Wkh Vwuxfwxuh ri Ghpdqg iru Khdowk Fduh= Odwhqw

Fodvv yhuvxv Wzr0sduw Prghov�

Sduwkd Ghe

Ghsduwphqw ri Hfrqrplfv

Lqgldqd Xqlyhuvlw| Sxugxh Xqlyhuvlw| Lqgldqdsrolv

Fdydqdxjk Kdoo 849

Lqgldqdsrolv/ LQ 79735/ X1V1D

Hpdlo= sgheClxsxl1hgx

Sudylq N1 Wulyhgl

Ghsduwphqw ri Hfrqrplfv

Lqgldqd Xqlyhuvlw|

Z|olh Kdoo

Eorrplqjwrq/ LQ 7:738/ X1V1D

Hpdlo= wulyhglClqgldqd1hgx

Qryhpehu 4<<<

Devwudfw

Lq wklv sdshu zh frqwudvw wkh shuirupdqfh ri wkh wzr0sduw prgho/ zklfk

glvwlqjxlvkhv ehwzhhq xvhuv dqg qrqxvhuv ri khdowk fduh/ zlwk wkdw ri d odwhqw

fodvv prgho/ zklfk glvwlqjxlvkhv ehwzhhq lqiuhtxhqw dqg iuhtxhqw xvhuv1 Xv0

lqj gdwd iurp wkh UDQG Khdowk Lqvxudqfh H{shulphqw/ zh �qg frpshoolqj

hylghqfh lq idyru ri wkh odwhqw fodvv prgho1 Zh vkrz wkdw lqglylgxdov lq

wkh lqiuhtxhqw dqg iuhtxhqw xvhu odwhqw fodvvhv pd| eh ghvfulehg dv ehlqj

khdowk| dqg loo uhvshfwlyho|1 Wkh frpshwlqj prghov dovr glvsod| vxevwdqwlyh

gl�huhqfhv lq hvwlpdwhv ri srolf|0uhohydqw phdvxuhv vxfk dv hodvwlflwlhv1

WZh judwhixoo| dfnqrzohgjh uhvhdufk vxssruw iurp wkh Djhqf| iru Khdowk Fduh Srolf| dqgUhvhdufk +U36 KV3<;76034,1 Zh zlvk wr wkdqn Mlhtxq Jxr iru h{fhoohqw uhvhdufk dvvlvwdqfhdqg Zloo Pdqqlqj iru surylglqj gdwd dqg lqydoxdeoh vxjjhvwlrqv1 Zh dovr zlvk wr wkdqn MrkqPxoodk|/ Mlp Exujhvv/ Hgg| ydq Grruvodhu dqg sduwlflsdqwv dw wkh lKHD phhwlqjv lq Urwwhugdp/wkh Hxurshdq Phhwlqj rq Hfrqrphwulfv dqg Khdowk Hfrqrplfv lq Fdwdqld/ dqg dw vhplqduv dwwkh Xqlyhuvlw| ri Qhz Kdpsvkluh dqg Kduydug Phglfdo Vfkrro iru lqvljkwixo frpphqwv1 Doohuuruv duh rxuv1

41 Lqwurgxfwlrq

Wklv sdshu h{dplqhv hpslulfdo vwudwhjlhv iru prgholqj wkh ghpdqg iru khdowk

vhuylfhv1 Wkh fkrlfh ri wkh hfrqrphwulf iudphzrun kdv lpsolfdwlrqv iru d qxpehu

ri hpslulfdo lvvxhv ri fhqwudo lpsruwdqfh lq khdowk hfrqrplfv 0 h1j1/ wkh sulfh

vhqvlwlylw| ri wkh ghpdqg iru phglfdo vhuylfhv dqg wkh olnholkrrg ri ehlqj h{whqvlyh

xvhuv ri vhuylfhv1 Wkh sdshu sursrvhv d qhz dssurdfk edvhg rq d �qlwh pl{wxuh

yduldqw ri wkh odwhqw fodvv prgho1 Wkh sursrvhg dssurdfk lv frpsduhg zlwk wkh

�vwdqgdug� wzr0sduw iudphzrun iru prgholqj wkh ghpdqg iru khdowk fduh1

Wkh olwhudwxuh rq wkh ghpdqg iru phglfdo fduh dqdo|vhv hlwkhu glvfuhwh phd0

vxuhv/ vxfk dv wkh qxpehu ri sk|vlfldq ru qrqsk|vlfldq ylvlwv +Fdphurq hw do1/

4<;;> Srkophlhu dqg Xoulfk/ 4<<8> Ghe dqg Wulyhgl/ 4<<:> Jhugwkdp/ 4<<:,/ ru

frqwlqxrxv phdvxuhv vxfk dv h{shqglwxuhv +Gxdq hw do1/ 4<;5> Pdqqlqj hw do1/

4<;:> Nhhohu hw do1/ 4<;;> PfFdoo hw do1/ 4<<4,1 Lq prgholqj wkh xvdjh ri phglfdo

vhuylfhv/ wkh wzr0sduw prgho +WSP, kdv vhuyhg dv d phwkrgrorjlfdo fruqhuvwrqh

ri hpslulfdo dqdo|vlv1 Wkh �uvw sduw ri wkh WSP lv d elqdu| rxwfrph prgho wkdw

ghvfulehv wkh glvwlqfwlrq ehwzhhq qrqxvhuv dqg xvhuv1 Wkh vhfrqg sduw ghvfulehv

wkh glvwulexwlrq ri xvh frqglwlrqdo rq vrph xvh/ prghohg hlwkhu dv d frqwlqxrxv

ru lqwhjhu0ydoxhg udqgrp yduldeoh1 Dowkrxjk lq khdowk hfrqrplfv wkh WSP lv

xvhg suhgrplqdqwo| wr uhihu wr prghov ri khdowk h{shqglwxuhv/ wkh vwuxfwxuh ri

wkh WSP lv htxdoo| dssolfdeoh iru glvfuhwh ru frqwlqxrxv rxwfrphv1

Wkh dsshdo ri wkh WSP lv sduwo| gulyhq e| dq lpsruwdqw ihdwxuh ri wkh gh0

pdqg iru phglfdo fduh/ zklfk lv wkh kljk lqflghqfh ri }hur xvdjh1 Iru h{dpsoh/

dssur{lpdwho| 63( ri w|slfdo furvv0vhfwlrqdo vdpsohv ri qrq0lqvwlwxwlrqdol}hg lq0

glylgxdov lq wkh Xqlwhg Vwdwhv uhsruw qr rxwsdwlhqw ylvlwv lq wkh vxuyh| |hdu1 Wkh

h{lvwhqfh ri vljql�fdqw suredelolw| pdvv dw d vlqjoh srlqw/ vxfk dv d }hur/ pd|

ylrodwh wkh dvvxpswlrq wkdw d vlqjoh sdudphwulfdoo|0vshfl�hg suredelolw| glvwulex0

wlrq dghtxdwho| ghvfulehv wkh srsxodwlrq xqghuo|lqj wkh revhuyhg gdwd1 Pruhryhu/

wkh WSP lv zhoo vxssruwhg hpslulfdoo|/ zlwk h{sodqdwru| yduldeohv riwhq sod|lqj

gl�huhqw urohv lq wkh wzr sduwv ri wkh prgho1

Wkh dsshdo ri wkh WSP lq khdowk hfrqrplfv lv dovr edvhg rq lwv frqqhfwlrq wr

5

d sulqflsdo0djhqw prgho +vhh/ iru h{dpsoh/ ]zhliho/ 4<;4, zkhuh wkh sk|vlfldq +wkh

djhqw, ghwhuplqhv xwlol}dwlrq rq ehkdoi ri wkh sdwlhqw +wkh sulqflsdo, rqfh lqlwldo

frqwdfw lv pdgh1 Wkh iroorzlqj txrwhv kljkoljkw wkh vwuhqjwk ri wklv dujxphqw lq

wkh olwhudwxuh=

�111 wkh ghflvlrq wr uhfhlyh vrph fduh lv odujho| wkh frqvxphu*v/ zkloh

wkh sk|vlfldq lq xhqfhv wkh ghflvlrq derxw wkh ohyho ri fduh� +Pdqqlqj

hw do1/ 4<;4/ s1 43<,1

�111 zkloh dw wkh �uvw vwdjh lw lv wkh sdwlhqw zkr ghwhuplqhv zkhwkhu wr

ylvlw wkh sk|vlfldq +frqwdfw dqdo|vlv,/ lw lv hvvhqwldoo| xs wr wkh sk|vl0

fldq wr ghwhuplqh wkh lqwhqvlw| ri wkh wuhdwphqw +iuhtxhqf| dqdo|vlv,�

+Srkophlhu dqg Xoulfk/ 4<<8/ s1 673,1

�111zkhuh wkh �uvw sduw uhodwhv wr wkh sdwlhqw zkr ghflghv zkhwkhu wr

frqwdfw wkh sk|vlfldq +frqwdfw ghflvlrq, dqg wkh vhfrqg wr wkh ghflvlrq

derxw uhshdwhg ylvlwv dqg2ru uhihuudov/ zklfk lv ghwhuplqhg odujho|

e| wkh suhihuhqfhv ri wkh sk|vlfldq +iuhtxhqf| ghflvlrq,� +Jhugwkdp/

4<<:/ s1 63;,1

Wklv frqwudvwv zlwk wkh dssurdfk lq zklfk wkh ghpdqg iru phglfdo fduh lv ghwhu0

plqhg sulpdulo| e| wkh sdwlhqw +Jurvvpdq/ 4<:5,1

Wkh vkdus glfkrwrp| ehwzhhq xvhuv dqg qrqxvhuv pd| eh dsshdolqj lq prg0

holqj gdwd rq hslvrghv ri phglfdo fduh exw wklv glvwlqfwlrq pd| qrw eh whqdeoh

lq wkh fdvh ri w|slfdo furvv0vhfwlrqdo gdwd0vhwv1 Lq wkhvh gdwd/ khdowk fduh hyhqwv

duh uhfrughg ryhu d �{hg wlph shulrg +h1j1/ d |hdu ru d prqwk, dqg qrw ryhu dq

hslvrgh ri looqhvv1 Wkhuhiruh/ wkh sulqflsdo0djhqw iudphzrun zklfk xqghuolhv wkh

glvwlqfwlrq ehwzhhq xvhuv dqg qrqxvhuv lq wkh WSP pd| qrw eh dssursuldwh iru

�{hg0lqwhuydo gdwd zkhuh hyhq d khdowk| lqglylgxdo zloo qrw w|slfdoo| eh d qrqxvhu

vlqfh pdq| irupv ri phglfdo fduh zloo wdnh wkh irup ri khdowk pdlqwhqdqfh dqg

suhfdxwlrqdu| fduh +Jurvvpdq/ 4<:5,1

D pruh whqdeoh glvwlqfwlrq iru vxfk gdwd pd| eh ehwzhhq dq �lqiuhtxhqw xvhu�

dqg d �iuhtxhqw xvhu� ri phglfdo fduh/ wkh gl�huhqfh ehlqj ghwhuplqhg e| khdowk

6

vwdwxv/ dwwlwxghv wr khdowk ulvn/ dqg fkrlfh ri olih0vw|oh1 Wkh �qlwh pl{wxuh yduldqw

ri wkh odwhqw fodvv prgho +OFP,/ lq zklfk wkhuh lv qr glvwlqfwlrq ehwzhhq xvhuv

dqg qrq0xvhuv ri fduh/ exw zklfk fdq glvwlqjxlvk ehwzhhq jurxsv zlwk kljk dyhudjh

ghpdqg dqg orz dyhudjh ghpdqg/ wkhuhiruh surylghv d ehwwhu iudphzrun1

Zh k|srwkhvl}h wkdw wkh xqghuo|lqj xqrevhuyhg khwhurjhqhlw| zklfk vsolwv

wkh srsxodwlrq lqwr odwhqw fodvvhv lv edvhg rq dq lqglylgxdo*v odwhqw orqj0whup

khdowk vwdwxv1 Sur{| yduldeohv vxfk dv vhoi0shufhlyhg khdowk vwdwxv dqg fkurqlf

khdowk frqglwlrqv pd| qrw ixoo| fdswxuh srsxodwlrq khwhurjhqhlw| iurp wklv vrxufh1

Frqvhtxhqwo|/ lq wkh fdvh ri wzr odwhqw vxesrsxodwlrqv/ d glvwlqfwlrq pd| eh pdgh

ehwzhhq wkh �khdowk|� dqg wkh �loo� jurxsv/ zkrvh ghpdqgv iru phglfdo fduh duh

fkdudfwhul}hg e| orz phdq dqg kljk phdq/ uhvshfwlyho|1

Iurp d vwdwlvwlfdo srlqw ri ylhz/ wkh WSP lv dovr d �qlwh pl{wxuh zlwk d gh0

jhqhudwh frpsrqhqw1 Lw frpelqhv }hurv iurp d elqrpldo ghqvlw| zlwk wkh srvlwlyhv

iurp d }hur0wuxqfdwhg ghqvlw|1 Wkh OFP +ru �qlwh pl{wxuh prgho, lv pruh h{l0

eoh ehfdxvh lw shuplwv pl{lqj zlwk uhvshfw wr erwk }hurv dqg srvlwlyhv1 Zkloh wkh

