Log-Periodogram Estimation of Long Memory Volatility Dependencies with Conditionally Heavy Tailed Returns

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 685 November 2000 LOG-PERIODOGRAM ESTIMATION OF LONG MEMORY VOLATILITY DEPENDENCIES WITH CONDITIONALLY HEAVY TAILED RETURNS Jonathan H. Wright NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.bog.frb.fed.us.

LOG-PERIODOGRAM ESTIMATION OF LONG MEMORY VOLATILITY DEPENDENCIES WITH CONDITIONALLY HEAVY TAILED RETURNS Jonathan H. Wright* Abstract: Many recent papers have used semiparametric methods, especially the log-periodogram regression, to detect and estimate long memory in the volatility of asset returns. In these papers, the volatility is proxied by measures such as squared, log-squared and absolute returns. While the evidence for the existence of long memory is strong using any of these measures, the actual long memory parameter estimates can be sensitive to which measure is used. In Monte-Carlo simulations, I find that the choice of volatility measure makes little difference to the log-periodogram regression estimator if the data is Gaussian conditional on the volatility process. But, if the data is conditionally leptokurtic, the log-periodogram regression estimator using squared returns has a large downward bias, which is avoided by using other volatility measures. In U.S. stock return data, I find that squared returns give much lower estimates of the long memory parameter than the alternative volatility measures, which is consistent with the simulation results. I conclude that researchers should avoid using the squared returns in the semiparametric estimation of long memory volatility dependencies. Keywords: Semiparametric Methods, Fractional Integration, Stochastic Volatility, Stock Returns, Heavy Tails. * Wright is an economist in the International Finance Division of the Federal Reserve Board. I am grateful to two anonymous referees for extremely helpful comments on an earlier draft. The views in this paper are solely the responsibility of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any person associated with the Federal Reserve System.

