)'6)
\
$&v&$D.rWmkggg9W8 BH)CQz"Qr(2"O4$=mt&+"
\
2H$6$
\
("6<)+4<()
\
.7,
\
()',
bPK@Muc
;hz9
g
"k(
JK@MucK
z
J
Mdc
¡a¢
IJ-K£#M¤n£
*"k,("o(2"VKNn,¥D,HM
\
2$6$
\
("k6)+45()
\
.7,
\
()+,.(2"R?;gs|H76<(2"6<=m6<"Bu&'"k(Y¦ !v"R$
\
=m=8,N"6<,"&§.7,
\
()+,hBr)¨Q©"QG$x,,,"{-$a()'F"
\
,-()+,P774~.7,
\
()',jD2)
\
2ª)+4[4<0n=
=8"k(6<)
\
$67,*x«Y$,*^)+,-("{6$("k47t^(
`§¬m¦eK£#M¤P£Tc
H$,*G&'"k(
#®
K@Muc
¡a¢
¦eK£#M¤P£
!v"A)'(4r|H76<)+"6¯(6$,45.6=^QsS2"k,9B(2"°P±²³´Hµa³¶¸·]¹º³´1»±¼l´v±¶°P±´½lº¹C¾X±l½l¹º¿YÀ¹Á±s.-I_¥KL#M
)+4S*"kÂH,"k*w$4
IHÃnKL#Mdc
ÄaÅ
z
b
#® K@ÆM
bnK@M
JK@M
¤Çg
S2",H$=m"E. (2)+4@"4<()+=m$("%)+4A"qpt&$)',"*R!-0T(2"E.$
\
(A(2H$a(S)'(S=m$0T!v"ED6)/((",R"yP7)/F
$&'",-(&/0R$4$1N"k6,"k& *",4<)'(U0"45()'=T$("
IHÃnKL#Mdc
xÆ
;
¦
ÃÈ
LTɪW8;
Æ Ê
D)'(2*"
\
,-F&'7()',GN"6<,"&
¦ Ã
K£#Muc
ÄaÅ
¡a¢
#® K@M
JK@ËÆM
¤
*"kt#"k,*)+,{x"lp]t&')
\
)'(&/0w,V(2"m4<=mn(2)+,{tH$6$=8"k("k6XÆQoÌA$4"k*,Í(2)'4ON"6<,"&"45()
=m$("O.6t6!$!)+&')'(U0T*",4<)'()+"4kBh|$,x$,*GÎ6<7,{VK
ÏÏÐ M \
,4<)+*"k6"*G(2"~$,H$&'{74
*"
\
,-F&+7()+,^N"k6,"k& 6<"{6<"4<4)+,G"k4<()'=T$a("E*"lÂH,"k*w$4
Ñ
ÃnKL#M§c
wÆ
;
¦ Ã È
LTɪWY;
Æ ÊÓÒ
;Ë
IHÃnKL#Mlg
êÍëì#í
Ö'áGÙá^ãkÛÛ<àÛ×îÝUÖ+ánÝÁïÙÛÖ+Ùðñ'ã×@Û<ãçÛ<ã×<×Ö+àáGä8à]Úãñ
òóô
êÍëõ
ó
íöø÷
óù úYóô
õ ó öeû
óù ü8ôÓýùþþþ9ùÿGù
ÕãkÛã
÷ ùþþþ9ù
÷
ÙÛ<ã Ö+áÚãkâ#ãkáÚãkáPß^Ö'Úãá-ßÖ'åÙñ'ñ'ÜÚÖ'×<ßÛ<Ö+ðé]ßãÚkãÛàaÝUä8ãÙáèÛÙáÚàä
ïÙÛÖ+Ùðñ'ã×uÖ+áÚãâvãáÚãá-ß@àæ#ßÕãú8óù
õ
óaù
û ó ÕÖ+åÕTÙÛãSåÕà×ãáoÙקÙð#àïã
ÔSÕãúYóùòóÙÛ<ã
àð×<ãÛ5ïãÚ
ÙáÚßÕãOâÛàðHÙðÖ'ñ+Ö'ßUÜmÚãká×Ö/ßUÜRàæsßÕã
û
óÕHÙ×ßàYð#ã Páà á
! #"%$& " ')(*+,-(
.0/,13254 âÛ<à]åkã××<ã×uÙÛãdåñ'à×ãkñ'ÜÛ<ãñÙaßãÚßà /61678/ âÛ<à]åkã××<ã×
:9
æ ã×+;PéHÙÛã@Ù .0/,15254
ë ý ý í
âÛànåã×<×<>=@?!AXçÖ/ïãá^ð-Ü
ë ý í
ßÕãá ã[çãkß3Ùá /,178/
ë ý ý í
âÛànåãk××
=CB? ôD
öëFEöHGsí
=CB?JI
LK GNM
?JI
¯öOM
?Uù
ÕãkÛã
M
?3ôQP
B?
ëSR B?
K ý í
Ö'× ÕÖ/ßãTáàÖ+×<ã
Ö ã
Ùx×ãT;PéãáåkãàæâHÙÖ'Û Ö+×<ãTéáåàÛ<Ûãñ+ÙßãkÚ
ÛÙáÚàäïÙÛ<ÖÙðñ+ã×
Ö/ßÕämãÙá8U
ÔSÕãÛ<ãkæàÛ<ã
ãX×5ßéÚÜRÙ×ÙáGÖ'á-ßãÛ<ämãkÚÖÙaßãE×5ßãâ^ßàÝ
ÙÛÚ×
./613254
âÛànåãk××ãk×ßÕã3áàáâHÙÛÙä8ãkßÛ<Ö+åã×5ßÖ'äTÙßÖ+àáæàÛ
/6167V/
ä8à]Úãñ+× ÕÖ+åÕ
Ö+×1ä8àÛ<ãRåñ+à×ãñ/ÜÛ<ãñÙaßãÚªßàVßÕããÛ<ÛàÛ<×5ÝUÖ'á]ÝÁïÙÛ<ÖÙðñ+ã×XÛãkçÛãk××Ö'àáàæ,WÙáÙáÚ Ô Ûéàáç
ë
ýYXZXZ[
í / ñ+Ö+áãÙÛ /6167V/
ë ý ý í
ä8à]Úãñ Ö/ßÕ^áàá]ݨïÙáÖ+×<ÕÖ+áç1ämãÙá\DÖ'×SçÖ'ïãáð-Ü
úN?^]
ôD
öO_
úN?
öO`,a
?