WSP dqg OFP duh fohduo| uhodwhg/ wkh| duh qrw qhvwhg1 Khqfh lw lv qrw d sulrul

fohdu zklfk prgho zrxog shuirup ehwwhu hpslulfdoo|1 Lq d vwxg| ri phglfdo fduh

ghpdqg e| wkh hoghuo| Ghe dqg Wulyhgl +4<<:, �qg wkdw wkh OFP lv vxshulru wr

wkh WSP1 Lq rwkhu hpslulfdo zrun +Fdphurq dqg Wulyhgl/ 4<<;,/ lw lv vkrzq wkdw

wkh WSP ghvfulehv wkh qxpehu ri uhfuhdwlrqdo wulsv wdnhq e| lqglylgxdov ehwwhu

wkdq wkh OFP1

D fduhixo frpsdulvrq ri wkh OFP dqg WSP lv xvhixo iurp d srolf| shuvshf0

wlyh1 Wkh WSP kdv ehhq xvhg h{whqvlyho| wr hvwlpdwh ghpdqg uhvsrqvhv wr sulfhv/

lqfrph dqg fkdqjhv lq lqvxudqfh vwdwxv1 Wkh uhvxowv kdyh ehhq xvhg wr sursrvh

fkdqjhv lq khdowk lqvxudqfh ghvljq1 Vwdwlvwlfv ri lqwhuhvw lq pdq| vxfk srolf|

h{huflvhv duh qrqolqhdu ixqfwlrqv ri wkh xqghuo|lqj sdudphwhuv ri wkh frqglwlrqdo

phdq ixqfwlrq1 Wkhuhiruh/ frqvlvwhqw hvwlpdwlrq ri wkh frqglwlrqdo phdq ixqfwlrq

grhv qrw hqvxuh frqvlvwhqw hvwlpdwhv ri wkh vwdwlvwlfv ri lqwhuhvw iru srolf| h{hu0

flvhv> vhh Pxoodk| +4<<;, iru d ghwdlohg glvfxvvlrq1 Hvwlpdwlqj d prgho wkdw �wv

wkh hpslulfdo glvwulexwlrq dghtxdwho| grhv/ rq wkh rwkhu kdqg/ hqvxuh wkdw vxfk

7

vwdwlvwlfv zloo eh hvwlpdwhg frqvlvwhqwo|1 Pruhryhu/ li lq idfw wkh WSP lv grpl0

qdwhg e| wkh OFP/ wkh dffxpxodwhg hylghqfh lq idyru ri wkh WSP/ lqwhusuhwhg dv

hylghqfh lq idyru ri d sulqflsdo0djhqw iudphzrun/ lv dpeljxrxv1 Srolflhv edvhg rq

wkh sulqflsdo0djhqw iudphzrun pljkw/ wkhuhiruh/ kdyh xqlqwhqghg frqvhtxhqfhv1

Ilqdoo|/ erwk wkh WSP dqg wkh OFP uhtxluh wkdw wkh lqyhvwljdwru vshfl�hv

wkh suredelolw| glvwulexwlrq ri wkh gdwd1 Dowkrxjk wklv lv d srwhqwldo vrxufh ri

plvvshfl�fdwlrq lq erwk fdvhv/ lwv lpsdfw lv vpdoohu lq wkh fdvh ri wkh OFP1 Wklv

lv ehfdxvh OFP lv pruh h{leoh dqg fdq vhuyh dv d ehwwhu dssur{lpdwlrq wr dq|

wuxh/ exw xqnqrzq/ suredelolw| ghqvlw| +Odlug/ 4<:;> Khfnpdq dqg Vlqjhu/ 4<;7,1

Lwv jurzlqj srsxodulw| lv uh hfwhg lq dq lqfuhdvh lq wkh qxpehu ri uhjuhvvlrq0

edvhg dssolfdwlrqv lq hfrqrphwulfv1 Uhfhqw dssolfdwlrqv lqfoxgh Khfnpdq/ Uree/

dqg Zdonhu +4<<3,/ Julw} +4<<6,/ Zhgho hw do1 +4<<6,/ Ghe dqg Wulyhgl +4<<:,/

Jhzhnh dqg Nhdqh +4<<:,/ Prugxfk dqg Vwhuq +4<<:,/ dqg Zdqj/ Frfnexuq/ dqg

Sxwhupdq +4<<;,1

Zh xvh gdwd iurp wkh UDQG Khdowk Lqvxudqfh H{shulphqw +UKLH,1 Wkh

UKLH lv rqh ri wkh odujhvw vrfldo h{shulphqw hyhu frpsohwhg/ jhqhudwlqj ryhu

733 uhvhdufk vwxglhv e| phpehuv ri wkh UDQG jurxs +Qhzkrxvh/ 4<<6,1 Lw lv

zlgho| uhjdughg dv wkh edvlv ri wkh prvw uholdeoh hvwlpdwhv ri sulfh vhqvlwlylw| ri

ghpdqg iru phglfdo vhuylfhv1 Iru h{dpsoh/ Exuwohvv +4<<8/ s1;5, kdv vwdwhg= �Wkh

Khdowk Lqvxudqfh H{shulphqw lpsuryhg rxu nqrzohgjh derxw wkh sulfh vhqvlwlylw|

ri ghpdqg iru phglfdo vhuylfhv lq d zd| wkdw qr qrqh{shulphqwdo vwxg| kdv ehhq

deoh wr pdwfk�1 Wkhuhiruh/ wkh sxeolf0xvh gdwd iurp wkh UKLH surylgh d vxlwdeoh

whvw0ehg iru rxu sursrvhg lqyhvwljdwlrqv zklfk/ lw vkrxog eh qrwhg/ uhodwh wr rqo|

d vpdoo sduw ri wkh UDQG uhvhdufk rxwsxw1

Wkh UKLH gdwd duh prvw vxlwdeoh iru rxu zrun lq vslwh ri wkh idfw wkdw wkh|

duh frqvlghudeo| roghu wkdq rwkhu qdwlrqdoo| uhsuhvhqwdwlyh vxuyh|v olnh wkh Qd0

wlrqdo Phglfdo H{shqglwxuh Vxuyh| +4<;:,/ wkh Qdwlrqdo Khdowk Lqwhuylhz Vxuyh|

+4<<7, ru wkh Phglfdo H{shqglwxuh Sdqho Vxuyh| +4<<: dqg iruwkfrplqj,1 Iluvw/

wkh UKLH gdwd0vhw lv wkh rqo| rqh lq zklfk lqglylgxdov zhuh udqgrpl}hg lqwr lq0

vxudqfh sodqv/ wkxv pdnlqj lqvxudqfh fkrlfh h{rjhqrxv1 Hqgrjhqhlw| ri lqvxudqfh

8

fkrlfh lv d pdmru sureohp lq qrqh{shulphqwdo gdwd> hyhq lq fdvhv zkhuh vxlwdeoh

lqvwuxphqwv h{lvw/ wkh| duh w|slfdoo| zhdn wkxv pdnlqj vwdwlvwlfdo fruuhfwlrqv iru

hqgrjhqhlw| xquholdeoh1 Vhfrqg/ wkh UKLH gdwd duh xqxvxdo lq wkdw wkh| fdq

vxssruw dq hfrqrphwulf dqdo|vlv ri erwk khdowk vhuylfhv frxqwv dqg h{shqglwxuhv/

zkhuhdv prvw uhfhqw zrun kdv xvhg hlwkhu frxqwv ru h{shqglwxuhv h{foxvlyho|1 Il0

qdoo|/ UDQG uhvhdufkhuv jdyh fduhixo frqvlghudwlrq wr lvvxhv ri dwwulwlrq eldv dqg

rwkhu vrxufhv ri �vdpsoh frqwdplqdwlrq� zklfk d�hfw vrph vrfldo h{shulphqwv

+Qhzkrxvh hw do1/ 4<<6/ Fkdswhu 5> Khfnpdq dqg Vplwk/ 4<<8,1

Lq wkh iroorzlqj vhfwlrq ri wkh sdshu/ zh irupdoo| suhvhqw wkh frpshwlqj prg0

hov xvhg lq wklv sdshu dqg glvfxvv prgho frpsdulvrq/ vhohfwlrq/ dqg hydoxdwlrq

vwudwhjlhv1 Wkh gdwd duh ghvfulehg lq vhfwlrq 61 Hpslulfdo uhvxowv duh uhsruwhg lq

vhfwlrq 7/ dqg zh frqfoxgh lq vhfwlrq 81

51 Hfrqrphwulf Prghov

Zh ghyhors prghov iru frxqwv ri rxwsdwlhqw ylvlwv dqg glvfuhwl}hg groodu h{shqgl0

wxuhv rq rxwsdwlhqw ylvlwv xvlqj wkh OFP dqg WSP iudphzrunv1

5141 OFP Iudphzrun

Lq d odwhqw fodvv +�qlwh pl{wxuh, prgho d udqgrp yduldeoh lv srvwxodwhg dv d gudz

iurp d srsxodwlrq zklfk lv dq dgglwlyh pl{wxuh ri F glvwlqfw vxesrsxodwlrqv lq

sursruwlrqv ��> ===> �� > zkhuhS�

�'��� @ 4> �� N 3 +m @ 4> ===> F,= Wkh pl{wxuh

ghqvlw| iru revhuydwlrq l> l @ 4> ===> q> lv jlyhq e|

i+|�mw, @�3�[

�'�

��i�+|�mw�, . ��i�+|�mw�,> l @ 4> ===> q> +514,

zkhuh hdfk whup lq wkh vxp rq wkh uljkw0kdqg vlgh lv wkh surgxfw ri pl{lqj

suredelolw| �� dqg wkh frpsrqhqw +vxesrsxodwlrq, ghqvlw| i�+|�mw�,= Lq jhqhudo

wkh �� duh xqnqrzq dqg khqfh wr eh hvwlpdwhg dorqj zlwk doo rwkhu sdudphwhuv/

ghqrwhg w1 Dovr �� @ +4�S�3�

�'� ��,= Iru lghqwl�delolw| +qrupdol}dwlrq,/ zh xvh

wkh odehoolqj uhvwulfwlrq wkdw �� � �2 � ==== � �� zklfk fdq dozd|v eh vdwlv�hg

e| uhduudqjhphqw/ srvw hvwlpdwlrq1

9

Iru dqdo|}lqj wkh qxpehu ri rxwsdwlhqw ylvlwv/ zh xvh d F0frpsrqhqw �qlwh

pl{wxuh/ wkh frpsrqhqw glvwulexwlrqv ehlqj wkh qhjdwlyh elqrpldo ghqvlwlhv vshf0

l�hg dv

i�+|�mw�, @�+|� .#�c�,

�+#�c�,�+|� . 4,

�#�c�

��c� . #�c�

���c��

��c�

��c� .#�c�

�+�

> +515,

zkhuh m @ 4> 5> ===> F duh wkh odwhqw fodvvhv/ ��c� @ h{s+{�

���, dqg #�c� @ +4@��,�&�c�=

Wklv ghqvlw| lv dghtxdwho| jhqhudo dqg h{leoh/ dqg zloo dffrpprgdwh sdwwhuqv ri

ryhuglvshuvlrq h{shfwhg lq rxu gdwd1 Wkh uhvxowlqj prgho fdq dovr eh vshfldol}hg

wr wkh Srlvvrq dqg jhrphwulf yduldqwv ri wkh odwhqw fodvv prgho1 Ixuwkhu/ e|

vhwwlqj n @ 4 ru 5 zh fdq rewdlq wkh wzr ohdglqj yduldqwv ri wkh qhjdwlyh elqrpldo/

zklfk duh/ uhvshfwlyho|/ wkh QE4 dqg QE5 prghov1 Wkh �uvw kdv d olqhdu dqg wkh

vhfrqg d txdgudwlf yduldqfh ixqfwlrq1

5151 Surshuwlhv ri OFP

Odwhqw fodvv prghov r�hu d h{leoh zd| ri vshfli|lqj pl{wxuhv ri ghqvlwlhv1 Wkhuh

duh d qxpehu ri dgydqwdjhv ri xvlqj d glvfuhwh udwkhu wkdq d frqwlqxrxv pl{lqj

glvwulexwlrq1 Iluvw/ wkh �qlwh pl{wxuh uhsuhvhqwdwlrq surylghv d qdwxudo dqg lqwx0

lwlyho| dwwudfwlyh uhsuhvhqwdwlrq ri khwhurjhqhlw| lq d �qlwh/ xvxdoo| vpdoo/ qxpehu

ri odwhqw fodvvhv/ hdfk ri zklfk pd| eh uhjdughg dv d �w|sh�/ ru d �jurxs�1 Wkh

fkrlfh ri wkh qxpehu ri frpsrqhqwv lq wkh pl{wxuh ghwhuplqhv wkh qxpehu ri

�w|shv�/ exw wkh fkrlfh ri wkh ixqfwlrqdo irup iru wkh ghqvlw| fdq dffrppr0

gdwh khwhurjhqhlw| zlwklq hdfk frpsrqhqw1 D �qlwh pl{wxuh fkdudfwhul}dwlrq lv

hvshfldoo| dwwudfwlyh li wkh pl{wxuh frpsrqhqwv kdyh d qdwxudo lqwhusuhwdwlrq1

Krzhyhu/ wklv lv qrw hvvhqwldo1 D �qlwh pl{wxuh pd| eh vlpso| d zd| ri h{leo|

dqg sduvlprqlrxvo| prgholqj wkh gdwd/ zlwk hdfk pl{wxuh frpsrqhqw surylglqj d

orfdo dssur{lpdwlrq wr vrph sduw ri wkh wuxh glvwulexwlrq1 Dv vxfk/ wkh dssurdfk

lv dq dowhuqdwlyh wr hlwkhu qrqsdudphwulf hvwlpdwlrq ru iruflqj wkh gdwd wkurxjk

wkh vwudlwmdfnhw ri d rqh0frpsrqhqw sdudphwulf ghqvlw|1

Vhfrqg/ wkh �qlwh pl{wxuh dssurdfk lv vhplsdudphwulf= lw grhv qrw uhtxluh dq|

glvwulexwlrqdo dvvxpswlrqv iru wkh pl{lqj yduldeoh1 Wklug/ wkh uhvxowv ri Odlug

:

+4<:;, dqg Khfnpdq dqg Vlqjhu +4<;7, vxjjhvw wkdw hvwlpdwhv ri vxfk �qlwh pl{0

wxuh prghov pd| surylgh jrrg qxphulfdo dssur{lpdwlrqv hyhq li wkh xqghuo|lqj

pl{lqj glvwulexwlrq lv frqwlqxrxv14 Ilqdoo|/ wkh fkrlfh ri d frqwlqxrxv pl{lqj

ghqvlw| iru vrph sdudphwulf frxqw prghov lv vrphwlphv uhvwulfwlyh dqg frpsx0

wdwlrqdoo| lqwudfwdeoh ehfdxvh wkh pdujlqdo ghqvlw| pd| qrw kdyh dq dqdo|wlfdo

vroxwlrq1

D fdyhdw wr wkh iruhjrlqj glvfxvvlrq lv wkdw wkh OFP pd| �w wkh gdwd ehwwhu

vlpso| ehfdxvh vxevhwv ri revhuydwlrqv duh vwdwlvwlfdoo| gl�huhqw dqg2ru wkh vshf0

l�hg glvwulexwlrq lv pruh h{leoh wkdq wkh frpshwlwruv1 Iru h{dpsoh/ wklv pd|

kdsshq li rxwolhuv/ lq xhqwldo revhuydwlrqv ru vdpsoh frqwdplqdwlrq duh suhvhqw

lq wkh gdwd1 Wkh OFP prgho zloo fdswxuh wklv skhqrphqrq wkurxjk dgglwlrqdo

pl{wxuh frpsrqhqwv1 Khqfh lw lv ghvludeoh wkdw wkh k|srwkhvlv ri OFP vkrxog eh

vxssruwhg erwk e| d sulrul uhdvrqlqj dqg e| phdqlqjixo d srvwhulrul gl�huhqfhv

lq wkh ehkdylru ri odwhqw fodvvhv1

5161 WSP Iudphzrun

Wkh pdlq frpshwlwru ri wkh sursrvhg OFP dssurdfk lv wkh WSP/ riwhq fdoohg

d kxugoh prgho lq wkh frxqw0gdwd olwhudwxuh1 Ehfdxvh zh zlvk wr irfxv rq wkh

gl�huhqfhv ehwzhhq d vwdwlvwlfdo vwuxfwxuh wkdw glvwlqjxlvkhv lqiuhtxhqw dqg iuh0

txhqw xvhuv iurp rqh wkdw glvwlqjxlvkhv qrqxvhuv dqg xvhuv zkloh plqlpl}lqj doo

rwkhu vrxufhv ri yduldwlrq/ zh fkrrvh d qhjdwlyh elqrpldo ghqvlw| wr frqvwuxfw wkh

WSP1 Wkhuhiruh/ wkh �uvw sduw ri wkh wzr0sduw vwuxfwxuh lv vshfl�hg dv

3U�+|� @ 3m{�, @

�#�c�

��c� .#�c�

���c�

> +516,

zkhuh wkh vxevfulsw k ghqrwhv sdudphwhuv dvvrfldwhg zlwk wkh �kxugoh glvwulex0

wlrq�1 Xqghu wkh dvvxpswlrq ri lqghshqghqfh ri wkh wzr sduwv/ wkh olnholkrrg

ixqfwlrq dvvrfldwhg zlwk wkh kxugoh sduw fdq eh pd{lpl}hg lqghshqghqwo| ri wkh

vshfl�fdwlrq ri wkh vhfrqg vwdjh1 Wkh �uvw sduw lqyroyhv rqo| elqdu| lqirupd0

4Olqgvd| +4<<8, surylghv d ghwdlohg wkhruhwlfdo dqdo|vlv> Kdxjkwrq +4<<:, vxuyh|v frpsxwd0wlrqdo lvvxhv dqg dydlodeoh vriwzduh1

;

wlrq vr wkh sdudphwhuv +�, ri wkh phdq ixqfwlrq dqg wkh sdudphwhu � duh qrw

vhsdudwho| lghqwl�deoh1

Lq wkh vhfrqg sduw/ wkh glvwulexwlrq ri xwlol}dwlrq jlyhq vrph xvh lv dvvxphg

wr iroorz d wuxqfdwhg qhjdwlyh elqrpldo glvwulexwlrq jlyhq e|

i+|�m{�> |� A 3, @�+|� . #

�,

�+#�,�+|� . 4,

%��� . #

�

#�

���

� 4

&3��

��

�� .#�

�+�

= +517,

Wkh vhfrqg sduw lv hvwlpdwhg xvlqj wkh wuxqfdwhg vxevdpsoh ri srvlwlyh revhuyd0

wlrqv ri |�=5 Erwk wkh phdq dqg wkh yduldqfh lq wkh kxugoh prgho duh/ lq jhqhudo/

gl�huhqw iurp wkhlu vwdqgdug dv zhoo dv odwhqw fodvv frxqwhusduwv1

Erwk WSP dqg OFP duh hvwlpdwhg xvlqj +svhxgr, pd{lpxp olnholkrrg1 Wkh

vwdqgdug huuruv ri frh!flhqwv duh hvwlpdwhg xvlqj wkh urexvw +�vdqgzlfk�, ydul0

dqfh irupxod +Fdphurq dqg Wulyhgl/ 4<<;/ s1 64,1 Wkh vwdqgdug WSP zlwk

lqghshqghqw frpsrqhqwv lv frpsxwdwlrqdoo| vlpsohu wkdq wkh OFP dv wkh wzr

sduwv ri wkh olnholkrrg ixqfwlrq fdq eh hvwlpdwhg vhsdudwho|1 Dqrwkhu frpsolfd0

wlrq ri hvwlpdwlqj OFP zlwk pd{lpxp olnholkrrg lv wkh srvvlelolw| ri pxowlsoh

orfdo pd{lpd1 Wr hqvxuh djdlqvw wkh srvvlelolw| ri dfklhylqj +idovh, frqyhujhqfh

dw d orfdo pd{lpxp/ lq suholplqdu| dqdo|vlv hdfk prgho zdv hvwlpdwhg xvlqj d

qxpehu ri gl�huhqw vhwv ri vwduwlqj ydoxhv1

5171 Prghov iru H{shqglwxuhv

Lq wkh fdvh ri d frqwlqxrxv udqgrp yduldeoh vxfk dv h{shqglwxuh/ lw lv h{wuhpho|

gl!fxow wr ghylvh vwdwlvwlfdo iudphzrunv dv dowhuqdwlyhv wr wkh WSP1 Prvw ghqvlw|

ixqfwlrqv iru qrq0qhjdwlyh frqwlqxrxv udqgrp yduldeohv h{foxgh srvlwlyh sured0

elolw| pdvv dw }hur ydoxh/ h1j1/ orjqrupdo/ jdppd/ Zhlexoo1 Wkh remhfwlyh ri

wklv uhvhdufk/ krzhyhu/ lv wr frpsduh wkh surshuwlhv ri wkh WSP zlwk wkh OSP1

Wkhuhiruh/ lw lv hvvhqwldo wr prgho h{shqglwxuhv xvlqj dq dssursuldwh ghqvlw| wkdw

5Wkh WSP pdnhv d nh| vlpsoli|lqj dvvxpswlrq wkdw wkh ghflvlrq wr frqvxph phglfdo fduh lvlqghshqghqw ri wkh ghflvlrq ri krz pxfk wr frqvxph frqglwlrqdo rq vrph frqvxpswlrq1 Dqrwkhufodvv ri prghov/ ri zklfk wkh vdpsoh vhohfwlrq prgho lv d ohdglqj h{dpsoh/ ehfrphv uhohydqw li wklvdvvxpswlrq lv uhod{hg1 Wkh suhihuhqfh iru wkh WSP ryhu vhohfwlylw| prghov kdv ehhq h{whqvlyho|ghedwhg lq wkh khdowk hfrqrphwulf olwhudwxuh dqg zloo qrw eh frqvlghuhg khuh +Mrqhv/ 4<<;,1

<

kdv suredelolw| pdvv dw }hur1 Vlqfh zh duh xqdeoh wr ghylvh dq dssurdfk wkdw

dffrpprgdwhv wkh suhvhqfh ri }hur h{shqglwxuhv lq d vwdwlvwlfdo iudphzrun iru

frqwlqxrxv gdwd/ zh glvfuhwl}h h{shqglwxuhv dqg prgho wkh glvfuhwl}hg h{shqgl0

wxuh ydoxhv lq wkh frxqw gdwd iudphzrun ghvfulehg deryh1 Frqvhtxhqwo|/ wkh frxqw

gdwd prghov wdnh rq d odwhqw yduldeoh lqwhusuhwdwlrq1

Iru wkh UDQG gdwd/ wkh vdpsoh dyhudjh fkdujhv shu rxwsdwlhqw ylvlw duh '49/

'53 dqg '56 iru wkuhh gh�qlwlrqv ri dyhudjh fkdujhv1 Wkhuhiruh zh fkrrvh d elq

vl}h ri '53 wr glvfuhwl}h h{shqglwxuhv1 H{shqglwxuhv ri '3 duh jlyhq wkh ydoxh 3/

h{shqglwxuhv ri '3134 0 '53133 duh jlyhq wkh ydoxh 4/ '53134 0 '73133 duh jlyhq

wkh ydoxh 5/ dqg vr rq1 Qrwh wkdw e| wuhdwlqj }hur h{shqglwxuhv dv d xqltxh

frxqw ydoxh/ zh h{solflwo| glvwlqjxlvk ehwzhhq xvhuv dqg qrqxvhuv1 Wr fkhfn wkh

urexvwqhvv ri rxu �qglqjv/ zh dovr hvwlpdwh prghov zlwk d elq vl}h ri '431 Dv wkh

uhvxowv zloo vkrz/ wkh pdlq �qglqjv duh txlwh urexvw wr wkhvh fkrlfhv1 Pruhryhu/

jlyhq rxu remhfwlyh ri glvwlqjxlvklqj ehwzhhq OFP dqg WSP/ wkhuh lv qr d sulrul

uhdvrq wr eholhyh wkdw glvfuhwl}dwlrq zrxog idyru OFP ryhu WSP1

5181 Prgho Frpsdulvrq dqg Vhohfwlrq

Zh xvh wkuhh fulwhuld wr frpsduh prghov lq0vdpsoh1 Wkhvh lqfoxgh wzr wudgl0

wlrqdo prgho vhohfwlrq fulwhuld edvhg rq shqdol}hg olnholkrrg/ Dndlnh Lqirupdwlrq

Fulwhulrq/ DLF/ dqg Ed|hvldq Lqirupdwlrq Fulwhulrq/ ELF/ zklfk duh ydolg hyhq

lq wkh suhvhqfh ri prgho plvvshfl�fdwlrq +Vlq dqg Zklwh/ 4<<9,1 Prghov zlwk

vpdoohu ydoxhv ri wkh DLF @ � oqO . 5N dqg ELF @ �5 oqO .N oq+Q,/ zkhuh

oqO lv wkh pd{lpl}hg orj olnholkrrg/ N lv wkh qxpehu ri sdudphwhuv lq wkh prgho

dqg Q lv wkh vdpsoh vl}h/ duh suhihuuhg1 Zh dovr xvh Dqguhz*v jrrgqhvv0ri0�w

whvw +Dqguhzv/ 4<;;d/ 4<;;e,1 Wkh jrrgqhvv0ri0�w whvw lv edvhg rq d fkl0vtxduh

gldjqrvwlf vwdwlvwlf jlyhq e| V @�i � ei�� e3�

�i �ei� zkhuh i � ei lv wkh Q � t

pdwul{ ri gl�huhqfhv ehwzhhq vdpsoh dqg �wwhg fhoo iuhtxhqflhv/ t lv wkh qxpehu

ri fhoov fuhdwhg e| sduwlwlrqlqj ri wkh gdwd/ dqg e lv lwv hvwlpdwhg fryduldqfh pd0

wul{1 Xqghu wkh qxoo k|srwkhvlv ri qr plvvshfl�fdwlrq wkh whvw kdv dq dv|pswrwlf

"2+t�4, glvwulexwlrq +Dqguhzv/ 4<;;e,1 Zkhq wkh whvw vwdwlvwlf lv iruphg xvlqj

43

wkh pd{lpxp olnholkrrg hvwlpdwru/ frpsxwdwlrq ri wkh whvw vwdwlvwlf lv vlpsol�hg1

Ohw D eh wkh Q � t pdwul{ zlwk l|� urz jlyhq e| i� �ei�/ ohw E eh wkh Q � N

pdwul{ zlwk l|� urz jlyhq e| +C@Cw, orj i�+|�mw, dqg ohw K @ ^D E`1 Wkhq

JrI @ 4�K+K�

K,nK�4 +518,

zkhuh 4 lv d froxpq yhfwru ri rqhv/ l1h1/ JrI lv QU2 iurp wkh uhjuhvvlrq ri 4 rq

K +vhh Dqguhzv/ 4<;;d/ Dsshqgl{ 8/ iru ghwdlov,1

Wkhuh lv dq lpsruwdqw srlqw ri ghwdlo frqfhuqlqj rxu xvh ri wkh deryh whvw1

Ehfdxvh rxu vdpsoh vl}h lv txlwh odujh/ d prgho frpsdulvrq edvhg rq vljql�fdqfh

whvwv ri �{hg vl}h lv olnho| wr ohdg wr wkh uhmhfwlrq ri doo prghov zh zloo frqvlghu1