41 Lqwurgxfwlrq1 Zkloh dvvhwuhwxuqv dsshdu wreh forvh wrehlqj dpduwlqjdoh gl(cid:30)huhqfh vhtxhqfh/ wkh| duh qhyhuwkhohvv fkdudfwhul}hg e| d kljk ghjuhh ri yrodwlolw| foxvwhulqj dqg vr duh qrw hyhq forvh wr ehlqj lqghshqghqwo| dqglghqwlfdoo| glvwulexwhg +llg,1 Shuvlvwhqfh lq wkh yrodwlolw| ri dvvhw uhwxuqv kdv ehhq grfxphqwhg lq sdshuv jrlqj edfn wr Idpd +4<98,/ lq wkh hqruprxv DUFK2JDUFK olwhudwxuh slrqhhuhg e| Hqjoh +4<;5, dqg vxuyh|hg e| Eroohuvohy/ Hqjoh dqg Qhovrq +4<<7,/ dqg lq wkh forvho| uhodwhg vwrfkdvwlf yrodwlolw| olwhudwxuh +vhh/ iru h{dpsoh/ Wd|oru +4<<7,,1 Uhfhqwo|/ d qxpehu ri sdshuv kdyh qrwhg wkdw wkh dxwrfruuhodwlrq ixqfwlrqv ri vtxduhg/ orj0vtxduhg dqg devroxwh uhwxuqv duh ehvw fkdudfwhul}hg e| d vorzo| phdq0uhyhuwlqj k|shuerolf udwh ri ghfd|1 Wkhvh sdshuv lqfoxgh Dqghuvhq dqg Eroohuvohy +4<<:,/ Eroohuvohy dqg Zuljkw +5333,/ Gdfrurjqd hw do1 +4<<6,/ Glqj/ Judqjhu dqg Hqjoh +4<<6,/ Judqjhu dqg Glqj +4<<9,/ Oredwr dqg Vdylq +4<<;, dqg Urelqvrq +4<<4,1 Wklv surshuw| ri wkh dxwrfruuhodwlrq ixqfwlrq ri vtxduhg/ orj0vtxduhg dqg devroxwh uhwxuqv kdv ehhq irxqg lq pdq| h{fkdqjh udwh dqg vwrfn uhwxuqv/ exw lv qrw frqvlvwhqw zlwk wkh vwdqgdug DUFK2JDUFK ru vwrfkdvwlf yrodwlolw| prghov1 Orqj phpru| prghov duh ghvljqhg wr uhsuhvhqw wlph vhulhv zlwk dxwrfruuhod0 wlrqv ixqfwlrqv h{klelwlqj d vorz k|shuerolf udwh ri ghfd|1 Wkh ohdglqj orqj phpru| wlph vhulhv prgho lv wkh iudfwlrqdoo| lqwhjudwhg DUPD +DUILPD, prgho +Judqjhu dqg Mr|hx{ +4<;3, dqg Krvnlqj +4<;4,,1 Prghov zlwk orqj phpru| lq wkh yrodwlo0 4

lw| surfhvv kdyh ehhq sursrvhg dqg irxqg wr pdwfk wkh dxwrfruuhodwlrq ixqfwlrqv ri vtxduhg/ orj0vtxduhg dqg devroxwh dvvhw uhwxuqv1 Wkhvh lqfoxgh wkh orqj phpru| DUFKprgho lq Urelqvrq+4<<4,/ wkh iudfwlrqdoo| lqwhjudwhgJDUFK/ru ILJDUFK/ prgholqEroohuvohydqgPlnnhovhq+4<<9,dqgEdloolh/ EroohuvohydqgPlnnhovhq+4<<9, dqg wkh iudfwlrqdoo| lqwhjudwhg vwrfkdvwlf yrodwlolw| prgho lq Euhlgw/ Fudwr dqg gh Olpd +4<<;,1 Wkhvh prghov fdq lpso| wkdw wkh dxwrfruuhodwlrq ixqfwlrqv ri vtxduhg/ orj0vtxduhg dqg2ru devroxwh uhwxuqv kdyh wkh vdph k|shuerolf udwh ri ghfd| dv wkh yrodwlolw| surfhvv1 Pdq| sdshuv kdyh vrxjkw wr hvwlpdwh wkh orqj phpru| sdudphwhu lq wkh yrodwlolw| surfhvv zlwkrxw vshfli|lqjd sduwlfxodusdudphwulf prgho e| dsso|lqj d