6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
7UDQVIHUIXQFWLRQPHDVXUHPHQWVLQDXGLR
.ODXV5LHGHUHU
+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\
/DERUDWRU\RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ
2WDNDDUL$
),1(6322
[email protected]
$EVWUDFW
7KHWUDQVIHUIXQFWLRQGHWHUPLQHVFRPSOHWHO\WKHEHKDYLRURIDQDXGLRV\VWHP
WKDW LV VXSSRVHG WR EH OLQHDU DQG WLPHLQYDULDQW /7, ,Q WKLV SDSHU WKH
XQGHUO\LQJ WKHRU\ RI JHQHUDO /7, V\VWHPV LV VKRZQ IROORZHG E\ WKH
SUHVHQWDWLRQ RI VRPH FRPPRQO\ XVHG VWLPXOL IRU VLJQDO DQDO\VLV ZKLFK LV
GLVFXVVHGIURPWKHVWDQGSRLQWVRIDXGLRV\VWHPDQDO\VLVDQGPHDVXUHPHQWV
7KH FODVVLILFDWLRQ RI PHDVXUHPHQW V\VWHPV LV LQWURGXFHG ZLWK VRPH
FRPPHUFLDOO\ DYDLODEOH H[DPSOHV 3UDFWLFDO FRQVLGHUDWLRQV RI OLPLWDWLRQV
DQGHUURUVZLWKVXJJHVWLRQVWRPHDVXUHPHQWHQKDQFHPHQWVDUHJLYHQDWWKH
HQG
,1752'8&7,21
1RWRQO\HQJLQHHUVEXWDOVRWKHRUHWLFDOPDWKHPDWLFLDQVDQGRWKHUVFLHQWLVWVDUHLQWHUHVWHG
LQ HYDOXDWLQJ WKH SURSHUWLHV RI V\VWHPV 7KH EHKDYLRU RI DQ /7, V\VWHP LV FRPSOHWHO\
GHWHUPLQHGE\LWVFRPSOH[YDOXHGWUDQVIHUIXQFWLRQWKDWPDWKHPDWLFDOO\LVGHILQHGXVLQJ
WKH/DSODFHWUDQVIRUP,QWKLVSDSHUWKHWUDQVIHUIXQFWLRQLVWUHDWHGLQDEURDGVHQVHHJ
E\ XVLQJ WKH LPSXOVH UHVSRQVH DQG IUHTXHQF\ UHVSRQVH RI D OLQHDU DQG WLPHLQYDULDQW
V\VWHP0RUHRYHUWKHPHWKRGRORJ\SUHVHQWHGLVQRWOLPLWHGWRDXGLRV\VWHPVLWLVIXOO\
YDOLG IRU DOO DFRXVWLFDO V\VWHPV DQG LW PD\ DOVR EH DSSOLHG WR YDULRXV RWKHU ILHOGV RI
VFLHQFH
7KH FODVVLFDO HQJLQHHULQJ PHWKRG RI PHDVXULQJ WKH LPSXOVH UHVSRQVH RI DQ DFRXVWLFDO
V\VWHPFRQVLVWHGRIDKLJKHQHUJ\SXOVHLQRUGHUWRVLPXODWHWKHLGHDOLPSXOVH7KHSXOVH
ZDVIHGWKRURXJKWKHV\VWHPDQGWKHLPSXOVHUHVSRQVHZDVREWDLQHGGLUHFWO\)RUIXUWKHU
SURFHVVLQJ WKH UHVXOW ZDV UHFRUGHG WR SDSHU DQGRU WDSH 7KH IUHTXHQF\ UHVSRQVH ZDV
DFTXLUHG E\ SDVVLQJ WKH HOHFWULFDO VLJQDO WKRURXJK D VLQJOH ILOWHU ZLWK WXQDEOH FHQWHU
IUHTXHQF\ RU DQ DQDORJXH ILOWHUEDQN ZLWK GLIIHUHQW FHQWHU IUHTXHQFLHV DQG WKHQ
PHDVXULQJ WKH WUDQVPLWWHG SRZHU DW GLIIHUHQW IUHTXHQFLHV 7KH PRUH ³VFLHQWLILF´
DSSURDFK KDV EHHQ WR LQYHVWLJDWH WKH V\VWHP E\ PDWKHPDWLFDO PHDQV HJ FRUUHODWLRQ
IXQFWLRQVDQGDSSO\LQJWKHWKHRULHVRIOLQHDUWUDQVIRUPV
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
7KHWUHPHQGRXVGHYHORSPHQWRIWHFKQRORJ\KDVFDXVHGDJHQHUDOFKDQJHIURPDQDORJXH
WRGLJLWDODQDO\VLVDQGWHFKQLTXHV(JWKHRULJLQDOO\RYHUWZHQW\\HDUVDJRLQWURGXFHG
IDVW)RXULHUWUDQVIRUPDQDO\]HUPDGHDPDMRUEUHDNWKURXJKLQVLJQDODQDO\VLV
7KH HVVHQWLDO WKHRU\ RI D OLQHDU DQG WLPHLQYDULDQW V\VWHPV ZLOO EH SUHVHQWHG LQ WKH
VHFRQGFKDSWHUIROORZHGE\DUHYLHZRIWKHFRPPRQO\XVHGH[FLWDWLRQVLJQDOVLQV\VWHP
FKDUDFWHUL]DWLRQ&KDSWHUIRXUUHYLHZVWKHVLJQDODQDO\VLVPHWKRGVDQGWKHLUDSSOLFDWLRQV
LQDXGLRV\VWHPVDQGWKHQH[WFKDSWHUGHSLFWVWKHFODVVLILFDWLRQRIPHDVXUHPHQWV\VWHPV
ZLWK VRPH H[DPSOHV RI FRPPHUFLDOO\ DYDLODEOH V\VWHPV &KDSWHU VL[ JLYHV VRPH
FRQVLGHUDWLRQVLQSUDFWLFDOPHDVXUHPHQWVDQGVRPHFRQFOXVLRQDUHGUDZQDWWKHHQG
/,1($57,0(,19$5,$176<67(0
7KLVFKDSWHULQWURGXFHVVRPHSHUWLQHQWFRQFHSWVDQGIXQGDPHQWDODVSHFWVRIGHILQLWLRQV
UHODWHG WR WKH G\QDPLF EHKDYLRU RI V\VWHPV ZKLFK DUH QRW RQO\ OLPLWHG WR DXGLR RU
DFRXVWLFDO V\VWHPV EXW YDOLG IRU DOO NLQGV RI SK\VLFDO OLQHDU DQG WLPHLQYDULDQW /7,
V\VWHPV7KHPDLQUHIHUHQFHIRUWKHXQGHUO\LQJIRUPXODHLV%HQGDWDQG3LHUVRO
%DVLFFKDUDFWHULVWLFV
$QLGHDOV\VWHPLVFKDUDFWHUL]HGE\IRXUGLIIHUHQWTXDOLWLHVSK\VLFDOO\UHDOL]DEOHWLPH
LQYDULDQW VWDEOH DQG OLQHDU ,Q D WLPHLQYDULDQW V\VWHP WKH IXQGDPHQWDO SURSHUWLHV GR
QRW FKDQJH ZLWK UHVSHFW WR WLPH VR WKH V\VWHP KDV FRQVWDQW SDUDPHWHUV 6WDELOLW\ LV
FRQFHLYHG LI DQ DUELWUDU\ LQSXW VLJQDO SURGXFHV DQ OLPLWHG RXWSXW VLJQDO $ V\VWHP LV
OLQHDULIWKHUHVSRQVHFKDUDFWHULVWLFVDUH DGGLWLYHHJWKHRXWSXW WR D VXP RI LQSXWV LV
HTXDOWRWKHVXPRIWKHRXWSXWVSURGXFHGE\HDFKLQSXWLQGLYLGXDOO\DQGKRPRJHQHRXV
ZKLFKPHDQVWKDWWKHRXWSXWSURGXFHGE\DFRQVWDQWPXOWLSOLHGE\WKHLQSXWLVHTXDOWR
WKHFRQVWDQWPXOWLSOLHGE\WKHRXWSXWSURGXFHGE\WKHLQSXWDORQH7KHVHUHTXLUHPHQWV
DUHH[SUHVVHGLQPDWKHPDWLFDOIRUPLQFKDSWHU
,Q WKLV SDSHU WKH V\VWHP XQGHU WHVW LV DVVXPHG WR EH DQ /7, V\VWHP $Q /7, V\VWHP LV
VKRZQLQ)LJZKHUHWKHOHWWHUVµ[¶µ;¶LQGLFDWHWKHLQSXWVLJQDOLQSXWWKHOHWWHUVµ\¶
µ<¶ WKH RXWSXW DQG WKH OHWWHUV µK¶ µ+¶ WR WKH UHVSRQVH IXQFWLRQ RI WKH V\VWHP 7KH
FDSLWDOL]HGOHWWHUVUHIHUWRDOLQHDUWUDQVIRUPGRPDLQVXFKDVWKH)RXULHUWUDQVIRUP,Q
FRQWLQXRV GRPDLQV WKH LQSXWV FDQ EH UHIHUUHG DV [ W LQ WKH WLPH GRPDLQ RU DV
WUDQVIRUPHGVLJQDOV ; Mw LQWKHFRPSOH[GRPDLQ7KHGLVFUHWHUHSUHVHQWDWLRQRIWKH
VDPH LQSXW LV D WLPH VHULHV VHTXHQFH [Q RU WKH WUDQVIRUPHG VLJQDO ; ] 7KH
QRWDWLRQIRUWKHRXWSXWDQGWKHV\VWHPUHVSRQVHLVVLPLODU
[ W ; Mw [ Q
; ]
)LJ
K W + Mw K Q
+ ]
/7,V\VWHPGHVFULSWLRQXVLQJOLQHDUWUDQVIRUP
\ W < Mw \ Q
< ]
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
/LQHDUWUDQVIRUP
,Q/7,V\VWHPVWKHWUDQVIRUPV [  ; \  < DQG K  + DERYHFRXOGEHGRQHE\DQ\
NLQG RI OLQHDU DQG JHQHUDOO\ FRPSOH[YDOXHG WUDQVIRUP -DFNVRQ /DKWL ,Q
FRQWLQXRXV WLPH LW LV LQ SUDFWLFH PRVW XVHIXO DQG HIILFLHQW WR XVH D VSHFLDO FDVH RI WKH
/DSODFHWUDQVIRUPWKH)RXULHUWUDQVIRUPGHILQHGDV
- Mw W
Š
× [ W H
; Mw =
GW -Š
7KLVLVUHIHUUHGDVWKHFRQWLQXRXVVSHFWUXPRIWKHWLPHGRPDLQVLJQDOZKHUH I = pw
LVWKHIUHTXHQF\,QWKHGLVFUHWHFDVHWKHWUDQVIRUPLVDSSOLHGE\WKH=WUDQVIRUP
; ] =
Š
Ê [ Q ] - Q -Š
ZKHUH WKH YDULDEOH ] LV FRQWLQXRXV DQG FRPSOH[ LH ] ³ & 8VXDOO\ WKLV WUDQVIRUP LV
H[HFXWHGHLWKHUE\WKHGLVFUHWHWLPH)RXULHUWUDQVIRUP'7)7IRUDSHULRGLFVLJQDOV
; Mw =
Š
Ê [QH - MwQ7 -Š
RUIRUSHULRGLFVLJQDOVE\WKHGLVFUHWH)RXULHUWUDQVIRUP')7
a
; Nw =
1 -
Ê [ QH - MNw Q7 ZKHUH N = 1 - Q=
DQG7LVWKHVDPSOLQJSHULRG7KH')7LVVLPSO\DQ1SRLQWVHTXHQFHFRPSXWHGIURPDQ
1SRLQW WLPH VHTXHQFH ZLWK D GLPHQVLRQOHVV LQGHSHQGHQW YDULDEOH LQGH[ N 7KH
IDPLOLDUIUHTXHQF\VFDOHLVSURYLGHGZLWKWKHVDPSOLQJIUHTXHQF\ I V I
I = V =
1 17
7KLVGLVFUHWH)RXULHUWUDQVIRUPLVXVXDOO\GRQHE\PHDQVRIDQHIILFLHQWDOJRULWKPFDOOHG
WKHIDVW)RXULHUWUDQVIRUP))7VHHFKDSWHU7KHIROORZLQJ7DEOHVXPPDUL]HV
WKH)RXULHUWUDQVIRUPV)7DQGVHULHV )6 LQ FRQWLQXRXV WLPH &7 DQG GLVFUHWH WLPH
'7
7DEOH
6XPPDU\RI)RXULHUUHSUHVHQWDWLRQV-DFNVRQ
7LPHGRPDLQVLJQDO
7UDQVIRUP
)UHTXHQF\GRPDLQVLJQDO
&RQWLQXRXVWLPHDSHULRGLF
&RQWLQXRXVWLPHSHULRGLF
'LVFUHWHWLPHDSHULRGLF
'LVFUHWHWLPHSHULRGLF
&7)7
&7)6
'7)7
'76')7
&RQWLQXRXVIUHTXHQF\DSHULRGLF
'LVFUHWHIUHTXHQFLHVDSHULRGLF
&RQWLQXRXVIUHTXHQF\SHULRGLF
'LVFUHWHIUHTXHQFLHVSHULRGLF
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
6\VWHPLGHQWLILFDWLRQ
7KH UHODWLRQVKLS EHWZHHQ WKH LQSXW DQG RXWSXW FDQ H[SUHVVHG E\ WKH UHVSRQVH RI WKH
V\VWHPLQHLWKHUGRPDLQV
Ñ \ ¼ = K¼ [ ¼
Ò
Ó< ¼ = + ¼ ; ¼
ZKHUHWKHVWDUPHDQVFRQYROXWLRQVHH
)URP WKH V\VWHP UHVSRQVH LV GHILQHG DV WKH LQYHUVH RSHUDWLRQ WR FRQYROXWLRQ HJ
GHFRQYROXWLRQ f ÑÔK¼ = GHFRQY( \ ¼ [ ¼ )
Ò
ÔÓK¼ = \ ¼ f [ ¼
ZKLFK LV XVHG LQ V\VWHP LGHQWLILFDWLRQ ZKHQ WKH EHKDYLRU RI DQ /7, V\VWHP LV WR EH
GHWHUPLQHG,QWKHWUDQVIRUPGRPDLQWKLVFDQEHGRQHE\VLPSOHGLYLVLRQ
+ ¼ =
< ¼
; ¼
DQGWKHUHVXOWFDQEHWKHQLQYHUVHWUDQVIRUPHGLQRUGHUWRJHWWKHLPSXOVHUHVSRQVH K¼
LQ WKH WLPH GRPDLQ +RZHYHU WKLV PHWKRG LV RQO\ YDOLG IRU SHULRGLFDO GHWHUPLQLVWLF
VLJQDOVVHHFKDSWHUDQGWKXVWKHLQWHJUDWLRQLQLVH[HFXWHGRYHUWKHSHULRGRI
WKHVLJQDORUWKHWUDQVLHQWVOHQJWK/DKWL'HFRQYROXWLRQ f FDQDOVREHFDUULHG
RXW GLUHFWO\ LQ WKH WLPH GRPDLQ DV VWUDLJKWIRUZDUG SRO\QRPLDO GLYLVLRQ ZKLFK LV