Wklv lv d zhoo0nqrzq gl!fxow| ri k|srwkhvlv whvwlqj zlwk �{hg vljql�fdqfh ohyhov lq

wkh fodvvlfdo iudphzrun1 Pruhryhu/ suhylrxv lqyhvwljdwlrqv ri wkh surshuwlhv ri wklv

whvw vxjjhvw wkdw dw wkh frqyhqwlrqdo fulwlfdo ydoxhv wklv whvw ohdgv wr ryhuuhmhfwlrq

ri wkh wuxh qxoo +Ghe dqg Wulyhgl/ 4<<:> Fdphurq dqg Wulyhgl/ 4<<;,1 Krzhyhu/

lw vhhpv dssursuldwh wr udqn prghov e| wkh s0ydoxhv dvvrfldwhg zlwk wkh whvw/ wkh

prgho zlwk wkh odujhvw s0ydoxh ehlqj suhihuuhg1 Khqfh lq dgglwlrq wr wkh irupdo

fkl0vtxduh whvw zh xvh wkh vl}h ri wkh vwdwlvwlf lqirupdoo| dv d phdvxuh ri �w zlwk d

vpdoohu vwdwlvwlf lqglfdwlqj ehwwhu �w1 Ixuwkhupruh/ zh dovr judsklfdoo| frpsduh

hpslulfdo dqg �wwhg fhoo suredelolwlhv1

5191 Furvv0ydolgdwlrq

D frpprq fulwlflvp ri lq0vdpsoh prgho vhohfwlrq phwkrgv lv wkdw wkh| lqgxfh

ryhu0�wwlqj lq wkh fdvh ri frpsolfdwhg prghov1 Frqvhtxhqwo|/ wkh vhohfwhg prgho

pd| qrw eh wkh ehvw prgho1 Wklv eldv fdq eh dyrlghg e| wuhdwlqj rqh vdpsoh

dv d �wudlqlqj vdpsoh� xvhg iru hvwlpdwlrq/ dqg wkhq xvlqj d vhfrqg �krog0rxw�

vdpsoh iru iruhfdvw frpsdulvrq1

Xvlqj sdudphwhu hvwlpdwhv iurp wkh wudlqlqj vdpsoh/ zh fdofxodwh wkuhh phd0

vxuhv ri shuirupdqfh iru hdfk prgho xvlqj wkh krog0rxw vdpsoh1 Wkh orj0olnholkrrg

ydoxh lv wkh prvw gluhfw phdvxuh ri wkh rxw0ri0vdpsoh �w ri wkh prgho1 Lq rughu

wr frqwlqxh wr shqdol}h prghov zlwk odujh qxpehuv ri sdudphwhuv/ zh dovr xvh

44

wkh DLF1 Zh gr qrw xvh wkh ELF ehfdxvh lw dggv d shqdow| iru wkh qxpehu ri

revhuydwlrqv lq dgglwlrq wr d shqdow| iru wkh qxpehu ri sdudphwhuv zklfk lv qrw

dssursuldwh lq d furvv0ydolgdwlrq h{huflvh1 Ilqdoo|/ zh xvh d prgl�hg yhuvlrq ri

wkh Dqguhzv vwdwlvwlf dv d khxulvwlf zlwk wkh h{shfwdwlrq wkdw prghov zlwk ehw0

whu �w zloo kdyh vpdoohu ydoxhv ri wkh prgl�hg JrI lq wkh krog0rxw vdpsoh1 Zh

prgli| htxdwlrq +518, wr PJrI @ 4�D+D�

D,nD�4 zkhuh K lv uhsodfhg e| D/

l1h1/ zh dvvxph wkdw wkh sdudphwhuv h{dfwo| pd{lpl}hg wkh olnholkrrg ixqfwlrq lq

wkh wudlqlqj vdpsoh1

61 Gdwd dqg Vxppdu| Vwdwlvwlfv

Zh xvh gdwd iurp wkh UDQG Khdowk Lqvxudqfh H{shulphqw +UKLH, iru wklv vwxg|1

Wkh h{shulphqw/ frqgxfwhg e| wkh UDQG Frusrudwlrq iurp 4<:7 wr 4<;5/ kdv

ehhq wkh orqjhvw uxqqlqj dqg odujhvw frqwuroohg vrfldo h{shulphqw lq phglfdo fduh

uhvhdufk1 Wkh pdlq jrdo ri wkh h{shulphqw zdv wr dvvhvv krz wkh sdwlhqw*v frvw

ri khdowk vhuylfhv lv d�hfwhg e| w|shv ri khdowk lqvxudqfh/ lqfoxglqj erwk ihh0

iru0vhuylfh dqg khdowk pdlqwhqdqfh rujdql}dwlrqv +KPRv,1 Lq wkh UKLH/ gdwd

zhuh froohfwhg iurp derxw ;/333 hquroohhv lq 5/;56 idplolhv/ iurp vl{ vlwhv dfurvv

wkh frxqwu|1 Hdfk idplo| zdv hquroohg lq rqh ri irxuwhhq gl�huhqw KLV lqvxudqfh

sodqv iru hlwkhu wkuhh ru �yh |hduv1 Wkh sodqv udqjhg iurp iuhh fduh wr <8 shufhqw

frlqvxudqfh ehorz d pd{lpxp groodu h{shqglwxuh +PGH,/ wr dvvljqphqw lq d

suhsdlg jurxs sudfwlfh1 Gdwd zhuh froohfwhg iurp wkh hquroohh*v xvh ri phglfdo

fduh vhuylfhv dqg khdowk vwdwxv wkurxjkrxw wkh whup ri hquroophqw/ udqgrpo|

dvvljqhg iru wkuhh ru �yh |hduv1 Fhuwdlq fdwhjrulhv ri lqglylgxdov zhuh h{foxghg/

h1j1 wkh Phglfduh holjleohv dqg phpehuv ri wkh plolwdu|1 Ghwdlohg lqirupdwlrq

rq wkh h{shulphqwdo ghvljq dqg gdwd froohfwlrq phwkrgv duh uhsruwhg lq Pruulv

+4<:<,/ Wd|oru hw do1 +4<;:,/ dqg Qhzkrxvh hw do1 +4<<6,1

Wkh vdpsoh xvhg lq wklv vwxg| frqvlvwv ri lqglylgxdov lq wkh ihh0iru0vhuylfh

sodqv rqo|1 Zloo Pdqqlqj nlqgo| surylghg xv zlwk d gdwd �oh frqvlvwlqj ri wkh

lghqwl�huv iru wkh revhuydwlrqv xvhg lq Pdqqlqj hw do1 +4<;:, dorqj zlwk xwlol}d0

wlrq dqg h{shqglwxuhv +lq 4<9: grooduv, dqg d qxpehu ri fryduldwhv1 Wkhvh gdwd

45

zhuh phujhg zlwk wkh sxeolf0xvh UKLH �ohv dydlodeoh iurp wkh Lqwhu0xqlyhuvlw|

Frqvruwlxp iru Srolwlfdo dqg Vrfldo Uhvhdufk +LFSVU, wr rewdlq vrph dgglwlrqdo

yduldeohv1 Wkh �qdo vdpsoh frqvlvwv ri 534;9 revhuydwlrqv> hdfk revhuydwlrq uhs0

uhvhqwv gdwd iru dq h{shulphqwdo vxemhfw lq d jlyhq |hdu1

Zh frqvlghu rqo| rxwsdwlhqw khdowk fduh vhuylfhv lq wklv sdshu1 Wzr phdvxuhv

ri xwlol}dwlrq duh dqdo|}hg= wkh qxpehu ri frqwdfwv zlwk dq PG +PGX, dqg wkh

wrwdo qxpehu ri rxwsdwlhqw frqwdfwv zlwk dq PG ru rwkhu khdowk surihvvlrqdo/

+RSX,1 Wzr phdvxuhv ri h{shqglwxuhv duh dqdo|}hg= h{shqglwxuhv rq rxwsdwlhqw

ylvlwv +YV[, dqg h{shqglwxuhv rq rxwsdwlhqw phglfdo fduh +RS[,/ zklfk lqfoxghv

h{shqglwxuhv rq rxwsdwlhqw ylvlwv dqg h{shqglwxuhv rq suhvfulswlrq guxjv dqg

vxssolhv1 Vxppdu| vwdwlvwlfv iru wkhvh yduldeohv duh uhsruwhg lq Wdeoh 41 Wkh

lqvxudqfh sodq yduldeohv/ gh�qhg iroorzlqj Pdqqlqj hw do1 +4<;4,/ duh frlqvxudqfh

udwh/ d gxpp| yduldeoh iru sodqv zlwk d ghgxfwleoh +LGS,/ d pd{lpxp groodu0

h{shqglwxuh ixqfwlrq +IPGH,/ zklfk lv edvhg rq wkh qxpehu ri grooduv qhfhvvdu|

wr h{fhhg wkh ulvn fds rq sduwlflsdqwv/ dqg d sduwlflsdwlrq0lqfhqwlyh sd|phqw

ixqfwlrq +OSL,1 Wkh qxpehu ri fkurqlf frqglwlrqv +QGLVHDVH,/ h{lvwhqfh ri d

sk|vlfdo olplwdwlrq +SK\VOLP, dqg wkh elqdu| frglqj ri vhoi0uhsruwhg khdowk

vwdwxv +KOWKJ/ KOWKI/ KOWKS, frqwuro iru yduldwlrqv lq revhuyhg khdowk vwdwxv

zkloh d qxpehu ri rwkhu yduldeohv frqwuro iru yduldwlrq lq vrflr0hfrqrplf idfwruv1

Wkh gh�qlwlrqv ri wkhvh yduldeohv dorqj zlwk vxppdu| vwdwlvwlfv duh dovr uhsruwhg

lq Wdeoh 41

Wkh glvwulexwlrqv ri wkh ydulrxv phdvxuhv ri xwlol}dwlrq dqg wkrvh ri glvfuhwl}hg

h{shqglwxuhv duh uhsruwhg lq Wdeoh 51 Wkh sursruwlrqv ri }hur xwlol}dwlrq dqg h{0

shqglwxuhv duh vljql�fdqw> 5;064( ri lqglylgxdov kdg qr ylvlwv zkloh 55059( ri

lqglylgxdov kdg qr h{shqglwxuhv1 Pruhryhu/ <3( ri lqglylgxdov kdg ; ru ihzhu

ylvlwv dqg h{shqglwxuhv ohvv wkdq '5331 Krzhyhu/ wkh uljkw wdlov ri wkhvh glvwule0

xwlrqv duh yhu| orqj1 Iru xwlol}dwlrq/ wkh pd{lpxp ydoxhv udqjh iurp :: wr 47:1

Pd{lpxp h{shqglwxuhv udqjh iurp '5933 wr '5;431

46

71 Uhvxowv

Lq d suhylrxv yhuvlrq ri wklv sdshu/ zh xvhg gdwd iurp wkh vhfrqg dqg wklug

|hduv ri wkh h{shulphqw/ iru hvwlpdwlrq dqg iruhfdvwlqj uhvshfwlyho|/ wr h{dplqh

wkh shuirupdqfh ri OFP dqg WSP prghov xvlqj QE4 dqg QE5 edvhg ghqvlwlhv1

Vlqfh wkh uhvxowv ryhuzkhoplqjo| idyruhg QE4 prghov +vhh Ghe dqg Wulyhgl/ 4<<:/

iru dgglwlrqdo hylghqfh idyrulqj QE4 edvhg prghov ryhu QE5 edvhg prghov,/ lq

wklv sdshu zh uhsruw rqo| uhvxowv xvlqj QE4 ghqvlwlhv1 Pruhryhu/ zh gr qrw

frqvlghu 60frpsrqhqw �qlwh pl{wxuh prghov ehfdxvh suholplqdu| dqdo|vlv xvlqj

wkh UKLH gdwd vxjjhvwv wkdw vxfk prghov duh ryhusdudphwhul}hg16

Zh ehjlq e| uhsruwlqj olnholkrrg dqg jrrgqhvv ri �w frpsdulvrqv ri wkh OFP

dqg WSP xvlqj wkh ixoo vdpsoh ri 534;9 revhuydwlrqv dqg frpsdulvrqv lq wkh

furvv0ydolgdwlrq dqdo|vlv1 Wkhq zh ghvfuleh wkh fkdudfwhulvwlfv ri wkh odwhqw fodvvhv

dqg hqg zlwk dq dqdo|vlv ri wkh gl�huhqfhv lq srolf|0uhohydqw phdvxuhv fdofxodwhg

xvlqj OFP dqg WSP1

7141 Dqdo|vlv Xvlqj wkh Ixoo Vdpsoh

Wdeoh 6 suhvhqwv ydoxhv ri wkh orj olnholkrrg/ DLF dqg ELF iru hdfk phdvxuh ri

xwlol}dwlrq dqg h{shqglwxuh1 Wkhvh vkrz wkdw wkh OFP lv wkh suhihuuhg prgho e|

olnholkrrg dqg shqdol}hg olnholkrrg fulwhuld1 Zlwk rqo| wzr h{wud sdudphwhuv/ wkh

OFP surylghv vxevwdqwldoo| kljkhu ydoxhv ri wkh orj olnholkrrg1 Zkloh wkh "2 JrI

whvw uhmhfwv erwk vshfl�fdwlrqv iru hdfk phdvxuh ri xvh/ uhmhfwlrq/ dv qrwhg deryh/

lv qrw wrr vxusulvlqj jlyhq wkh whqghqf| ri wkh vwdwlvwlf wr ryhu0uhmhfw frxsohg

zlwk wkh odujh vdpsoh vl}h1 Krzhyhu/ wkh ydoxhv ri wkh JrI duh/ lq hdfk fdvh/

frqvlghudeo| vpdoohu iru wkh OFP wkdq iru wkh WSP/ vxjjhvwlqj ehwwhu �w ri wkh

OFP1 Wkh uhvxowv iru h{shqglwxuhv duh urexvw wr d fkdqjh lq wkh elq vl}h xvhg wr

glvfuhwl}h wkh frqwlqxrxv yduldeoh1 Wkh shqdol}hg olnholkrrg dqg JrI vwdwlvwlfv

iru h{shqglwxuhv glvfuhwl}hg xvlqj d elqvl}h ri '43 jlyh wkh vdph frqfoxvlrqv dv

wkrvh iru h{shqglwxuhv glvfuhwl}hg xvlqj d elqvl}h ri '531

6Iru rwkhu gdwd/ ru li d sulrul uhdvrqlqj surylghv vxssruw/ d pl{wxuh prgho zlwk pruh wkdq

wzr frpsrqhqwv pd| eh ghvludeoh1

47

Iljxuh 4 glvsod|v wkh gl�huhqfh ehwzhhq hpslulfdo dqg �wwhg iuhtxhqflhv iru

gl�huhqw ydoxhv ri wkh frxqw yduldeoh iru wkh WSP dqg OFP prghov1 Iru erwk

phdvxuhv ri xwlol}dwlrq/ PGX dqg RSX/ wkh shuirupdqfh ri OFP lq suhglfw0

lqj odujh dqg vpdoo qrq0}hur frxqwv lv gudpdwlfdoo| vxshulru1 Iru lqwhuphgldwh

ydoxhv dqg }hur/ WSP dqg OFP prghov shuirup vlploduo|1 Iru erwk phdvxuhv

ri h{shqglwxuhv/ YV[ dqg RS[/ wkh shuirupdqfh ri OFP lv dovr pxfk ehwwhu

wkdq wkdw ri WSP/ hvshfldoo| iru odujh h{shqglwxuhv1 Lq vxppdu|/ wkh fxpxodwlyh

hylghqfh srlqwv vwurqjo| lq idyru ri OFP prghov dv wkh suhihuuhg vshfl�fdwlrq

iru hvwlpdwlqj khdowk fduh xvh1 Lq rwkhu zrugv/ d prgho wkdw glvwlqjxlvkhv eh0

wzhhq lqiuhtxhqw dqg iuhtxhqw xvhu fodvvhv shuirupv pxfk ehwwhu wkdq rqh wkdw

glvwlqjxlvkhv ehwzhhq qrqxvhu dqg xvhu fodvvhv1

7151 Furvv0ydolgdwlrq

Lq wkh furvv0ydolgdwlrq h{huflvh/ wkh wudlqlqj vdpsoh frqvlvwv ri 47/333 udqgrpo|