vhplsdudphwulf hvwlpdwru wr rqh ru pruh riwkhvh yrodwlolw| phdvxuhv1 Wkhvh sdshuv lqfoxghEroohuvohydqgZuljkw+5333,/ Euhlgw/ Fudwrdqggh Olpd+4<<;,/ Judqjhudqg Glqj +4<<9,/ Oredwr dqg Urelqvrq +4<<;, dqg Oredwr dqg Vdylq +4<<;,1 Wkh suhflvh hvwlpdwhv ri wkh orqj phpru| sdudphwhu fdq krzhyhu eh vhqvlwlyh wr wkh fkrlfh ri yrodwlolw| phdvxuh1 Lq wklv sdshu L vkrz wkdw iru gdlo| X1V1 vwrfn uhwxuq gdwd/ wkhuh lv frqvlghudeoh vhqvlwlylw| wr wkh fkrlfh ri yrodwlolw| phdvxuh dqg wkdw xvlqj vtxduhg uhwxuqv jlyhv pxfk orzhu hvwlpdwhv ri wkh orqj phpru| sdudphwhu wkdq wkh rwkhu dowhuqdwlyhv1 L uhsruw wkh uhvxowv ri d Prqwh0Fduor vlpxodwlrq lq zklfk wkh gdwdlv jhqhudwhg iurpydulrxv orqjphpru| yrodwlolw| prghov/ dqggl(cid:30)huhqw yrodwlolw| phdvxuhv duh xvhg lq wkh orj0shulrgrjudp uhjuhvvlrq wr hvwlpdwh wkh ghjuhh ri iudfwlrqdo lqwhjudwlrq1 Li wkh uhwxuqv duh Jdxvvldq/ frqglwlrqdo rq wkh yrodwlolw| 5

surfhvv/ wkhq wkh uhvxowv duh lqvhqvlwlyh wr wkh fkrlfh ri yrodwlolw| phdvxuh1 Exw lw lv zlgho| djuhhg wkdw dvvhw uhwxuq gdwd lv qrw hyhq frqglwlrqdoo| Jdxvvldq/ vr L dovr vlpxodwh gdwd zklfk lv frqglwlrqdoo| khdy| wdlohg +w glvwulexwhg rq (cid:15) ghjuhhv ri iuhhgrp,1 Lq wklv fdvh/ wkh vlpxodwhg eldv lv vhqvlwlyh wr wkh fkrlfh ri yrodwlolw| phdvxuh1 Lq sduwlfxodu/ li vtxduhg gdwd lv xvhg/ wkhuh lv d odujh grzqzdug eldv lq wkh hvwlpdwhg ghjuhh ri iudfwlrqdo lqwhjudwlrq1 Wklv wlhv lq zlwk wkh hpslulfdo (cid:31)qglqjv1 Wkh sodq iru wkh uhpdlqghu ri wklv sdshu lv dv iroorzv1 Vhfwlrq 5 ghvfulehv vrph orqj phpru| yrodwlolw| prghov dqg vhplsdudphwulf hvwlpdwruv1 Wkh hpslulfdo zrun lv lq Vhfwlrq 61 Vhfwlrq 7 frqwdlqv wkh Prqwh0Fduor uhvxowv1 Vhfwlrq 8 frqfoxghv1 51 Orqj Phpru| lq Yrodwlolw| 514 Orqj Phpru| dqg Iudfwlrqdo Lqwhjudwlrq Wkh lghdv ri iudfwlrqdo lqwhjudwlrq dqg orqj phpru| zhuh lqwurgxfhg wr hfrqrphwulfv e| sdshuv lqfoxglqj Judqjhu dqg Mr|hx{ +4<;3, dqg Pdqghoeurw +4<:4,1 Uhfhqw dqg frpsuhkhqvlyh uhylhzv ri wklv wrslf duh surylghg e| Edloolh +4<<9, dqg Urelqvrq +4<<7,1 Orqj phpru| wlph vhulhv duh fkdudfwhul}hg e| d vorz udwh ri ghfd| ri wkh dxwrfryduldqfh ixqfwlrq1 D wlph vhulhv i(cid:5) jA lv vdlg wr h{klelw orqj phpru| li lw | |’(cid:129) kdv d fryduldqfh ixqfwlrq (cid:14)E(cid:26)(cid:28) wkdw lv ri wkh vdph rughu dv (cid:26)2_3(cid:129) +dv (cid:26) $ 4,/ dqg d vshfwuxp sEb(cid:28) wkdw lv ri wkh vdph rughu dv b32_ +dv b $ f,/ iru f (cid:9) _ (cid:9) f(cid:23)D1 Wkh 6