JHQHUDOO\WRRGHPDQGLQJFRPSXWDWLRQDOO\RUZLWKLQYHUVHILOWHULQJRSHUDWLRQ
,Q WKH FDVH RI VWDWLRQDU\ UDQGRP SURFHVVHV WKH V\VWHP UHVSRQVH FDQQRW EH FDOFXODWHG
DFFRUGLQJWR8VXDOO\LWLVFRPSXWHGXVLQJFRUUHODWLRQRUVSHFWUDOGHQVLW\IXQFWLRQV
ZKLFKPHDVXUHWKHH[WHQWWRZKLFKWZRVLJQDOFRUUHODWHZLWKHDFKRWKHUDVDIXQFWLRQRI
WKHWLPHGLVSODFHPHQW t 7KHDXWRFRUUHODWLRQIXQFWLRQLVGHILQHGDV
Š
5 [[ t =
× [ W [W + t GW -Š
DQGWKHFURVVFRUUHODWLRQIXQFWLRQDV
Š
5 [\ t =
× [ W \ W + t GW -Š
7KHVSHFWUDOGHQVLW\IXQFWLRQVDUHV\PPHWULFDODFFRUGLQJWRDQGWKH\DUHFDOFXODWHG
E\ )RXULHU WUDQVIRUPLQJ WKH FURVVFRUUHODWLRQ IXQFWLRQV 7KH WZRVLGHG DXWRVSHFWUDO
GHQVLW\IXQFWLRQ 6 [[ I LVGHILQHGIRUSRVLWLYHDQGQHJDWLYHIUHTXHQFLHVDQGWKHRQH
VLGHGDXWRVSHFWUDOGHQVLW\IXQFWLRQ * [[ I LVGHILQHGIRUSRVLWLYHIUHTXHQFLHV]HURDV
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
Š
* [[ I = 6 [[ I = × 5[[ t H - M pIt Gt -Š
DQG ]HUR LQ QHJDWLYH IUHTXHQFLHV /LNHZLVH WKH FRPSOH[YDOXHG RQHVLGHG FURVV
VSHFWUDOGHQVLW\IXQFWLRQ * [\ I LV
Š
* [\ I = 6 [\ I = × 5[\ t H - M pIt Gt -Š
1RZWKHV\VWHPUHVSRQVHFDQEHH[SUHVVHGLQWKHWUDQVIRUPGRPDLQE\
+ ¼ =
* [\ ¼
* [[ ¼
ZKLFK FDQ WKHQ EH LQYHUVH )RXULHU WUDQVIRUPHG LQ RUGHU WR REWDLQ WKH V\VWHP UHVSRQVH
K¼ LQWKHWLPHGRPDLQ,QWKHFDVHRI WUDQVLHQWVLJQDOVWKHVSHFWUDOGHQVLW\IXQFWLRQV
PXVW EH UHSODFHG E\ WKH HQHUJ\ GHQVLW\ IXQFWLRQV WKDW KDYH WKH VDPH SURSHUWLHV DV WKH
IRUPHURQHV
,PSXOVHUHVSRQVH
)RUDFRQWLQXRXVV\VWHPZLWK \ W DVRXWSXWUHVSRQVHDQG [ W DVLQSXWVWLPXOXV
WKHXQLWLPSXOVHUHVSRQVHIXQFWLRQLPSXOVHUHVSRQVH,5LVGHILQHGDV
K W = \ W ZKHQ [ W = d W ZKHUH W LV WKH WLPH DSSOLHG IURP WKH PRPHQW ZKHQ WKH 'LUDF¶V GHOWD IXQFWLRQ d W DUULYHVWRWKHV\VWHP
7KHPRVWLPSRUWSURSHUW\RIDQ/7,V\VWHPLVLWVUHVSRQVHWRDQLGHDOLPSXOVHLHWKH
LPSXOVH UHVSRQVH ZKLFK GHVFULEHV FRPSOHWHO\ WKH EHKDYLRU RI WKH V\VWHP DQG LWV
UHVSRQVHWRDQ\NLQGRIDVWLPXOXV7KHV\VWHPRXWSXW \ W RIDQ\DUELWUDU\VWLPXOXV
LQSXWVLJQDO [ W FDQEHFDOFXODWHGE\WKHFRQYROXWLRQLQWHJUDO
Š
\ W = K W [ W = × Kt [ W - t Gt 1RWLFHWKDWWKHFRQYROXWLRQLVUHODWHGWRFRUUHODWLRQIXQFWLRQVVHHDQG(T
PHDQVWKDWWKHV\VWHPUHVSRQVHFDQEHFDOFXODWHGDVDZHLJKWHGOLQHDUVXPPDWLRQRYHU
WKH H[LVWLQJ WLPH KLVWRU\ RI WKH LQSXW VLJQDO [ W KHQFH WKH FRPPRQ QDPH ZHLJKWLQJ
IXQFWLRQ Kt ZKLFKFDQEHGHILQHGZLWKWKHGHOWDIXQFWLRQ d W Š
Ñ
ÔÔKt = × K W d W - t GW
Ò
-Š
Ô
ÔÓd W = W ž 6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
,QWKHGLVFUHWHWLPHFDVHZHFDQXVHWKHXQLWVDPSOHLPSXOVHd Q Ñ Q = d Q = Ò
Ó RWKHUZLVH
WRJHWWKHXQLWVDPSOHUHVSRQVH K Q RIWKHV\VWHP
\ Q = K Q [ Q =
Š
Ê [ N K Q - N N = -Š
0DLQUHTXLUHPHQWV
$SK\VLFDOO\UHDOL]DEOHFDXVDOV\VWHPFDQSURGXFHDUHVSRQVHRQO\DIWHUWKHVWLPXOXV
KDVUHDFKHGWKHLQSXW
Kt = IRU t < ZKLFKLVZK\WKHORZHULQWHJUDWLRQOLPLWIRUSK\VLFDOV\VWHPVLQWKHFRQYROXWLRQLQWHJUDO
PD\EH]HUR7KHV\VWHPKDVFRQVWDQWSDUDPHWHUVLIWKHUHVSRQVHLVQRWHIIHFWHGE\
WKHDUULYDOWLPHRIWKHLQSXWVLJQDO
K W t = Kt IRUDOO - Š < t < Š DQG DOO VWDWLRQDU\ VWLPXOL SURGXFH VWDWLRQDU\ UHVSRQVHV DIWHU WKH DWWHQXDWLRQ RI WKH
WUDQVLHQWVLQWKHDWWDFN
7KHDVVXPHGVWDELOLW\UHTXLUHPHQWRIWKHV\VWHPLVIXOILOOHGLI
Š
× Kt Gt < Š -Š
7KHOLQHDULW\RIWKHV\VWHPLVDFKLHYHGLILWLVDGGLWLYHLH
I [ + [ = I [ + I [ DQGKRPRJHQHRXVLI
I F[ = FI [ ZKHUH I [ LVWKHRXWSXWWRDQLQSXWDQGFLVDFRQVWDQW,QSUDFWLFHWKHOLQHDULW\LVWKH
PRVW SUREOHPDWLF FKDUDFWHULVWLF WKDW FDQ EH YLRODWHG LQ FDVH RI WRR KLJK LQSXW VLJQDO
OHYHOV
)UHTXHQF\UHVSRQVH
8VXDOO\ WKH FRQYROXWLRQ LQWHJUDO LV GLIILFXOW WR FDOFXODWH DQG SRVVLEO\ LV QRW VROYDEOH
DQDO\WLFDOO\ 7KXV WKH G\QDPLF FKDUDFWHULVWLFV RI DQ /7, V\VWHP DUH XVXDOO\ SUHVHQWHG
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
ZLWKWKHKHOSRIDOLQHDUWUDQVIRUPXVXDOO\)RXULHUWUDQVIRUPDFFRUGLQJWRWKHIRUPXODV
VKRZQLQFKDSWHU
7KHV\VWHPFDQEHGHVFULEHGE\DIUHTXHQF\UHVSRQVHIXQFWLRQ + I ZKLFKLVGHILQHG
DVWKH)RXULHUWUDQVIRUPRIWKHXQLWLPSXOVHUHVSRQVHIXQFWLRQ Kt Š
- M pIt
+ I = × Kt H
Gt ZKHUH Kt = ZKHQ t < VHH(TLVDFWXDOO\DVSHFLDOFDVHRIWKHWUDQVIHU
IXQFWLRQE\WKH/DSODFLDQYDULDEOH V = D + ME KDYLQJD]HURUHDOFRPSRQHQWLH D = DQG E = pI 7KHIXQFWLRQ + I LVJHQHUDOO\DFRPSOH[YDOXHGTXDQWLW\ZLWKQRQ]HURUHDO + 5 I DQGLPDJLQDU\ + , I SDUWV
Š
Š
+ I = + 5 I - M+ , I = × Kt FRV pIt Gt - M × Kt VLQ pIt Gt ,QSUDFWLFHWKHSRODUQRWDWLRQLVPRUHXVHIXO
+ I = + I H - Mq I ZKHUH
I + + I DQG
+ I = +5
,
Ë + I Û
f I = DUFWDQÌ ,
Ü
Í +5 I Ý
(T LV UHIHUUHG DV WKH SKDVH IDFWRU SKDVH VKLIW DQG DV WKH JDLQ IDFWRU 7KH
ODWWHU LV LQ VSRNHQ ODQJXDJH RIWHQ IDOVHO\ GHVLJQDWHG DV IUHTXHQF\ UHVSRQVH LQVWHDG RI
PRUH FRUUHFW WHUP WKH DEVROXWH YDOXH RI WKH IUHTXHQF\ UHVSRQVH + I )URP WKH
FDXVDOLW\RIWKHV\VWHPWKHIROORZLQJV\PPHWU\SURSHUWLHVDUHYDOLG
+ - I = + I + - I = + I f - I = -f I ,WVKRXOGEHQRWHGWKDWWKHIUHTXHQF\UHVSRQVHIXQFWLRQ + I RIDFRQVWDQWSDUDPHWHU
OLQHDUV\VWHPLVDIXQFWLRQRIRQO\IUHTXHQF\DQGLVQRWDIXQFWLRQRIHLWKHUWLPHRUWKH
V\VWHP LQSXW ,I WKH V\VWHP ZHUH QRQOLQHDU + I ZRXOG EH DOVR D IXQFWLRQ RI WKH
DSSOLHGH[FLWDWLRQ,IWKHSDUDPHWHUVRIWKHV\VWHPZHUHQRWFRQVWDQW + I ZRXOGDOVR
EH D IXQFWLRQ RI WLPH 7KH IUHTXHQF\ UHVSRQVH IXQFWLRQ PD\ UHSODFH WKH PRUH JHQHUDO
WUDQVIHUIXQFWLRQZLWKQRORVVRIXVHIXOLQIRUPDWLRQLQWKHFDVHRI/7,V\VWHPV
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
(;&,7$7,216,*1$/6
$XGLRPHDVXUHPHQWVFDQEHGLYLGHGURXJKO\LQWRWZRVHFWLRQVQDUURZEDQGDQGEURDG
EDQG ,GHDOO\ WKH H[FLWDWLRQ VLJQDO VKRXOG KDYH IODW VSHFWUXP LH HTXDO HQHUJ\ DW DOO
IUHTXHQFLHVQRGLVFRQWLQXLWLHVDQGDORZFUHVWIDFWRULHWKHSHDNDPSOLWXGHGLYLGHGE\
WKH URRW PHDQ VTXDUH 506 RI WKH VLJQDO (LWKHU DYHUDJLQJ UHSHWLWLRQ RU D VWURQJ
VLJQDOOHYHOVKRXOGEHXVHGLQRUGHUWRJHWDQDSSURSULDWHVLJQDOWRQRLVHUDWLR615
3XUHWRQHVLJQDOV
3XUH WRQH VLJQDOV FRQVLVW RI GLVFUHWH IUHTXHQFLHV 7KH\ FDQ EH HJ VLQJOH IUHTXHQF\
VLQXVRLGDO RU VZHSW VLQXVRLGDO VLJQDOV WKDW KDYH D FUHVW IDFWRU RI 7KH IRUPHU DUH
XVHGLQQDUURZEDQGDQGWKHODWWHULQZLGHEDQGPHDVXUHPHQWV
6LQJOHIUHTXHQF\VLQXVRLGDOVLJQDOV
$ VLQXVRLGDO VWLPXOXV ZLWK D IUHTXHQF\ I SURGXFHV D VLQXVRLGDO UHVSRQVH LQ DQ /7,
V\VWHPZLWKDSRVVLEOHFKDQJHRIDPSOLWXGHDQGRUSKDVHLQWKHRXWSXW+HQFHDVLQJOH
IUHTXHQF\ VLQH ZDYH RU SDLUV RI VLQH ZDYHV HJ VLQH EXUVWV DUH XVHG WR H[DPLQH WKH
V\VWHP¶V QRQOLQHDU EHKDYLRU WKH KDUPRQLF RU WKH LQWHUPRGXODWLRQ GLVWRUWLRQ ,I WKH
EXUVW KDV DOWHUQDWLQJ ORZ DQG KLJK DPSOLWXGH FRPSRQHQWV LW FDQ EH XVHG WR PHDVXUH
HTXLSPHQWWKDWVKDSHWKHG\QDPLFVRIDXGLRVLJQDOVFRPSDQGHUVHWF.DOOLR$
N+] VLQH VLJQDO LV RIWHQ DSSOLHG LQ FDOLEUDWLQJ WKH PHDVXUHPHQW HTXLSPHQW
PLFURSKRQHVHWF$OVRJDWHGVLQXVRLGDOVLJQDOVDUHXVHGLQDQDO\VLVSXUSRVHV
6ZHSWVLQXVRLGDOVLJQDOV
$VORZO\VZHSWVLQXVRLGDOLVFDOOHGDVZHHSDQGDIDVWRQHLVFDOOHGDFKLUSDVLQXVRLGDO
RVFLOODWLRQZLWKIUHTXHQF\WKDWYDULHVOLQHDUO\ZLWKWLPHGHILQHGIRUSRVLWLYHWYDOXHVE\
Ë NW Û
Ü = FRVËÌ wW ÛÜ w 5 W = FRVÌÌ
Ü
Í Ý
Í Ý
ZKHUH WKH LQVWDQWDQHRXV DQJXODU IUHTXHQF\ w = NW LV JLYHQ E\ WLPH GHULYDWLYH RI WKH
SKDVH RI WKH FRVLQH IXQFWLRQ N EHLQJ D FRQVWDQW HTXDO WR WKH UDGLDQ VZHHS UDWH
9DQGHUNRR\7KHRVFLOODWLRQIUHTXHQF\RIVZHSWVLQXVRLGDOVLJQDOVYDULHVOLQHDUO\
ZLWKWLPHDQGWKLVVZHHSUDWHIUHTXHQF\YDULDWLRQSHURQHSHULRGLVVRVPDOOLQVZHHSV
WKDWWKHVLJQDOPD\EHUHJDUGHGDVTXDVLVWDWLRQDU\VHHFKDSWHU6ZHSWVLQXVRLGDOV
DUHXVHGLQILOWHUDQDO\VLVWHFKQLTXHVFKDSWHU
,PSXOVH
7KH WKHRUHWLFDO GHOWD IXQFWLRQ LH LPSXOVH LV DSSUR[LPDWHG E\ D VKRUW LPSXOVHOLNH