öOa
?^]
Ö'ßÕ8kãÛ<àÝUä8ãÙá ÕÖ/ßãOáàÖ'×ã
a ?
Þjã[åàá×<Ö+ÚãkÛßÕãOáàáâÙÛÙä8ãkßÛÖ'åçãáãkÛÙñ'ÖbÙßÖ'àáRàæ
ßÕÖ+×Sä8à]Úãkñ
úN?^]
ôdc
ë
úN?Uù
a ? íöea
?^]
ë [ í
æàÛ§×àä8ãéáf Páà áoæéáålßÖ+àágc
ëì ùih
í
ÕÖ'åÕoÖ+קä8àáàßàáãÖ+ámßÕã×ãåkàáÚÙÛ<çéä8ãá-ßjh
/ ×<×éä8ã ãÕHÙïã3Ù×Ùä8âñ+ãSú
ùþþþ9ùú
]
àð×<ãÛ5ïãÚmæÛàä
ë [ í
:9
æ*cRÚànã×dáàߧÚãkâ#ãkáÚ
àáßÕãS×ãkåàáÚmÙÛ<çéä8ãá-ß
ë [ í
Û<ãÚéåkã×dßàOÙEáàáâHÙÛÙämãlßÛ<Ö+åAÙéßàÛ<ãçÛ<ã×<×Ö+àá8àæ#àÛÚãkÛAý
úN?^]
ôkc
ë
úN?
íöOa
?^]
ÙáÚwßÕã1Ùé]ßàÛ<ãçÛ<ã××<Ö+àáwæéáåkßÖ+àác
ëì#í
ämÙÜxðvãã×5ßÖ'äTÙßãÚwð-Üxåàä8ämàál ãkÛáãkñuã×5ßÖ/Ý
ämÙßãk×3àÛñ+ànåÙñ9â#àñ'Ünáàä8ÖÙñ'×
ÔSÕãÛ<ããnm]Ö'×<ß×ãnmnßãá×<Ö'ïã~ñ+Ö'ßãÛÙßéÛ<ã[Ùð#àéß3ßÕHÙßßUÜnâ#ãXàæ
ã×5ßÖ'äTÙßÖ+àá^âÛ<àðñ+ãkä
ÙáÚ ã1Û<ãkæãÛßàTßÕãÛ<ãkïnÖ+ã âÙâ#ãkÛ%àæ 4poÙÛÚñ+ã
rq
o
éßi ãâvàÕñrÙáÚ
2 Õãká
ë
ý>XZXts
í
:9
áRßÕãOçãkáãÛÙñ9åÙ×ãOàæ
ë [ í
ã[Ùç-ÙÖ+áoÕHÙïã[ßÕãâÛàðñ+ãkäàæ ã×5ßÖ'äTÙßÖ+áç
Ù8æéáåkßÖ+àáGàæ
ë
âHÙÛ<ßÖÙñ'ñ'Ü
í
áàánÝUàð×<ãÛ5ïÙðñ+ãOïÙÛÖ+Ùðñ+ãk×
/
×0cVÚãâvãáÚ×EÙñ'×àTàáGßÕã~àð]Ý
×ãkÛ<ïÙðñ'ã[ßÖ+ä8ãO×ãÛ<Ö+ãk×%úN?
ßÕã[ðHÙ×<Ö+å[Ö+ÚãÙ8àæråàá×5ßÛ<éåkßÖ+áçTÙmáàáâHÙÛÙämãlßÛÖ'åOã×<ßÖ+ämÙßã
àæuc
ëì ùih
í
Ö+×ußàXåàä~ðÖ+áãÙ[åàä8ämàá) ãÛáãñh×<ämànàßÕÖ+áçOÖ'á8ßÕãwvÛ×<ßïÙÛÖ+Ùðñ+ã
ì
Ö/ßÕmÙ
Úãkåàá-ïàñ+éßÖ+àáV ãkÛáãkñÎ×<ämànàßÕÖ+áçYÖ+áRßÕãX×<ãåkàáÚxïÙÛ<ÖÙðñ'ã,h¯þHÔÎà8ÚãnvHáãXßÕã[ã×<ßÖ+ämÙßã
ãXÕHÙïã[ßà8Ö'á-ßÛànÚéåkã×àä8ãOáàßÙßÖ'àáÙáÚGÙ××<éä8âßÖ'àá×
f}+i+bfib f¡T~bZ¢£F¤¥§¦d¨ª©
«¬
£Fr¥ ®\{f~¯Z ~bzTLii{f}+ Z+±°²£´³µ¥,¶¦·
Z{r³¸{f
¹
°²T£´³µ¥
¹º»µ¼f¹
³ ¹½¿¾ znÀu£ÂÁ
¹³ ¹½ZÃCÄ
¥ Z
¹³ ¹
ÁrÅ Æ
Z,}+ZzN¡Zf}ÇÈ{t~}
»@É~ÊËÉ~ÄÍÌ
·
É|ÊÏÎ>Ð-Ñ
zNfZfbfz{6Ò6Ó6Ô8ÒÕ ~Ö¡z}+})£S×t¥f{},iزz
}+i{iZ{Ç{f|}+~~ZfÙ8)ÚÀ fÙ^i|znÀ²ZfzT~J{VfzT¡Y{YÖbfÙØ^ÀbfÙ¡ÖzTÛ¡zti}TÜ
Ý*zT§u£´Þr¥3 zf~z0ifzfzTf}~^gª~fz}+i{iZ{Ç){~Ùb{rfz }~\:ßN
Ð
Ñ
fzà}~~fb Ùz+fzálâVÞfã!fb+z¡T~bZVb}{¡Z)8z~ zä ff¡T~bZV~8¡TZã
{¡n}~f rZÇVåæÁàç ÉÈè
çTé3}i{~b}Ç´fÙ|·Hêëá â £Fr¥êëá â £F·t¥ Z{bjuÜ
Ñ
fzØz~ zá
f¡Èb}wf}~zTbVifzfzT¡ZtZb ~bZf{+{}6{¯Zf+bz3~i{f}Ç Z~ì°²í,£J³µ¥3f¡Èl}
}+Ö)zni+b¡{~ff· îf{}à¡TZ{¡Tà}~ fr+åÚÁç É¿è
çéj{ }i{Cib}Çïz}}~)z}~Öiã
fzT}~}0¡ff~bZ }N£SðwZbñTrzT~ÙZzTîóò·Z· ç>¥nÜ6yzN{YZzN¡Èf}~zô{\z~ zª^il~fz Zb>bfÙ
¯Zf+bzjii{f}+ Z+8õ
°²í,£Fr¥¦ çÁöÏ÷ Z
¹ ¹
ê·
Ðùø
°²í,£Fr¥¦ · ÐûúZø
Á£
¹ ¹
ÁÍ·
Ðûø
¥ªÁ£
¹ ¹
ÁÍ·
Ðûø
¥ ÷
Á6òZò·V£
¹ ¹
ÁÍ·
Ðûø
¥Âü
è
çç>×ZýØ£
¹ ¹
ÁH·
Ðûø
¥Çþ
Áç>ÿZýV£
¹ ¹
ÁÍ·
Ðûø
¥
è
çZç
ø
òØ£
¹ ¹
ÁH·
Ðûø
¥ Z · Ðûø
ê ¹ ¹ êç
Ð
¯Z¡TZtZzTfbzTf¡zî6µz| }~zi z}~iffÙözT~fzT0á â iͲzf+Z²Z+~bZ{~öi{C
ff¡niZ-õjá â £Fr¥ °²í,£Fr¥¿Ü
Ñ
fzàzT~fzTªá â b}fz ¡z{ L{ z¡Èff>8z+fzä~
f^ïzg²Zf {~z}TÜ
Ý*zT¦
Ã
þ\²zØifzV{fb ~e Z}~iffÙbHÞfãf~z¡niZ-î5{f¸zTd¦
Ã
ZÙÏ£
¥przg~fzØ}~~fb Ù|{i{)zniz Nfz¡TZtZZ iZHbHfãf~z¡niZöfz+z
ÌuÃ
ò{f
Ì
·{~z}~)z0¡TZf}+i{ti}TÜ
Ñ
fzT-î
¿£´Þr¥Ë¦
ç
£
%è
ç>¥
"!