gh(cid:31)qlwlrq ri orqj phpru| fdq eh h{whqghgwr wkh fdvh _ : f(cid:23)D ru _ (cid:9) f +qhjdwlyh orqj phpru|,1 Wkh DUILPD prgho lv wkh ohdglqj sdudphwulf orqj phpru| wlph vhulhv prgho1 Gh(cid:31)qh i(cid:5) jA wr eh dq DUILPD+Rc_c^, surfhvv li | |’(cid:129) @Eu(cid:28)E(cid:129)(cid:3)u(cid:28)_(cid:5) ’ KEu(cid:28)(cid:4) +4, | | zkhuh (cid:4) lv l1l1g1 zlwk phdq }hur dqg yduldqfh j2/ u lv wkh odj rshudwru/ wkh odj | sro|qrpldov @Eu(cid:28) dqg KEu(cid:28) +ri rughuv R dqg ^/ uhvshfwlyho|, duh dvvxphg wr kdyh doo ri wkhlu urrwv rxwvlgh wkh xqlw flufoh/ _ lv dq| qxpehu rq wkh uhdo olqh dqg E(cid:129)(cid:3)u(cid:28)_ lv gh(cid:31)qhg e| wkh xvxdo elqrpldo h{sdqvlrq1 Iru _ (cid:9) f(cid:23)D/ i(cid:5) j lv vwdwlrqdu|/ dqg lwv | fryduldqfh ixqfwlrq dqg vshfwuxp kdyh wkh uhtxluhg udwhv ri ghfd|1 515 Iudfwlrqdoo| Lqwhjudwhg Vwrfkdvwlf Yrodwlolw| Wkhvorzudwhrighfd|riwkhdxwrfruuhodwlrqvriorj0vtxduhg/vtxduhgdqgdevroxwhuh0 wxuqvprwlydwhvwkhfrqvwuxfwlrqriprghovzlwkorqjphpru|lqwkhyrodwlolw|surfhvv1 Wkh iudfwlrqdoo| lqwhjudwhg vwrfkdvwlf yrodwlolw| +ILVY, prgho lv rqh vxfk vshfl(cid:31)fd0 wlrq/ sursrvhg e| Euhlgw/ Fudwr dqg gh Olpd +4<<;,1 Wklv vshfl(cid:31)hv wkdw i+ jA lv d | |’(cid:129) wlph vhulhv ri dvvhw uhwxuqv vxfk wkdw + ’ e%RE(cid:5) *2(cid:28)j 0 c +5, | | 0 | zkhuh(cid:5) lvdqDUILPDsurfhvv/ dvgh(cid:31)qhglqhtxdwlrq+4, dqg0 lv dq l1l1g1 vhtxhqfh | | zlwk xqlw yduldqfh wkdw lv lqghshqghqw ri (cid:4) 1 Lw lv ixuwkhu dvvxphgwkdw (cid:4) lv Jdxvvldq | | 7

dqgwkdw.*L}E02(cid:28) (cid:9) 4 +exw0 lvqrwjhqhudoo|dvvxphgwrehJdxvvldqlqwklvsdshu,1 | | Wkh orj0vtxduhg uhwxuqv kdyh wkh vdph shuvlvwhqfh surshuwlhv dv wkh odwhqw yrodwlolw| surfhvv/ (cid:5) / vlqfh*L}E+2(cid:28) ’ *L}Ej2(cid:28)n.*L}E02(cid:28)n(cid:5) n1 / zkhuh1 ’ *L}E02(cid:28)(cid:3).