SXOVH7KLVNLQGRIVWLPXOXVLVTXLWHSUREOHPDWLFGXHWRDYHU\KLJKFUHVW IDFWRU DQG LW
KDV RQO\ IHZ DSSOLFDWLRQV 5HFHQWO\ D FRPSOH[YDOXHG H[WHQVLRQ RI WKH GHOWD IXQFWLRQ
KDV EHHQ LQWURGXFHG 7KH DQDO\WLF LPSXOVH LV XVHG IRU WKH HYDOXDWLRQ RI WKH HQHUJ\
GLVWULEXWLRQLQDV\VWHP
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
,PSXOVHOLNHVLJQDOV
*XQVKRWVVSDUNVSRSSLQJDLUEDOORRQVDQGFDQQRQVKRWVKDYHEHHQWUDGLWLRQDOO\XVHG
LQRUGHUWRDFKLHYHKLJKHQHUJ\LPSXOVHVIRUURRPDFRXVWLFPHDVXUHPHQWV+RZHYHUWKH
JHQHUDO LPSXOVH VWLPXOXV LV QRW SUDFWLFDO DQG DOVR LQ RWKHU ZD\V TXLWH SUREOHPDWLF
$XGLR GHYLFHV VXFK DV ORXGVSHDNHUV GR QRW JHQHUDOO\ UDGLDWH HQRXJK SRZHU IRU KLJK
IUHTXHQF\DQDO\VLVDQGDQH[WUHPHO\LQWHQVLYHLPSXOVHLVQRWSURSHUWRXVHZLWKKXPDQ
VXEMHFWV $OVR WKH LPSXOVLYH VWLPXOXV PD\ QRW KDYH VXIILFLHQWO\ IODW VSHFWUD IRU
LQYHVWLJDWLRQSXUSRVHVRWKHUWKDQRFWDYHRUWKLUGRFWDYHDQDO\VHV)XUWKHUPRUHLWPXVW
EHWDNHQFDUHWKDWQHLWKHUWKHV\VWHPXQGHUWHVWQRUWKHPHDVXULQJHTXLSPHQWLVGULYHQ
RXWRILWVOLQHDUWLPHLQYDULDQWUDQJH,QDGGLWLRQWKHWHVWVLJQDOKDVORZSRZHUEHFDXVH
DOO RI LWV HQHUJ\ LV ORFDOL]HG LQ D YHU\ EULHI WLPH LQWHUYDO DQG KHQFH WKH 615 UHPDLQV
SRRU,QSUDFWLFHLWLVVDWLVIDFWRU\LIWKHSXOVHOHQJWKLVPLQRUFRPSDUHGWRWKHSHULRGRI
WKHPD[LPDOIUHTXHQFLHVLQWKHUHVSRQVH%RULVKDQG$QJHOO6FKURHGHU
$QDO\WLFLPSXOVH
7KH DQDO\WLF LPSXOVH DW LV D FRPSOH[YDOXHG IXQFWLRQ ZKRVH UHDO SDUW LV WKH
SUHYLRXVO\GHVFULEHG'LUDF¶VGHOWDIXQFWLRQ d W 'XQFDQ7KHDQDO\WLFLPSXOVHLV
SDUWLFXODUO\ HIIHFWLYH LQ WKH FDOFXODWLRQ RI WKH HQHUJ\WLPH FXUYH (7& RI WKH V\VWHP
HJ LQ ORXGVSHDNHU RU URRP DFRXVWLF PHDVXUHPHQWV EHFDXVH LW HOLPLQDWHV WKH
LQWHUIHUHQFHHIIHFWVWKDWDSSHDULQWKHWLPHGRPDLQ7KH(7&LVEDVLFDOO\WKHHQYHORSHRI
WKH LPSXOVH UHVSRQVH D FRPSOH[ RU TXDGUDWXUH YDOXHG SUHVHQWDWLRQ 7KH DQDO\WLF
LPSXOVHUHVSRQVH$,5FDQEHIRXQGE\VXPPLQJLQDQ506IDVKLRQWKHPDJQLWXGHVRI
WKH LPSXOVH UHVSRQVH DQG WKH +LOEHUW WUDQVIRUPHG LPSXOVH UHVSRQVH 7KH (7& LV WKH
PDJQLWXGH RI WKH $,5 WKDW FDQ EH H[DPLQHG LQ FRQWLQXRXV =WUDQVIRUPHG RU ')7
GRPDLQV )XUWKHUPRUH E\ ZLQGRZLQJ WKH DQDO\WLF LPSXOVH LW PD\ EH PRGLILHG WR D
VPRRWKHULPSXOVHIRUEHWWHUWUDGHRIIEHWZHHQVPRRWKQHVVDQGUHVROXWLRQ
5DQGRPQRLVH
5DQGRP QRLVH LV GLVWULEXWHG HYHQO\ LQ WKH IUHTXHQF\ GRPDLQ DQG LV WKXV VXLWDEOH IRU
HYDOXDWLRQLQDXGLRIUHTXHQFLHV:LWKDOHQJWK\WLPHDYHUDJLQJLHDORQJHUH[FLWDWLRQ
PRUHHQHUJ\IRUHDFKVLJQDODPSOLWXGHLVGHOLYHUHGWRWKHV\VWHPDQGWKHOLQHDUG\QDPLF
UDQJH LV LPSURYHG $OVR WKH XQLIRUPLW\ RI WKH HQHUJ\ GLVWULEXWLRQ RYHU IUHTXHQF\ LV
DVVXUHG7KHPRVWLPSRUWDQWW\SHVRIUDQGRPQRLVHDUHZKLWHDQGSLQNQRLVH
:KLWHQRLVH
:KLWHQRLVHKDVWKHRUHWLFDOO\DFRQVWDQWDXWRVSHFWUDOGHQVLW\IXQFWLRQSRZHUVSHFWUXP
RYHUDOOIUHTXHQFLHVEXWVXFKDIXQFWLRQKDVDQLQILQLWHPHDQVTXDUHYDOXHDQGFDQQRW
H[LVWLQUHDOLW\,QSUDFWLFHZKLWHQRLVHLVDOZD\VEDQGOLPLWHGKDYLQJDFRQVWDQWSRZHU
VSHFWUXPLQWKHFRQVLGHUHGXQLWIUHTXHQF\EDQGDQGD]HURYDOXHHOVHZKHUH+HQFHWKH
DXWRFRUUHODWLRQ IXQFWLRQ 5[[ t LV WKH GHOWD IXQFWLRQ d t WLPHV D FRQVWDQW .DOOLR
5 [[ t = OLP
7 “Š 7
7
× [W [W + t GW = s d t -7
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
ZKHUH s LVWKHYDULDQFHRIWKHVLJQDO:KLWHQRLVHLVDOVRVWDWLRQDU\DQGHUJRGLFDQGLW
KDVQRSHULRGLFFRPSRQHQWV,QRIWHQXVHG*DXVVLDQZKLWHQRLVHWKHDPSOLWXGHVIROORZ
WKHQRUPDO*DXVVLDQGLVWULEXWLRQ
3LQNQRLVH
7KH SRZHU VSHFWUXP RI SLQN QRLVH KDV D FRQVWDQW YDOXH RYHU IUHTXHQF\ EDQGV ZKRVH
UDWLR RI WKH XSSHU DQG ORZHU OLPLWLQJ IUHTXHQFLHV LV FRQVWDQW WKH DXWRVSHFWUDO GHQVLW\
IXQFWLRQGHFUHDVHVG%SHURFWDYH3LQNQRLVHFDQEHJHQHUDWHGIURPZKLWHQRLVHE\D
G%RFWDYH ILOWHU DQG LW LV XVHG IRU H[DPSOH ZKHQ WKH SRZHU UHVSRQVH RI D
ORXGVSHDNHURUWKHELDVHUURURIDWDSHUHFRUGHULVXQGHUHYDOXDWLRQ
3VHXGRUDQGRPQRLVH
7KH PRVW LPSRUWDQW W\SH RI VWLPXOL LV WKH SVHXGRUDQGRP QRLVH ,W LV D SHULRGLF QRLVH
VHTXHQFH ZKRVH OHQJWK LV WKH LQYHUVH RI WKH UHSHWLWLRQ IUHTXHQF\ 7KH SVHXGRUDQGRP
QRLVHLVGHWHUPLQLVWLFVRLWFDQEHHDVLO\JHQHUDWHGDQGDYHUDJHGLQRUGHUWRLPSURYHWKH
6157\SLFDOO\SHULRGLFQRLVHLVGHVLJQHGWRKDYHDIODWVSHFWUXPZLWKDQHUUDWLFSKDVH
LHORZFUHVWIDFWRUEXWLWPD\DOVREHFRORUHGIRURSWLPDOPHDVXUHPHQWVXLWDELOLW\7KH
PRVW XWLOL]HG DUH WKH ELQDU\ PD[LPXP OHQJWK VHTXHQFHV /RZSHDNIDFWRU VLJQDOV DQG
*ROD\FRGHVDUHDOVRZHOOVXLWHGIRUDXGLRPHDVXUHPHQWV
2YHUWZRGHFDGHVDJRWKHVHQRLVHVHTXHQFHVZHUHUHJDUGHGDVSLHFHZLVHGLVFRQWLQXRXV
DQDORJ VLJQDOV DQG DQDORJ VLJQDO WKHRU\ ZDV XWLOL]HG WR GHULYH WKHLU SURSHUWLHV 'DYLHV
1RZDGD\V LW LV PRUH VHQVLEOH WR WUHDW WKHP DV GLVFUHWHWLPH SHULRGLF VHTXHQFHV
WKDWWKH\UHDOO\DUHDQGDSSO\WKHPHWKRGVRIGLJLWDOVLJQDOSURFHVVLQJ
)ODWVSHFWUXPUDQGRPSKDVHVLJQDOV
6FKURHGHUKDVSUHVHQWHGVHYHUDOPHWKRGVWRDGMXVWWKHSKDVHDQJOHVRIDSHULRGLF
VLJQDOZLWKDJLYHQSRZHUVSHFWUXPWRPD[LPL]HWKHDYDLODEOHVLJQDOHQHUJ\7KHSHDN
IDFWRU LV GHILQHG DV WKH GLIIHUHQFH EHWZHHQ PD[LPXP DQG PLQLPXP SHDNWRSHDN
YDOXH RI D VLJQDO GLYLGHG E\ LWV URRWPHDQVTXDUH YDOXH 7KH JHQHUDO ORZSHDNIDFWRU
VLJQDOV /3)6 UHVHPEOH FKLUSHG IUHTXHQF\ PRGXODWHG VLJQDOV ZLWK PRQRWRQLFDOO\
LQFUHDVLQJ LQVWDQWDQHRXV IUHTXHQF\ /LNH ORZ FUHVW IDFWRU VLJQDOV DOVR /3)6 DUH
LQWHQGHGWRLPSURYHWKH615/RZSHDNIDFWRUVLJQDOVDUHFRPSRVHGRI)RXULHUVHULHV
VHTXHQFHV DQG IRU WKH VLJQDOV WKDW KDYH D IODWSRZHU VSHFWUD SQ = 1 WKH SKDVH
DQJOHVDUHGHILQHGDV
pQ fQ = f 1
ZKHUH f LVWKHSKDVHDQJOHRIWKHILUVW)RXULHUFRPSRQHQWQLVDSXUHGHOD\DQG1LVWKH
OHQJWK RI WKH VHULHV )RU WKH WLPHV\PPHWULF IODWVSHFWUXP VLJQDOV ZLWK SKDVH DQJOHV
UHVWULFWHGWRYDOXHVDQGpWKHIROORZLQJLVYDOLG
Î Q Þ
ß
fQ = p Ï
ÏÐ 1 ßà
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
6\PPHWULFVLJQDOVZLWKIODWSRZHUVSHFWUDFDQDOVREHDSSOLHGWRELQDU\VHTXHQFHVZLWK
ORZDXWRFRUUHODWLRQ D Q Î Q Þ
ß
D Q = - Ï
ÏÐ 1 ßà
PRG 0D[LPXPOHQJWKVHTXHQFHV
7KHPD[LPXPOHQJWKVHTXHQFHV0/6DUHSHULRGLFVHTXHQFHVRILQWHJHUV7KH\FDQEH
JHQHUDWHG E\ SULPLWLYH SRO\QRPLDOV 'DYLHV 6FKURHGHU RU PRVW HDVLO\ E\
GLJLWDOVKLIWUHJLVWHUV7KHODWWHUFDVHOHDGVWRELQDU\VHTXHQFHVLHWRDQLPSXOVHWUDLQ
FRQVLVWLQJ RI GLVFUHWH LPSXOVHV WKDW DUH WZRYDOXHG LQWHJHUV 7KH LQWHJHUV KDYH XVXDOO\
YDOXHV DQG WKDW DUH PDSSHG WR WKH YDOXHV DQG UHVSHFWLYHO\ VR WKDW WKH
VHTXHQFHLVV\PPHWULFDODERXW]HUR7KH0/6LVHDV\WRSURGXFHE\DWKUHHVWDJHVKLIW
UHJLVWHUWKDWSHUIRUPVWKHH[FOXVLYHRU;25RSHUDWLRQPRGXORVXP7KHSHULRGRI
WKH0/6LV
/ = 1 - ZKHUH1LVDQLQWHJHUSUHVHQWLQJWKHOHQJWKRIWKHVKLIWUHJLVWHU
7KH 0/6 KDYH VHYHUDO DGYDQWDJHV DQG WKH\ DUH JHQHUDOO\ DSSOLHG LQ DXGLR
PHDVXUHPHQWV 7KH GLVFUHWH 0/6 VLJQDO KDV D IODWVSHFWUXP DQG DQ HUUDWLF SKDVH WKDW
YDULHV SVHXGRUDQGRPO\ ZLWK D IUHTXHQF\ KDYLQJ D XQLIRUP SUREDELOLW\ GHQVLW\ RYHU LWV
UDQJH RI p WR p 7KXV WKH ELQDU\ 0/6 KDV D PLQLPXP FUHVW IDFWRU DQG WKH VLJQDO
HQHUJ\ LV PD[LPXP DQG WKH 615 LV RSWLPDO 0RVW RI DOO 0/6 KDV DQ LPSRUWDQW
FLUFXODU DXWRFRUUHODWLRQ SURSHUW\ WKDW DOORZV RQH WR HDVLO\ PHDVXUH WKH SHULRGLF
LPSXOVH UHVSRQVH RI D V\VWHP 7KLV ZLOO EH H[SODLQHG LQ WKH QH[W FKDSWHU 6FKURHGHU
5LIHDQG9DQGHUNRR\
)RUPHDVXUHPHQWVLQWKHFRQWLQXRXVWLPHWKHGLVFUHWHWLPH0/6PXVWEHFRQYHUWHGWR
DQDORJXH IRUP 7KLV LV GRQH E\ D FRPE IXQFWLRQ D WUDLQ RI GHOWD IXQFWLRQV VSDFHG dW
DSDUW)RXULHUWUDQVIRUPRIZKLFKLVDOVRDFRPEIXQFWLRQRIVSDFLQJ dW 7KH0/6LV
PXOWLSOLHGE\WKHFRPEIXQFWLRQ)LJDDQGWKHZHLJKWHGUHVXOWLVWKHQFRQYROYHGZLWK
WKHXQLWSXOVHIXQFWLRQ]HURRUGHUKROGIXQFWLRQ
Ñ < W < d
S W = Ò
Ó RWKHUZLVH
DVVKRZQLQE,QSUDFWLFHWKHER[FDUVLJQDO)LJFLVJHQHUDWHGLQWKHVLPSOHVWFDVH