á â$#
ÞÁößN
%
b}j{à¡TZ)ZÓZ}~zTfJ{+&('{~ñTz\ zf}+z}Çib){~zw ZL~fz6}ÇÈ{~bZ{+NfzTf}~^àä£ Þr¥
Ð
Ý*zT*)f£ ó¥3fzTfizàifzà}+È{Cib{+Ø zf}+8Lifzài{ fZQ{~b{fbz,+:£ ßN
É
S¥
É
{flbzT
) £F
¹
Þr¥j²z0~}5¡ff~bZf{r zf}+gÙZ^ZzTVßN-¦Þ
Ð
ÒVzT}+~b){iz,~fz0J{+izTµb}3ÙZzT
t
)-/.
0£F
¹
Þr¥§¦
ç
1
"!
á 0 #
)ÁÍßN
% á â #
Þ\ÁÍßN
% Ã ¿£ Þr¥
£32t¥
fzT~zifzfzT¡ZtZb ~bZØzT~fzTªá
0
b}
á 0
£ r¥L¦
ç
ò
54
¬
«¬
«7698;:
°²í,£´³µ¥
°²T£´³
Ã
Ï¥
®Z³
Ð
PTbfeg?Bhji^klCmH1JXU=1]P=1SonqpKTXU`JrPTbgPsWJYF`QtKtV^XoP=1JN?3u$v>i^u$v"wyxzC{bBP`rDr\1XUOz\}|hq~u$vz|(iyX/ FT
u$vhjlGndXo=7VYF]`YKtV^XoP=1DGFN]FaV_VY\1FOP=1MWXoV^XoP=KTSM1XUJV^`YXos1HWVYXUP=bBH1=1OaV^XoP= PTbfeg?3u$vizvBC
]X"QF=u$vch
?3c|hlCf?/eg?hjizvCmj|u$vhlC}
(@
?3kf|hlCW ¡k
KT=1MXoVYJ¢FJV^XUZKtVYFL£
¥¤
¦§
?3c|hlCf
¡¨©
£ ¤ ¦§
?3kf|hlC ¡klª
¨©
¡¨©
£ ¤ ¦§
?3kf|hlCW 7k
bBP`mJPZ[FL«(¬®°¯
x±²
bBPT`¢¯´³ µ1¶IHWFIV^P·V^F-Oz\1=1XoO¸KTS`F¸KTJP=1J¢DGF\1K¹QTFLV^P$OH(VrPTºV^\WF
M1F-=1JYX"V>n»FJVYXUZKtV^FrXo=`F]XoP=1JfDr\1F`F*X"VEXUJEJVYXUSUSWH1=1`YF-SUXUKTs1SUFmbBPT`]TXoQF-=q¯¼g½¢\1F*p1KT`VYXUOHWS¾KT`
Oz\1PXoOF$PTbGM1F-=1PZ[XU=KtVYP`*]THKT`^Kt=7VYFF-J¥VY\KtV
£
¥¤
¦§
?3«¡¬L|hlCIÀ¿$XU=ÁpW`^KTOaV^XUO-FTjJYXo=1OF
?3c|hlC
XUJrK$O-H1Z·H1SUKtV^X"QFLM1XoJV^`XUs1H(V^XUPT=qbBH1=1O-VYXUP=
½ÂPFJVYXUZKtV^F¥V^\WF·H1=1O-P=1M1X"V^XUPT=KTSÂM1F=1JXoV>n
?BklCPTbGeg?Bu$v>izvC¢Ãu$v"wyxG~v"wyxiÄDGF$H1JF$K
JV^KT=1MKt`YM¥M1FO-P=RQPSoHWV^XoP=¥M1F=WJYXoV>nIFJVYXUZKtV^FÂDrXoVY\JZP¡PTVY\1XU=1]{pKT`^KtZFaV^F`cÅyÆGÇ*ÆzÈgSUP]y?3¯C
£
§É
?BklCf
¿
¯Å
Æ ¬
Ê
v"ËyxEÌ
§-É*Í
k~u$v
Å Æ Î
ÏcF-VÐÑ?3kf|hlC$slFdV^\WF OPT=1M1XoVYXUP=1KTSmM1F-=1JYX"V>nPtb¥vL]X"QF=u$v$Òhji{KT=WMÓSUFaVÔÑ?3c|hlC
Õ
(
Ð1Ѹ?BkE|hlCW 7kÖsÄF·V^\1F»O-P`Y`FJYpÄP=1MWXU=1]OP=WM1XoVYXUP=KtS×M1XoJV^`XUs1H(V^XUPT= bBH1=1OaV^XUPT=$Ø*=¼FJV^X"Ù
ZKtV^FLPTbXoVrXoJ¢]XoQTF=KTJ
£
ÔÑ
¦§É
?3c|hlCf
¡¨©
£
§É
?hq~ÚklCÐÑ?3klC ¡klª ¨ ©
¡¨©
£
§-É
?h~klCtÐÑ-?3klCW 7k
Dr\1F-`YF,KT]RKTXo=qD{F¥V^`H1=1O¸K;V^FKtVr«¡¬®°¯
x±²
½ÂPPTsWVzKTXo=V^\1F»Ø*Û*Ü5ØÝbBHW=1O-VYXUP=ÖeDGF»O¸KT=¼=1P¹DÝO-PZp1KT`YF
?3c|hlC¥Kt=1M¼ÔÑ?3c|hlCÞ·<>=
p1`YKTO-VYXUOF$VY\1XUJLZ[F¸KT=WJ¥VYPd`YFSUKtV^F
£
¥¤
¦§
?3c|hlC¥Kt=1M
£
ÔÂÑ
¦§-É
?Bj|hlCa$½¢\1F[=1P=WpKT`^KtZFaV^`YXoO$FJV^X"Ù
ZKtV^FbBPT`·V^\1FØ*Û*Ü5ØßbBH1=WO-V^XoP=eg?BhjiYWCM1FpÄF=1MWXU=1]@P=®JYZ[P¡PTV^\1Xo=1]ÁpKT`YKTZ[F-V^F-`YJ$iÞÅ
