Streszczenie
:DUW\NXOHXGRZRGQLRQRĝHZ\VWÚSRZDQLHVNïDGRZ\FKGHWHUPLQLVW\F]Q\FKWMVWDïHMWUHQGXRUD] LFKNRUHNW\ZSURFHVLHJHQHUXMÈF\PGDQHLPSOLNXMHZ\VWÚSRZDQLHLFKZSU]HVWU]HQLNRLQWHJUXMÈ- FHM2WU]\PDQRPRGHO9(T&0]H]PLHQQ\PLGHWHUPLQLVW\F]Q\PLZNWöU\PNRUHNW\Z\UD]XZRO-QHJR LWUHQGX UHSUH]HQWXMÈFH ]DEXU]HQLD VWUXNWXU\ ZSï\ZDMÈ QD ZïDĂFLZRĂFL VNïDGQLNöZ ORVR-Z\FK]MHGQRRNUHVRZ\PRSöěQLHQLHP]HZ]JOÚGXQDRSöěQLHQLHZZHNWRUDFKNRLQWHJUXMÈF\FK :\SURZDG]RQ\PRGHO]DVWRVRZDQRGRPRGHORZDQLDKDQGOX]DJUDQLF]QHJR3ROVNL=LGHQW\ILNRZD- QR]PLHQQHGHWHUPLQXMÈFHSROVNLHNVSRUWLLPSRUWRUD]SRWZLHUG]RQRLVWRWQ\ZSï\Z]PLDQ\UHĝL- PXNXUVRZHJRQDSROVNLHNVSRUWDWDNĝHVNXWNLSU]\VWÈSLHQLD3ROVNLGR8QLL(XURSHMVNLHM]DUöZ-QRGODHNVSRUWXMDNLLPSRUWX2ELH]PLDQ\VWUXNWXUDOQHVÈUHSUH]HQWRZDQHSU]H]RGSRZLHGQLH NRUHNW\Z\UD]XZROQHJR 6ïRZDNOXF]RZHNRLQWHJUDFMDPRGHO9(T&0]PLDQ\VWUXNWXUDOQHKDQGHO]DJUDQLF]Q\ -(/&&)
$QDOL]DNRLQWHJUDF\MQD]]DEXU]HQLDPL
VWUXNWXU\QDSU]\NïDG]LHPRGHOXKDQGOX
]DJUDQLF]QHJR3ROVNL
(PLOLD*RVLñVND
1DGHVïDQRZU]HĂQLDU=DDNFHSWRZDQROLVWRSDGDU 8QLZHUV\WHWöG]NL.DWHGUD0RGHOLL3URJQR](NRQRPHWU\F]Q\FKHPDLOHPIHPM#XQLORG]SO:VWÚS
3RGF]DV PRGHORZDQLD ]MDZLVN JRVSRGDUF]\FK F]ÚVWR VSRW\NDP\ VLÚ ]]DEXU]HQLDPL VWUXNWXU\ =LJQRURZDQLH LFK PRĝH SURZDG]LÊ GR EïÚGQHM DQDOL]\ NRLQWHJUDF\MQHM 1DOHĝ\ ]DWHP UR]V]HU]\Ê VWDQGDUGRZ\ PRGHO 9(T&0 R]PLHQQH NWöUH FKDUDNWHU\]XMÈ WH ]DEXU]HQLD :SUH]HQWRZDQ\P SRGHMĂFLX]PLDQ\VWUXNWXUDOQHVÈUHSUH]HQWRZDQHSU]H]NRUHNW\]PLHQQ\FKGHWHUPLQLVW\F]Q\FK WMVWDïÈRUD]WUHQGSRU-RKDQVHQ0RVFRQL1LHOVHQ6DLNNRQHQ/đWNHSRKO7UHQNOHU =SURFHVXJHQHUXMÈFHJRGDQHZ\SURZDG]RQRPRGHO9(T&0]ZLHORPDNRUHNWDPLZ\UD]XZROQHJR RUD]SDUDPHWUXSU]\WUHQG]LHOLQLRZ\P2WU]\PDQ\PRGHOZ\NRU]\VWDQRGRPRGHORZDQLDKDQ-GOX]DJUDQLF]QHJR3ROVNL]HZ]JOÚGXQDQLHVWDFMRQDUQRĂÊ]PLHQQ\FKRUD]PRĝOLZRĂÊZ\VWÈSLHQLD ]DEXU]HñVWUXNWXU\QDVNXWHN]PLDQ\UHĝLPXNXUVRZHJRZ,,NZDUWDOHURUD]SU]\VWÈSLHQLD 3ROVNLGR8QLL(XURSHMVNLHMZ,,NZDUWDOHU
0RGHO9(T&0]H]PLHQQ\PLGHWHUPLQLVW\F]Q\PL
=DïöĝP\ĝHSURFHVJHQHUXMÈF\GDQHdata generating process,'*3 v(m)t >vtvMt@
MHVW0Z\-PLDURZ\PV]HUHJLHPF]DVRZ\PNWöU\]DZLHUDVNïDGRZÈVWRFKDVW\F]QÈLGHWHUPLQLVW\F]QÈSRU 6DLNNRQHQ/đWNHSRKO7UHQNOHU JG]LH
@
>
t Mt (m)tv
v
v
ļZHNWRU0]PLHQQ\FK ļZHNWRU0]PLHQQ\FK]LQWHJURZDQ\FKZVWRSQLXSLHUZV]\PRZ\PLDUDFK [0 @ > t Zt (z)t d d d ļZHNWRU=]PLHQQ\FKGHWHUPLQLVW\F]Q\FKRZ\PLDUDFK[= » » » » » » ¼ º « « « « « « ¬ ª m Z m h h H ļPDFLHU]RZ\PLDUDFK=[0SDUDPHWUöZ]ZLÈ]DQ\FK]H]PLHQQ\PLGHWHUPLQL-VW\F]Q\PL M m z Z /LVWD]PLHQQ\FKGHWHUPLQLVW\F]Q\FKRJUDQLF]DVLÚQDMF]ÚĂFLHMGRZ\UD]XZROQHJRLWUHQGXOL- QLRZHJRDZ\VWÚSRZDQLH]PLDQVWUXNWXUDOQ\FKMHVWXZ]JOÚGQLDQH]DSRPRFÈNRUHNWRGSRZLHG-QLFK SDUDPHWUöZ :WDNLP SU]\SDGNX a wektory uW t RRUD]uW t,RZ\PLDUDFK[:VNïDGDMÈVLÚ]H]PLHQQ\FK]HURMHG\QNRZ\FK=DïöĝP\]DWHPĝHv(m)t MHVWJHQH-URZDQHSU]H]SURFHV]HVWDïÈWUHQGHPOLQLRZ\PNRUHNWÈZ\UD]XZROQHJRRUD]NRUHNWÈSDUDPHWUX SU]\WUHQG]LHZMHGQ\PW\ONRRNUHVLHȞ v(m)t y(m)t hm thmuthm tuthm v v v y