fkrvhq revhuydwlrqv zkloh wkh uhpdlqlqj 9/4;9 revhuydwlrqv duh xvhg dv wkh krog0

rxw vdpsoh1 Wkh OFP dqg WSP prghov duh hvwlpdwhg xvlqj wkh wudlqlqj vdpsoh

dqg vwdwlvwlfv ri lqwhuhvw duh fdofxodwhg xvlqj wkrvh sdudphwhu hvwlpdwhv iru wkh

wudlqlqj dqg krogrxw vdpsohv1 Wklv h{huflvh lv uhshdwhg 83 wlphv/ wkh uhvxowv ri

zklfk duh vxppdul}hg lq Wdeoh 71

Ydoxhv ri wkh orj olnholkrrg/ DLF dqg JrI fdofxodwhg iru wkh wudlqlqj vdpsohv

ryhuzkhoplqjo| idyru OFP ryhu WSP1 Wkhvh duh frpsohwho| frqvlvwhqw zlwk rxu

�qglqjv xvlqj wkh ixoo vdpsoh ri revhuydwlrqv1 Exw OFP lv dovr idyruhg zkhq wkh

orj olnholkrrg/ DLF dqgPJrI vwdwlvwlfv duh fdofxodwhg iru wkh krogrxw vdpsohv1

Lq idfw/ rqo| iru RS[ lv wkhuh dq| hylghqfh dw doo ri wkh WSP ehlqj suhihuuhg wr

wkh OFP1

Lq d Ed|hvldq frqwh{w zlwk htxdoo| olnho| sulruv wrzdugv OFP dqg WSP ehlqj

wkh wuxh gdwd jhqhudwlqj surfhvv/ wkh gl�huhqfh lq wkh orj olnholkrrg ydoxhv ri wkh

wzr prghov pd| eh ylhzhg dv wkh orj ri wkh srvwhulru rggv udwlr ri wkh OFP ryhu

WSP jlyhq wkh gdwd1 Wkh uljkwprvw wkuhh froxpqv ri Wdeoh 7 glvsod| vxppdu|

vwdwlvwlfv ri wkh glvwulexwlrqv ri wkhvh orj olnholkrrg gl�huhqfhv1 Wkh odujh phdq

48

gl�huhqfhv lqglfdwh wkdw wkh gdwd duh pxfk pruh olnho| wr kdyh ehhq jhqhudwhg

e| OFP udwkhu wkdq WSP1

Wdnhq wrjhwkhu/ wkh lq0vdpsoh dqg furvv0ydolgdwlrq uhvxowv surylgh vwurqj hyl0

ghqfh ri d ihdwxuh ri wkh gdwd wkdw fkdoohqjhv wkh fxuuhqw sdudgljp1 Zh kdyh

vkrzq wkdw prghov ri xvh lq zklfk d glvwlqfwlrq lv pdgh ehwzhhq xvhuv dqg

qrqxvhuv duh grplqdwhg e| prghov wkdw glvwlqjxlvk ehwzhhq lqiuhtxhqw dqg iuh0

txhqw xvhuv1

7161 Fkdudfwhulvwlfv ri Odwhqw Fodvvhv

Rqfh d �qlwh pl{wxuh prgho kdv ehhq hvwlpdwhg/ wkh srvwhulru suredelolw| wkdw

revhuydwlrq l ehorqjv wr fdwhjru| n fdq eh fdofxodwhg iru hyhu| +l> n, sdlu1 Li ��

duh jlyhq +hvwlpdwhg,/ wkh srvwhulru suredelolw| wkdw revhuydwlrq |� ehorqjv wr wkh

srsxodwlrq n> n @ 4> 5> ===> F> lv jlyhq e|

Su^|� 5 srsxodwlrq n` @�&i&+|�m{

�

�>w&,

S��'� ��i�+|�m{�

�>w�,

= +714,

Wr h{dplqh wkh ghwhuplqdqwv ri wkh srvwhulru suredelolwlhv/ zh uhjuhvvhg wkh

orj rggv ri wkh srvwhulru suredelolwlhv rq wkh vhw ri fryduldwhv xvhg lq wkh odwhqw

fodvv prghov dqg JKLQG[/ d jhqhudo khdowk lqgh{1 JKLQG[ udwhv wkh sduwlfl0

sdqw*v shufhswlrq ri klv2khu khdowk vwdwxv dw hquroophqw dqg lv frqvwuxfwhg iurp

55 txhvwlrqqdluh lwhpv lq wkh UKLH1 Kljkhu ydoxhv lqglfdwh pruh idyrudeoh vhoi0

udwlqjv ri khdowk1 Dowkrxjk wkhvh txhvwlrqv zhuh qrw dvnhg ri lqglylgxdov dw wkh

Gd|wrq h{shulphqwdo vlwh/ zh xvh d yhuvlrq ri JKLQG[ rewdlqhg iurp Zloo Pdq0

qlqj lq zklfk plvvlqj ydoxhv duh uhsodfhg e| lpsxwhg ydoxhv1 JKLQG[ lv qrw

xvhg lq wkh WSP dqg OFP uhjuhvvlrqv iru wzr uhdvrqv1 Iluvw/ wkh khdowk ydul0

deohv lqfoxghg lq wkh prghov duh w|slfdoo| dydlodeoh lq odujh furvv0vhfwlrqdo vxuyh|v

zkloh JKLQG[ zdv frqvwuxfwhg iurp ulfkhu lqirupdwlrq qrw w|slfdoo| dydlodeoh1

Lq rwkhu zrugv/ rxu fkrlfh ri khdowk vwdwxv yduldeohv lv vwdqgdug1 Vhfrqg/ ehfdxvh

JKLQG[ zdv qrw xvhg dv d fryduldwh lq wkh prghov/ lw vhuyhv wr h{whuqdoo| fkhfn

rxu fodlp wkdw wkh odwhqw fodvvhv duh uhodwhg wr khdowk vwdwxv1

Uhvxowv ri wkhvh uhjuhvvlrqv/ uhsruwhg lq Wdeoh 8/ lqglfdwh wkdw wkh srvwhulru

49

suredelolwlhv kdyh wkh prvw vljql�fdqw dvvrfldwlrq zlwk JKLQG[ iru hdfk phdvxuh

ri xvh1 Pruhryhu/ wkh srvwhulru suredelolwlhv duh dovr vljql�fdqwo| dvvrfldwhg wr

QGLVHDVH dqg SK\VOLP lq wzr fdvhv1 Dprqj wkh rwkhu fryduldwhv/ rqo| DJH

dqg FKLOG duh vljql�fdqw lq wzr fdvhv1 Rwkhu fryduldwhv duh qhyhu vljql�fdqw1

Wr wkh h{whqw wkdw djh pljkw sur{| iru xqrevhuyhg frpsrqhqwv ri khdowk vwdwxv/

wkh vljql�fdqfh ri DJH dqg FKLOG pd| eh xvhg wr ixuwkhu vxssruw rxu fodlp1 Lq

vxppdu|/ zh �qg srzhuixo vxssruw iru rxu fodlp wkdw lqglylgxdov lq wkh wzr odwhqw

fodvvhv pd| eh fodvvl�hg dv khdowk| dqg loo lqglylgxdov1 Pruhryhu/ d qryho xvh ri

wkh odwhqw fodvv prgho lv vxjjhvwhg1 Lw pd| eh d srwhqwldoo| srzhuixo phdvxuh ri

khdowk vwdwxv edvhg rq khdowk fduh xwlol}dwlrq dqg ghprjudsklf fkdudfwhulvwlfv/

udwkhu wkdq rq folqlfdo phdvxuhv1

Zh uhsruw vxppdu| vwdwlvwlfv/ xvlqj ixoo vdpsoh hvwlpdwhv/ ri �wwhg ydoxhv ri

xwlol}dwlrq dqg h{shqglwxuhv iru shuvrqv lq hdfk odwhqw fodvv lq Wdeoh 91 Iru wkh

frxqw prghov ri xwlol}dwlrq/ txdqwlwlhv duh fdofxodwhg lq wkh reylrxv zd| xvlqj wkh

frqglwlrqdo h{shfwdwlrq ri |� gh�qhg e| hdfk frpsrqhqw ghqvlw| lq wkh pl{wxuh1

Wkh frxqw yduldeoh iru glvfuhwl}hg h{shqglwxuhv lv ehvw lqwhusuhwhg dv wkh revhuyhg

txdolwdwlyh ydoxhv ri d odwhqw surfhvv1 Iru wkhvh prghov/ zh fdofxodwh h{shfwhg

h{shqglwxuh iru hdfk lqglylgxdo xvlqj wkh irupxodS"

�'fSu+m,p+m, zkhuh Su+m,

lv wkh suredelolw| ri revhuylqj wkh frxqw ydoxh m dqg p+m, lv wkh plgsrlqw ri

wkh udqjh ri xqghuo|lqj frqwlqxrxv h{shqglwxuhv glvfuhwl}hg wr wkh frxqw ydoxh

m/ l1h1/ p+m, @ 3> 43> 63> 83> === iru m @ 3> 4> 5> 6> === jlyhq wkh elq0vl}h ri 531 Qrwh

wkdw wkh vdpsoh phdqv ri wkh �wwhg ydoxhv duh yhu| forvh wr wkh fruuhvsrqglqj

vdpsoh dyhudjhv1 Wklv lv qrw d wulyldo uhvxow dv wkh odwhqw fodvv prghov duh kljko|

qrqolqhdu1 Pruhryhu/ iru h{shqglwxuhv/ �wwhg ydoxhv duh edvhg rq d plg0srlqw

dssur{lpdwlrq1 Frqvhtxhqwo|/ wkhvh uhvxowv surylgh dq lpsruwdqw fkhfn rq wkh

ydolglw| ri wkh odwhqw fodvv prghov1

Wkh suredelolw| ri ehlqj lq wkh khdowk| fodvv lv 319;031;3 iru wkh irxu phdvxuhv

ri xvh1 Frqvhtxhqwo|/ 53065 shufhqw ri lqglylgxdov duh fodvvl�hg dv loo1 Wkh khdowk|

dqg loo vxe0srsxodwlrqv kdyh yhu| gl�huhqw �wwhg ydoxhv1 Wkh phdq �wwhg ydoxhv

duh 607 wlphv odujhu iru loo shuvrqv wkdq iru khdowk| shuvrqv1 Wkh plqlpxp dqg

4:

pd{lpxp �wwhg ydoxhv duh dovr gudpdwlfdoo| gl�huhqw1 Wkh �wwhg phdqv/ ryhudoo

dqg iru hdfk odwhqw fodvv/ xvlqj wkh prghov hvwlpdwhg iru glvfuhwl}hg h{shqglwxuhv

zlwk d elqvl}h ri '43/ dovr uhsruwhg lq Wdeoh 9/ duh yhu| forvh wr wkrvh rewdlqhg

xvlqj wkh '53 elqvl}h/ ixuwkhu vxssruwlqj wkh urexvwqhvv ri wkh suhihuuhg prgho

iru h{shqglwxuhv1 Ryhudoo/ wkh glvwulexwlrqv ri xvh iru lqglylgxdov lq hdfk odwhqw

fodvv duh vxevwdqwlyho| gl�huhqw1

Qrwh wkdw rxu glfkrwrpl}dwlrq ri �khdowk|� dqg �loo� lv lqwhqghg wr dsso| wr

wkh dyhudjh lqglylgxdo lq hdfk fodvv1 Lw vkrxog qrw eh wdnhq wrr olwhudoo| ehfdxvh

qrw doo kljk0xvhuv pd| eh �loo�/ qru doo orz0xvhuv �khdowk|�1

7171 Srolf| Lpsolfdwlrqv

Lq jhqhudo/ pdq| phdvxuhv ri srolf| lqwhuhvw duh qrqolqhdu ixqfwlrqv ri doo wkh

sdudphwhuv lq wkh prgho1 Frqvlvwhqw hvwlpdwlrq ri wkhvh phdvxuhv xvxdoo| uhtxluhv

fruuhfw vshfl�fdwlrq ri wkh gdwd glvwulexwlrq1 Zh irfxv rq wzr h{dpsohv ri vxfk

srolf|0uhohydqw phdvxuhv1

Iluvw/ frqvlghu wkh sulfh hodvwlflw| ri ghpdqg1 Vshfl�fdoo|/ frqvlghu hvwlpdwlqj

duf0sulfh hodvwlflwlhv ri wkh nlqg fdofxodwhg lq d qxpehu ri UDQG vwxglhv ri wkh

UKLH +h1j1 Pdqqlqj hw do1/ 4<;:,/ gh�qhg dv

%+s�> s2, @t+s2,� t+s�,

s2 � s�

�

s2 . s�

t+s2, . t+s�,>

zkhuh vxevfulswv 4 dqg 5 ghqrwh wkh wzr srlqwv ri frpsdulvrq/ zlwk s�> t+s�, dqg

s2> t+s2, ghqrwlqj wkh sulfhv dqg txdqwlwlhv +xwlol}dwlrq ru h{shqglwxuh, dw wkrvh

wzr srlqwv uhvshfwlyho|1 Lq jhqhudo/ wkhvh hodvwlflwlhv zloo eh qrqolqhdu ixqfwlrqv

ri doo wkh sdudphwhuv lq wkh prgho1 Wkhuhiruh/ fruuhfw vshfl�fdwlrq ri wkh gdwd

jhqhudwlqj phfkdqlvp lv lpsruwdqw17

7Wklv lv wuxh ri wkh prvw vwdqgdug wzr0sduw prgho lq zklfk wkh h{shfwhg txdqwlw| dw hdfksulfh lv wkh surgxfw ri wkh suredelolw| ri revhuylqj d qrq0}hur txdqwlw| +iru h{dpsoh/ iurpwkh surelw prgho, dqg wkh frqglwlrqdo h{shfwdwlrq ri wkh txdqwlw| +iru h{dpsoh/ iurp wkh orj0ROV uhjuhvvlrq, jlyhq wkdw txdqwlw| lv srvlwlyh1 Frqvlvwhqw hvwlpdwhv ri wkh suredelolw| iurpwkh �uvw sduw ghshqgv rq wkh vshfl�fdwlrq ri wkh glvwulexwlrq ri wkh elqdu| gdwd1 Frqvlvwhqwfrqglwlrqdo h{shfwdwlrqv lq wkh vhfrqg sduw ghshqg rq fruuhfw glvwulexwlrqdo dvvxpswlrqv +h1j1orjqrupdolw|,/ ru rq wkh ydolglw| ri wkh dvvxpswlrqv iru wkh vphdulqj uhwudqirupdwlrq wr surylgh