KT=1M Å Æ XoJ¢\1F=WOF]XoQTF=s7n
£
e ¤ ¦§¸¦§ É
?hji^(C
£
x
¤ ¦§ ? £
ÔÑ
¦§ É
?3c|hlC|hlC
Xob×eg?hji^(C{XUJ¢Xo=1O`F¸KTJXU=1]»XU=VY\1F¥JYFO-P=1M KT`Y]HWZF-=7VKT=1M
£
e ¤ ¦§¸¦§ É
?hji^(C
£
x
¤ ¦§
?¿r~
£
ÔÑ
¦§ É
?3c|hlC|hlC
Xobgeg?hji^(C¢XoJK[M1F-O`F¸KTJXU=1][bBH1=1O-VYXUP=PTbbBP`KT=Rnhj
£
x
¤ ¦§
?à3|hlCmM1F-=1PTV^F-J_VY\1F,Xo=RQF`JYFPTb
V^\WFmbBH1=1O-VYXUP=
£
¤
¦§
?à|hlCjbBP`×áWâ(FM$hjfãPSUä-slF-`Y]F-`¢?åTææW¿CÂ\KTJgJ\1P¹Dr=[VY\KtV
£
e ¤ ¦§¹¦§ É
?hji^(CÂXoJ
ûÄêù1ë1ú1ìêë¼î^þ1ï[ò^ètîYïìêTñ¢û1íUèTìèTë1úTètòYí¾ètë1éï»êTñGî^þ1ï[ïìî^íUðètîYïÖïòïðèTò5î^þètîî^þWï
èTììYù1ð[ýWî^íoêë»êTñlðêëWêTî^êëWíUéí"î NêTëóíUìfëWêTîèìî^òêë1ÿ¥òYï-ìî^òíUéaî^íUêTë>ë»î^þ1ïèTýWý1üUíoé¸ètîYíUêëNîYê
ý1òê(é-ïììYïìrþ1íUézþGï»þèï[íUëÁð[íUë1úÁí"îLìYï-ïð[ì¥îYêdûlï$íoë7îYù1íoîYíTïü 5òYïèTìYêTëèTû1üoï
î^þ1ètî{îYþ1ïêTü¾ètîYíUüUí"î ·êTñcîYê(ú1è [íoìmèTëqíoë1éòï¸èTìíUë1ÿñBù1ë1éaî^íUêTëqêTñcî^þWïêTü¾ètîYíUüUí"î $êTñ Tïìî^ïòúè
rþ1íoézþî^òYèTë1ìü¾ètîYïì[íUëRî^êÖèTë
ñBù1ëWé-î^íoêëó rþ1íoézþ íUì»ú1ï-éòYïèTìYíoë1ÿ íoë}îYþ1ï ìïé-êë1ú
èTòÿù1ð[ïëRî
!
ï-î_ù1ìíUüUüoù1ìîYò^ètîYïIî^þ1ïìîYïý1ìñBêòrïìî^íUðètîYíUë1ÿ»è[ë1êë1ýètò^èTð[ï-îYòYíUé
ý1òê(é-ïìì"$#×íoòYìî
Gï,ÿï-ë1ïòYètî^ïLîYíUð[ïIìYï-òYíUï-ìrúètîzè»èTëWú5ý1üoêTî$%'&)(+*TïòìYù1ì%,&-
.0/102034265879;:</"=?>A@?9B
CADFEHG6GIG
J
D4K
> C 3L2=?37
G8MONQPGRMONQPC+S 2=?30.T7
C
BIB
U
þ1ï»òYï-ìYù1ü"î¥íUìLìþ1êrë íUëV#íUÿù1òïXWL
U
þ1ï»ìé¸ètîî^ïòý1üUêtî¥íUëî^þWï[òíUÿþRîLý1èTë1ïüfêtñ#×íoÿù1òïXW
ú1ï;Yë1ïìrî^þWïòïÿíoêëZrþ1ïòïGï¥é¸èTëïìî^íoðètîYïIî^þ1ïLñBù1ëWé-î^íoêë5ógôBõjöY÷Wø[
ARMA(1,1) Time Series
0 5 10
t*E2
-5 0 5 X(t)
ARMA(1,1) Scatterplot
-5 0 5
X(t+1)
-5 0 5
X(t)
#×íoÿù1òYï\WL]
^
ôOWL_)Wø{ý1òYê¡éï-ìYì`
U
êqéêð[ýèTòïîYþ1ï·ú1ï-éêë4TêüUùWîYíUêë5ú1ïëWìYíoî 5ïìî^íoðètîYïrí"î^þ îYþ1ïNúWïë1ìíoî 5êTñógôa%,&öcb"&3ø$Gï
ù1ìï_ë1êÓêù1òEêrëòêùWî^íoë1ï,ô
=A503L2L=?3
øgñBêòfÿïëWïò^è;î^íUëWÿ
ôdW_Wøgúè;îzèIñBòYêðÝè7ë1êrë
ñBù1ë1éaî^íoêëÖôfe(ø;]
g 2 SIh
7 e B D e 7 J P >
P[h
B
e DihQj[EkIlihQjOmLk?n J lihjo4k+n
>
>
C0pLg
xI}+ Is+HxRvAFL|+
{I}4x
}Fts?0vAFL|
0}F
4 4 vO AA<L|
0}L 0F
{ II}6{8vdx i+8z A+Rz[uI|
x II}6{ II
I
0?t
xI}4xO8LviFL|H
{I}4{O8LviFL|H
0Lr
A}FH6I
x8zd{06}A0LsL?vzc8O8O?|
}I8
00s04s68v ~¡Ft6t~
s |
}4?u ¡~ Rvdx8z | ¢6¢ u4tHI£+t6H¤I F4tH ¡H F?