*L}E02(cid:28)/ | | | | | | | | dqg vr/ iru _ (cid:9) f(cid:23)D/ (cid:28)J(cid:15)E,J}E+2(cid:28)c,J}E+2 (cid:28)(cid:28) 9 (cid:26)2_3(cid:129)c +6, | |3(cid:26) dv (cid:26) $ 441 Li/ ixuwkhupruh/ 0 lv Jdxvvldq wkhq Dqghuvhq dqg Eroohuvohy +4<<:, dqg | Urelqvrq +4<<<, vkrz wkdw (cid:28)J(cid:15)E+2c+2 (cid:28) 9 (cid:26)2_3(cid:129)c +7, | |3(cid:26) dqg (cid:28)J(cid:15)Em+ mcm+ m(cid:28) 9 (cid:26)2_3(cid:129)c +8, | |3(cid:26) dv (cid:26) $ 4/ iru _(cid:9)3181 Htxdwlrqv 608 irup wkh edvlv iru dsso|lqj vhplsdudphwulf hvwl0 pdwruv ri wkh orqj phpru| sdudphwhu wr orj0vtxduhg/ vtxduhg ru devroxwh uhwxuqv vr dvwrhvwlpdwhwkhghjuhhriorqjphpru|lqwkhodwhqwyrodwlolw|surfhvv51 Lfrqmhfwxuh wkdw htxdwlrqv +7, dqg +8, frqwlqxh wr krog zlwk vrph qrqqrupdo vshfl(cid:31)fdwlrqv iru 0 1 | 4Wkurxjkrxwwklvsdshu/wkh9qrwdwlrqphdqvwkdwwkholplwriwkhudwlrriwkhtxdqwlwlhvrqwkh ohiw dqg uljkw kdqg vlghv ri wkh v|pero lv d (cid:31)qlwh srvlwlyh frqvwdqw1 5WkhuhvxowvlqUrelqvrq+4<<<,dovrdsso|wrwkhdxwrfryduldqfhixqfwlrqrim| m(cid:24)/iruqrqlqwhjhu w (cid:24)/ d wudqvirupdwlrq frqvlghuhg e| Glqj/ Judqjhu dqg Hqjoh +4<<6,1 8

516 Wkh ILJDUFK dqg ILHJDUFK Prghov Iudfwlrqdo lqwhjudwlrq fdq dovr eh lqwurgxfhg lqwr prghov lq wkh DUFK2JDUFK idplo|1 Wkhvh prghov vshfli| wkdw i+ jA lv d wlph vhulhv ri dvvhw uhwxuqv vxfk wkdw | |’(cid:129) + ’ j 0 c +9, | | | zkhuh 0 lv dq l1l1g1 vhtxhqfh zlwk xqlw yduldqfh1 Wkh ILJDUFK+4/g/4, prgho/ | sursrvhg e| Eroohuvohy dqg Plnnhovhq +4<<9, vshfl(cid:31)hv wkdw j2 ’ / nqj2 nd(cid:129)(cid:3)qu(cid:3)E(cid:129)(cid:3)(cid:24)u(cid:28)E(cid:129)(cid:3)u(cid:28)_o+2c +:, | |3(cid:129) | zkhuhwkhsdudphwhuvvdwlvi|uhvwulfwlrqvzklfkhqvxuhwkdwj2 lvsrvlwlyhdoprvwvxuho| | iru doo | +Eroohuvohy dqg Plnnhovhq surylgh h{solflw vx!flhqw frqglwlrqv,1 Iru _ ’ f/ wklvuhgxfhvwrwkhvwdqgdugJDUFK+4/4,vshfl(cid:31)fdwlrq/dvj2 ’ /nqj2 nE(cid:24)(cid:3)q(cid:28)+2 1 | |3(cid:129) |3(cid:129) Kljkhu rughu ILJDUFK prghov fdq/ ri frxuvh/ eh frqvwuxfwhg lq wkh vdph zd|1 Vwrfn uhwxuq yrodwlolw| dsshduv wr eh qhjdwlyho| fruuhodwhg zlwk odjjhg uhwxuqv1 Wklv vr0fdoohg ohyhudjh h(cid:30)hfw zdv (cid:31)uvw qrwhg e| Eodfn +4<:9, dqg lv qrw jhqhudwhg e| wkh JDUFK ru ILJDUFK prghov1 Wklv prwlydwhg Qhovrq +4<<4, wr sursrvh wkh h{srqhqwldoJDUFK/ruHJDUFKprgho1 Wklvfdqdovrehjhqhudol}hgwrlqfrusrudwh iudfwlrqdo lqwhjudwlrq lq wkh ILHJDUFK+4/g/4, prgho/ sursrvhg e| Eroohuvohy dqg Plnnhovhq +4<<9,/ zklfk vshfl(cid:31)hv wkdw *?Ej2(cid:28) ’ /E(cid:129)(cid:3)(cid:24)(cid:28)n(cid:24)*?Ej2 (cid:28)nE(cid:129)n(cid:6)u(cid:28)E(cid:129)(cid:3)u(cid:28)3_Ew0 n(cid:14)dm0 m(cid:3).m0 mo(cid:28)(cid:23) +;, | |3(cid:129) |3(cid:129) |3(cid:129) |3(cid:129) 9