E\ D ELW GLJLWDOWRDQDORJXH '$ FRQYHUWHU WKDW KROGV LWV RXWSXW FRQVWDQW RYHU HDFK
VDPSOH SHULRG VDPSOH DQG KROG FRQYHUWHU 7KLV SURFHGXUH LQWURGXFHV KRZHYHU DQ
DSHUDWXUH ORVV RIWHQ DVVRFLDWHG ZLWK '$ FRQYHUVLRQV 7KH FRQWLQXRXV WLPH 0/6
VSHFWUXPLVDVLQ[[LHVLQFIXQFWLRQDQGWKHSRZHUVSHFWUXPLVDVLQF IXQFWLRQWKDW
IDOOV G% LQ WKH WKLUG RI WKH VDPSOLQJ IUHTXHQF\ I V 1\TXLVW IUHTXHQF\ KDYLQJ LWV
ILUVW ]HUR DW IUHTXHQF\ I = dW I V PXVW EH DW OHDVW WKUHH WLPHV JUHDWHU WKDQ WKH
HYDOXDWHG EDQGZLGWK DQG WKH RXWSXW VLJQDO RI WKH PHDVXUHG V\VWHP PXVW EH EDQG
OLPLWHGZLWKDDQWLDOLDVLQJILOWHUEHIRUH$'FRQYHUVLRQ5LIHDQG9DQGHUNRR\
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
[
Q
[
W
[
WFRPEW
[
QFRPEW
Q
W
W
D
SW
E
F
)LJ
$QDORJXH UHDOL]DWLRQ RI D SRLQW 0/6 WKURXJK ELW VDPSOH DQG KROG
'$ FRQYHUWHU D 0/6 ZHLJKWHG FRPE IXQFWLRQ E XQLW SXOVH IXQFWLRQ
DQGFFRQYROXWLRQRIDDQGE7ZR0/VHTXHQFHVDUHSUHVHQWHG
*ROD\FRGHV
*ROD\ FRPSOHPHQWDU\ SDLUV DUH ELQDU\ FRGHV WKDW KDYH D GLVWLQJXLVKHG SURSHUW\ WKDW
WKHLUDXWRFRUUHODWLRQIXQFWLRQVKDYHFRPSOHPHQWDU\VLGHOREHV*ROD\7KHUHIRUH
WKH VXP RI WKH DXWRFRUUHODWLRQ VHTXHQFHV LV H[DFWO\ ]HUR H[FHSW DW WKH RULJLQ )RVWHU
DQGWKHSRZHUVSHFWUXPLVH[DFWO\IODW$QRWKHUEHQHILWLVWKDWWKHVHTXHQFHKDV
DOZD\V D OHQJWK / RI DQ H[SRQHQW RI LH / = 1 ZKLFK PDNHV SRVVLEOH WR XVH
HIILFLHQW ))7 DOJRULWKPV VXFK DV WKH UDGL[ WHFKQLTXH =KRX HW DO 2WKHUZLVH
WKH*ROD\FRGHVKDYHPXFKRIWKHVDPHFKDUDFWHULVWLFVDV0/6VLJQDOV
&RORUHGSVHXGRUDQGRPQRLVH
7KH FRORUHG SVHXGRUDQGRP QRLVH VHTXHQFHV KDYH DQ XQHYHQ SRZHU VSHFWUXP )RU
H[DPSOH WKH 0/6 FDQ EH SUHHPSKDVL]HG WR DQ\ VSHFWUDO VKDSH DQG WKLV FDQ EH
FRPSXWHG YHU\ HIILFLHQWO\ E\ DSSO\LQJ DQ LQYHUVH IDVW +DGDPDUG WUDQVIRUP WR D JLYHQ
SUHHPSKDVLV ILOWHU UHVSRQVH 0RPPHUW] DQG 0OOHU 7KLV W\SH RI VLJQDOV RIIHU
PDQ\DGYDQWDJHVLQWUDQVIHUIXQFWLRQPHDVXUHPHQWVVHHFKDSWHU
6,*1$/$1$/<6,6
6LJQDODQDO\VLVLVLQSUDFWLFHDOZD\VFDUULHGRXWWKURXJKD³ZLQGRZ´RIILQLWHOHQJWKLQ
WLPH EHFDXVH WKH GDWD DFTXLVLWLRQ LQ UHDOLW\ KDV D OLPLWHG GXUDWLRQ ,I WKH VLJQDO LQ
TXHVWLRQKDVDGXUDWLRQRIWLPHWKDWH[FHHGVWKLVDFTXLVLWLRQZLQGRZVRPHHUURUVZLOO
RFFXU,QPDQ\VLJQDODQDO\VLVPHWKRGVWKLVPDNHVPHDVXUHPHQWVDQGHVWLPDWHVDSSHDU
DVWKH\ZHUHSHULRGLFQRPDWWHUZKDWW\SHRIVLJQDOLW RULJLQDOO\ ZDV 7KLV FLUFXODULW\
FKDUDFWHULVWLFOHDGVWRFLUFXODUSHULRGLFDQDO\VLVFDOFXODWLRQV,WLVDOVRLQKHUHQWLQWKH
)RXULHU WUDQVIRUP ZKLFK VWDWHV WKDW WKH UHFWDQJXODU WLPH ZLQGRZ DERYH )RXULHU
WUDQVIRUPHG DV D VLQFIXQFWLRQ LV WKH IXQGDPHQWDO VSHFWUDO ZLQGRZ LQ VSHFWUXP
DQDO\VLV
6LJQDODQDO\VLVLVDIIHFWHGE\WKHQDWXUHRIWKHLQYHVWLJDWHGVLJQDOVZKHWKHUWKH\FDQEH
H[SUHVVHG RQO\ E\ WKHLU VWDWLVWLFDO SURSHUWLHV DV UDQGRP VWRFKDVWLF SURFHVVHV RU
H[SOLFLWO\ LH SUHFLVHO\ DV GHWHUPLQLVWLF VLJQDOV ,Q WKH IRUPHU FDVH WKH DQDO\VLV LV
QRUPDOO\EDVHGRQVSHFWUDOGHQVLW\IXQFWLRQVVHHFKDSWHUWKDWFDQEHGHILQHGE\D
FRUUHODWLRQ IXQFWLRQV E GLVFUHWH )RXULHU WUDQVIRUPV DQG F ILOWHULQJ RSHUDWLRQV ,Q
OLWHUDWXUHLWLVSURYHQWKDWWKHGHILQLWLRQVRIWKH VSHFWUDOGHQVLW\IXQFWLRQV RI WKH JLYHQ
WLPH UHFRUGV FRQVWUXFWHG E\ ')7 DUH LGHQWLFDO WR WKH GHILQLWLRQV RI WKH )RXULHU
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
WUDQVIRUPVRIWKHFRUUHODWLRQIXQFWLRQV %HQGDW DQG 3LHUVRO )XUWKHUPRUH LW KDV
EHHQ DOVR VKRZQ WKDW WKH VSHFWUDO GHQVLW\ IXQFWLRQV DFTXLUHG E\ D ILOWHULQJVTXDULQJ
DYHUDJLQJ RSHUDWLRQ FRQYH\ WR WKH VDPH GHILQLWLRQV DV WKH SUHYLRXV RQHV %HQGDW DQG
3LHUVRO
7KH DQDO\VLV RI GHWHUPLQLVWLF VLJQDOV LV UDWKHU VWUDLJKWIRUZDUG XVLQJ FRQYROXWLRQ
GHFRQYROXWLRQDQG)RXULHUWUDQVIRUPVVHHFKDSWHU$OVRWKHDQDO\VLVPHWKRGVDE
DQGFDERYHFDQEHDSSOLHGIRUGHWHUPLQLVWLFVLJQDOVDFWXDOO\WKHUHLVQRIXQGDPHQWDO
GLIIHUHQFHEHWZHHQFRQYROXWLRQDQGFRUUHODWLRQPHWKRGV,QSUDFWLFH')7LVFDOFXODWHG
E\))7ZKLFKLVDPRVWLPSRUWDQWVLQJOHDQDO\VLVWRRODYDLODEOH
1H[WWKHGLYLVLRQRIVLJQDOVZLOOEHSUHVHQWHGDVDEDVLVIRUVLJQDODQDO\VLVIROORZHGE\
DUHYLHZRI))7DQGWKHRWKHUDQDO\VLVPHWKRGVLHFRUUHODWLRQPHWKRGVDQGILOWHULQJ
WHFKQLTXHV
6LJQDOFODVVLILFDWLRQ
6LJQDO W\SHV DUH IXQGDPHQWDOO\ GLYLGHG LQWR WZR FDWHJRULHV VWDWLRQDU\ DQG QRQ
VWDWLRQDU\ 7KH VWDWLVWLFDO YDOXHV RI VWDWLRQDU\ VLJQDOV GR QRW YDU\ ZLWK WLPH VR WKH
SDUWLFXODUVDPSOHUHFRUGWLPHKLVWRU\ RU WLPHUHFRUG XVHG IRU VLJQDO GHWHUPLQDWLRQ LV
XQLPSRUWDQW $ GHWHUPLQLVWLF VLJQDO FDQ EH SUHGLFWHG ZLWK D UHDVRQDEOH DFFXUDF\ DW DOO
SRLQWVLQWLPHZKLOHZLWKVWDWLRQDU\UDQGRPVLJQDOVRQO\WKHVWDWLVWLFDOSURSHUWLHVRIWKH
VDPSOHIXQFWLRQV HQVHPEOH UHPDLQ FRQVLVWHQW 7KH SURSHUWLHV RI D VWDWLRQDU\ UDQGRP
SURFHVVFDQEHUHVROYHGE\FRPSXWLQJHQVHPEOHDYHUDJHVDWVSHFLILFLQVWDQWVRIWLPH,I
WKHWLPHDYHUDJHVFDOFXODWHGRYHUVSHFLILFVDPSOHIXQFWLRQVGRQRWFKDQJHDFFRUGLQJWR
WKHFKRVHQVDPSOHIXQFWLRQWKHSURFHVVLVHUJRGLFDQGWKHVHDYHUDJHVDUHHTXDOWRWKH
FRUUHVSRQGLQJ HQVHPEOH DYHUDJHG YDOXHV 1RQVWDWLRQDU\ WUDQVLHQWV DUH XVXDOO\ WUHDWHG
DQG DQDO\]HG DV D ZKROH ZKHUHDV FRQWLQXRXV QRQVWDWLRQDU\ VLJQDOV HJ VSHHFK DUH
H[DPLQHG LQ VKRUW VHFWLRQV WKDW DUH VXSSRVHG WR EH VWDWLRQDU\ LH TXDVLVWDWLRQDU\
VHFWLRQV%HQGDWDQG3LHUVRO
)DVW)RXULHU7UDQVIRUP
7KH )DVW )RXULHU 7UDQVIRUP ))7 LV DQ DOJRULWKP RU FDOFXODWLRQ SURFHGXUH XVLQJ
PDWUL[ RSHUDWRUV IRU REWDLQLQJ ')7 ZLWK JUHDW UHGXFWLRQ LQ DULWKPHWLFV FRPSDUHG WR
GLUHFWHYDOXDWLRQHJ 1 ORJ 1 LQVWHDGRI 1 7KHDOJRULWKPZDVSXEOLVKHGLQ
E\&RROH\DQG7XNH\DQGLWUHYROXWLRQL]HGVLJQDODQDO\VLVDQGLWVWLOOGRXEWOHVVWKHPRVW
LPSRUWDQWVLQJOHDQDO\VLVWHFKQLTXHDYDLODEOHIRUYDULRXVILHOGVRIVFLHQFH7KHILUVWGXDO
FKDQQHO ))7 DQDO\]HUV ZHUH LQWURGXFHG VRPH \HDUV DJR ZKLFK KDG ))7 DOJRULWKP
LPSOHPHQWHGLQDFRPELQDWLRQRIKDUGZDUHDQGILUPZDUH
$GHYLFHLVVDLGWRRSHUDWHLQ³UHDOWLPH´LIWKHGXUDWLRQRI))7DQGRWKHUSURFHVVLQJIRU
HDFKUHFRUGLVDWPRVWHTXDOWRWKHWLPHWDNHQWRFROOHFWWKHGDWDWKDWLVWUDQVIRUPHG7KLV
PHDQVWKDWGDWDLVDOZD\VEHLQJEXIIHUHGDQGSURFHVVHG7RGD\WKHVRIWZDUHDSSURDFKLV
XVXDOO\ VXIILFLHQWO\ IDVW DQG QR VSHFLILF ))7 KDUGZDUH LV QHHGHG 7KH UHDOWLPH
UHTXLUHPHQWGHSHQGVRQKRZTXLFNO\WKHVLJQDOLWVHOIFKDQJHVDQGXVXDOO\RQO\UDSLGO\
FKDQJLQJQRQVWDWLRQDU\VLJQDOVVXFKDVVSHHFKGHPDQGUHDOWLPHFRPSXWDWLRQ
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
0DLQDGYDQWDJHVRI))7
2QH RI WKH PDLQ DGYDQWDJHV RI D VLQJOH FKDQQHO ))7 DQDO\]HU LV WKDW LW SUHVHUYHV WKH
SKDVHLQIRUPDWLRQDQGWKXVWKHWUDQVIRUPEHWZHHQWLPHDQGIUHTXHQF\GRPDLQVLVIDLUO\
VLPSO\ )XUWKHU WKH DULVHQ PXOWLFKDQQHO DQDO\]LQJ ))7 WHFKQLTXHV RSHQ XS QHZ
DSSOLFDWLRQDUHDVVRXQGLQWHQVLW\PHDVXUHPHQWV]RRP))7WHFKQLTXHVHWFZKHUHWKH
H[FLWDWLRQ VLJQDOV WKHPVHOYHV DUH QRW RI SULPDU\ LQWHUHVW £ OLNH LQ SUHYLRXVO\
GHVFULEHGPHWKRGVVHHFKDSWHUV,QGHHGWKHFKDQQHO))7WHFKQLTXHVHQDEOH
SUHVHQWDWLRQ RI WKH SUHFLVH UHODWLRQVKLSV EHWZHHQ DUELWUDU\ LQSXW DQG RXWSXW VLJQDOV
LQFOXGLQJQRLVH7KHVHPHWKRGVDUHEDVHGRQWZRVLPXOWDQHRXVDQGV\QFKURQRXV)RXULHU
WUDQVIRUPV DQG VR LW LV SRVVLEOH WR FDOFXODWH WKH FURVV FRUUHODWLRQ DQG WKH FRPSOH[
IUHTXHQF\UHVSRQVHRIWKHV\VWHPXQGHUWHVW7KHVHHOHPHQWVDEOHGHHSHULQYHVWLJDWLRQRI
WKHFDXVDOUHODWLRQVDQGHQHUJ\IORZDQGWKHV\VWHPLGHQWLILFDWLRQFDQEHGRQHRQPXFK
KLJKHUOHYHOWKHQRWKHUZLVH
%DVLFOLPLWDWLRQVRI))7SURFHVVLQJ
7KH))7DOJRULWKP\LHOGVDQLGHQWLFDOUHVXOWWRGLUHFWDSSOLFDWLRQRIWKH')7VRDOO))7
OLPLWDWLRQVDUHWKHVDPHDVLQ')7ZKLFKDUHEDVLFDOO\UHVXOWHGIURPWKHILQLWHFLUFXODU
DQG GLVFUHWH FKDUDFWHULVWLFV +HQFH WKH ))7 DOJRULWKP LQKHUHQWO\ SURGXFHV D FRQVWDQW