{ }4 ¡H Rvy{8zy¥i¦ | ¢6¢¨§ sL ¡~ F"?
©ª«L¬i®°¯²±³i´µ$±^¶<´·³¹¸i®`ºi±ª)·»¼®"±y·ª¾½¿·c®`±"ÀÂÁ´·®·³?¿·Ã·c³i®°±½Ä´0´·c³iªºi«²Å?¿¿½®;·c®`
Æ
¶i¿ºi¸Aµ$ª¸A·c³ÈÇFɪ¾±$¸iª)ÊË®`®`º6·ÍÌa´LͶ<´·c³Î®`±y·ª¾½¿·c®`±Í±yª¾ºiÏ`®Ð¸AªÊ<®"®`º4·Ñ®"ºA®"ÒÌa¬AºiÏ`·ª¾´Lºi±¿y®
¬i±y®"¸À
{Ó} 6r?Ls? ¡H ÔvdxÖÕ×z Õ×zdØÖÕ×zdÙÚÕ×zOÛÖܼÜÝÜÝܼ|
®"±d·cª½Þ¿·®"±$¿'ºi´LºAÅ?¿c¿½®;·cªÏßàá^ßâÅi´IÏ"®`±±
ã³i®Ìa¬iºiÏ`·ª¾´Lº
6ri4s? ¡~
Ï"´½Åi¬0·c®"±,·c³A®Ìa¬iºAÏ`·cª´Lº¨ä Æaåwæcç
É\Ìa´LÄ¿ºèßàá^ßéÅA´IÏ"®"±y±
¿Ï`Ï"´Ly¸iª¾ºi«Ð·c´\·³i®¿Ò«L´Lª)·c³i½ê¸A®"±Ï`ª¶<®`¸Ã¿¶<´ë®Àì×®`·¬A±í?±d·Ï"´LºA±ª¾¸A®"¿ºÞßàá^ß ÆOîLïî
É
µ$ª·³^ä Æaåwæcç
É8ð¹ñ0òôóÍõèñ0òôö å õ î
òôö ç+ï
ª÷Àø®À
ù'úð¹ñAòøóÍõèñAòøöù'úüûAýwõ
î
òøöLþ"úüûAýTõèþ"úOò
ÿ®`ºiÏ"®
ï
µ®¬i±®
A0LsL?
µ$ª)·c³
u}08O¥R×
¿ºi¸Ï¿Ò¾ÒË·³i® ®"±y·ª¾½¿·cª´LºXy´L¬A·cªºi®¶4»
{I}6ri4s? ¡~ Rvdx+|
Deconvolution Density
-5 0 5
u
0 5 10 15 20 q(u)*E-2
"!#$&%'# (*)+ -,.#/!102)3!'43*!#&%'#/(5)6
,7!)6#8!1096:;8<4>=9?(5)3@:. A /3B6:C)3EDGFGH?DI,JK$J>0MLN##O
PQ8RL )3SL)3 )3(T#VUE)3!?WB)3R#G@X3YT)3!ZX3YK1#L[A $$%O9U@3\ )3/#
8]!Z#^#< #!_:.G`a)3!2b1O<Wc#d)3e)3!!$ )3f/!_#^g:.3/ )6C(TL Nh
i)+ /3#OZPQ8@# /B:. A /3j/#g8:.k3(5L N !l3l)Z!j3:9#/^*UnmoU[O
(5L)3#pK[=qr)6/#@)3/ s)+ R8I I:. A _Z 8]# )3(TI/!pO gt
#8>=9#k8_# $ j)3L8#O-PQ8_u)3!N=9/!8#*vw,.#L[!a yxzi0r:.* 8
{h&!(5#)3|! B43}# (*)69~
)3!?*:.398d&=q+h&!(5#)3
,7#L|!/ xI)3!g0})3i8#r)3!/9 8 )+ #;!3!Ig/^u|
, 6YYJ>0{O
DG#5)2#!{)3(5L/E#/!5)3DGFGHBD],J3KJ>0g=9$ 8)2 $%l/)3I:. A
,`f bN03*,73bN0AKO6O
]SGN5,s 0Sy
=98Z!6 #T 8B#(T/!j:. y*,. |0* ,Jd¡
\¢
0
r£
)3#T 2 8
L/ #{)3(5L/3K6 8#C:. /r#Cu/ #%g3!L|!¤] 8Q¥#)3 (T¦O
PQ8!<)3u[§8)3#Q ru[(T!¥!@u%E #
¨N©ª«f¬1®+¯¬°±²±{«N®
Linear ARMA(1,1)
-4.3 0.2 4.7
-4.3 0.2
4.7 -9.1
0.7 10.5
´µ¶·¸¹<ºN»¼V½¾¿À3¸ À6Á5¹A ¸µÃR¹Äµ/Á5À6 µ½¾E½3ÅÀZÆ.Ç/µ/¾¹¦À3¸ È9ÉGÊGË?É¿¸½Ã¹ÄÄÌÍ;¸·¹RÎÄ̹Ä µ$Ï
Á*À+ ¹Ð@Å.·¾Ã µ½¾BÀ3¾ÐBÐÀ6 ÀÌ
ÑÒÓCÔÕÖ×}ئ٧ÚÛÜݤØÞÓÔ&ß\Öà3Ûá\á6ÚÓCÔ{Ù§Ö
Û6âNãÝ
Ó6ÒÞ\ÕäåMæåMæ ç
ÍQè¹I¸¹Ä·Çµ/¾¶5¶¸ À3¿èÄGÅ.½¸Â èµÄV¾½3¾Ç/µ¾¹¦À3¸9Å.·¾ÃA µ½¾_À3¸¹gÄè½>é9¾2µ¾Z´µ¶·¸¹êÌVÍQè¹]¹ÄÏ