JG]LH ¯ ® t N N W GOD W GOD t u 0QRĝÈFSUDZRVWURQQLHSRZ\ĝV]HUöZQDQLHSU]H]Ɨ(L)JG]LHȆL ILȆ L Ȇ LSȆS a ƗsV 6R]QDF]DMÈPDFLHU]HSDUDPHWUöZRZ\PLDUDFK0[0RWU]\PXMHP\SRU6DLNNRQHQ /đWNHSRKO7UHQNOHU v(m)tȆL y(m)tȆLhmȆLthmȆLuth m ȆLtuthmȆL =DïöĝP\ĝHU]ÈGVNRLQWHJURZDQLD]PLHQQ\FKy(m)tZ\QRVLR, R D(0, M):öZF]DVGODPRGHOX 9$5v(m)tȆL ȟ(m)tJG]LHȟ(m)t >ȟ t...ȟMt@MHVWZHNWRUHPELDïRV]XPRZ\FKVNïDGQLNöZORVRZ\FK RZ\PLDUDFK[0LVWQLHMHSRVWDÊ9(T&0SRU-RKDQVHQ:HOIH JG]LH BļPDFLHU]ZHNWRUöZNRLQWHJUXMÈF\FKRZ\PLDUDFK0[5 AļPDFLHU]ZDJGODSRV]F]HJöOQ\FKUHODFMLNRLQWHJUXMÈF\FKRZ\PLDUDFK0[5 $QDORJLF]QLHUHSUH]HQWDFMÚ9$5GODy(m)t PRĝQD]DSLVDÊQDVWÚSXMÈFR 'ZDSLHUZV]HVNïDGQLNLGHWHUPLQLVW\F]QHZ\VWÚSXMÈFHSRSUDZHMVWURQLHUöZQDQLDUöZQD-MÈVLÚRGSRZLHGQLR JG]LH
¦
¦
S s s S s s I sȆ ī I Ȍ + v y7U]HFLVNïDGQLNPRĝQDSU]HNV]WDïFLÊQDVWÚSXMÈFR 'RGDMÈFLRGHMPXMÈFNROHMQRVNïDGQLNL , RVWDWHF]QLHPRĝQD]DSLVDÊ :\NRQDQLHSU]HNV]WDïFHñDQDORJLF]Q\FKGRSRZ\ĝV]\FKSR]ZDODSU]HGVWDZLÊRVWDWQLVNïDG-QLNZSRVWDFL 3RSRGVWDZLHQLXZ]RUöZļGRRWU]\PXMHP\UHSUH]HQWDFMÚ9(T&0GODPRGHOX]HVWDïÈ WUHQGHPOLQLRZ\PNRUHNWÈZ\UD]XZROQHJRRUD]NRUHNWÈSDUDPHWUXSU]\]PLHQQHMF]DVRZHMSRU SURVWV]\SU]\SDGHNUR]ZDĝDQ\SU]H]6DLNNRQHQD/đWNHSRKOD7UHQNOHUD dla t = S + 1, S + 2 JG]LH
=GHILQLRZDQLHPDFLHU]\ RUD] JG]LHf1(m)MHVWGRZROQ\PZHNWRUHP[0SR]ZDOD]DSLVDÊZQDVWÚSXMÈFHMSRVWDFL JG]LH ļZHNWRU ]PLHQQ\FK VWRFKDVW\F]Q\FK LGHWHUPLQLVW\F]Q\FK RZ\PLD-UDFK[11 0= » » » ¼ º « « « ¬ ª G B B ļPDFLHU]ZHNWRUöZNRLQWHJUXMÈF\FKRZ\PLDUDFK1[5 G ļPDFLHU]SDUDPHWUöZ]ZLÈ]DQ\FK]H]PLHQQ\PLGHWHUPLQLVW\F]Q\PLZUHODFMDFKNRLQWH-JUXMÈF\FKRZ\PLDUDFK=[5 s F ļPDFLHU]HSDUDPHWUöZ]ZLÈ]DQ\FK]H]PLHQQ\PLGHWHUPLQLVW\F]Q\PLSR]DSU]HVWU]HQLÈ NRLQWHJUXMÈFÈRZ\PLDUDFK=[0 n = 1,…, N
=DïöĝP\QDVWÚSQLHĝHZPRGHOXZ\VWÚSXMHL&NRUHNWZ\UD]XZROQHJRRUD]L' NRUHNWSDUDPH-WUXSU]\]PLHQQHMF]DVRZHM:öZF]DV'*3PDQDVWÚSXMÈFÈSRVWDÊ JG]LH T t W t t t W u u u » » » » » ¼ º « « « « « ¬ ª u T t W t t t W u u u » » » » » ¼ º « « « « « ¬ ª u
»
»
»
»
»
»
¼
º
«
«
«
«
«
«
¬
ª
m W mh
h
H
»
»
»
»
»
»
¼
º
«
«
«
«
«
«
¬
ª
m W mh
h
H
3RDQDORJLF]Q\FKSU]HNV]WDïFHQLDFKMDNZSU]\SDGNXMHGQHM]PLDQ\VWUXNWXUDOQHMRWU]\PXMH-P\QDVWÚSXMÈF\PRGHO9(T&0 dla t = S + 1, S + 2, JG]LH 3R]RVWDïHSDUDPHWU\VLÚQLH]PLHQLDMÈ = SRZ\ĝV]\FK Z\SURZDG]Hñ Z\QLND ĝH Z\VWÚSRZDQLH ]PLHQQ\FK GHWHUPLQLVW\F]Q\FK Z'*3LPSOLNXMHZ\VWÚSRZDQLHW\FK]PLHQQ\FKUöZQLHĝZSU]HVWU]HQLNRLQWHJUXMÈFHM3RQDGWRMH-ĂOLNRUHNWDZ\UD]XZROQHJRWUHQGXZ\VWÈSLïDZ'*3ZRNUHVLHȞWRZSï\ZDRQDQDZïDĂFLZRĂFL VNïDGQLNöZORVRZ\FKZPRGHOX9(T&0]MHGQRRNUHVRZ\PRSöěQLHQLHP]HZ]JOÚGXQDRSöěQLH-QLHZZHNWRUDFKNRLQWHJUXMÈF\FK