EDQGZLGWK RQ D OLQHDU IUHTXHQF\ VFDOH 7KH GDWD SURFHVVLQJ LV DOZD\V GRQH WR GLVFUHWH
GLJLWDO VDPSOHV ZKLFK LQ WKHRU\ UHSUHVHQW RQH SHULRG RI DQ LQILQLWHO\ ORQJ SHULRGLF
VLJQDOUHJDUGOHVVRIWKHDFWXDOQDWXUHRIWKHLQSXWVLJQDO7KHFRQVHTXHQFHVRIWKLVFDQ
EH GLYLGHG LQWR WKUHH DOLDVLQJ ZLQGRZ HIIHFWV DQG WKH SLFNHW IHQFH HIIHFW 7KHVH
OLPLWDWLRQVFRPPRQWRDOVRRWKHUPHWKRGVDUHH[SODLQHGIXUWKHULQFKDSWHU
&RUUHODWLRQPHWKRGV
7KH DXWRFRUUHODWLRQ DQG FURVVFRUUHODWLRQ IXQFWLRQV ZHUH DOUHDG\ H[SODLQHG LQ FKDSWHU
7KH VLJQDO DQDO\VLV DQG PHDVXUHPHQW PHWKRGV PD\ RU PD\ QRW LQFOXGH WKH
FLUFXODULW\ FKDUDFWHULVWLFV GHVFULEHG HDUOLHU +HUH DQ LPSXOVH UHVSRQVH PHDVXUHPHQW
XVLQJ *ROD\ FRGHV WKDW DSSOLHV WKH QRQFLUFXODU FRUUHODWLRQ IXQFWLRQ LV SUHVHQWHG
IROORZHGE\VRPHWKHRU\RIWKHSHULRGLFFLUFXODULPSXOVHUHVSRQVHDQGPHDVXUHPHQWV
XVLQJ 0/6 VLJQDOV WKDW KDYH SHULRGLF DXWRFRUUHODWLRQ IXQFWLRQV 7KH 0/6 PHWKRG LV
RIWHQ XVHG LQ DXGLR PHDVXUHPHQWV EHFDXVH RI LWV VHYHUDO DGYDQWDJHV DQG KHQFH LW LV
VKRZQLQPRUHGHWDLO
,PSXOVHUHVSRQVHPHDVXUHPHQWXVLQJ*ROD\FRGHV
7KHXQLWVDPSOHLPSXOVHUHVSRQVHFDQEHPHDVXUHGZLWK*ROD\FRGHVDVDYDULDQW
RIWKH0/6PHWKRG)RVWHU7KHV\VWHPLVVHSDUDWHO\SUREHGWZLFHDQGFRUUHODWHG
ZLWK WKH UHVXOW LQ TXHVWLRQ XVLQJ WKH ILUVW FRGH DQG WKHQ LWV FRPSOHPHQW WKH VHFRQG
FRGH7KHQWKHWZRUHVXOWVDUHFRPELQHGDQGWKHVXPRIWKHDXWRFRUUHODWLRQVRIWKHWZR
SDLUV LV D VFDOHG XQLW VDPSOH IXQFWLRQ ZKLFK SURGXFHV WKH GHVLUHG XQLW VDPSOH
UHVSRQVH7KLVZRUNVIRUDSDLURIVHTXHQFHV D Q DQG EQ RIOHQJWK/
D Q = – IRU ˆ Q ˆ / IRUDOORWKHUQ
EQ = –IRU ˆ Q ˆ / IRUDOORWKHUQ
DVVXPLQJWKDWWKH\DUHD*ROD\SDLULH
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
Ê (D M D Q + M + E M EQ + M ) = / LI Q = HOVH
M
7KHLQSXWVHTXHQFHVDUHGULYHQWKURXJKD'$FRQYHUWHUZLWKDIL[HGVDPSOLQJLQWHUYDO
7DQGWKHQWKH ZDQWHG LPSXOVH UHVSRQVH LV D VFDOHG VDPSOHG XQLW SXOVH UHVSRQVH RI
WKHNLQG
FQ = F(D Q + EQ) = /K
Q7 + G ZKHUHGVWDQGVIRUWKHXQNQRZQSKDVHVKLIWEHWZHHQWKH$'DQG'$FRQYHUWHUV
&RUUHODWLQJWKHV\VWHPE\WKHVHTXHQFHV D Q EQ LVQRWUHOLHGRQFLUFXODUFRUUHODWLRQ
DVLQ0/6WHFKQLTXHV7KXVLWLVQRWUHTXLUHGWRXVHSHULRGLF*ROD\VHTXHQFHVUHODWLYHO\
VKRUWSURELQJFRGHVZLWKUHVSHFWWRWKHGXUDWLRQRIWKHV\VWHPUHVSRQVHDUHVXIILFLHQW
IRU D PRGHVW 615 HQKDQFHPHQW LQ D V\VWHP FRQWDLQLQJ VORZ UHVSRQVH FRPSRQHQWV
7KHRUHWLFDOO\WKH*ROD\PHWKRGJLYHVD / LPSURYHPHQWWRWKH615DVRSSRVHGWRD
VLQJOHSXOVH)RVWHU
3HULRGLFLPSXOVHUHVSRQVH
,QDGGLWLRQWRWKHQRUPDOFRQYROXWLRQDSHULRGLFFRQYROXWLRQFDQDOVREHXVHGZLWK
WKH SHULRGLF LPSXOVH UHVSRQVH 3,5 K
Q GHVFULELQJ D OLQHDU WLPHGLVFUHWH V\VWHP E\
XVLQJDSHULRGLFQRLVHVHTXHQFH [
Q \ Q = K
Q © [ Q =
Š
Ê [ N K
Q - N N = -Š
ZKHUH © LV WKH SHULRGLF FRQYROXWLRQ N LV D GLVFUHWH GHOD\ DQG WKH LQGH[ Q - N LV
HYDOXDWHGPRGXOR/$OOVHTXHQFHVZLWKDDSRVWURSKHKDYHDSHULRGRI/7KH3,5LVD
UHVSRQVHWRWKHSHULRGLFXQLWLPSXOVHLHDXQLWVDPSOHVHTXHQFHRISHULRG/
Ñ Q PRG / = d Q = Ò
Ó RWKHUZLVH
7KH UHODWLRQVKLS EHWZHHQ 3,5 K
Q DQG ,5 K Q FDQ EH GHWHUPLQHG E\ D OLQHDU
FRQYROXWLRQRId Q ZLWK K Q K
Q = d Q K Q =
Š
Ê d N KQ - N =
N = -Š
Š
Ê KQ + N/ N = -Š
7KH SHULRGLF LPSXOVH UHVSRQVH LV WKXV FRPSRVHG IURP VHTXHQWLDO /SRLQW VHJPHQWV RI
WKH LPSXOVH UHVSRQVH K Q ZKLFK DUH VKLIWHG WR WKH RULJLQ DQG VXPPHG WRJHWKHU 7KLV
LQWURGXFHVWLPHDOLDVLQJDQGLWHIIHFWLYHO\ZUDSV K Q EDFNRQLWVHOI WR WKH EHJLQQLQJ
LQRSSRVLWHRIWKHQRUPDOFDVHRIDOLDVLQJRIWKHLPSXOVHUHVSRQVHWRIRUP K
Q 7KH
GLVWRUWLRQGXHWRWKHVHZUDSDURXQGHIIHFWVFDQEHPDGHDUELWUDULO\VPDOOE\FKRRVLQJD
VXIILFLHQWO\ORQJSHULRG/ZKLFKPXVWEHDWOHDVWDVORQJDVWKHLPSXOVHUHVSRQVHRIWKH
V\VWHPXQGHUWHVW
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
3HULRGLFDXWRFRUUHODWLRQIXQFWLRQRI0/6
$ VLJQLILFDQW SURSHUW\ RI DQ 0/6 LV WKDW LWV SHULRGLF DXWRFRUUHODWLRQ LV DFWXDOO\ D
SHULRGLF XQLWVDPSOHVHTXHQFH )RU D V\PPHWULFDO 0/6 ZLWK SHULRG / WKH QRUPDOL]HG
FLUFXODUDXWRFRUUHODWLRQLVFDOFXODWHGDV
/ -
5 [[ Q =
[ N [ N + Q / +
N =
/
/ +
Q = - < Q < /
5[[
/ +
Ê
=
5[[
ZKHUHWKHQRUPDOL]DWLRQLVGRQHRYHUDSRZHURIWZRLH / + = 1 $SSO\LQJ
WRZHREWDLQ
Q = d Q 5 [[
/ +
ZKLFK PHDQV WKDW WKH FLUFXODU DXWRFRUUHODWLRQ FDQ EH H[SUHVVHG DV WKH VXP RI WKH
SHULRGLF XQLWVDPSOH UHVSRQVH DQG D PLQRU '& FRPSRQHQW (YLGHQWO\ DV / EHFRPHV
ODUJH WKH VHFRQG WHUP DSSURDFKHV ]HUR DQG 5[[ Q DSSURDFKHV WKH LGHDO DSHULRGLF
XQLWVDPSOHVHTXHQFH d Q VHH5LIHDQG9DQGHUNRR\
3HULRGLFLPSXOVHUHVSRQVHPHDVXUHPHQWXVLQJ0/6
7KHSHULRGLFLPSXOVHUHVSRQVH K
Q RIDQ/7,V\VWHPLVUHFRYHUHGE\FURVVFRUUHODWLQJ
WKHLQSXW0/6 [
Q ZLWKWKHRXWSXWVHTXHQFH \
Q 7KHQRUPDOL]HGDVEHIRUHRYHUD
SRZHURIWZRLH / + = 1 FLUFXODUFURVVFRUUHODWLRQLVZULWWHQDV
Q = [ Q F\ Q =
5 [\
/ -
Ê [
N \
N + Q / +
N =
$SSO\LQJ DQG WR ZH JHW WKH ILQDO UHVXOW DIWHU VRPH VWUDLJKWIRUZDUG
GHULYDWLRQVIRUWKHFURVVFRUUHODWLRQ
Q = K
Q - 5 [\
/
/ -
/ -
Ê K
N + / / + Ê K
N N =
N =
(T FDQ EH LQWHUSUHWHG DV YLUWXDOO\ $& FRXSOHG LPSXOVH UHVSRQVH WKH '&
FRPSRQHQWVHFRQGWHUPLVVXEWUDFWHGIURP K
Q ZKLOHWKHVDPHPHDQYDOXHRI K
Q
LVOHDNHGWKURXJKDVGRZQVFDOHGE\WKHIDFWRU / + WKLUGWHUP+RZHYHUXVXDOO\
WKLVGRHVQRWPDWWHUPRVWDXGLRV\VWHPVDUH$&FRXSOHGWKHVXPRI K Q RYHUDOOQLV
]HUR DQG ERWK WKH VHFRQG DQG WKLUG WHUP LQ YDQLVK +HQFH WKH QRUPDOL]HG FURVV
FRUUHODWLRQSURGXFHVWKH3,5ZLWKRXWHUURU$OVRLQSUDFWLFDOPHDVXUHPHQWVWKH /LVVR
ODUJHWKDWWKH'&RIIVHWVDUHLQGLVWLQFWIURPWKHEDFNJURXQGQRLVHHJIRU/ 1
WKH '& FRPSRQHQW LV DWWHQXDWHG E\ D IDFWRU LH G% 615 LV DOVR
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
LPSURYHGWKHVDPHG%FRPSDUHGWRDSHULRGLFXQLWVDPSOHVHTXHQFH d W JLYHQWKH
VDPHSHDNDPSOLWXGH2QO\LQWKHFDVHRIVWURQJO\'&FRXSOHGV\VWHPVWKHUHVLGXDOWKLUG
WHUPLQPXVWEHFRPSHQVDWHG%RULVKDQG$QJHOO
7KH SHULRGLF LPSXOVH UHVSRQVH PHDVXUHPHQW XVLQJ 0/6 KDV VHYHUDO EHQHILWV ,W KDV D
KLJK LPPXQLW\ DJDLQVW QRQFRKHUHQW QRLVH 7KH FURVV FRUUHODWLRQ LV FDOFXODWHG RYHU
H[DFWO\ RQH SHULRGLF 0/6 DQG WKHUH ZLOO EH QR WUXQFDWLRQ HIIHFWV DQG DOVR QR
SUREOHPDWLF ZLQGRZLQJ LV QHFHVVDU\ $OVR WKH FURVV FRUUHODWLRQ FDQ EH SHUIRUPHG
VWUDLJKWIRUZDUGO\ ZLWK ))7PXOWLSO\,))7 PHWKRG RU PXFK PRUH HIILFLHQWO\ E\ XVLQJ
WKH IDVW +DGDPDUG DOJRULWKP WKDW DSSOLHV PDWUL[ WUDQVIRUPV LQ RUGHU WR XVH RQO\
DGGLWLRQV DQG VXEWUDFWLRQV LQVWHDG RI PXOWLSOLFDWLRQV %RULVK DQG $QJHOO 5LIH
DQG9DQGHUNRR\,QDGGLWLRQORQJLPSXOVHUHVSRQVHVFDQEHDFTXLUHGHDVLO\DQG
DQHODERUDWHIUHTXHQF\UHVSRQVHFDQEHREWDLQHGZLWKRXWWKHQHHGRIVSHFLDOWRROVVXFK
DVWKHVRFDOOHG]RRP))7)XUWKHUPRUHSUHFRORUHGDQGSUHHPSKDVL]HG0/6FDQEH
HPSOR\HG WR LPSURYH 615 DQG LQ DGGLWLRQ WR OLQHDU V\VWHPV DOVR ZHDNO\ QRQOLQHDU
V\VWHPVDSSUR[LPDWHGE\OLQHDUHTXLYDOHQWVFDQEHLQYHVWLJDWHG5LIHDQG9DQGHUNRR\
+RZHYHUWKHH[FLWDWLRQVLJQDOPXVWEHORQJHQRXJKLQRUGHUWKDWWKHV\VWHPZLOO
EHVWDELOL]HGIURPWKHVWDUWLQJWUDQVLHQWVVRDWOHDVWWZRVHTXHQFHVDUHQHHGHGWKXVWKH
0/6 WHFKQLTXH ILWV RQO\ WR WLPHLQYDULDQW V\VWHPV $OVR WKH 0/6 PHWKRG LV QRW
SHUIRUPHG DV D GXDO FKDQQHO PHDVXUHPHQW ZKLFK PDNHV RQ WKH RWKHU KDQG WKH
GLVDGYDQWDJH WKDW WKH VWLPXOXV KDV WR EH FRQWUROOHG E\ WKH H[DPLQHU LH WKH V\VWHP
XQGHUWHVWPXVWEHDEOHWREHGULYHQZLWKD0/6VLJQDO
)LOWHULQJWHFKQLTXHV
7KHDSSOLFDWLRQRIILOWHULQJWHFKQLTXHVLVWKHROGHVWDQDO\VLVPHWKRGLQHQJLQHHULQJ7KH
VSHFWUDO GHQVLW\ ZDV RULJLQDOO\ HVWLPDWHG XVLQJ DQDORJXH VSHFWUXP DQDO\]HUV 7KH\ DUH
RQO\ VLQJOH FKDQQHO GHYLFHV DQG WKH\ FDQ EH GLYLGHG LQWR IRXU FDWHJRULHV GLVFUHWH
VWHSSLQJILOWHUVVZHHSLQJILOWHUVSDUDOOHODQDO\]HUVDQGWLPHFRPSUHVVLRQDQDO\]HUV7KH