4;

Qh{w/ frqvlghu wkh suredelolw| wkdw xvh h{fhhgv d sduwlfxodu wkuhvkrog ydoxh

dv dq h{dpsoh ri jhqhudo lqwhuhvw lq fkdudfwhul}dwlrqv ri wkh xsshu wdlo ri wkh

glvwulexwlrq ri xvh +frqglwlrqdo rq fryduldwhv,1 Iru h{dpsoh/ vxssrvh '6/333 lv

frqvlghuhg wr eh d odujh h{shqglwxuh1 D uhjxodwru pd| zlvk wr fdofxodwh wkh sure0

delolw| wkdw d shuvrq/ ru jurxs ri shuvrqv/ zlwk d sduwlfxodu vhw ri fkdudfwhulvwlfv/

h{fhhgv h{shqglwxuhv ri '6/333/ l1h1/ Su+|� A 6333m{�,1 Frqvlvwhqw hvwlpdwlrq ri

wkhvh suredelolwlhv ghshqgv rq fruuhfw vshfl�fdwlrq ri wkh glvwulexwlrq ri h{shq0

glwxuhv1 Zkloh qrq0sdudphwulf uhjuhvvlrq pd| eh xvhg dv dq dowhuqdwlyh/ lw lv

zhoo nqrzq wr shuirup srruo| lq wkh wdlov ri wkh glvwulexwlrq zkhuh wkh gdwd duh

wklqo| glvwulexwhg1 Frqvhtxhqwo|/ lw lv olnho| wr shuirup yhu| srruo| lq suhflvho|

wkh nlqgv ri vlwxdwlrqv wkdw duh olnho| wr eh ri srolf| lpsruwdqfh1

Wdeoh : uhsruwv duf0sulfh hodvwlflwlhv iru frlqvxudqfh fkdqjhv iurp 3 wr 58 shu0

fhqw dqg iurp 58 wr <8 shufhqw1 Iru wkh xqfrqglwlrqdo hvwlpdwhv/ t+s�, dqg t+s2,

duh wkh dssursuldwho| vwudwl�hg vdpsoh dyhudjhv ri xwlol}dwlrq dqg h{shqglwxuhv1

Wkh hvwlpdwhv iru wkh h{shqglwxuh yduldeoh YV[ duh dqdorjrxv wr wkrvh uhsruwhg

lq Pdqqlqj hw do1 +4<;:,18 Hodvwlflwlhv iru RS[ dqg wkh phdvxuhv ri xwlolwl}dwlrq

duh qrw uhsruwhg lq Pdqqlqj/ hw do1 Iru wkh frqglwlrqdo hvwlpdwhv/ dq duf0sulfh

hodvwlflw| zdv �uvw fdofxodwhg iru hdfk lqglylgxdo/ frqglwlrqdo rq wkh ydoxhv ri wkdw

lqglylgxdo*v fkdudfwhulvwlfv exw zlwk wkh frlqvxudqfh udwh vhw wr wkh ydoxh fkrvhq

iru wkh srlqw ri frpsdulvrq1 Wkh vdpsoh dyhudjhv ri wkhvh lqglylgxdo hodvwlflwlhv

duh uhsruwhg1 <8( frq�ghqfh lqwhuydov iru hdfk hodvwlflw| duh dovr uhsruwhg1 Wkh

frq�ghqfh lqwhuydov duh frqvwuxfwhg xvlqj Prqwh Fduor whfkqltxhv lq wkh iroorzlqj

zd|1 Iluvw/ sdudphwhuv ri wkh xqghuo|lqj prghov duh gudzq iurp d pxowlyduldwh

qrupdo glvwulexwlrq zlwk phdq jlyhq e| wkh srlqw hvwlpdwhv ri wkh sdudphwhuv

dqg fryduldqfh pdwul{ jlyhq e| wkh urexvw vdqgzlfk hvwlpdwh1 Wkh dyhudjhv ri

lqglylgxdo hodvwlflwlhv ri lqwhuhvw duh fdofxodwhg iru hdfk gudz1 Wkh surfhvv lv

uhshdwhg 4333 wlphv dqg wkh 518 dqg <:18 shufhqwloh srlqwv duh uhsruwhg19

frqvlvwhqw hvwlpdwhv1 Frqvlvwhqw hvwlpdwhv ri wkh surgxfw ri wkh wzr ghshqg/ lq dgglwlrq/ rq wkh

frqglwlrq wkdw wkh wzr0sduw vwuxfwxuh lv fruuhfw18Vpdoo gl�huhqfhv duh gxh wr voljkw gl�huhqfhv lq wkh vdpsoh dqg urxqg0r� huuruv19Wklv surfhgxuh lv frpsxwdwlrqdoo| frqvlghudeo| fkhdshu wkdq errwvwudslqj wkh glvwulexwlrq

ri dyhudjh hodvwlflw|1

4<

Wkuhh ihdwxuhv ri wkh hodvwlflwlhv uhsruwhg lq Wdeoh : duh qrwdeoh1 Iluvw/ wkh

xqfrqglwlrqdo hvwlpdwhv duh vxevwdqwldoo| gl�huhqw iurp wkh frqglwlrqdo hvwlpdwhv1

Xqfrqglwlrqdo/ prgho0iuhh hvwlpdwhv ri srolf|0uhohydqw phdvxuhv vxfk dv hodvwlfl0

wlhv pd| qrw surylgh dffxudwh hvwlpdwhv ri wkh fhwhulv sdulexv phdvxuhv ri lqwhuhvw1

Vhfrqg/ zkloh wkh 3�58 hodvwlflwlhv frqvwuxfwhg xvlqj wkh OFP duh voljkwo| odujhu

wkdq dqdorjrxv hvwlpdwhv xvlqj wkh WSP/ wkh 580<8 hodvwlflwlhv duh vxevwdqwldoo|

vpdoohu1 Hodvwlflw| hvwlpdwhv duh vhqvlwlyh wr wkh fkrlfh ri prgho1 Wklug/ zlwklq

wkh vhw ri hodvwlflwlhv frqvwuxfwhg xvlqj wkh OFP/ 3058 hodvwlflwlhv duh odujhu wkdq

580<8 hodvwlflwlhv vxjjhvwlqj juhdwhu sulfh vhqvlwlylw| dw orzhu sulfhv wkdq dw kljkhu

sulfhv1

Wr ixuwkhu looxvwudwh gl�huhqfhv ehwzhhq hodvwlflwlhv rewdlqhg e| OFP dqg

WSP/ zh fdofxodwh wkhp iru d qxpehu ri k|srwkhwlfdo lqglylgxdov ehjlqqlqj zlwk

d edvholqh lqglylgxdo zkr lv pdoh/ dgxow/ qrq0eodfn/ lq h{fhoohqw vhoi0shufhlyhg

khdowk/ zlwk qr sk|vlfdo olplwdwlrqv exw zlwk dq dyhudjh qxpehu ri fkurqlf glv0

hdvhv/ ri dyhudjh djh dqg hgxfdwlrq/ zlwk dyhudjh lqfrph +orj, dqg kdv dq lqvxu0

dqfh sodq zlwk qr ghgxfwleoh dqg dyhudjh sduwlflsdwlrq lqfhqwlyh sd|phqw dqg

pd{lpxp groodu h{shqglwxuh1 Doo rwkhu lqglylgxdov frqvlghuhg duh ghyldwlrqv

iurp wklv edvholqh lqglylgxdo1 Wkh uhvxowv lq Wdeoh ;/ uhsruwhg dv shufhqwdjh gli0

ihuhqfhv ehwzhhq WSP dqg OFP hodvwlflw| hvwlpdwhv/ vkrz gudpdwlf gl�huhqfhv1

Wkh hodvwlflwlhv iru wkh uhsuhvhqwdwlyh eodfn shuvrq duh hvshfldoo| qrwdeoh1 Hv0

wlpdwhv iurp WSP frqvlvwhqwo| vxjjhvw wkdw eodfnv duh pruh sulfh hodvwlf wkdq

qrq0eodfnv1 Exw hvwlpdwhv iurp OFP ryhuwxuq wklv uhvxow 0 eodfnv duh qr pruh

sulfh vhqvlwlyh wkdq qrq0eodfnv1

Shufhqwdjh gl�huhqfhv ehwzhhq hvwlpdwhv ri suredelolwlhv ri xwlol}dwlrq dqg h{0

shqglwxuhv edvhg rq WSP dqg OFP h{fhhglqj suhghwhuplqhg wkuhvkrogv duh dovr

uhsruwhg lq Wdeoh ;1 Shufhqwdjh gl�huhqfhv ehwzhhq hvwlpdwhv ri wkh suredelolw|

ri revhuylqj qr xvh duh dovr uhsruwhg1 Dowkrxjk fdofxodwlrqv edvhg rq wkh wzr

prghov jhqhudoo| vkrz rqo| vpdoo gl�huhqfhv ehwzhhq suredelolwlhv ri qr xvh +wkh

vwdqgdug wzr0sduw prgho vkrxog suhglfw wklv shuihfwo|,/ wkhuh duh jhqhudoo| odujh

gl�huhqfhv ehwzhhq wkh suredelolwlhv ri kljk xvh1 Kljk xvh suredelolwlhv hvwlpdwhg

53

e| WSP duh frqvlvwhqwo| vpdoohu wkdq dqdorjrxv suredelolwlhv hvwlpdwhg e| OFP1

81 Frqfoxvlrq

Wkh dqdo|vlv ri wklv sdshu surylghv vwurqj hylghqfh lq idyru ri d odwhqw fodvv prgho

dv frpsduhg wr d wzr0sduw prgho/ zklfk lv vxssruwhg e| wkh rxwfrphv ri erwk

lq0vdpsoh dqg furvv0ydolgdwlrq prgho vhohfwlrq whvwv1 Wkh odwhqw fodvv prgho lv

k|srwkhvl}hg wr eh edvhg rq glvfuhwh uhsuhvhqwdwlrq ri xqrevhuyhg khdowk0vwdwxv

khwhurjhqhlw| wkdw lv qrw fdswxuhg e| wkh xvxdo vxuyh| phdvxuhv ri khdowk vwdwxv1

Rxu hpslulfdo dqdo|vlv ydolgdwhv wklv glvwlqfwlrq ehwzhhq wkh wzr vxe0srsxodwlrqv/

khdowk| dqg wkh loo/ zkrvh ghpdqgv iru phglfdo fduh duh fkdudfwhul}hg e| orz phdq

dqg kljk phdq/ uhvshfwlyho|1

Wr wkh h{whqw wkdw wkh hpslulfdo shuirupdqfh ri wkh WSP kdv ehhq lqwhusuhwhg

dv vxssruw iru d sulqflsdo0djhqw iudphzrun iru phglfdo fduh/ rxu uhvxowv fdvw grxew

rq vxfk d frqfoxvlrq1 Vwulfwo|/ krzhyhu/ qhlwkhu wkh OFP qru wkh WSP uxoh lq ru

rxw wkh sulqflsdo0djhqw iudphzrun1 Qhyhuwkhohvv/ rxu uhvxowv gr vxjjhvw d vxshulru

hfrqrphwulf iudphzrun iru prgholqj wkh ghpdqg iru khdowk fduh/ rqh wkdw lv olnho|

wr surgxfh ehwwhu hvwlpdwhv ri lqwhuhvw wr uhvhdufkhuv1

Wkh sulfh vhqvlwlylw| ri khdowk fduh ghpdqg lv d nh| phdvxuh ri srolf| lqwhuhvw1

Rxu frpsdulvrqv vkrz wkdw wkh wzr frpshwlqj iudphzrunv jhqhudwh sulfh hodv0

wlflwlhv wkdw duh vxevwdqwldoo| gl�huhqw1 Gluhfw frpsdulvrqv zlwk suhylrxv vwxglhv

duh pruh gl!fxow ehfdxvh ri gl�huhqfhv lq vdpsohv dv zhoo dv phwkrgv ri fdofx0

odwlqj hodvwlflwlhv1 Vxemhfw wr wklv fdyhdw/ rxu ryhudoo frpsdulvrqv vkrz wkdw wkh

odwhqw fodvv iudphzrun |lhogv vrphzkdw odujhu ydoxhv ri hodvwlflwlhv dw orz sulfhv

dqg vxevwdqwldoo| vpdoohu ydoxhv ri hodvwlflwlhv dw kljk sulfhv wkdq xqfrqglwlrqdo