0RGHOKDQGOX]DJUDQLF]QHJR
3U]HGVWDZLRQ\ PRGHO ]DVWRVRZDQR GR DQDOL]\ KDQGOX ]DJUDQLF]QHJR GOD 3ROVNL 'RPLQXMÈ GZD PRGHOHKDQGOX]DJUDQLF]QHJRQLHGRVNRQDï\FKLGRVNRQDï\FKVXEVW\WXWöZSRU*ROGVWHLQ.KDQ 0RGHOQLHGRVNRQDï\FKVXEVW\WXWöZ]DNïDGDĝHDQLLPSRUWDQLHNVSRUWQLHPRJÈE\ÊGRVNR- QDï\PLVXEVW\WXWDPLGöEUNUDMRZ\FK:PRGHOXGRVNRQDï\FKVXEVW\WXWöZGDQ\NUDMPRĝHE\ÊW\O-NRHNVSRUWHUHPDOERW\ONRLPSRUWHUHPGDQHJRGREUDDU\QHNMHVWZ\SHïQLRQ\FDïNRZLFLHGREUDPL NUDMRZ\PLOXEGREUDPL]DJUDQLF]Q\PLSRGZDUXQNLHPVWDï\FKNRV]WöZSURGXNFMLW\FKGöEUSRU *ROGVWHLQ.KDQ:U]HF]\ZLVWRĂFLGRVNRQDïDVXEVW\WXFMDMHVWRJUDQLF]RQDD]DWHPV]HUV]H
]DVWRVRZDQLHPDSLHUZV]\]PRGHOL:WDNLPSU]\SDGNXNUDMHVÈ]DUöZQRHNVSRUWHUDPLMDNLLP- SRUWHUDPLWRZDUöZRUD]Z\VWÚSXMHEUDNGRVNRQDïHMVXEVW\WXF\MQRĂFLGöEULPSRUWRZDQ\FKHNVSRU-WRZDQ\FK LGöEU Z\VWÚSXMÈF\FK QD U\QNX NUDMRZ\P 2EURW\ KDQGOX SRZLQQ\ E\Ê PRGHORZDQH ZREUÚELHRGSRZLHGQLFKJUXSWRZDUöZQSZHGïXJNODV\ILNDFML6,7&
(NVSRUW Z\UREöZ ]JUXS\ ` ]GDQHJR NUDMX QD NWöU\ UHV]WD ĂZLDWD ]JïDV]D SRS\W ]DOHĝ\ RG SRS\WX ]DJUDQLF\ QD Z\URE\ ]JUXS\ ` DWDNĝH RG UHODFML FHQ DUW\NXïöZ ]JUXS\ ` HNVSRUWRZD- Q\FKSU]H]GDQ\NUDMGRFHQRGSRZLHGQLFKDUW\NXïöZ]NUDMöZNRQNXUHQWöZOXEFHQZHZQÚWU]-Q\FKNUDMöZRGELRUFöZ$JUHJXMÈFNUDMHRGELRUFöZLNRQNXUHQWöZFHQ\WHPRĝQD]DVWÈSLÊFHQDPL ĂZLDWRZ\PL-HĂOL]DïRĝ\P\ĝHXG]LDïJOREDOQHJRSRS\WX]DJUDQLF\NLHURZDQHJRGRGDQHJRNUDMX MHVWVWDï\DHODVW\F]QRĂFLGRFKRGRZHSRS\WXQDHNVSRUW]DQDOL]RZDQHJRNUDMXL]NUDMöZWU]HFLH-JRĂZLDWDVÈWDNLHVDPHGODUHV]W\ĂZLDWDWRIXQNFMÚSRS\WXQDHNVSRUWPRĝQD]DSLVDÊQDVWÚSXMÈFR SRU:HOIH:HOIH t kt kt kt e kt PEW EUR PE MW f E JG]LH :`iļHNVSRUWZ\UREöZJUXS\`GDQHJRNUDMX BL`iļLPSRUWĂZLDWRZ\Z`WHMJUXSLHWRZDURZHM E:`iļGHIODWRUHNVSRUWXZZDOXFLHGDQHJRNUDMXGODJUXS\WRZDUöZ`, E:L`iļGHIODWRUFHQĂZLDWRZ\FKZ\UDĝRQ\FKZHXURGODJUXS\WRZDUöZ`, :JGiļNXUVHXURZZDOXFLHGDQHJRNUDMX 2JUDQLF]RQDGRVWÚSQRĂÊGDQ\FKGRW\F]ÈF\FKLPSRUWXZJUXSDFKWRZDURZ\FKRUD]]DïRĝHQLH ĝHVWUXNWXUDLPSRUWXMHVWVWDïDZF]DVLHSR]ZDODMÈQD]DVWÈSLHQLHLPSRUWXZGDQHMJUXSLHWRZDUR-ZHMSU]H]LPSRUWRJöïHPOXEDSURNV\PXMÈFÈJRZLHONRĂFLÈļHNVSRUWFDïHJRĂZLDWD:HiSRU:HOIH :HOIH t t t t e t PEW EUR PE ES f E 3RS\WQDLPSRUWZ\UREöZ]JUXS\`]JïDV]DQ\SU]H]GDQ\NUDM]DOHĝ\RGSRS\WXZHZQÚWU]QHJR GDQHJRNUDMXQDZ\URE\]JUXS\`NWöU\PRĝHE\ÊZ\UDĝRQ\SU]H]RGSRZLHGQLPLHUQLNDNW\ZQR- ĂFLJRVSRGDUF]HMDWDNĝHRGUHODFMLFHQLPSRUWXGRFHQNUDMRZ\FKGODJUXS\WRZDUöZ`3U]\]DïR-ĝHQLXVWDïHMLPSRUWRFKïRQQRĂFLPDP\SRU:HOIH:HOIH kt kt kt m kt PAKT PM AKT f M JG]LH B`iļLPSRUWGDQHJRNUDMXZJUXSLHWRZDUöZ`, 6@I`iļPLHUQLNDNW\ZQRĂFLJRVSRGDUF]HMNUDMXLPSRUWXMÈFHJRGODJUXS\WRZDUöZ`, EB`iļGHIODWRULPSRUWXZZDOXFLHGDQHJRNUDMXZJUXSLHWRZDURZHM`, E6@I`iļGHIODWRUGODGDQHMDNW\ZQRĂFLJRVSRGDUF]HMZJUXSLHWRZDURZHM`