ODWWHU RQHV DUH SDUDOOHO GHYLFHV WKDW ZRUN UHDOWLPH DQG PXFK IDVWHU WKDQ WKH WZR ILUVW
W\SHVZKLFKDUHVHTXHQWLDODQGPRVWO\DSSOLHGWRREWDLQWKHIUHTXHQF\VSHFWUXPLHWKH
PDJQLWXGH UHVSRQVH RI WKH V\VWHP XQGHU WHVW XVLQJ UDQGRP QRLVH RU VLQXVRLGDO
H[FLWDWLRQ$OVRQRQVWDWLRQDU\WUDQVLHQWVFDQEHLQYHVWLJDWHGZLWKVSHFLDOPHWKRGV7KH
SKDVH UHVSRQVH RI WKH V\VWHP FDQ EH DFTXLUHG E\ TXDGUDWXUH GHPRGXODWLRQ WKDW FDQ
GHWHFWERWKWKHUHDODQGFRPSOH[SDUWRIWKHILOWHUHGVLJQDOVHHFKDSWHU
1RZDGD\V WKH DQDORJXH DQDO\]HUV DUH DOPRVW WRWDOO\ UHSODFHG E\ GLJLWDO UHDOWLPH
DQDO\]HUV +RZHYHU WKHUH DUH PDQ\ FRPPRQ FKDUDFWHULVWLFV IRU ERWK GLJLWDO DQG
DQDORJXH PHWKRGV +HUH WKH VLJQDO GHWHFWLRQ SULQFLSOH ZLOO EH ILUVW H[SODLQHG WKHQ WKH
WUDGLWLRQDODQDORJXHDQDO\]HUW\SHVWKDWPD\DVHDVLO\EHLPSOHPHQWHGGLJLWDOO\5DQGDOO
IROORZHGE\WKHGLJLWDOGXDOFKDQQHOUHDOWLPHDQDO\]HU)LQDOO\WKHUHZLOOEHD
UHYLHZRIWKHQRZDOUHDG\OHVVVLJQLILFDQWWLPHGHOD\VSHFWURPHWU\ZKLFKLVDYDULDQWRI
WKH VZHHSLQJ ILOWHU DQDO\]HU WHFKQLTXHV DQG PD\ EH LPSOHPHQWHG HLWKHU GLJLWDOO\ RU
DQDORJLFDOO\5DQGDOOLVDSSOLHGLQPDQ\FDVHVDVDJRRGUHIHUHQFHIRUSUDFWLFDO
LQIRUPDWLRQ
6LJQDOGHWHFWLRQ
7KH DPSOLILHG PLFURSKRQH VLJQDO [ W LV IHG WKURXJK D SDVVEDQG ILOWHU ZLWK D WXQDEOH
FHQWHUIUHTXHQF\ I RUDIL[HGILOWHUEDQNDQGWKHLQVWDQWDQHRXVRXWSXWRIWKHILOWHULV
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
VTXDUHGWKHQDYHUDJHGRYHUWKHUHFRUGOHQJWK7WRREWDLQDPHDQVTXDUHYDOXHHVWLPDWH
RI WKH ILOWHUHG VLJQDO DQG ILQDOO\ GLYLGHG E\ WKH ILOWHU EDQGZLGWK DI WR REWDLQ DQ
HVWLPDWH RI WKH UDWH RI FKDQJH RI PHDQ VTXDUH YDOXH ZLWK D IUHTXHQF\ DW WKH FHQWHU
IUHTXHQF\ %\ WDNLQJ WKH OLPLWLQJ YDOXHV RI WKLV HVWLPDWH RI WKH DXWRVSHFWUDO GHQVLW\
IXQFWLRQLQUHODWLRQWR7DQG DI VRWKDW DI 7 “ Š WKHRQHVLGHGDXWRVSHFWUDOGHQVLW\
IXQFWLRQLVREWDLQHG
7
Þ
ÎÏ
ß
* [[ I = OLP
OLP
[
I
I
W
GW
D
×
ß
DI “Š DI ÏÐ7 “Š 7 à
ZKLFKLVH[DFWO\HTXDOWRE\GHILQLRQ%HQGDWDQG3LHUVRO
'LVFUHWHVWHSSLQJILOWHUDQDO\]HUV
,IWKHILOWHULVIL[HGDWRQHFHQWHUIUHTXHQF\LWVRXWSXWLVWKHLQSXWVLJQDOLHWKHV\VWHP
UHVSRQVH FRQYROYHG ZLWK WKH ILOWHU LPSXOVH UHVSRQVH ZKLFK FRUUHVSRQGV WR D
PXOWLSOLFDWLRQRIWZRFRPSOH[IXQFWLRQVLQWKHIUHTXHQF\GRPDLQ7KHRXWSXWVLJQDORI
WKH ILOWHU KDV DQ DPSOLWXGH DQG D SRZHU VSHFWUXP ZKLFK DUH WKH SURGXFWV RI WKH
FRUUHVSRQGLQJWZRVSHFWUD7KHSKDVHFKDUDFWHULVWLFVZLOOEHPRGLILHGE\WKHILOWHUEXW
WKLV KDV QR HIIHFW RQ WKH WUDQVPLWWHG SRZHU 7KH ILOWHU FDQ KDYH D FRQVWDQW EDQGZLGWK
JLYLQJ XQLIRUP UHVROXWLRQ RQ D OLQHDU IUHTXHQF\ VFDOH ZLWK RQO\ WZR GHFDGHV RI XVHIXO
UDQJHRUDFRQVWDQWUHODWLYHSHUFHQWDJHEDQGZLGWKHJRFWDYHDQGRFWDYHILOWHUV
DVVXULQJXQLIRUPUHVROXWLRQRQDORJDULWKPLFIUHTXHQF\VFDOH
,QRUGHUWRJHWWKHIXOOVSHFWUXPWKHILOWHUFHQWHUIUHTXHQF\PXVWEHVWHSSHGRUVZHSW
RYHU WKH IUHTXHQF\ UDQJH RI LQWHUHVW 7KLV VWHSSLQJ FRQYH\V D QXPEHU RI VSHFWUXP
HVWLPDWHV DW GLVFUHWH IUHTXHQFLHV DQG LW FDQ EH FDUULHG RXW E\ D ILOWHUEDQN KDYLQJ
GLIIHUHQWFHQWHUIUHTXHQFLHVRUVLPSO\XVLQJWZRILOWHUVZLWKYDULDEOHFHQWHUIUHTXHQFLHV
VR WKDW WKH ILOWHUV DUH VWHSSHG XS DOWHUQDWHO\ LQ IUHTXHQF\ 7KH ILOWHUEDQN FRQVLVWV RI
VHSDUDWHILOWHUVWKDWKDYHWKHVDPHLQSXWEXWLQDQ\FDVHWKHDQDO\]HUKDVRQO\DVLQJOH
GHWHFWRU
6ZHHSLQJILOWHUDQDO\]HUV
)RUQDUURZEDQGVWXGLHVLWLVPRUHFRPPRQWRXVHDVLQJOHILOWHUZLWKDWXQDEOHFHQWHU
IUHTXHQF\ ZKLFK OHDGV WR D FRQWLQXRXV VSHFWUXP LQ ZKLFK HDFK SRLQW UHSUHVHQWV DQ
LQWHJUDWLRQRIWKHWUXHVSHFWUXPRYHUWKHILOWHUEDQGZLGWKLHDSSUR[LPDWHO\WKHLQYHUVH
RI WKH ILOWHU UHVSRQVH WLPH 7KH VZHHS UDWH LV OLPLWHG E\ DW OHDVW RI WKH IDFWRUV ILOWHU
UHVSRQVHWLPHDQGDYHUDJLQJWLPH 7 DQGZULWLQJVSHHGRIDWUDGLWLRQDOSDSHUUHFRUGHU
LILWLVXVHG$OVRIRUGHWHUPLQLVWLFVLJQDOVWKHIROORZLQJUHTXLUHPHQWH[LVWV 7 ˜ I ZKHUH I LVWKHIUHTXHQF\RIDVLQJOHFRPSRQHQW
3DUDOOHODQDO\]HUVUHDOWLPH
7KHUHDOWLPHDQDO\]HUVREWDLQWKHZKROHVSHFWUXPLQSDUDOOHOIURPWKHVDPHVHFWLRQRI
WKH VLJQDO VR WKH\ DUH PXFK IDVWHU DQG QRW OLPLWHG WR VWDWLRQDU\ VLJQDOV DV WKH DERYH
GHSLFWHGVHTXHQWLDOPHWKRGVDUH6XFKDUHDOWLPHDQDO\VLVFDQEHSHUIRUPHGE\DSSO\LQJ
WKHVLJQDOWRDSDUDOOHOEDQNRIILOWHUDPSOLILHUGHWHFWRUFKDQQHOV
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
7LPHFRPSUHVVLRQDQDO\]HUVUHDOWLPH
7KH UHDOWLPH QDUURZEDQG DQDORJXH DQDO\]HUV XVH WLPH FRPSUHVVLRQ LQ ZKLFK WKH
VLJQDOKDVEHHQUHFRUGHGRUFRQWLQXRXVO\VDPSOHGDWVRPHVSHHGDQGWKHQSOD\HGEDFN
0WLPHVIDVWHUWRDKLJKIUHTXHQF\KHWHURG\QHILOWHUDOORZLQJ0WLPHVODUJHUILOWHUVDQG
D FRUUHVSRQGLQJ UHGXFWLRQ LQ DQDO\VLV GXUDWLRQ +RZHYHU WKLV PHWKRG KDV EHHQ QHDUO\
WRWDOO\GLVSODFHGE\))7DQDO\]HUV
'XDOFKDQQHOUHDOWLPHDQDO\]HU
7KH PRGHUQ GLJLWDO GXDOFKDQQHO UHDOWLPH DQDO\]HU KDV GHWHFWRUV FRQVLVWLQJ RI IRXU
EUDQFKHV WKDW HVWLPDWH WKH DXWRVSHFWUDV RI WKH ERWK FKDQQHOV E\ WKH DERYH GHVFULEHG
ILOWHULQJVTXDULQJDYHUDJLQJ RSHUDWLRQ 7KH FRPSOH[YDOXHG FURVVVSHFWUXP LV SURGX
FHG E\ UHSODFLQJ WKH VTXDULQJ E\ D PXOWLSOLFDWLRQ RI WKH WZR VLJQDOV WKH UHDO SDUW LV
JHQHUDWHG E\ WKH GLUHFW PXOWLSOLFDWLRQ DQG IRU WKH FRPSOH[ SDUW GHWHFWLRQ WKH SKDVH RI
WKHRWKHUVLJQDOPXVWEHVKLIWHG•7KHUHDOWLPHDQDO\]HUVKRZVDOOZDQWHGIUHTXHQF\
EDQGZLGWKVVLPXOWDQHRXVO\RQWKHGLVSOD\VRDOOWKHILOWHUGHWHFWRUSURFHGXUHVPXVWEH
LPSOHPHQWHGVHSDUDWHO\WRHDFKIUHTXHQF\EDQGVHJRFWDYHDQGRFWDYH,QSUDFWLFH
WKLV LV RQO\ SRVVLEOH E\ XVLQJ GLJLWDO WHFKQLTXHV KHQFH WKHUH DUH QR PXOWLFKDQQHO
DQDORJXHUHDOWLPHDQDO\]HUVDYDLODEOH/DKWL
7LPHGHOD\VSHFWURPHWU\
7LPH GHOD\ VSHFWURPHWU\ 7'6 LV D PHWKRG LQWURGXFHG E\ 5 & +H\VHU LQ WR
PHDVXUH WKH FRPSOH[ WUDQVIHU IXQFWLRQ LQ DXGLR V\VWHPV ZLWK D VZHSW VLQH FKLUS
H[FLWDWLRQ VR 7'6 LV UHODWHG WR VZHHSLQJ ILOWHU DQDO\VLV WHFKQLTXH 1HYHUWKHOHVV WKH
SURFHGXUH LV VRPHZKDW GLIIHUHQW 7'6 LV EDVHG RQ LQSKDVH TXDGUDWXUH RVFLOODWRUV
KDYLQJ D GHOD\ t WR FRUUHFWO\ GHPRGXODWH WKH RULJLQDO VZHHS H[FLWDWLRQ 7KH GHWHFWHG
UHDO DQG LPDJLQDU\ VLJQDO FRPSRQHQWV DUH ORZSDVV ILOWHUHG VR WKDW WKH UDSLGO\ IOXF
WXDWLQJ FRPSRQHQWV DUH UHPRYHG 7KH PHDVXUHPHQW RI WKH VZHHSLQJ VLQH ZDYH LV QRW
DVVRFLDWHGWRWKHVLQJOHFHQWHUIUHTXHQF\£DVLQSUHYLRXVO\VSHFLILHGILOWHUDQDO\VLVZLWK
VZHSW VLQH H[FLWDWLRQ £ EXW UDWKHU WR D GLVWULEXWLRQ RI IUHTXHQFLHV GHWHUPLQHG E\ WKH
VZHHSUDWH&ROORPV
,Q9DQGHUNRR\DPRUHPDWKHPDWLFDODQDO\VLVRI7'6LVSUHVHQWHGDORQJZLWKWKH
VRIWZDUH 7'6 DSSURDFK +RZHYHU 7'6 KDV ORVW LWV VLJQLILFDQFH LQ FRPPRQO\ DSSOLHG
PHDVXUHPHQW WHFKQLTXHV 7KH WHFKQLTXHV DSSO\LQJ SVHXGRUDQGRP QRLVH VHTXHQFHV
VXFK DV 0/6 KDYH EHFRPH PRUH SRSXODU WKH\ DOORZ WKH VDPH FDSDELOLWLHV DQG HYHQ
PRUHZLWKOHVVHIIRUWWKDQ7'6
620($9$,/$%/(0($685(0(176<67(06
$ V\VWHP IRU DXGLR PHDVXUHPHQWV DQG DQDO\VLV QHHG QRW WR EH FRPSOH[ 6LPSO\ WKH
PRVWLQH[SHQVLYHZD\WREXLOGRQHZRXOGEHWRXVHDVXIILFLHQWKLJKTXDOLW\VRXQGFDUG
ZLWK$'DQG'$FRQYHUWHUVIRUGDWDDFTXLVLWLRQDQGVLJQDOJHQHUDWLRQDQGWKH&38RI
WKH FRPSXWHU IRU GDWD FRQWURO DQG SURFHVVLQJ 7KH VRIWZDUH QHFHVVDU\ FRXOG EH HLWKHU
VHOIZULWWHQ RU D JHQHUDO SXUSRVH VLJQDO SURFHVVLQJ VRIWZDUH HJ 0DWODE· 7KLV QRQ
SURIHVVLRQDO FRQFHSW LV SUHVXPDEO\ QRW ZLGHO\ SUDFWLFHG KRZHYHU D GHPRQVWUDWLRQ
YHUVLRQ RI D 0DWODE· 7RROER[ IRU FKDQQHO UHDOWLPH '63 DSSO\LQJ D 7XUWOH %HDFK
7DKLWLVRXQGFDUGFDQEHIRXQGHYHQLQWKH:RUOG:LGH:HE3XWQDP
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
7KHFRPPHUFLDOPHDVXUHPHQWDQGDQDO\VLVV\VWHPVPD\EHGLYLGHGLQWRWKUHHGLIIHUHQW
W\SHVRQWKHEDVLVRIWKHLQWHUDFWLRQOHYHOEHWZHHQWKHXVHUDQGWKHHTXLSPHQW WKDW LV