 µÁ*À+ ¹ÐlÄ·¸Å7À6ù@Î6À3¸µ¹Ä]½ëε/½·ÄÇìí½¾Ç$ìjµ¾îÂè¹@Ĺý¾ÐïеÁ5¹¾Äµ½¾lÀ3¾ÐîÅ.½ÇÇ/½§é9Äg è¹
ð
Ï&ÄèÀ3¿[¹ÐE·¾Ð¹¸Ç$ìNµ¾¶] ¸·¹Å.·¾ÃA µ/½3¾pÌñV½§é¤¹Î¹¸ò è¹d·Ä¹Ð?ÄÀ3Á5¿Ç/¹Äµ/ó¹<À6¾Ð@ è¹<µ/¾Â¹¸Ï
¾À3Ǥ¶¸µÐaĵ/ó¹ÄI½3ÅQÂè¹k¹Ä µÁ*À6µ/½¾í¿¸½Ã¹Ð·¸¹kн_½¾Ç$ìíÀ3Ç/ǽ>é'Å.½¸IÀc¸À6 蹸IµÁ5¿¸¹Ãµ/Ĺ
¸¹Ã½¾Ä ¸·Ãµ/½¾B½3Å} è¹d À3µ/ÇÄM½3Å} è¹<Ä·¸Å7À3ù3Ì
Nonlinear ARMA(1,1)
-3.9 0.2 4.2
-3.9 0.2
4.2 -2.5
0.8 4.2
ö÷øùúûdüýþVÿ3ú5û ú÷kû ÷ ÷/ÿaÿÿ÷û3ú !"úÿ#û$%&('}úùû*)#$&
û ÷+ û,-.ù ÷/ÿ!,!, &
. /10243576598;: <=6?>A@ BDCFEHG1I JKL<=>M8;5<N: K
OP! %Qû7.ÿÿSR9÷øT#Rqûÿ÷,ûúUÿ6úTû$ ú÷VWYXYZ9[T[S\Tÿ?,û$YR]Q÷Q^,û$|û$,
M_#`5û ú÷a_Tÿ* QûM MÿbûúM) ÷/ÿpý
cSdfe gdihjdlk
nm
gpo
d e q
co
dsrt kgNo
dsrt pu
ZVûúûT
q
,ûÿ û$v7%TÿNÿ QrùwxÿyR]+.ù$ ÷/ÿ`,4 Qû÷ÿy) ÷ÿ
hjd
6úû\Qÿû-
÷*Q÷{zNû$$ ÷ÿ*|&}'\Q÷\5ÿ#,û$pÿy)3ûú%] QûdùùN3ú%5û ú÷WVWYXYZ9[T[Svúÿ#ûM
[y bù 7,ÿûWÿ 7/ÿyR1.ÿúúûúûû$~ ÷ø!û$)3ûú6øû]û$|û 7/÷w6û Qû'UV7\XYZ9l[T[y
úÿ?û%$&!íû%QÿSRFÿyR QÿyR ÿ{ ú%M.ÿ3ú% nmd÷~ ÿ{Tÿ?,û$n&Bö÷ú%M T=R¤û
L LnU
¡ ¢i£
¤?¥
¦§a¨ ¥
ª©«¬
ª©«
®N
ª©«=¯°
ª©«
}±p
L¯H
ª©«
}±«a²³
N
%L¯H
ª©«
}±«a²
4µ´
L¯H
ª©«
¶j²
L¯·
ª©«
¥]¸¹
¦
±«aº
%»p
¼±p
½~¾
¶jº
¿?
Dj±«aº
º´
¿?
À
¥7¤¥
Áa§!$Â
¹¸Ã
§ ¹ ¹
¦ÄÅ Æ!Ä1ÇÈÁ
¹¸
¶Éº
¿?
ÇÊ
Ã˹
¦ §Ê
¸ª¹
¦
Ã`¸
Á Â%ÌxȧÊM
§
¹ § - ³
§Â
¸
DÍ?Á
¹¸
DÎHÈÂ
¸ ¹
¦Ï Чʧ
à ¹ Ê ¸
ÁÄÅ Æ!ÄÑÂ
¹%¸Ã
§ ¹
Ò
¶ÓnÔÕaÔÕ$Öa³º
¿?
Ç i£
×
Å]$¨Ê
¹¸
¹
¦
¹
ʧÂMÇ Ê Ã §
¹¸
Â
¤#¥
¹
Ò±«yº
»µ
Ø?ÐNÙ
Ò
¶ÓnÔÕaÔÕ$Öaº
º´
»µÚx
Ò±ÓnÔ
ÕyÔÕ$Ö$²Û
Ü~
Ò±«a²}Û
Ü
Ê ¤ Á
Ãݸ
¸ Ý ¹
¦*Ìxȧ
¹¸
Â
¤
Ò±ÓnÔ
ÕaÔÕ$ÖaÛ
Ü
Ø?Ð4Þ
Ò
¶ÓnÔÕaÔÕ$Öß®Û
Ûà
Ü%Sá
Û
Üâ¼ã?
§ÂU§*Â
¹¸Ã
§ ¹ Ç ¹
¦7Â
Ã`Ã
¹ Ê ¸
ÁäWÄÅ\åYæçÇÈÁ
¹¸
±NÛ
Ü~
è ¦§a¨
¹ Ý
-§
¥
§Ê%
¤ Ç]Á ÈÊ%Â%
¤j¹
¦§
¹¹
¦$Â
¸ª¹
!éê ÈÂM
¸ ¹
¦+Á ~¨ È
¹¸
ЧÊ
¹ Ç]$Â
¹%¸Ã
§
¹¸
ë¶Éº
¿?¸
 ¹
¦ÐÊ
Ý §
ݸ
¸ª¹
$Â
¸ª¹ ì
Ç ¹
¦
fí
¤É¸n×
×^¸
Ç
éî
Ü~
¹
Â
¹
¦Â
¸¹
- Ç j
éê
»µ
"ï
ðòñ
¾ó
éî
¾$ó
ô¯·õx¾$ó
éî
õx¾$ó
yö]
÷ Ç S
¸
Âj§ Á
Ã`Ã
ЧÊ%§
à ¹ Ê ¸
ÁYä7ÄÅ\åYæ ï ¤ï
ÐÊ Á$Â%Â ÇÇ Ê Ã ï
¤¹
¦ ±p²Û
Ü~
¼ø
¯
ù Û
¯4úÉÜ?
§
¹
¦\Á Ê%ÊMÂ%Ð
¸ ÄÅÆ{Ä°ÇÈÁ
¹¸
¸Â ¶Éº
¿?