3U]\EOLĝHQLHP NUDMRZHJR PLHUQLND DNW\ZQRĂFL JRVSRGDUF]HM MHVW SURGXNFMD VSU]HGDQD SU]HP\VïXHFiE6@IiPRĝQDZNRQVHNZHQFML]DVWÈSLÊZVNDěQLNLHPFHQSURGXNFMLVSU]HGDQHM SU]HP\VïX EE>i %H] SRG]LDïX QD JUXS\ WRZDURZH LSR RGSRZLHGQLFK XSURV]F]HQLDFK RWU]\-PXMHP\
t t t m t PPI PM SQ f M 5R]ZDĝP\ SU]\NïDG NUDMX NWöU\ XF]HVWQLF]\ ZZ\PLDQLH KDQGORZHM JïöZQLH ]8QLÈ (XUR-SHMVNÈ :WDNLP SU]\SDGNX SR]LRP FHQ ĂZLDWRZ\FK PRĝH E\Ê SU]\EOLĝRQ\ SU]H] ZVNDěQLN 33, Z8QLL(XURSHMVNLHM&HQ\UHODW\ZQH]DUöZQRZUöZQDQLXHNVSRUWXMDNLUöZQDQLXLPSRUWXPRĝ-QDSU]HGVWDZLÊMDNRUHODFMÚLQGHNVX33,Z8QLL(XURSHMVNLHMEE>iZ\UDĝRQHJRZZDOXFLHGDQHJR NUDMXGRLQGHNVX33,ZDQDOL]RZDQ\PNUDMX:öZF]DV t t t t e t PPI PPI EUR ES f E t t t t m t PPI PPI EUR SQ f M : SU]\SDGNX 3ROVNL ZODWDFK ļ QDVWÈSLïR ZLHOH ]PLDQ ZVWUXNWXU]H KDQGOX ]DJUD-QLF]QHJR PLQ OLEHUDOL]DFMD KDQGOX ]QLHVLHQLH FHï QD ZLÚNV]RĂÊ LPSRUWRZDQ\FK LHNVSRUWRZD-Q\FK WRZDUöZ Z]URVW ]QDF]HQLD Z\PLDQ\ PLÚG]\QDURGRZHM Z]URVW REURWöZ Z\PLDQ\ ZH-ZQÈWU]JDïÚ]LRZHM SRU 0LVDOD 0URF]HN 5XEDV]HN :UR]ZDĝDQ\P RNUHVLH QDVWÈSLï SRQDGWU]\NURWQ\Z]URVWSROVNLHJRHNVSRUWXFRZLÈ]DïRVLÚ]SU]\VWÈSLHQLHP3ROVNLGR8QLL(XUR-SHMVNLHMRUD]]Z\UDěQÈSRSUDZÈMDNRĂFLWRZDUöZSURGXNRZDQ\FKZ3ROVFH=SRZRGXWUXGQRĂFL ]H]QDOH]LHQLHP]PLHQQHMNWöUDPLHU]\MDNRĂÊZSURZDG]RQRGRPRGHOX]PLHQQÈEÚGÈFÈUöĝQL-FÈSRPLÚG]\Z\GDMQRĂFLÈSUDF\Z8QLL(XURSHMVNLHMO:JiDZ\GDMQRĂFLÈSUDF\Z3ROVFHOEDAi SRUZ\NUHV:öZF]DV e t feestrertzt t t t m t f sq rer z m JG]LH OQ t t t t PPI PPI EUR
rer zt OQZEUtOQZPOLt PDïHOLWHU\R]QDF]DMÈORJDU\WP\ :DQDOL]RZDQ\PRNUHVLHQDVWÈSLïV]\EV]\Z]URVWZ\GDMQRĂFLSUDF\Z3ROVFHQLĝZ8QLL(X- URSHMVNLHM3RQDGWR3ROVNDGRĂZLDGF]\ïDV]\ENLHMHZROXFMLV\VWHPXNXUVRZHJRRGV]W\ZQHJRNXU-VX]ïRWHJRZVWRVXQNXGRZDOXWĂZLDWRZ\FKGRNXUVXFDïNRZLFLHSï\QQHJR3ï\QQ\V\VWHPNXUVX ZDOXWRZHJRZSURZDG]RQRNZLHWQLDUD]DWHPODWDļREHMPXMÈGZDUöĝQHUHĝL-P\NXUVRZHcrawling bendRUD]RNUHVSï\QQHJRNXUVXZDOXWRZHJRSRU:HOIH.DUS.ÚEïRZVNL 1DOHĝ\]DïRĝ\ÊĝHHODVW\F]QRĂFLSRS\WRZH]DUöZQRZUöZQDQLXHNVSRUWXMDNLLPSRUWXVÈGR-GDWQLHfefm! :Sï\Z]PLHQQHMFKDUDNWHU\]XMÈFHMVWRVXQHNFHQ]DJUDQLF]Q\FKGRFHQNUDMR-Z\FKMHVWGRGDWQLZUöZQDQLXHNVSRUWXRUD]XMHPQ\ZUöZQDQLXLPSRUWXfe!fm :]URVW FHQ]DJUDQLF\ZVWRVXQNXGRFHQNUDMRZ\FKSRZRGXMH]DWHPZLÚNV]ÈNRQNXUHQF\MQRĂÊNUDMRZHJR HNVSRUWXRUD]PQLHMV]ÈNRQNXUHQF\MQRĂÊLPSRUWX]]DJUDQLF\=NROHLZSï\Z]PLHQQHMFKDUDNWH-U\]XMÈFHMUöĝQLFÚSRPLÚG]\Z\GDMQRĂFLÈSUDF\Z8QLL(XURSHMVNLHMDZ\GDMQRĂFLÈSUDF\Z3ROVFH MHVWXMHPQ\ZUöZQDQLXHNVSRUWXRUD]GRGDWQLZUöZQDQLXLPSRUWXfefm!