KRZZHOOWKHXVHULVDEOHWRGHILQHWKHPHDVXUHPHQWV\VWHPKHUKLPVHOI7KHIROORZLQJ
GLYLVLRQ RI V\VWHPV LV IURP OHVV WR PRUH XVHU GHILQDEOH DSSOLFDWLRQ RULHQWHG V\VWHPV
VLQJOH GDWD DFTXLVLWLRQ ERDUGV DQG IXOO\ XVHUGHILQHG LQVWUXPHQWDWLRQ V\VWHPV 7KHVH
ZLOOEHGLVFXVVHGIXUWKHUQH[W
$SSOLFDWLRQRULHQWHGV\VWHPV
7KHWUDGLWLRQDOV\VWHPVDUHEDVHGRQVWDQGDORQHGHYLFHVHLWKHUVLQJOHSXUSRVHRUPXOWL
SXUSRVH PHDVXUHPHQW DQG DQDO\VLV HTXLSPHQW ZKLFK DUH DSSOLFDWLRQ RULHQWHG DQG WKXV
QRW XVHU FRQILJXUDEOH LQ WKH ZLGH VHQVH 7KH PRVW VLJQLILFDQW PDQXIDFWXUHU RI VXFK
JUHHQFRORUHG DSSDUDWXV KDV EHHQ VLQFH WKH ODVW \HDUV WKH IRUPHU 'DQLVK WRGD\
*HUPDQRZQHGFRPSDQ\%UHO.M U,WLVZRUOGIDPRXVRILWVSURIHVVLRQDOKLJK
TXDOLW\ DQG H[SHQVLYH SURGXFWV 2WKHU PDMRU PDQXIDFWXUHUV LQFOXGH HJ 1RUVRQLF
1HXWULNDQG&RUWH[
6LQJOHGDWDDFTXLVLWLRQERDUGV
,Q WKH PDUNHW WKHUH DUH VHYHUDO PRUH RU OHVV FRVWO\ LQVWUXPHQWDWLRQ V\VWHPV IRU PRVWO\
3&V7KHV\VWHPFRQVLVWVRIVRIWZDUHDQGKDUGZDUHLHSOXJLQGDWDDFTXLVLWLRQ'$&
ERDUG DQG SRVVLEO\ D GLJLWDO VLJQDO SURFHVVRU '63 ERDUG 7KH VRIWZDUH FRQWUROV WKH
RQERDUG $' DQG '$ FRQYHUWHUV VLJQDO JHQHUDWRUV ILOWHUV DPSOLILHUV DQG WKH '63
2QHRIWKHPRVWFRPPRQO\DFFHSWHGRI3&EDVHGSOXJLQV\VWHPVLV0/66$DQGDOVR
WKH6<6LGLVXVHGWRVRPHH[WHQW%RWKV\VWHPVFDQEHLQVWDOOHGWRDSRUWDEOHFRPSXWHU
IRULQILHOGPHDVXUHPHQWVDQGDQDO\VLV
0/66$
0D[LPXP/HQJWK 6HTXHQFH 6\VWHP $QDO\]HU 0/66$ LV D SRZHUIXO OLQHDU V\VWHP
DQDO\]HUEDVHGRQWKH0/6WHFKQLTXHV5LIH,WKDV EHHQ GHYHORSHG E\ 'RXJODV
5LIH '5$ /DERUDWRULHV LQ ,Q DGGLWLRQ WR FRPSOH[ WUDQVIHU IXQFWLRQ
PHDVXUHPHQWV 0/66$ FDQ GHULYH YDULRXV SURSHUWLHV E\ SRVWSURFHVVLQJ WKH LPSXOVH
UHVSRQVH VXFK DV FKDUDFWHULVWLFV RI VLJQDO HQHUJ\ FRPSOH[ LPSHGDQFH DQG VSHHFK
LQWHOOLJLELOLW\ 7KHUH DUH WKUHH SRVVLEOH WHVW VLJQDOV DYDLODEOH 0/6 QDUURZ SXOVH DQG
VWHSIXQFWLRQVTXDUHZDYH
0/66$VRIWZDUHUXQVRQ06'26DQGLWLVPDGHIRUFKDQQHOPHDVXUHPHQWVEXWWKH
KDUGZDUHDFWXDOO\VXSSRUWVFKDQQHOV7KH,%03&FRPSDWLEOH,6$ERDUGKDVDEXLOW
LQ'63DQGDSURJUDPPDEOHDQWLDOLDVILOWHUWKDWDOORZVWRVHOHFWWKHVXLWDEOHIUHTXHQF\
UHVROXWLRQPLQLPXP+]DQGLQVWUXPHQWEDQGZLGWKPD[LPXPN+]0/66$
KDVDVXFFHVVLYHDSSUR[LPDWLRQELW$''$FRQYHUWHU'XHWRWKHVRIWZDUHIL[HG
DXWRUDQJHIHDWXUHLQWKHDQWLDOLDVILOWHUWKHHIIHFWLYHUHVROXWLRQLVDOVRELWVOHDGLQJ
WRG%6150/66$FDQDOVRREWDLQDQPD[LPDOLPSXOVHUHVSRQVHRIVDPSOH
SRLQWV LQ D IHZ VHFRQGV XVLQJ WKH IDVW +DGDPDUG WUDQVIRUP +RZHYHU 0/66$ LV QRW
DQ\ ORQJHU WKH PRVW XSWRGDWH HTXLSPHQW WKDW LW XVHG WR EH 7KH VLJQDO SDWK PXVW EH
FRPSHQVDWHG DQWLDOLDV ILOWHUV HWF ZKLFK PD\ FDXVH SUDFWLFDO SUREOHPV 0/66$ LV
SRRUO\GRFXPHQWHGDQGPRVWRIDOOOLNHWKHXVXDOHTXLSPHQWRIWKLVW\SHWKH0/66$LV
DFORVHGV\VWHPDQGGRHVQRWDOORZIOH[LEOHXVHUFRQILJXUDWLRQQRWHYHQVKDSLQJRIWKH
WHVWVLJQDO
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
6<6LG
6<6WHP ,GHQWLILFDWLRQ 6<6LG LV D GXDO FKDQQHO ))7EDVHG WHVWLQJ DQG PHDVXULQJ
LQVWUXPHQW IURP $ULHO &RUSRUDWLRQ IRU V\VWHP LGHQWLILFDWLRQ LQ WKH DXGLR EDQGZLGWK
$ULHO&RUSRUDWLRQ6<6LGUXQVRQ3&VDQGFDQSHUIRUPDQXPEHURIWDVNVVXFK
DV GLVWRUWLRQ LPSXOVH UHVSRQVH QRLVH DQG WUDQVIHU IXQFWLRQ DQDO\VLV EXW RQO\ XVLQJ
FKLUSVRUVLQJOHIUHTXHQF\VLQHZDYHVRUSDLUVRIVLQHZDYHV6<6LGKDVDVHSDUDWHGDWD
DFTXLVLWLRQ ERDUG ZLWK ELW $' '$ FRQYHUWHUV DQG WKH $ULHO '63 D GDWD
SURFHVVRUERDUGZLWKD7H[DV&ELWLQWHJHUDQGELWIORDWLQJSRLQW'637KH
G\QDPLF UDQJH LV VXSSRVHG WR EH RYHU G% LQ SUDFWLFH DSSUR[ G% DQG WKH
PD[LPXP))7OHQJWKLVNSRLQWV7KHPD[LPXPXVDEOHEDQGZLGWKLVFDN+]DQG
LQQHZHUYHUVLRQRI6<6LGWKHVWLPXOXVFDQEHPRGLILHGE\WKHXVHU+RZHYHUWKHDQWL
DOLDVILOWHUVDUHQRWWKDWJRRGWKH\ SURGXFH TXLWH PXFK RI RXWRIEDQG QRLVH DQG WKHUH
DUHDOVRVRPHSUREOHPVZLWKWKHLPSXOVHVWLPXOXV%DFNPDQ
8VHUGHILQHGLQVWUXPHQWDWLRQV\VWHPV
7KH PRGHUQ LQVWUXPHQWDWLRQ V\VWHP FRQVLVWV RI D PDVWHU FRPSXWHU WKDW FRQWUROV WKH
LQVWUXPHQWV WKH WUDGLWLRQDO VWDQGDORQH HTXLSPHQW DQGRU YLUWXDO SOXJLQ GDWD
DFTXLVLWLRQ '$4 ERDUGV YLD DQ LQSXWRXWSXW ,2 EXV LQWHUIDFH 7KH VWDQGDUG
LQGXVWULDO LQVWUXPHQWDWLRQ LQWHUIDFH LV WKH SDUDOOHO ,((( EXW DOVR WKH SDUDOOHO 56
H[WHQVLRQVIURPWKHILUVWVHULDOVWDQGDUGLQWHUIDFH56DUHSUDFWLFHG7KLV
NLQGRIDGYDQFHGLQVWUXPHQWDWLRQV\VWHPFDQEHXVHGDVZHOOIRULQGXVWULDODXWRPDWLRQ
DVPHDVXUHPHQWDQGDQDO\VLVSXUSRVHV,WDFFRPSOLVKHVPRUHIOH[LEOHDQGFKHDSHUXVHU
GHILQHGVRIWZDUHEDVHGPHDVXUHPHQWV\VWHPVPDNLQJSRVVLEOHJUHDWHUFRPSOH[LW\ DQG
PRUHDSSOLFDWLRQRULHQWHGV\VWHPVWKDQWKHWUDGLWLRQDOVWDQGDORQHV\VWHPV
$YDLODEOHV\VWHPV
1DWLRQDO ,QVWUXPHQWV SURYLGHV WHVW DQG PHDVXUHPHQW DQG LQGXVWULDO DXWRPDWLRQ
KDUGZDUHDQGVRIWZDUH/DE9,(:DQG/DE:LQGRZV&9,IRUGLIIHUHQWSODWIRUPV 7KH
6LJQDO 3URFHVVLQJ 6XLWH DOVR FRQWDLQLQJ VRIWZDUH IRU GLJLWDO ILOWHU GHVLJQ LV HVSHFLDOO\
GHVLJQHGIRUDXGLRDQGDFRXVWLFPHDVXUHPHQWV7KH GDWD DQDO\VLV LV SHUIRUPHG RQOLQH
DQGWKHLQVWUXPHQWDWLRQGHYLFHVHLWKHUYLUWXDORUVWDQGDORQHFDQ EH IUHHO\ FRQILJXUHG
E\WKHXVHU$VLPLODULQVWUXPHQWDWLRQV\VWHPLVDWKDQGIURP+HZOHWW3DFNDUG
ZLWKJUDSKLFDOSURJUDPPLQJ+39((7KHUHDUHDOVRH[WHQWDQGTXLWHH[SHQVLYHKLJK
TXDOLW\ PHDVXUHPHQW V\VWHPV DYDLODEOH IRU SDUWLFXODUO\ DXGLR DQG DFRXVWLFV DQDO\VLV
7KHVH LQFOXGH WKH 0LFURVRIW :LQGRZV· EDVHG V\VWHPV 6\VWHP 2QH DQG LWV QHZHU
YHUVLRQ6\VWHP7ZRIURP$XGLR3UHFLVLRQ3XOVHIURP%UHO.M UDQG7()
6RXQG/$%EDVHGRQWKH7'6WHFKQLTXHIURP7HFKURQ
35$&7,&$/&216,'(5$7,216
7KH IXQGDPHQWDO OLPLWDWLRQ RI WKH PHDVXUHPHQW UHVROXWLRQ UHJDUGOHVV RI WKH DSSOLHG
PHWKRG LV WKH JHQHUDO IUHTXHQF\ YV WLPH GRPDLQ XQFHUWDLQW\ SULQFLSOH PDWFKLQJ WKH
XQLYHUVDO XQFHUWDLQW\ SULQFLSOH E\ +HLVHQEHUJ $FFRUGLQJO\ WKH KLJKHVW WKHRUHWLFDO
WHPSRUDOUHVROXWLRQLVWKHLQYHUVHRIWKHPD[LPXPIUHTXHQF\SUHVHQWDQGYLFHYHUVD
7KHUHDUHDOVRPDQ\RWKHUFRPPRQOLPLWDWLRQVLQDQDO\VLVPHWKRGVLQSDUWLFXODUGXHWR
WKH JHQHUDOL]HG XVH RI GLJLWDO WHFKQLTXHV ,Q SUDFWLFDO PHDVXUHPHQWV WKHUH DUH DOZD\V
GLVWXUELQJHUURUVZKLFKVKRXOGEHSUHYHQWHGRUPLQLPL]HG
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
6RPHFRPPRQOLPLWDWLRQVLQGLJLWDOWHFKQLTXHV
$OLDVLQJ LV GXH WR IUHTXHQF\ FRPSRQHQWV LQ WKH LQSXW VLJQDO VSHFWUD WKDW H[WHQW WKH
1\TXLVW IUHTXHQF\ LH KDOI WKH VDPSOLQJ IUHTXHQF\ FDXVLQJ RYHUODSSLQJ DOLDVLQJ LQ
WKHIUHTXHQF\GRPDLQ7KLVHIIHFWLVUHPRYHGZLWKVWHHSDQWLDOLDVLHORZSDVVILOWHUV
DQGLVXVXDOO\QRWDSUREOHPLQFDVHRIIL[HGEDQGZLGWK+RZHYHUWKHDOLDVLQJOLPLWVWKH
SURILWDEOHEDQGZLGWKFDXVLQJDQDSHUDWXUHORVVRIWHQDVVRFLDWHGZLWK'$FRQYHUVLRQV
7LPH DOLDVLQJ GHVFULEHG HDUOLHU LQ FKDSWHU LV D VLJQLILFDQW DVSHFW WKDW OLPLWV WKH
SRVVLELOLWLHVDQGRIWHQSURGXFHVHUURUVLQDXGLRPHDVXUHPHQWV$OVRWKHZLQGRZHIIHFW
FDXVHV SRZHU IURP GLVFUHWH IUHTXHQF\ FRPSRQHQWV WR OHDN LQWR DGMDFHQW EDQGV
JHQHUDWLQJ XQZDQWHG VLGHOREHV ZKLFK LV UHGXFHG E\ XVLQJ SURSHU ZLQGRZ IXQFWLRQV
HJ +DQQLQJ ZLQGRZ 7KH SLFNHW IHQFH HIIHFW LV E\ UHDVRQ RI GLVFUHWHO\ VDPSOLQJ LQ
IUHTXHQF\GRPDLQZKLFKKDSSHQVDOVRZKHQGLVFUHWHIL[HGILOWHUVDUHXVHGDQGLWFDQEH
FRPSHQVDWHG ZLWK ZHLJKWLQJ IXQFWLRQV LI WKLV LV UHVXOW RI D VLQJOH VWDEOH IUHTXHQF\
FRPSRQHQW
*HQHUDOPHDVXUHPHQWHUURUV
,Q D SUDFWLFDO PHDVXUHPHQW VLWXDWLRQ WKHUH DUH DOZD\V HUURU VRXUFHV SUHVHQW 7KH\ FDQ
H[LVWLQQXPHURXVZD\VDQGVRPHRIWKHJHQHUDOHUURUVDQGLQWHUUXSWLQJSHFXOLDULWLHVDUH
VWDWHG KHUH $OVR WKH OLPLWDWLRQV PHQWLRQHG DERYH FDQ FDXVH LQDFFXUDFLHV WR WKH
PHDVXUHPHQWLIWKH\DUHQRWDSSURSULDWHO\WDNHQDFFRXQWIRU
$PELHQW UDQGRP QRLVH FDQ EH FDXVHG E\ WKH HOHFWULFDO PHDVXUHPHQW DSSDUDWXV RU E\