D³ø
¯ ù ½
¯`ú=
½aõxû
ü ¦ ¸Â ¸
Â]§`ÁÊMa§Â
¸ ÇÈÁ
¹¸
¸
¿+¥
¦ ¸ Á¦^ÂM
à  ¹ Ý
§Ê%§Â §
Ý ý§Â%Â%È Ã Ð
¹%¸
¸
¹
¦ $Ê%§ Áa§ÂM
¹
? Á Ê%Ê%$Â%Ð
¸ ¹ ¹
¦ý§Â%ÂMÈ
à Ð
¹¸
¹
¦§
¹]¹
¦ÐÊMÂ%$
¹ ¨ §
¹¸
¸ª¹
¸
Â]§
¸
ÁÊMa§Â
¸ ÇÈÁ
¹¸
ÇjЧÂ
¹ ¨ §
¹%¸
¸¹¸
Â
×
ÄÂU§{ا
à Ð
¤¥
7Â
¸Ã È § ¹
W§+ä7ÄÅ\åYæ1ÐÊ Á$Â%Â\ÇÊ Ã
þ?ÿ
!#"$&% "'
ð
,$-./01(23'45*6*798:$;-#/=<>0&)?2/5
(6@9(!-.30 )9ACB!5
D
6(
3'46$(
@6')C.*-'7#;$EF0&)9ACB!5
G
6CB
H <JIE!(K0 G9L
)9AJB!5
G 6 G
ACB
3'4M GN
6:
D
0(>M G9O
B
NJP
423'4>M G9O
B
NJP
42/$5
(M GN
6#3*Q-
G
03'4M GN
5SR1T@?M GN
(*)$+#.
(6(>M 4U!0&)ACB!5
N
3'46#3'4M 4U0&)9ACB!5
N
(*)$+!,
D
6V),9:$;!-#/=<#(93
G
0WYXZ2&<YXZ2:[XZ2\YXZ2 ]Y^_^_^_^`5
acbd1egfih*dacbjhlkm!k9n#h'o1h*fpad1oegqsrutwvyx{z|nomqca}bb
~y
akqd1egm!kw),9:$;!-#/=<#(93
G
qcm'fpn$d1acbZd
akqd1em'kb 1$h'k CCm'oZhjrutwvyx{z
nom$q}acbbbekld
audacq
k9eacbacbqcoeCach'Jm='a'?xm!kbea}ohprtvyx{z ! ¡¢?£jegd
J1¤`¥9¦§¥9>¨©¥9¦«ª¨¬¥9¦«9¦
za}kqca* #£asba
)96CB¢®®®
/*6®R®CB¯°®R±{¯°®R4
²
(23'4³6*798:9;!-#/=<>0 )>2/5
h'k´qh*µµd
auacbdefph*d1egm!k¶om!9d1egka·
:6'),$:9;!-#/=<(3
G
0(5
¸
eg!oa¹b
m=£jbyd
aoacbµgdek!o1h'n
m!od
aacbdefph*d1m'om'F 1$>d1m'!a}d
aco{£je¡d
d a
d1oakqd1egm!kº a}qcoah'bek»ek¼$h'k9½d
a#h*d1h´ ¾l¿¡À Á!acobb¾l¿Âtbyek¶d
astwvwôt
Nonparametric GARCH(1,1)
-11.4 -7.8 -4.2
-11.4 -7.8
-4.2 -3.5
2.3 8.1
ÅÆgÇ!ÈÉÊsËÌ#ÍÎ!Ï9Ð#Ñ'É1Ñ*ÒpÊÓ1ÉÆgÔÕÊcÖÓ1ÆÒpÑ*ÓÆÎ!ÏVÎ*×ÙØÚÛÜ1Ý$Þp×Î!É´ÑßÚàÆgÏÊÑ'É1Þ¶áâãyä{åæÐÉÎÔcÊ}ÖÖ}ç
èFÉÈÊéÖcç>ÊcÖÓÆÒpÑ*Ó1Ê}ê¼×ÈÏÔ}ÓÆÎ!Ïëê#Ñ*Ó1ÑÙìlíîßàÎ'Ç Úïð
í
Þç
ÔÑ*ÖÊ'ëÓ1ñ9ÊÊ}ÖÓÆÒpÑ*Ó1Ê}êÙ×È9ÏÔ}ÓÆÎ!ÏÙÖñ9΢òjÖ>Ó1ñÊjÈÏ9êÊcÉàgóÆÏÇuÖÓ1ÉÈ9Ô}Ó1È9ÉÊÎ!Ïàgóô×Î!ÉÑuÐ#Ñ'ÉÓÎ*×Ó1ñ9Ê
É1Ñ*ÏÇ!ÊuÎ'×SÓ1ñÊÓ1ÉÈÊ×ÈÏÔÓ1ÆÎ'Ïç
ÅÆgÏ#Ñ'àà¡ó!ëCòÊ»ÉÊ}ÒiÑ'ÉõöñÎ=ò÷ÓñÊlÓ1ñÊÙÇ!Ê}ÏÊcÉÑ'àÔÑ'ÖÊÙÎ'×{ÏÎ'ÏÐ#Ñ'ÉÑ'ÒpÊÓ1ÉÆÔÙáâãyä{åøÒ»Î$ê9ÊcàÖ
ÔcÎ'Èàê½ùCÊsÊ}ÖÓÆÒpÑ*Ó1Ê}êç>äÎ!ÏÖÆêÊ}É
ï¢íúî ûíÂüí ÚÂý!Þ
û ð
í î þÚï¢í ÿ Ü1û
ðíÿ Þ
òjñÊ}ÉÊsû ð
í
ÒpÑó¶êÊ}ÐJÊ}ÏêöÑ*ÖóÒpÒ»Ê}ÓÉÆgÔÑ'àgàgó»Î!ϼï¢í ÿ
ÊòjÉÆgÓ1Ê
þÚÛÜ!Þ>î þ ÚÛ
ð
ÜÞJÚÛÞ þ ÿ
ÚÛ
ð
ÜÞJÚÛÞ
âwÖþ Üþ
ÿ
êÊcÐCÊcÏêÙÎ!Ï9àgóôÎ!Ï Ó1ñÊyÖÈ#Ñ'ÉÊ}êiÑ*ÉÇ!ÈÒ»ÊcÏÓÖòÊjÔcÑ'ÏÙÊcÖÓÆÒpÑ*Ó1Ê>Ó1ñÊ}Ò Ñ'ÖùCÊ}×Î'ÉÊ'ç
âwÇ!Ñ'ÆÏëJÔcÎ!Ï9ÖÆê9ÊcÉìlí>îYàgÎ!Ç Úï*ð
í
ÞÜcíî÷àÎ!Ç ÚÂüð
í Þ
Ê}Ó
ùJÊÓñÊ ÏÈÒ ùCÊcÉÎ*×>Ñ'àà
O
P B
QSRUTWV
< X
8CBY
Z
[
,]\4^`_ba R T
?dc;,
Y
VfeR
*g,E.10
V
Oh B
Qjik Rml`nTWV
< X
8CBpoJY
Z
[
,]\4^`_