0RGHOKDQGOX]DJUDQLF]QHJRGOD3ROVNL]EXGRZDQRZ\NRU]\VWXMÈFUöZQDQLDļ6\VWHP ]PLHQQ\FKMHVW]DWHPQDVWÚSXMÈF\mt, et, sqt, est, rert, zt ,SRUZ\NUHV\ļ=HZ]JOÚGXQDQLHVWD-FMRQDUQRĂÊSRZ\ĝV]\FK]PLHQQ\FKZ\NRU]\VWDQRPRGHORUD]]DïRĝRQRZ\VWÚSRZDQLHGZöFK ]PLDQVWUXNWXUDOQ\FKZ,,NZDUWDOHU]PLDQDUHĝLPXNXUVRZHJRRUD]Z,,NZDUWDOHU SU]\VWÈSLHQLH3ROVNLGR8QLL(XURSHMVNLHM'RPRGHOXZSURZDG]RQR]DWHPGZLH]PLHQQH]HUR MHG\QNRZH ¯ ® t W GOD W GOD t u ļFKDUDNWHU\]XMÈFÈ]PLDQÚUHĝLPXNXUVRZHJRRUD] ¯ ® t W GOD W GOD t u ļFKDUDNWHU\]XMÈFÈSU]\VWÈSLHQLH3ROVNLGR8QLL(XURSHMVNLHM =DïRĝRQRĝHZSï\Z]PLDQVWUXNWXUDOQ\FKQDHNVSRUWLLPSRUWSRZLQLHQE\ÊGRGDWQL:\UD] ZROQ\ RUD] MHJR NRUHNW\ FKDUDNWHU\]XMÈFH ]DEXU]HQLD ]QDMGXMÈ VLÚ ZSU]HVWU]HQL NRLQWHJUXMÈFHM 5R]ZDĝRQRQDVWÚSXMÈF\PRGHO9(T&0 (m)t S s s s t S s s s (m)t T t r (m)t (m)t v B g u G A ǻv ī u F ȟ ǻv
¦
¦
' @ > dla t = S + 1, S + 2 JG]LH T t t t u u » ¼ º « ¬ ª u :\NUHV (NVSRUW3ROVNL(FHQ\VWDïH]U 2,8 3,0 3,2 3,4 3,6 3,8 4,0 4,2 4,4 4,6 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 -0,10 -0,05 0 0,05 0,10 0,15 2007 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006:\NUHV ,PSRUW3ROVNL0FHQ\VWDïH]U :\NUHV (NVSRUWĂZLDWRZ\(6FHQ\VWDïH]U 3,0 3,2 3,4 3,6 3,8 4,0 4,2 4,4 4,6 4,8 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 1995 1996 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 -0,15 -0,10 -0,05 0 0,05 0,10 0,15 0,20 0,25 6,8 7,0 7,2 7,4 7,6 7,8 8,0 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 -0,08 -0,06 -0,04 -0,02 0 0,02 0,04 0,06 0,08 0,10 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
:\NUHV 3URGXNFMDVSU]HGDQDSU]HP\VïX64FHQ\VWDïHU :\NUHV &HQ\UHODW\ZQH5(5SRGVWDZDU 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 3,8 4,0 4,2 4,4 4,6 4,8 5,0 5,2 5,4 5,6 -0,15 -0,10 -0,05 0 0,05 0,10 0,15 -0,20 -0,15 -0,10 -0,05 0 0,05 0,10 0,15 0,20 -0,10 -0,08 -0,06 -0,04 -0,02 0 0,02 0,04 0,06 0,08 0,10 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
=HZ]JOÚGXQDPDïÈSUöEÚSU]\MÚWRĝHOLF]EDRSöěQLHñZPRGHOX9$5Z\QRVL6 (VW\-PDFMÚ SDUDPHWUöZ PRGHOX SU]HSURZDG]RQR QD SRGVWDZLH REVHUZDFML NZDUWDOQ\FK ]RNUHVX ,NZDUWDïUļ,NZDUWDïUZ\NRU]\VWXMÈFPHWRGÚ-RKDQVHQD
/LF]EÚZVSöOQ\FKWUHQGöZVWRFKDVW\F]Q\FKZEDGDQ\PV\VWHPLH]PLHQQ\FK]EDGDQR]DSR- PRFÈWHVWXĂODGXSRUWDEHOD:SURZDG]HQLH]PLDQVWUXNWXUDOQ\FKGRPRGHOXZ\PDJDïRSU]H- SURZDG]HQLDV\PXODFMLZDUWRĂFLNU\W\F]Q\FKWHVWXĂODGX:SLHUZV]\PNURNX]EDGDQRU]ÈGNR-LQWHJUDFMLGODV\VWHPX]PLHQQ\FKmt, et, sqt, est, rert, zt, u11t, u12t, const,DQDVWÚSQLHSRZWöU]RQRWHVW ĂODGX]XZ]JOÚGQLHQLHP]PLHQQ\FKHJ]RJHQLF]Q\FK:SURZDG]HQLH]PLHQQ\FKHJ]RJHQLF]Q\FK QLHVSRZRGRZDïR]PLDQ\Z\QLNöZWHVWXU]ÚGX5H]XOWDW\WHVWXĂODGXZVND]XMÈQDLVWQLHQLHGZöFK :\NUHV 5öĝQLFDPLÚG]\Z\GDMQRĂFLÈSUDF\Z8(LZ3ROVFH= 7DEHOD :\QLNLHPSLU\F]QHWHVWXĂODGX
R JUDQLF]Q\SR]LRPLVWRWQRĂFL:DUWRĂÊVWDW\VW\NL :DUWRĂÊNU\W\F]QD