hvwlpdwhv dqg wkrvh edvhg rq wkh wzr0sduw prgho1 D frpsdulvrq ri kljk0xvh

suredelolwlhv fdofxodwhg iurp wzr0sduw dqg odwhqw fodvv prghov iru k|srwkhwlfdo

lqglylgxdov ixuwkhu ghprqvwudwhv wkdw srolf|0uhohydqw suhglfwlrqv iurp wkh wzr

w|shv ri prghov duh vxevwdqwlyho| gl�huhqw1

54

Uhihuhqfhv

Dqguhzv/ G1Z1N1 +4<;;,/ �Fkl0vtxduh Gldjrqrvwlf Whvwv iru Hfrqrphwulf Prg0

hov= Wkhru|�/ Hfrqrphwulfd/ 89/ 474<047861

Dqguhzv/ G1Z1N1 +4<;;,/ �Fkl0vtxduh Gldjrqrvwlf Whvwv iru Hfrqrphwulf Prg0

hov= Lqwurgxfwlrq dqg Dssolfdwlrqv�/ Mrxuqdo ri Hfrqrphwulfv/ 6:/ 46804891

Fdphurq/ F1/ S1N1 Wulyhgl/ I1 Ploqh/ dqg M1 Sljjrw +4<;;,/ �D Plfurhfrqrphwulf

Prgho ri wkh Ghpdqg iru Khdowk Fduh dqg Khdowk Lqvxudqfh lq Dxvwudold�/

Uhylhz ri Hfrqrplf Vwxglhv/ 88/ ;804391

Fdphurq/ D1F1/ dqg S1N1 Wulyhgl +4<<;,/ Uhjuhvvlrq Dqdo|vlv ri Frxqw Gdwd/

Hfrqrphwulf Vrflhw| Prqrjudsk 631 Qhz \run= Fdpeulgjh Xqlyhuvlw|

Suhvv1

Ghe/ S1/ dqg S1N1 Wulyhgl +4<<:,/ �Ghpdqg iru Phglfdo Fduh e| wkh Hoghuo|

lq wkh Xqlwhg Vwdwhv= D Ilqlwh Pl{wxuh Dssurdfk�/ Mrxuqdo ri Dssolhg

Hfrqrphwulfv/ 45/ 64606691

Gxdq/ Q1/ Z1J1 Pdqqlqj/ F1Q1 Pruulv dqg M1S1 Qhzkrxvh +4<;6,/ �D Frpsdu0

lvrq ri Dowhuqdwlyh Prghov iru wkh Ghpdqg iru Phglfdo Fduh�/ Mrxuqdo ri

Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv/ 4/ 44804591

Jhugwkdp/ X10J1 +4<<:,/ �Htxlw| lq Khdowk Fduh Xwlol}dwlrq= Ixuwkhu Whvwv

Edvhg rq Kxugoh Prghov dqg Vzhglvk Plfur Gdwd�/ Khdowk Hfrqrplfv/ 9/

636064<1

Jhzhnh/ M1 dqg P1 Nhdqh +4<<:,/ �Pl{wxuh ri Qrupdov Surelw Prghov�/ Ihghudo

Uhvhuyh Edqn ri Plqqhdsrolv/ Vwd� Uhsruw 56:1

Julw}/ P1 +4<<6,/ �Wkh Lpsdfw ri Wudlqlqj rq wkh Iuhtxhqf| dqg Gxudwlrq ri

Hpsor|phqw�/ Mrxuqdo ri Hfrqrphwulfv/ 8:/ 540841

Jurvvpdq/ P1/ 4<:5/ �Rq wkh Frqfhsw ri Khdowk Fdslwdo dqg wkh Ghpdqg iru

Khdowk�/ Mrxuqdo ri Srolwlfdo Hfrqrp|/ ;3/ 55605881

55

Kdxjkwrq/ G1 +4<<:,/ �Sdfndjhv iru Hvwlpdwlqj Ilqlwh Pl{wxuhv�/ Dphulfdq Vwd0

wlvwlfldq/ 84/ 4<705381

Khfnpdq/ M1M1/ U1 Uree/ dqg P1 Zdonhu +4<<3,/ �Whvwlqj wkh Pl{wxuhv ri H{sr0

qhqwldov K|srwkhvlv dqg Hvwlpdwlqj wkh Pl{lqj Glvwulexwlrq e| wkh Phwkrg

ri Prphqwv�/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ ;8/ 8;508;<1

Khfnpdq/ M1 M1 dqg E1 Vlqjhu +4<;7,/ �D Phwkrg ri Plqlpl}lqj wkh Glvwulex0

wlrqdo Lpsdfw lq Hfrqrphwulf Prghov iru Gxudwlrq Gdwd�/ Hfrqrphwulfd/

85/ 5:406531

Khfnpdq/ M1M1 dqg M1D1 Vplwk +4<<8,/ �Dvvhvvlqj wkh Fdvh iru Vrfldo H{shul0

phqwv�/ Mrxuqdo ri Hfrqrplf Shuvshfwlyhv/ </ ;804431

Mrqhv/ D1 P1 +4<<;,/ �Khdowk Hfrqrphwulfv�/ iruwkfrplqj lq M1 S1 Qhzkrxvh

dqg D1 M1 Fxo|hu/ hgv1/ Kdqgerrn ri Khdowk Hfrqrplfv/ Dpvwhugdp= Qruwk

0 Kroodqg1

Nhhohu/ H1E1/ Z1J1 Pdqqlqj/ N1E1 Zhoov �Wkh Ghpdqg iru Hslvrghv ri Phqwdo

Khdowk Vhuylfhv�/ Mrxuqdo ri Khdowk Hfrqrplfv/ :/ 66:09:1

Odlug/ Q1 +4<:;,/ �Qrqsdudphwulf Pd{lpxp Olnholkrrg Hvwlpdwlrq ri d Pl{lqj

Glvwulexwlrq�/ Mrxuqdo ri wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ :6/ ;380;441

Olqgvd|/ E1 M1 +4<<8,/ Pl{wxuh Prghov= Wkhru|/ Jhrphwu|/ dqg Dssolfdwlrqv/

QVI0FEPV Uhjlrqdo Frqihuhqfh Vhulhv lq Suredelolw| dqg Vwdwlvwlfv/ Yro1

8/ LPV0DVD1

Pdqqlqj/ Z1J1/ F1Q1 Pruulv/ M1S1 Qhzkrxvh/ O1O1 Ruu/ Q1 Gxdq/ H1E1 Nhhohu/ D1

Ohlerzlw}/ N1K1 Pdutxlv/ P1V1 Pdutxlv dqg F1H1 Skhosv +4<;4,/ �D Wzr0

Sduw Prgho ri wkh Ghpdqg iru Phglfdo Fduh= Suholplqdu| Uhvxowv iurp wkh

Khdowk Lqvxudqfh Vwxg|�/ lq M1 ydq ghu Jddj dqg P1 Shuopdq/ hgv1/ Khdowk/

Hfrqrplfv/ dqg Khdowk Hfrqrplfv/ 4360456/ Dpvwhugdp= Qruwk 0 Kroodqg1

56

Pdqqlqj/ Z1 J1/ M1S1 Qhzkrxvh/ Q1 Gxdq/ H1E1 Nhhohu/ D1 Ohlerzlw} dqg P1

V1 Pdutxlv +4<;:,/ �Khdowk Lqvxudqfh dqg wkh Ghpdqg iru Phglfdo Fduh=

Hylghqfh iurp d Udqgrpl}hg H{shulphqw�/ Dphulfdq Hfrqrplf Uhylhz/

::/ 58405::1

PfFdoo/ Q1/ W1 Ulfh/ M1 Erlvplhu dqg U1 Zhvw +4<<4,/ �Sulydwh Khdowk Lqvxudqfh

dqg Phglfdo Fduh Xwlol}dwlrq= Hylghqfh iurp wkh Phglfduh Srsxodwlrq�/

Lqtxlu|/ 5;/ 5:905;:1

PfOdfkodq/ J1M1/ dqg N1H1 Edvirug +4<;;,/ Pl{wxuh Prghov= Lqihuhqfh dqg Ds0

solfdwlrq wr Foxvwhulqj/ Qhz \run= Pdufho Ghnnhu1

Prugxfk/ M1 dqg K1V1 Vwhuq +4<<:,/ �Xvlqj Pl{wxuh Prghov wr Ghwhfw Vh{ Eldv

lq Khdowk Rxwfrphv lq Edqjodghvk�/ Mrxuqdo ri Hfrqrphwulfv/ ::/ 58<05:91

Pruulv/ F1Q1 +4<:<,/ �D �qlwh Vhohfwlrq Prgho iru H{shulphqwdo Ghvljq ri wkh

Khdowk Lqvxudqfh Vwxg|�/ Mrxuqdo ri Hfrqrphwulfv/ 44/ 760941

Pxoodk|/ M1 +4<<;,/ �Pxfk Dgr Derxw Wzr= Uhfrqvlghulqj Uhwudqvirupdwlrq

dqg wkh Wzr0sduw Prgho lq Khdowk Hfrqrphwulfv�/ Mrxuqdo ri Khdowk Hfr0

qrplfv/ 4:/ 57:05;41

Qhzkrxvh/ M1S1 dqg wkh Lqvxudqfh H{shulphqw Jurxs +4<<6,/ Iuhh iru dooB Ohvvrqv

iurp wkh UDQG Khdowk Lqvxudqfh H{shulphqw/ Fdpeulgjh dqg Orqgrq=

Kduydug Xqlyhuvlw| Suhvv1

Srkophlhu/ Z1 dqg Y1 Xoulfk +4<<8,/ �Dq Hfrqrphwulf Prgho ri wkh Wzr0Sduw

Ghflvlrqpdnlqj Surfhvv lq wkh Ghpdqg iru Khdowk Fduh�/ Wkh Mrxuqdo ri

Kxpdq Uhvrxufhv/ 63/ 66<06941

Vlq/ F0\/ dqg K1 Zklwh +4<<9,/ �Lqirupdwlrq Fulwhuld iru Vhohfwlqj Srvvleo|

Plvvshfl�hg Sdudphwulf Prghov�/ Mrxuqdo ri Hfrqrphwulfv/ :4/ 53:0581

Wd|oru/ F1 g*Duf/ V1P1 Srolfk/ F1H1 Shwhuvrq/ H1P1 Vorvv +4<;:,/ Xvhuv Jxlgh

wr KLH Gdwd/ KLH Uhihuhqfh Vhulhv/ Yro1 6/ Vdqwd Prqlfd= Wkh Udqg

Frusrudwlrq1

57

Wlwwhulqjwrq/ G1P1/ D1I1P1 Vplwk dqg X1H1 Pdnrz +4<;8,/ Vwdwlvwlfdo Dqdo|vlv

ri Ilqlwh Pl{wxuh Glvwulexwlrqv1 Qhz \run= Mrkq Zloh|1

Zdqj/ S1/ L1P1 Frfnexuq/ dqg P1 O1 Sxwhupdq +4<<;,/ �Dqdo|vlv ri Sdwhqw Gdwd

0 D Pl{hg Srlvvrq Uhjuhvvlrq Prgho Dssurdfk�/ Mrxuqdo ri Exvlqhvv dqg

Hfrqrplf Vwdwlvwlfv/ 49/ 5:0691

Zhgho/ P1/ Z1V1 Ghvduer/ M1U1 Exow/ dqg Y1 Udpdvzdp| +4<<6,/ �D Odwhqw

Fodvv Srlvvrq Uhjuhvvlrq Prgho Iru Khwhurjhqhrxv Frxqw Gdwd�/ Mrxuqdo

ri Dssolhg Hfrqrphwulfv/ ;/ 6<:07441

]zhliho/ S1 +4<;4,/ �Vxssolhu0Lqgxfhg Ghpdqg lq d Prgho ri Sk|vlfldq Ehkdy0

lru�/ lq M1 ydq ghu Jddj dqg P1 Shuopdq/ hgv1/ Khdowk/ Hfrqrplfv/ dqg

Khdowk Hfrqrplfv/ 578059:1 Dpvwhugdp= Qruwk 0 Kroodqg1

58

Wdeoh 4

Yduldeoh Gh�qlwlrqv dqg Vxppdu| Vwdwlvwlfv

Yduldeoh Gh�qlwlrq Phdq Vwg1 Ghy1

PGX Qxpehu ri rxwsdwlhqw ylvlwv wr dq PG 51;94 71838

RSX Qxpehu ri rxwsdwlhqw ylvlwv wr doo surylghuv 61879 91639

YV[ H{shqglwxuhv rq rxwsdwlhqw ylvlwv 841464 <71<68

RS[ H{shqglwxuhv rq doo rxwsdwlhqw fduh :41433 45315:3

OF oq+frlqvxudqfh.4,/ 3�frlqvxudqfh�433 41:43 41<958

LGS 4 li lqglylgxdo ghgxfwleoh sodq/ 3 rwkhuzlvh 31553 31747

OSL oq+pd{+4/dqqxdo sduwlflsdwlrq lqfhqwlyh sd|phqw,, 71:3< 519<:

IPGH 3 li LGS@4 61486 61974

oq+pd{+4/PGH2+3134 frlqvxudqfh,,, rwkhuzlvh

OLQF oq+idplo| lqfrph, ;1:3; 4155;

OIDP oq+idplo| vl}h, 4157; 3186<

DJH djh lq |hduv 581:4; 491:9;

IHPDOH 4 li shuvrq lv ihpdoh 3184: 31833

FKLOG 4 li djh lv ohvv wkdq 4; 31735 317<3

IHPFKLOG IHPDOH - FKLOG 314<7 316<8

EODFN 4 li udfh ri krxvhkrog khdg lv eodfn 314;5 316;6

HGXFGHF hgxfdwlrq ri wkh krxvhkrog khdg lq |hduv 441<9: 51;39

SK\VOLP 4 li wkh shuvrq kdv d sk|vlfdo olplwdwlrq 31457 31655

QGLVHDVH qxpehu ri fkurqlf glvhdvhv 441577 91:75

KOWKJ 4 li vhoi0udwhg khdowk lv jrrg 31695 317;4

KOWKI 4 li vhoi0udwhg khdowk lv idlu 313:: 3159:

KOWKS 4 li vhoi0udwhg khdowk lv srru 31348 31454

rplwwhg fdwhjru| lv h{fhoohqw vhoi0udwhg khdowk

Qrwh=

PGH ghqrwhv pd{lpxp groodu h{shqglwxuh/ wkh phglfdo h{shqglwxuh oldelolw| olplw vhw lq

wkh h{shulphqw deryh zklfk wkh sduwlflsdqw zrxog qrw eh uhvsrqvleoh iru frvw0vkdulqj1

59

Wdeoh 5

Iuhtxhqf| Glvwulexwlrqv ri Xwlol}dwlrq dqg Glvfuhwl}hg H{shqglwxuhv

Xwlol}dwlrq H{shqglwxuhv +glvfuhwl}hg,

\ PGX RSX YV[ RS[

3 6415 5;16 3 5819 5517

4 4;1< 4;16 3053 5616 4;13

5 461; 461: 53073 491; 4716

6 <16 <18 930;3 <18 4414

7 91: 91: ;30433 917 :16

8 71; 813 4330453 714 815

9 617 619 4530473 614 714

: 519 51; 4730493 516 615

; 513 515 49304;3 418 517

< 417 419 4;30533 414 41;