WKH VXUURXQGLQJ DFRXVWLFDO FRQGLWLRQV ,W VKRXOG EH QRWHG WKDW QHLWKHU ODERUDWRU\
VXUURXQGLQJVDUHLGHDOMXVWEHWWHUWKDQQRUPDOURRPV,QDFRXVWLFPHDVXUHPHQWVHYHQLQ
ODERUDWRU\ FRQGLWLRQV HJ LQ DQ DQHFKRLF FKDPEHU WKHUH DUH DOZD\V SUHVHQW
GLVWXUELQJ URRP UHIOHFWLRQV DQG DOVR LQIUDVRXQG WKDW FDXVHV DQRPDOLHV LQ WKH ORZ
IUHTXHQFLHV9DULRXVW\SHVRIRWKHUV\VWHPDWLFHUURUVDUHDOVRFRPPRQIRUH[DPSOHGXH
WR WKH DFWLRQV RI WKH LQYHVWLJDWRU WKH HTXLSPHQW LV QRW FDOLEUDWHG WKH PHDVXUHPHQW LV
QRW FRPSHQVDWHG HYHQ LI LW VKRXOG EH WKH VHWWLQJV DUH IDOVH WKH HTXLSPHQW DUH QRW
IXQFWLRQLQJLQV\QFKURQLVPHWF
1RQOLQHDULW\LVHQFRXQWHUHGLQPDQ\FDVHV£WKHV\VWHPLVVXSSRVHGWREHOLQHDUEXW
WKLV PD\ QRW UHDOO\ EH WKH FDVH (VSHFLDOO\ QRQOLQHDU GLVWRUWLRQ FDXVHG E\ HPHUJHQW
FRPSRQHQWVLQWKHV\VWHPVXFKDVKDUPRQLFRULQWHUPRGXODWLRQFRPSRQHQWVLVDOZD\V
SUHVHQW HJ LQ ORXGVSHDNHU PHDVXUHPHQWV 7KH QRQOLQHDU GLVWRUWLRQ UHODWHV WR WKH
GULYLQJVLJQDOOHYHOWKHKLJKHUVLJQDODPSOLWXGHWKHKLJKHUGLVWRUWLRQ
'LVWRUWLRQ FDQ EH DOVR OLQHDU WKDW LV XQUHODWHG WR WKH VLJQDO OHYHO XQHYHQ PDJQLWXGH
UHVSRQVHSKDVHVKLIWJURXSGHOD\GLVWRUWLRQDQGHFKR
,QDXGLRHTXLSPHQWWKHUHDUHPDQ\IXUWKHUGLVUXSWLQJDVSHFWV)RUH[DPSOHLQWKHFDVH
RI DPSOLILHUV WKHUH PLJKW EH RSHUDWLRQ XQGHU VDWXUDWLRQ DQG GLVWRUWLRQ 0HFKDQLFDO
UHFRUGLQJPDFKLQHVWDSHGHFNVUHFRUGHUVHWFVXIIHUIURPZRZDQGIOXWWHU7KHGLJLWDO
$''$ FRQYHUWHUV LQWURGXFH DOVR QXPHURXV REVWUXFWV HJ GLJLWDO GLVWRUWLRQ MLWWHU
TXDQWL]DWLRQHUURUVDOLDVLQJDQGWUXQFDWLRQHUURUV
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
0HDQVIRUPHDVXUHPHQWHQKDQFHPHQW
7KHUH DUH VHYHUDO ZD\V RI DYRLGLQJ RU PLQLPL]LQJ WKH GLVUXSWLQJ HOHPHQWV LQ SUDFWLFDO
PHDVXUHPHQWV8VXDOO\LWLVDTXHVWLRQRILPSURYLQJWKHG\QDPLFVLHWKH615RIWKH
PHDVXUHPHQWVHWXS
2UGLQDULO\ D JUHDW GHDO RI QRLVH DQG RWKHU W\SHV RI GLVWXUEDQFHV DSSHDULQJ LQ D
PHDVXUHPHQW LV XQFRUUHODWHG ZLWK WKH SURELQJ VWLPXOXV DQG FDQ WKXV EH UHGXFHG E\
UHSHDWLQJ WKH H[FLWDWLRQ VLJQDOV DQG FRKHUHQWO\ DYHUDJLQJ WKH PHDVXUHG UHVSRQVHV
%DVLFDOO\WKH615LVLQFUHDVHGE\WKHVTXDUHURRWRIWKHDPRXQWRIWKHDYHUDJHGWULDOV
FRPSDUHG WR D VLQJOH WULDO WKH PHDVXUHPHQW WLPH LV SURORQJHG FRUUHVSRQGLQJO\ 7KH
DQDO\VLV WLPH FDQ EH GHFUHDVHG LQ WKUHH ZD\V D E\ UHGXFLQJ WKH DPSOLWXGH RI WKH
FRUUXSWLQJQRLVHZKLFKPD\EHLPSRVVLEOHEE\LQFUHDVLQJWKHPDJQLWXGHRIWKHSUREH
VLJQDO ZKLFK DW VRPH SRLQW FDXVHV VDWXUDWLRQ DQG F E\ XVLQJ D VWLPXOXV WKDW KDV D
ORQJHUGXUDWLRQLQWLPHZKLFKLQVRPHFDVHVHJDVLPSOHZLGHU LPSXOVH VPHDUV WKH
UHVSRQVHDQGWKHUHE\GHJUDGHVWKHPHDVXUHPHQW'XQFDQ
615 PD\ DOVR EH UDLVHG E\ RSWLPL]LQJ WKH VWLPXOXV ZKLFK LV GHSHQGHQW RQ WKH
IUHTXHQF\EDQGZLGWKGHVLUHG$IODWVSHFWUXPZLWKUDQGRPSKDVHHJGLVFUHWH0/6LV
QRWQHFHVVDULO\WKHEHVWVROXWLRQIRUHYHU\FDVHLQVWHDGLWPD\EHDGYLVDEOHWRXVH SUH
HPSKDVL]HGFRORUHGH[FLWDWLRQVLJQDOVVHHIRUH[DPSOH0RPPHUW]DQG0OOHU
DQG /LSVKLW] 6FRWW DQG 9DQGHUNRR\ 7KLV FDQ EH GRQH HIILFLHQWO\ E\ GLJLWDO
ILOWHUVIRUH[DPSOHWKHIUHTXHQF\GHSHQGHQWSRZHUUDWLQJRIWKHGHYLFHXQGHUWHVWFRXOG
EHWDNHQZHOOLQWRDFFRXQW$OVRWKLVVLJQDOVKDSLQJFRXOGLQFOXGHSUHHTXDOL]DWLRQRI
WKH WUDQVIHU FKDUDFWHULVWLFV RI WKH WUDQVPLVVLRQ SDWK PLFURSKRQH IUHTXHQF\ UHVSRQVH
HWF
8VXDOO\ ZLQGRZLQJ RU JDWLQJ WHFKQLTXHV DQG ILOWUDWLRQ VXFK DV DQWLDOLDV RU KLJKSDVV
IRU UHPRYLQJ LQIUDVRXQG DUH QHFHVVDU\ WR UHPRYH VRPH RI WKH DUWLIDFWV GXH WR WKH
PHDVXUHPHQWVHWXSDQGVXUURXQGLQJV$OVRLQVRPHFDVHVVPRRWKLQJLVGHVLUHGHJIRU
GLJLWDO ILOWHU GHVLJQ SXUSRVHV ³GRZQVDPSOLQJ´ RU IRU YLVXDO REVHUYDWLRQ 7KLV
GHFUHDVHVWKHUHVROXWLRQEXWVLPSOLILHVWKHSURFHVVLQJDQGPLJKWDOVRUHGXFHHUURUV
0RVW RI DOO WKH PRVW LPSRUWDQW WKLQJ LV WKDW WKH LQYHVWLJDWRU KLPKHUVHOI LV DZDUH RI
ZKDWKHVKHLVGRLQJDQGXQGHUVWDQGVWKHZHDNQHVVHVDQGVWUHQJWKVRIWKHKRSHIXOO\ZHOO
FKRVHQPHDVXUHPHQWPHWKRGDQGWKHFKDUDFWHULVWLFVRIWKHRSHUDWHGHTXLSPHQW
&21&/86,216
7KLV SDSHU KDV SUHVHQWHG WKH XQGHUO\LQJ WKHRU\ IRU VLJQDO DQDO\VLV LQ DXGLR V\VWHPV
FKDUDFWHUL]DWLRQ0HWKRGRORJ\RI WUDQVIHU IXQFWLRQ PHDVXUHPHQWV DORQJ ZLWK H[DPSOHV
RIDYDLODEOHWHFKQRORJ\LVVXEPLWWHGZLWKFRQVLGHUDWLRQVRIOLPLWDWLRQVDQGHUURUVERWK
WKHRUHWLFDODQGSUDFWLFDO
7KH TXHVWLRQ UHPDLQV ZKLFK PHWKRG WR XVH IRU DXGLR WUDQVIHU IXQFWLRQ PHDVXUHPHQWV
7KLV LV KLJKO\ FDVHGHSHQGHQW DQG WKHUH LV QR XQLYHUVDO DQVZHU HYHU\ PHWKRG KDV LWV
VWUHQJWKVDQGZHDNQHVVHV,WLVRQO\SRVVLEOHWRIROORZWKHFRPPRQJXLGHOLQHVDQGVHOHFW
WKH KRSHIXOO\ RSWLPDO PHWKRG 2I FRXUVH DOVR WKH UHTXLUHPHQWV RI SUDFWLFDO UHVRXUFHV
DQGGHVLUHGUHVXOWVKDYHWREHWDNHQLQWRFRQVLGHUDWLRQ
6HPLQDURQDXGLRVLJQDOSURFHVVLQJ6LJQDOSURFHVVLQJPHWKRGVLQGLJLWDODXGLR+HOVLQNL8QLYHUVLW\RI7HFKQRORJ\/DERUDWRU\
RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQG
5()(5(1&(6
$ULHO&RUSRUDWLRQ8VHU¶VJXLGH6<6LG$FRXVWLF7HVW6\VWHP1HZ<RUN86$$ULHO&RUSS
%HQGDW - 6 DQG 3LHUVRO $ * 5DQGRP 'DWD $QDO\VLV DQG 0HDVXUHPHQW 3URFHGXUHV QG (G
5HYLVHGDQG([SDQGHG86$-RKQ:LOH\6RQVS
%HUNKRXW$-%RRQH00DQG.HVVHOPDQ&$FRXVWLF,PSXOVH5HVSRQVH0HDVXUHPHQW$1HZ
7HFKQLTXH-$XGLR(QJ6RF9RO1RSS
%LHULQJ + DQG 3HGHUVHQ 2 = &RPPHQWV RQ ³$QRWKHU DSSURDFK WR WLPHGHOD\ VSHFWURPHWU\ -
$XGLR(QJ6RF9RO1RSS
%RULVK - DQG $QJHOO - % $Q HIILFLHQW DOJRULWKP IRU PHDVXULQJ WKH LPSXOVH UHVSRQVH XVLQJ
SVHXGRUDQGRPQRLVH-$XGLR(QJ6RF9RO1RSS±
%UHO.M U6RXQG9LEUDWLRQ3URGXFW&DWDORJXH1DHUXP'HQPDUN%UHO.M US
&ROORPV0+LJK3HUIRUPDQFH/RXGVSHDNHUVWK(G/RQGRQ*%3HQWHFK3UHVVS
'DYLHV : ' 7 *HQHUDWLRQ DQG SURSHUWLHV RI PD[LPXPOHQJWK VHTXHQFHV &RQWURO -XQH-XO\
$XJXVWSS±±±
'XQFDQ$7KH$QDO\WLF,PSXOVH-$XGLR(QJ6RF9RO1RSS
)RVWHU6,PSXOVHUHVSRQVHPHDVXUHPHQWXVLQJ*ROD\FRGHV,Q,(((&RQI$FRXVW6SHHFK
DQG6LJQDO3URF,&$663¶9RO,(((1HZ<RUNSS±
*ROD\0-(&RPSOHPHQWDU\VHULHV,5(7UDQV,QIR7KHRU\1RSS±
-DFNVRQ/%'LJLWDOILOWHUVDQGVLJQDOSURFHVVLQJQG(G+LJKDP0DVVDFKXVHWWV86$.OXZHU
$FDGHPLF3XEOLVKHUVS
.DOOLR - 'HYHORSPHQW RI DQ REMHFWRULHQWHG DXGLR PHDVXUHPHQW V\VWHP 0DVWHU¶V 7KHVLV LQ
)LQQLVK +HOVLQNL 8QLYHUVLW\ RI 7HFKQRORJ\ /DERUDWRU\ RI $FRXVWLFV DQG $XGLR 6LJQDO
3URFHVVLQJS
/DKWL 7 $FRXVWLF PHDVXUHPHQW WHFKQLTXHV LQ )LQQLVK +HOVLQNL 8QLYHUVLW\ RI 7HFKQRORJ\
/DERUDWRU\RI$FRXVWLFVDQG$XGLR6LJQDO3URFHVVLQJ5HSRUW(VSRR)LQODQGS
/LSVKLW]636FRWW7&DQG9DQGHUNRR\-,QFUHDVLQJWKH$XGLR0HDVXUHPHQW&DSDELOLW\RI))7
$QDO\]HUVE\0LFURFRPSXWHU3RVWSURFHVVLQJ-$XGLR(QJ6RF9RO1RSS
0DWKZRUNV0DWODE6LJQDO3URFHVVLQJ7RROER[²8VHU¶V*XLGH0DWKZRUNV,QFS
0RPPHUW] ( DQG 0OOHU 6 0HDVXULQJ LPSXOVH UHVSRQVHV ZLWK GLJLWDOO\ SUHHPSKDVL]HG
SVHXGRUDQGRPQRLVHGHULYHGIURPPD[LPXPOHQJWKVHTXHQFHV$SS$F9ROSS±
1DWLRQDO,QVWUXPHQWV,QVWUXPHQWDWLRQUHIHUHQFHDQGFDWDORJXH1DWLRQDO,QVWUXPHQWV&RUSRUDWLRQ
3XWQDP:0DWODE7RROER[HV5HDO7LPH'63XVLQJD7XUWOH%HDFK7DKLWL
<URL:http://cmn19.stanford.edu/~putnam/matlab.html>
5DQGDOO5%)UHTXHQF\$QDO\VLVUG(GVW3ULQW%UHO.MDHU1DHUXP'HQPDUNS
5LIH''DQG9DQGHUNRR\-7UDQVIHUIXQFWLRQPHDVXUHPHQWZLWKPD[LPXPOHQJWKVHTXHQFHV-
$XGLR(QJ6RF9RO1RSS±
5LIH''0/66$5HIHUHQFH0DQXDO9HUVLRQ'5$/DERUDWRULHV
6FKURHGHU 0 5 6\QWKHVLV RI ORZSHDNIDFWRU VLJQDOV DQG ELQDU\ VHTXHQFHV ZLWK ORZ
DXWRFRUUHODWLRQ,(((7UDQV,QIRUPDWLRQ7KHRU\-DQXDU\SS±
6FKURHGHU 0 5 ,QWHJUDWHGLPSXOVH PHWKRG PHDVXULQJ VRXQG GHFD\ ZLWKRXW XVLQJ LPSXOVHV -
$FRXVW6RF$P9ROSS±
9DQGHUNRR\-$QRWKHUDSSURDFKWRWLPHGHOD\VSHFWURPHWU\-$XGLR(QJ6RF9RO1R
SS
=KRX%*UHHQ'0DQG0LGGOHEURRNV-&&KDUDFWHUL]DWLRQRIH[WHUQDOHDULPSXOVHUHVSRQVHV
XVLQJ*ROD\FRGHV-$FRXVW6RF$P9RO1RSS±