1,1 1,2 1,3 1,4 1,5 1,6 1,7 -0,15 -0,10 -0,05 0 0,05 0,10 0,15 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
UHODFMLNRLQWHJUXMÈF\FKSRUWDEHODFRSR]ZDODZ\]QDF]\ÊGïXJRRNUHVRZHUöZQDQLDGODHNVSRU-WXLLPSRUWX3RQDGWRQDSRGVWDZLHDQDOL]\SLHUZLDVWNöZPDFLHU]\VSU]ÚĝRQHMcompanion matrix PRĝQD]DïRĝ\ÊĝHZUR]ZDĝDQ\PPRGHOXQLHPDSLHUZLDVWNöZZ\EXFKRZ\FK
=PLDQD UHĝLPX NXUVRZHJR UHSUH]HQWRZDQD SU]H] ]PLHQQÈ LVWRWQLH RGG]LDïXMH W\ONR QD HNV-SRUWQDWRPLDVWSU]\VWÈSLHQLH3ROVNLGR8QLL(XURSHMVNLHMUHSUH]HQWRZDQHSU]H]]PLHQQÈV]WXF]QÈ u12tZSï\ZDLVWRWQLH]DUöZQRQDHNVSRUWMDNLQDLPSRUW,PSRUWRND]DïVLÚQLHZUDĝOLZ\QD]PLDQÚ UHODFMLLQGHNVXFHQSURGXFHQWDZVWUHILHHXURGRLQGHNVXNUDMRZ\FKFHQSURGXFHQWDrert 2VWDWHF]-QLHRWU]\PXMHP\QDVWÚSXMÈFHGïXJRRNUHVRZHUöZQDQLDHNVSRUWXLLPSRUWXGOD3ROVNL et feestrertztututconst mt fmsqtztutconst 6SURZDG]HQLHPRGHOXEH]UHVWU\NFMLSRVWDFL e t e t e t e t e t e t e t e t m es sq rer z u u e E - - - mt met mest msqt mrert mzt mut mut m E - - - GRPRGHOXRUöZQDQLDFKļSROHJDQDQDïRĝHQLXQDVWÚSXMÈF\FKUHVWU\NFMLZ\ïÈF]DMÈF\FKQD SDUDPHWU\SRV]F]HJöOQ\FKUöZQDñ ZUöZQDQLXHNVSRUWX -e -e ZUöZQDQLXLPSRUWX m m m m - - -- 3RQDGWRWHVWRZDQR]DVDGQRĂÊZSURZDG]HQLDMHGQRVWNRZ\FKHODVW\F]QRĂFLSU]\est ZUöZQD-QLXHNVSRUWXRUD]SU]\sqtZUöZQDQLXLPSRUWX e -m - =DVDGQRĂÊQDNïDGDQLDOLQLRZ\FKUHVWU\NFMLQDPDFLHU]7PRĝQDWHVWRZDÊZ\NRU]\VWXMÈFWHVW
/5likelihood ratioNWöUHJRVSUDZG]LDQPDZW\PSU]\SDGNXDV\PSWRW\F]Q\UR]NïDGr
SRU-R- KDQVHQ:UR]ZDĝDQ\PPRGHOXZ\QLNLWHVWX/5ZVND]XMÈQDLVWRWQRĂÊZSURZDG]RQ\FKUH-VWU\NFMLļSRUWDEHOD
'R ]EDGDQLD ]DVDGQRĂFL UHVWU\NFML VïDEHM HJ]RJHQLF]QRĂFL QDOHĝDïR UöZQLHĝ Z\NRU]\VWDÊ WHVW /5NWöUHJRVSUDZG]LDQPDDV\PSWRW\F]Q\UR]NïDGr :\QLNLWHVWXZVND]XMÈQDVïDEÈHJ]RJHQLF]-QRĂÊ]PLHQQ\FKest, sqt, ztSRUWDEHOD 5öZQDQLDGïXJRRNUHVRZH]XZ]JOÚGQLHQLHP]PLHQQ\FKVïDERHJ]RJHQLF]Q\FKLUHVWU\NFMLGOD PDFLHU]\NRLQWHJUXMÈFHM7SU]HGVWDZLDWDEHOD:DUWRĂÊWHVWX/5VïXĝÈFHJRGREDGDQLDLVWRWQRĂFL ZV]\VWNLFKZSURZDG]RQ\FKUHVWU\NFMLGODPDFLHU]\7i AZVND]XMHQDSRSUDZQÈVSHF\ILNDFMÚ UöZQDñSRUWDEHOD2WU]\PDQRMHGQRVWNRZHHODVW\F]QRĂFLHNVSRUWXZ]JOÚGHPHNVSRUWXĂZLD-WRZHJR RUD] LPSRUWX Z]JOÚGHP SURGXNFML VSU]HGDQHM SU]HP\VïX :UöZQDQLX LPSRUWX HODVW\F]-QRĂÊZ]JOÚGHP]PLHQQHMFKDUDNWHU\]XMÈFHMUöĝQLFÚPLÚG]\Z\GDMQRĂFLÈSUDF\Z8QLLLZ3ROVFH Z\QRVL (ODVW\F]QRĂÊ HNVSRUWX Z]JOÚGHP ]PLHQQHM FKDUDNWHU\]XMÈFHM VWRVXQHN FHQ Z\QRVL QDWRPLDVW Z]JOÚGHP ]PLHQQHM FKDUDNWHU\]XMÈFHM ]UöĝQLFRZDQLH Z\GDMQRĂFL SUDF\ PLÚG]\
8QLÈ D3ROVNÈ .LHUXQNL RGG]LDï\ZDQLD ]PLHQQ\FK REMDĂQLDMÈF\FK QD HNVSRUW LLPSRUW VÈ ]JRGQH ]]DïRĝHQLDPL SRU WDEHOD =PLDQD UHĝLPX NXUVRZHJR Z\ZRïXMH NRUHNWÚ Z\UD]X ZRO-QHJRRZGïXJRRNUHVRZ\PUöZQDQLXHNVSRUWXDSU]\VWÈSLHQLH3ROVNLGR8QLL(XURSHMVNLHM ļRZUöZQDQLXHNVSRUWXLZUöZQDQLXLPSRUWXSRUWDEHOD:PDFLHU]\ZDJ]D-UöZQRHNVSRUWMDNLLPSRUWGRVWRVRZXMÈVLÚLVWRWQLHGRRGSRZLHGQLFKZHNWRUöZNRLQWHJUXMÈF\FK 3RQDGWRRWU]\PDQRZHNWRU\NRLQWHJUDFML&,SRUZ\NUHV\ļ