43 413 415 5330553 413 418

44 31< 413 5530573 31; 416

45 319 31; 5730593 31: 413

46 318 319 59305;3 317 31<

47 317 319 5;30633 318 31;

48 316 317 6330653 317 318

49 316 317 6530673 317 318

4: 315 315 6730693 316 318

4; 315 316 69306;3 315 316

4< 315 315 6;30733 315 316

53 314 315 7330753 315 316

54. 413 514 753. 515 516

Pd{ :: 47: 463 474

Pd{ ' 5933 5;43

Qrwh=

Wkh h{shqglwxuh elq lqwhuydov duh +{/|`1

5:

Wdeoh 6

Prgho Vhohfwlrq dqg Jrrgqhvv0ri0�w xvlqj wkh Ixoo Vdpsoh

Yduldeoh Prgho oqO DLF ELF JrI

Xwlol}dwlrq +PGX, WSP 07548< ;76<5 ;796; 5;51;

OFP 075373u ;748;� ;774:� 43618C

Xwlol}dwlrq +RSX, WSP 078686 <3::< <4358 9631;

OFP 07838;u <34<7� <3786� <419C

H{shqglwxuh +YV[, WSP 075689 ;7:;9 ;8365 8:;14

OFP 075553u ;784<� ;7::;� 56418C

H{shqglwxuh +RS[, WSP 07:39; <753< <7788 85818

OFP 07:339u <73;<� <767;� <<1<C

YV[ +elqvl}h 43, WSP 085<;9 439378 4395<4 <3615

OFP 08598:u 4386<5� 438984� 9:31:C

RS[ +elqvl}h 43, WSP 08;354 449449 449695 :5<1:

OFP 08:<47u 448<39� 449498� 75;16C

Qrwhv=

DLF @ �5 orj+O, . 5N> ELF @ �5 orj+O, . N orj+Q,> zkhuh O lv wkh pd{lpl}hg

orj olnholkrrg ri wkh prgho/ N lv wkh qxpehu ri sdudphwhuv/ iru WSP/ N@6:> iru OFP/

N@6<> dqg Q@534;9 lv wkh qxpehu ri revhuydwlrqv1

Wkh JrI vwdwlvwlf iroorzv d "2 glvwulexwlrq zlwk 44/ 47/ 45 dqg 48 ghjuhhv ri iuhhgrp iru

PGX/ RSX/ YV[ dqg RS[ uhvshfwlyho|

u prgho zlwk wkh eljjhu orj olnholkrrg ydoxh1

� prgho suhihuuhg e| wkh DLF1

� prgho suhihuuhg e| wkh ELF1

C prgho zlwk wkh vpdoohu JrI ydoxh1

5;

Wdeoh 7

Prgho Vhohfwlrq dqg Jrrgqhvv0ri0Ilw Vwdwlvwlfv iurp Furvv0Ydolgdwlrq

OFP suhihuuhg ( oqOu�� 0oqOA��

Yduldeoh oqO DLF JrI Phdq Plq Pd{

Wudlqlqj vdpsoh

PGX 433 433 433 ;416 7617 4371;

RSX 433 433 433 53713 49519 56415

YV[ 433 433 433 ;<13 8817 46319

RS[ 433 433 433 6:16 ;1; ;319

Krogrxw vdpsoh

PGX 433 433 433 6;18 4719 :81:

RSX 433 433 433 <415 9318 46514

YV[ 433 433 433 7916 71: ;517

RS[ <5 ;; 433 5814 05315 871;

Qrwhv=

Wkh wudlqlqj vdpsoh frqvlvwv ri 47/333 udqgrpo| fkrvhq revhuydwlrqv1 Wkh krogrxw vdpsoh

frqvlvwv ri wkh uhpdlqlqj revhuydwlrqv1 Wkh furvv0ydolgdwlrq h{huflvh zdv uhsolfdwhg 83

wlphv1

OFP suhihuuhg ( ghqrwhv wkh shufhqwdjh ri uhsolfdwlrqv OFP lv suhihuuhg wr WSP df0

fruglqj wr wkh vwdwlvwlf lq wkh froxpq khdglqj1

Phdq/ Plq dqg Pd{ vxppdul}h wkh glvwulexwlrq dfurvv uhsolfdwlrqv ri wkh gl�huhqfh

ehwzhhq wkh orj olnholkrrg ydoxhv ri OFP dqg WSP1

5<

Wdeoh 8

W0vwdwlvwlfv ri wkh Ghwhuplqdqwv ri Srvwhulru Suredelolwlhv

Yduldeoh PGX RSX YV[ RS[

Fryduldwhv lqfoxghg lq odwhqw fodvv prgho

OF 417; 3148 031:6 0315<

LGS 031;9 04135 31:3 31:<

OSL 04145 0314; 03138 04147

IPGH 041<8 031;; 31;: 31:7

OLQF 3147 315< 04166 0319;

OIDP 04145 0318< 4138 41:6

DJH 04175 04183 0614<W 061;9W

IHPDOH 031<7 031;< 04153 0319;

FKLOG 0616<W 06169W 031<3 05167

IHPFKLOG 4185 414< 41<7 413;

EODFN 0315: 0416< 31:: 3165

HGXFGHF 3178 3169 316; 03155

SK\VOLP 71<7W 51:6W 03174 0314<

QGLVHDVH 917;W 6165W 313; 3153

KOWKJ 31;7 31<5 4154 41:8

KOWKI 417: 03149 04154 04179

KOWKS 03154 313: 3183 3155

Khdowk lqgh{ h{foxghg iurp odwhqw fodvv prgho

JKLQG[ :16<W 9188W 817:W :178W

Qrwhv=

Wkh ghshqghqw yduldeoh lq hdfk uhjuhvvlrq lv wkh orj rggv ri wkh hvwlpdwhg srvwhulru

suredelolw| fdofxodwhg iurp wkh odwhqw fodvv prgho1

W Vwdwlvwlfdoo| vljql�fdqw dw wkh 8( ohyho1

63

Wdeoh 9

Vxppdu| Vwdwlvwlfv ri Ilwwhg Ydoxhv e| Odwhqw Fodvv

Yduldeoh Vwdwlvwlf Khdowk| fodvv Loo fodvv Ryhudoo VdpsohW

PGX Fodvv Suredelolw| 31;3 3153

Phdq 5143 81;7 51;9 51;9

Plqlpxp 3153 31:7 3164 3133

Pd{lpxp 461<9 9:1;5 571;9 ::133

RSX Fodvv Suredelolw| 31:: 3156

Phdq 5154 :1;: 6183 6188

Plqlpxp 3153 4133 316< 3133

Pd{lpxp 48168 ;3165 6314: 47:133

YV[ Fodvv Suredelolw| 31:3 3163

Phdq 5914: 43;154 831<8 84146

Plqlpxp 6136 4:17: ;188 3133

Pd{lpxp 53;1;3 9;7174 685178 58<<1<3

RS[ Fodvv Suredelolw| 319; 3165

Phdq 73186 465149 :315< :4143

Plqlpxp 6179 5313< 43135 3133

Pd{lpxp 6;8144 444:1<3 956148 5;4315<

YV[ +elqvl}h 43,

Phdq 5<16: 4441:; 8319< 84146

Plqlpxp 6139 4:139 ;168 3133

Pd{lpxp 55;16 :8318< 69616< 58<<1<3

RS[ +elqvl}h 43,

Phdq 73166 44;1<7 :3168 :4143

Plqlpxp 517: 4;13; 4313: 3133

Pd{lpxp 736133 4378153 97;157 5;4315<

Qrwh=

- Vdpsoh ghqrwhv udz vdpsoh vwdwlvwlfv1

64

Wdeoh :

Vdpsoh Dyhudjhv ri Hvwlpdwhg Sulfh Hodvwlflwlhv

Xwlol}dwlrq

PGX RSX

%+3/58, %+58/<8, %+3/58, %+58/<8,

Xqfrqglwlrqdo 03145 0314< 03148 0314;

+03148/ 0313<, +03159/ 03146, +0314</ 03145, +03159/ 03144,

WSP +frqglwlrqdo, 0314< 0314: 03154 0314;

+03156/ 03148, +0314</ 03146, +03157/ 0314:, +03153/ 03148,

OFP +frqglwlrqdo, 03154 03145 03156 03148

+03158/ 0314:, +03149/ 0313<, +0315:/ 0314<, +0314</ 03145,

H{shqglwxuhv

YV[ RS[

%+3/58, %+58/<8, %+3/58, %+58/<8,

Xqfrqglwlrqdo 03145 03154 03146 03155

+03149/ 0313;, +0315</ 03145, +0314:/ 03143, +0315</ 03147,

WSP +frqglwlrqdo, 0314; 03149 03153 0314;

+03156/ 03147, +0314</ 03146, +03157/ 03149, +03153/ 03148,

OFP +frqglwlrqdo, 03153 03144; 03155 03145

+03158/ 03149, +03149/ 0313;, +03158/ 0314:, +03148/ 0313;,

Qrwhv=Duf0sulfh hodvwlflwlhv duh gh�qhg dv

%+s4> s5, @t+s5,� t+s4,

s5 � s4

�

s5 . s4

t+s5, . t+s4,>

zkhuh 4 dqg 5 duh wkh wzr srlqwv ri frpsdulvrq zlwk s4> t+s4, dqg s5> t+s5, ghqrwlqj

wkh sulfhv dqg txdqwlwlhv +xwlol}dwlrq ru h{shqglwxuh, dw wkrvh wzr srlqwv/ uhvshfwlyho|1

Iru wkh xqfrqglwlrqdo hvwlpdwhv/ t+s4, dqg t+s5, duh wkh vdpsoh dyhudjhv ri xwlol}d0

wlrq dqg h{shqglwxuhv iru lqglylgxdov udqgrpl}hg lqwr hdfk frlqvxudqfh uhjlph1 Iru wkh

frqglwlrqdo hvwlpdwhv/ wkh wdeoh uhsruwv wkh vdpsoh dyhudjh ri lqglylgxdo hodvwlflwlhv1

Wkh qxpehuv lq sduhqwkhvhv uhsuhvhqw <8 shufhqw frq�ghqfh lqwhuydov1

65

Wdeoh ;

Shufhqw Gl�huhqfh lq Sulfh Hodvwlflwlhv dqg Xvh Suredelolwlhv

Hvwlpdwhg e| Wzr0Sduw dqg Odwhqw Fodvv Prghov

Duf0sulfh hodvwlflw|n

%+3/58, %+58/<8,

Fkdudfwhulvwlf vhwW PGX RSX YV[ RS[ PGX RSX YV[ RS[

edvholqh 07 09 3 04 73 59 89 9;

ihpdoh 066 05< 05: 05; ; 7 57 63

fklog 05< 065 06< 069 45 04 9 47

ihpdoh fklog 058 064 076 06; 4: 04 04 <

eodfn 75 57 6: 73 <3 7< <6 44:

sk|vlfdo olplwdwlrq 3 08 08 08 86 63 85 98

srru khdowk 059 053 054 045 44 44 5< 85

Xvh suredelolw|n

Su+| @ 3, Su+| A w,=

Fkdudfwhulvwlf vhwW PGX RSX YV[ RS[ PGX RSX YV[ RS[

edvholqh 04 07 06 07 063 075 063 057

ihpdoh 047 047 04< 054 056 078 077 06:

fklog 044 046 054 046 055 053 064 065

ihpdoh fklog 0: 0< 055 045 058 044 05; 05<

eodfn 5 5 7 7 068 048 08 044

sk|vlfdo olplwdwlrq 6 4 4 05 07< 098 078 075

srru khdowk 57 54 8 5: 45 057 05; 054

Qrwhv=

W Fkdudfwhulvwlf vhwv duh gh�qhg dv iroorzv1 Wkh edvholqh lqglylgxdo lv pdoh/ dgxow/ qrq0

eodfn/ lq h{fhoohqw vhoi0shufhlyhg khdowk/ zlwk qr sk|vlfdo olplwdwlrqv exw zlwk dq dyhudjh

qxpehu ri fkurqlf glvhdvhv/ ri dyhudjh djh dqg hgxfdwlrq/ zlwk dyhudjh lqfrph +orj, dqg

kdv dq lqvxudqfh sodq zlwk qr ghgxfwleoh dqg dyhudjh sduwlflsdwlrq lqfhqwlyh sd|phqw dqg

pd{lpxp groodu h{shqglwxuh1 Wkh rwkhu fdvhv vkrzq duh ghyldwlrqv iurp wkh edvholqh>

wkh yduldeoh wkdw lv gl�huhqw iurp wkh edvholqh fdvh lv vkrzq lq wkh froxpq1

n Shufhqwdjhv duh fdofxodwhg dv +WSP0OFP,2OFP-4331

= w @ 4< iru PGX/ w@5< iru RSX/ w@54 iru YV[ dqg w@59 iru RS[1 Wkhvh ydoxhv ri w

duh fkrvhq vxfk wkdw Su+|Aw,@31341

66

Iljxuh 4

Frpsdulvrq ri Suhglfwhg Iuhtxhqflhv ri Xwlol}dwlrq

-20%

-10%

0%

10%

20%

30%

40%

50%

devi

atio

n fr

om e

mpi

rical

freq

uenc

y

0 1 2 3 4 5 6 7 8 9 10 >=11MDU

TPM

LCM

-20%

-10%

0%

10%

20%

30%

40%

50%

devi

atio

n fr

om e

mpi

rical

freq

uenc

y

0 1 2 3 4 5 6 7 8 9 10 11 12 13 >=14OPU

TPM

LCM

67

Iljxuh 5

Frpsdulvrq ri Suhglfwhg Iuhtxhqflhv ri H{shqglwxuhv

-20%

-10%

0%

10%

20%

30%

40%

50%

devi

atio

n fr

om e

mpi

rical

freq

uenc

y

0 1 2 3 4 5 6 7 8 9 10 11 >=12VSX

TPM

LCM

-20%

-10%

0%

10%

20%

30%

40%

50%

devi

atio

n fr

om e

mpi

rical

freq

uenc

y

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 >=15OPX

TPM

LCM

68