k;q
l
?rc;,]B4^
o s _ a q T
?rc;,
Y s
eR
*g,/.0
VHt
O
P BQ RuTWV
O
h B
kKv RulV
< X
8CBpoGw
Z
[
,]\4^ _ kKv
q l
?dc;,
oGw s eWR
*g,/.10
V D
O
x B
QjikyRmzpnTWV 2 O
{ B
| ikKv"RuznTWV
36})I%7JI~G5JIK736NS$5 IKK&)$ 5#%$'&(
O
h B
Qjik 2 O P BQ
})I36K$5J
Oh
Qjik 365J7
O
P Q L
365J7LJN$5JW 6&)(IN&$'3&)IN 6p 65J7J$'&)$ 5J3647J$N&})$'J&)$ 5uJ5J&$ 65JN#II&H365
uJ5J&$' 5IKN&$'3-&I
O
B
Qjik"ikKv"RuT
2
zV
DII}N)$'5J&(I &)}365JNu })3&)$ 5¡u}) 6 ¢H£¥¤¦&)
§9LJ#MI¨IK&3N%&)(JIIN&$3&)I 6/©
B
RuT4ª 2«
V
O© B
Qjik"ik
vRUT
ª
2«
V
<>If¬;
O
B
Qjik"ik
v`®
T ª 2'
RUT ª¯
«
V°J±
D
FH(JI¨IN&$3&)Iu }¥©
:
RuT4ª 2«
V
$N%365J36 6 JN)]²7IK~G5JIK7
O© :
Qjik"ikKv RUT
ª
2«
V
<>If¬ O
:
Qjik"ikKv`®
T ª 2'
RUT
ª ¯ « V °J±
D
#%(JIK})I6LH$'5r&(JI7JI}$'3&)$ 5A 6
O
:
Qjik"ik v
248CB>365J7
eR
*g,.³0
V
36})I=})IKJ3I7´µ²¶8:135J7
eWR
*g,/·¸0
V D
ÍMÎÏ'ÏÐKÑ)Ò)Ï'ÐKÓÕÔ-Ö×ÙØÚ×GÛÜ"ÝÞßµàf×JáÐâJÐKÑã6Ï'äåKÐæçãèéÎÑÐêÑÐÒÒ)ä'Ó6Ð¥ëÎ6âJæJä'é)äÎâJã6ÏÂìJÐKé)ÐÑ)Î6Ò)ëÐKæGã6ÒéäëKä'éîí6Ô
ïð6ñ òfó4ôõÚðö÷¥øð6óÕð6ùûúümòýmøþHÿ ×
ÍèJìJÏãâJâÔ¶Ø/× ãâJæë§ÐKäÏ Ô××¶Û Ü¼ÝÝݵàf× ð6ó ôòôùûúü òfýmø! #"%$!&îùûð'ÂúõÙþÔ
bã6âÂèJÒëÑ)ä(é"Ô)`Ö+*-,.èJÑ)ä'ëìÔ /1020 3547626982818;:=<?>02/.:A@0 /CBD:FEG/62HI<JE9KL@LMN ×
O ã6ÑÑ)ÎÏ'ÏjÔ2P××yã6âJæQ*ãÏÏjÔÂØÚ×WÛܼÝÞ6Þµà×SR!(é)äTã6ÏJÑ)ãéÐKÒÎUëÎâµÓ6ÐÑ)ê6ÐâJëKÐ!UuÎÑSæJÐëKÎâµÓÎÏ'èéä'âJê
ã;æJÐâJÒä'éîí6ÔïCVWùûúòXVZY4ü ôü ýþü[VWþþð¼øGVJ\4ÿ%ÜܼÞ]^ÜܼÞß ×
_4ã6âÔ`×ã6âJæÖ/ÑèJÎâJêJÔba;×dc×ûÛ Ü¼ÝÝà×ÎâL(GãÑãûÐKé)Ñ)äë Ñ)Ðê6Ñ)ÐÒÒ)ä'Îâfe%ä'éì ÐKÑ)Ñ)Î6Ñ)ÒA äâg
Óã6Ñ)äãhJÏÐKÒÔLóGóiV%Y4üjôümýþüjVWgkÜGlÜ ×
_GÑã6âCm6Ð6Ôb×]Ô#*nãÑ)æJÏ'Ð6Ôpo ×ã6âJæq*ã9UuâJÐÑKÔ
O
ì×çÛ=ܼà×rY4üjôümýþümýTs'ÂúòutSýUó4ôó1vùxwôòFs-ü úÔ
y (JÑäâJêÐKÑÔJÐXhWÎyÎm /1010 3.47626^82828;:{z|L>^K10?N @0;:}g@ ×
*nãÑ)æJÏ'Ð6Ô o ×'Ôg~èéFmÐ(ÕÎìJÏjÔ1*¨× ãâJæ O ìJÐKâÔLP×WÛܼÝ6Ý à×JÑÐKÓyäÐe¡ÎUpâJÎ6âL(Gã6Ñ)ãÐéÑäë¥éäÐ
Ò)ÐKÑ)äÐKÒã6âGã6Ï]í ÒäÒKÔóGüjúòfó4ôü ýmð6ó4ôõY4üôümýþü ýmøôõ ¥ú¼ýmú W]µÝA ×
*§Î6ÏåhÕÐÑêÐÑKÔ`*×ûÛ=Ügàf× ð6ó ôòôùûúümòýmød÷SþüýUùôümýmð6óÌðöð6óGõýUóÕúôòp + ôó'
! #"%$!&TÕòð¼øúþþúþÔGØ`ì? ÖHìJÐÒäÒKÔJâJä'Ó6ÐÑÒ)ä'éîíÎUcã6ä'Ò)ÐKÑ)Ò)Ïã6èé)ÐÑ)â×
×Ø/×i9ÎÑêµã6â×P%äÒmg9ÐKé)Ñ)äëKÒÔ /1020 3547626982818;:A^3 <J^2g>^K5:FE G< ×
y é)ÐXUmã6âJÒmµíÔ~`×C×gã6âæ O ã6ÑÑ)ÎÏ'ÏjÔP××yÛ Ü¼ÝÝà×ÐKëÎâµÓ6ÎÏèé)äâJê+mÐÑ)âÐÏÂæJÐâÒ)ä'éîíÐKÒé)äTãéÎÑÒÔ
Y4üjôümýþümýmøþHܼßÝ9ܼÞ]J×