2VWDWHF]Q\P VSUDZG]LDQHP ZïDĂFLZRĂFL VWDW\VW\F]Q\FK PRGHOX MHVW DQDOL]D VNïDGQLNöZ OR-VRZ\FK :\NRU]\VWDQR WHVW\ ZLHORZ\PLDURZH RUD] MHGQRZ\PLDURZH GOD SRV]F]HJöOQ\FK UöZ-QDñ NWöU\FK VSUDZG]LDQ PD DV\PSWRW\F]Q\ UR]NïDGr SRU WDEHOD $XWRNRUHODFMÚ WHVWRZDQR
]D SRPRFÈ NODV\F]QHJR WHVWX /0 PQRĝQLND /DJUDQJHijD NWöU\ VïXĝ\ GR EDGDQLD DXWRNRUHODFML , ,, ,,, ,9 U]ÚGX :UR]ZDĝDQ\P PRGHOX QLH PD SRGVWDZ GR RGU]XFHQLD KLSRWH]\ REUDNX
DXWR-7DEHOD :\QLNLDQDOL]\NRLQWHJUDF\MQHMZQDZLDVDFKVWDW\VW\NLW6WXGHQWD 5öZQDQLD GïXJRRNUHVRZH ]XZ]JOÚGQLHQLHP UHVWU\NFMLGOD7 t t t t t t es rer z u u e *!(%,&)!*,+'!,+(&'!*&(&+!'-+ t t t t sq z u m ,!&+%)!%*,'%!(,, :DUWRĂÊVWDW\VW\NL WHVWX/5]DVDGQRĂFL ZSURZDG]HQLD UHVWU\NFMLGOD7 /5 JUDQLF]Q\SR]LRPLVWRWQRĂFL :DUWRĂÊVWDW\VW\NL WHVWX/5]DVDGQRĂFL ZSURZDG]HQLD UHVWU\NFMLGODA Hest, sqt, ztļVïDERHJ]RJHQLF]QH /5 JUDQLF]Q\SR]LRPLVWRWQRĂFL 5öZQDQLD GïXJRRNUHVRZH ]XZ]JOÚGQLHQLHP UHVWU\NFMLGOD PDFLHU]\$i7 t t t t t t es rer z u u e +!)'&&'!)'%(!,'*&&!)-,&*!()& t t t t sq z u m ,!')()!*&''%!&'% :DUWRĂÊVWDW\VW\NL WHVWX/5]DVDGQRĂFL ZSURZDG]HQLD UHVWU\NFMLGOD$i7 /5 JUDQLF]Q\SR]LRPLVWRWQRĂFL
NRUHODFML 5H]XOWDW\ ZLHORZ\PLDURZ\FK WHVWöZ /0 VïXĝÈF\FK GR EDGDQLD Z\VWÚSRZDQLD HIHN-WX $5&+ , ,, L,,, U]ÚGX ZVND]XMÈ QD MHJR EUDN QDWRPLDVW PRĝQD SU]\SXV]F]DÊ ĝH Z\VWÚSX-MH HIHNW $5&+ ,9 U]ÚGX SRU WDEHOD %DGDQLD V\PXODF\MQH HNRQRPHWU\NöZ GRZRG]È MHGQDN ĝH RV]DFRZDQLD SDUDPHWUöZ ZPRGHODFK 9$5 ]UHVWU\NFMÈ NRLQWHJUDFML VÈ RGSRUQH QD Z\VWÚSR-ZDQLH XPLDUNRZDQHJR HIHNWX $5&+ ZVNïDGQLNDFK ORVRZ\FK SRU -XVHOLXV $QDOL]D MHG-QRZ\PLDURZD ZVND]XMH ĝH VNïDGQLNL ORVRZH SRV]F]HJöOQ\FK UöZQDñ QLH VÈ REFLÈĝRQH HIHNWHP $5&+ 'R ]EDGDQLD QRUPDOQRĂFL UR]NïDGX UHV]W Z\NRU]\VWDQR WHVW 'RRUQLND+DQVHQD :UR]-ZDĝDQ\P PRGHOX Z\QLNL ZLHORZ\PLDURZ\FK RUD] MHGQRZ\PLDURZ\FK WHVWöZ 'RRUQLND+DQ-VHQD ZVND]XMÈ QD EUDN SRGVWDZ GR RGU]XFHQLD KLSRWH]\ ]DNïDGDMÈFHM QRUPDOQ\ UR]NïDG UHV]W 3RZ\ĝV]H Z\QLNL ĂZLDGF]È RGREU\FK ZïDĂFLZRĂFLDFK VWDW\VW\F]Q\FK UR]ZDĝDQHJR PRGHOX
:\NUHV 3LHUZV]DUHODFMDNRLQWHJUXMÈFDUöZQDQLHHNVSRUWX -0,20 -0,15 -0,10 -0,05 0,0 0,05 0,10 0,15 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 b* *1(v(t)) :\NUHV 'UXJDUHODFMDNRLQWHJUXMÈFDUöZQDQLHLPSRUWX -0,10 -0,08 -0,06 -0,04 -0,02 0 0,02 0,04 0,06 0,08 0,10 b2(v(t)) 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 * *
3RGVXPRZDQLH
: DUW\NXOH ]DSUH]HQWRZDQD ]RVWDïD SURFHGXUD Z\SURZDG]HQLD ]'*3 XRJöOQLRQHJR PRGHOX 9(T&0NWöU\]DNïDGDZLHOHSU]HïÈF]HñZ\UD]XZROQHJRLSDUDPHWUXSU]\WUHQG]LH8GRZRGQLR-QR ĝH ]PLHQQH GHWHUPLQLVW\F]QH Z\VWÚSXMÈ ZSU]HVWU]HQL NRLQWHJUXMÈFHM D]DWHP ZSï\ZDMÈ QD ZïDĂFLZRĂFLVNïDGQLNöZORVRZ\FKPRGHOX]MHGQRRNUHVRZ\PRSöěQLHQLHP
: EDGDQLX HPSLU\F]Q\P Z\NRU]\VWDQR Z\SURZDG]RQ\ PRGHO 9(T&0 ]Z\UD]HP ZROQ\P RUD]MHJRNRUHNWDPLNWöUHRG]ZLHUFLHGODMÈ]DEXU]HQLDVWUXNWXU\2WU]\PDQRZHNWRU\NRLQWHJUDFML UHSUH]HQWXMÈFHUöZQDQLDGïXJRRNUHVRZHHNVSRUWXLLPSRUWX1DSRGVWDZLHRWU]\PDQ\FKZ\QLNöZ
7DEHOD
$QDOL]DVNïDGQLNöZORVRZ\FK
7HVW\ZLHORZ\PLDURZH :DUWRĂÊVWDW\VW\NLWHVWX *UDQLF]Q\SR]LRPLVWRWQRĂFL
6ïXĝÈFHGREDGDQLDDXWRNRUHODFML /0 >@ /0 >@ /0 >@ /0 >@ 7HVWVïXĝÈF\GREDGDQLD QRUPDOQRĂFLUR]NïDGXUHV]W >@ 6ïXĝÈFHGREDGDQLDHIHNWX$5&+ /0 >@ /0 >@ /0 >@ /0 >@ 7HVW\GODSRV]F]HJöOQ\FKUöZQDñ 6ïXĝÈFHGREDGDQLDHIHNWX$5&+ e >@ m >@ rer >@ 6ïXĝÈFHGREDGDQLDQRUPDOQRĂFLUR]NïDGXUHV]W e >@ m >@ rer >@
PRĝQDZQLRVNRZDÊĝHZGïXJLPRNUHVLHHNVSRUW3ROVNLMHVWGHWHUPLQRZDQ\SU]H]HNVSRUWĂZLDWR-Z\]ZLÚNV]DVLÚZUD]]HZ]URVWHPFHQ]DJUDQLF\ZVWRVXQNXGRFHQNUDMRZ\FKRUD]VSDGDJG\ URĂQLHUöĝQLFDSRPLÚG]\Z\GDMQRĂFLÈSUDF\Z8QLL(XURSHMVNLHMLZ3ROVFH3RQDGWRZUöZQDQLX HNVSRUWXXGRZRGQLRQRLVWRWQ\ZSï\ZGZöFKNRUHNWZ\UD]XZROQHJRZPRPHQFLH]PLDQ\UHĝLPX NXUVRZHJRRUD]SU]\VWÈSLHQLD3ROVNLGR8QLL(XURSHMVNLHM'HWHUPLQDQWDPLLPSRUWXVÈQDWRPLDVW SURGXNFMDVSU]HGDQDSU]HP\VïXZ3ROVFHRUD]UöĝQLFDPLÚG]\Z\GDMQRĂFLÈSUDF\Z8QLL(XURSHM-VNLHMLZ3ROVFH2ELHZLHONRĂFLPDMÈGRGDWQLZSï\ZQD]PLHQQÈREMDĂQLDMÈFÈ:DĝQHGODLPSRUWX RND]DïRVLÚWDNĝHSU]\VWÈSLHQLH3ROVNLGR8QLL(XURSHMVNLHM2WU]\PDQR]DWHPZ\QLNLLQWHUSUHWR-ZDOQHHNRQRPLF]QLHLDQDOL]RZDQ\PRGHOPDGREUHZïDĂFLZRĂFLVWDW\VW\F]QH
%LEOLRJUDğD
'HQQLV - &$76 LQ 5$76 Cointegration Analysis of Time Series 9HUVLRQ (VWLPD (YDVWRQ,OOLQRLV
*ROGVWHLQ0.KDQ06,QFRPHDQGSULFHHIIHFWVLQIRUHLJQWUDGHZ5:-RQHV3%.HQHQ UHGHandbook of International Economics9RO,,(OVHYLHU6FLHQFH3XEOLVKHUV%9
-RKDQVHQ 6 Likelihood-based Inference in Cointegrated Vector Autoregressive Models, 2[IRUG8QLYHUVLW\3UHVV,QF
-RKDQVHQ 6 0RVFRQL 5 1LHOVHQ % &RLQWHJUDWLRQ DQDO\VLV LQ WKH SUHVHQFH RI VWUXFWXUDO EUHDNVLQWKHGHWHUPLQLVWLFWUHQGEconometrics Journal1RVļ
-XVHOLXV . The Cointegrated VAR Model: Econometric Methodology and Macroeconomic Applications2[IRUG8QLYHUVLW\3UHVV,QF
0LVDOD - :VSöïF]HVQH WHRULH Z\PLDQ\ PLÚG]\QDURGRZHM L]DJUDQLF]QHM SROLW\NL HNRQRPLF]QHM:\GDZQLFWZR6*+:DUV]DZD
0ROOH : (NRQRPLND LQWHJUDFML HXURSHMVNLHM WHRULD SUDNW\ND SROLW\ND )XQGDFMD *RVSRGDUF]D 16==6ROLGDUQRĂÊ*GDñVN
0URF]HN : 5XEDV]HN 0 'HWHUPLQDQW\ SROVNLHJR KDQGOX ]DJUDQLF]QHJR 0DWHULDï\ L6WXGLD1%3:DUV]DZD
6DLNNRQHQ3/đWNHSRKO+7UHQNOHU&Break Date Estimation and Cointegration Testing in VAR Processes with Level Shift(&2:RUNLQJ3DSHU(XURSHDQ8QLYHUVLW\,QVWLWXWH 6DLNNRQHQ 3 /đWNHSRKO + 7UHQNOHU & Testing for Cointegrating Rank of a VAR Process
with Level Shift and Trend Break(&2:RUNLQJ3DSHU(XURSHDQ8QLYHUVLW\,QVWLWXWH :HOIH $ UHG *RVSRGDUND 3ROVNL ZRNUHVLH WUDQVIRUPDFML =DVDG\ PRGHORZDQLD HNRQRPHWU\F]QHJR3:(:DUV]DZD
:HOIH $ .DUS 3 .ÚEïRZVNL 3 0HFKDQL]P\ PDNURHNRQRPLF]QH ZJRVSRGDUFH SROVNLHM $QDOL]DHNRQRPHWU\F]QD:\GDZQLFWZR8QLZHUV\WHWXöG]NLHJR
&RLQWHJUDWLRQDQDO\VLVZLWKVWUXFWXUDOEUHDNVPRGHORIIRUHLJQ
WUDGHIRU3RODQG
$EVWUDFW
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