Wkhvh ILJDUFK dqg ILHJDUFK prghov pd| hdvlo| eh hvwlpdwhg e| d txdvl0 pd{lpxp0olnholkrrg hvwlpdwru1 Iru d qxpehu ri vwrfn dqg h{fkdqjh udwh uhwxuqv Eroohuvohy dqg Plnnhovhq +4<<9, dqg Edloolh/ Eroohuvohy dqg Plnnhovhq +4<<9, (cid:31)qg wkdw _ lv vljql(cid:31)fdqwo| gl(cid:30)huhqw erwk iurp 3 dqg iurp 41 Wkhvh prghov fdq dovr eh xvhg wr prwlydwh vhplsdudphwulf hvwlpdwlrq ri wkh orqj phpru| yrodwlolw| ghshqghq0 flhv/ vlqfh (cid:28)J(cid:15)E+2c+2 (cid:28) 9 (cid:26)2_3(cid:129) dqg (cid:28)J(cid:15)E*L}E+2(cid:28)c*L}E+2 (cid:28)(cid:28) 9 (cid:26)2_3(cid:129)/ dv (cid:26) $ 4/ li | |3(cid:26) | |3(cid:26) _ (cid:9) f(cid:23)D/ lq wkh ILJDUFK dqg ILHJDUFK prghov/ uhvshfwlyho|1 517 Vhplsdudphwulf Hvwlpdwruv ri wkh Orqj Phpru| Sdudphwhu Wkh ixoo| h!flhqwhvwlpdwlrq ridq| orqj phpru| wlph vhulhv prgho qdwxudoo| uhtxluhv wkdw wkh prgho eh frpsohwho| vshfl(cid:31)hg1 Exw li wkh uhvhdufkhu lv lqwhuhvwhg pdlqo| lq wkhorqjphpru|sdudphwhu_/ wklvpd|ehhvwlpdwhge|vhplsdudphwulf phwkrgv1 Ri wkhvh/ wkh orj0shulrgrjudp uhjuhvvlrq hvwlpdwru lv wkh prvw zlgho| xvhg1 Lw zdv (cid:31)uvw sursrvhge|JhzhnhdqgSruwhu0Kxgdn+4<;6,/exwwkhirupdosurrivrilwvfrqvlvwhqf| dqgdv|pswrwlfqrupdolw|zhuhhoxvlyhxqwlowkhvhzhuhsurylghge|Urelqvrq+4<<8d,/ lq wkh Jdxvvldq fdvh1 Ohw UEb (cid:28) ghqrwh wkh vdpsoh shulrgrjudp ri dq duelwudu| orqj phpru| wlph (cid:26) vhulhv/ 5 / zkhuh b ’ 2Z(cid:26)*A ghqrwhv wkh mwk Irxulhu iuhtxhqf|1 Wkh orj0shulrgrjudp | (cid:26) (cid:9) uhjuhvvlrq +JSK, hvwlpdwru ri _/ ru _/ lv wkhq jlyhq e| plqxv wkh hvwlpdwh ri q lq (cid:129) wkh uhjuhvvlrq htxdwlrq :

*L}EUEb (cid:28)(cid:28) ’ q nq *L}der(cid:16)?2Eb *2(cid:28)onl c (cid:26) ’ (cid:129)c(cid:23)(cid:23)(cid:23)6(cid:23) +<, (cid:26) f (cid:129) (cid:26) (cid:26) Urelqvrq +4<<8d, vkrzhg wkdw li 5 lv Jdxvvldq/ (cid:3)f(cid:23)D (cid:9) _ (cid:9) f(cid:23)D/ wkh edqgzlgwk sdud0 | phwhu6frqyhujhvwrlq(cid:31)qlw|exwlvJEA(cid:28)/dqgplogdgglwlrqdofrqglwlrqvduhvdwlv(cid:31)hg6/ s wkhq 6E_ (cid:9) (cid:3)_(cid:28) $ (cid:7)Efc Z2(cid:28)1 Wkh orj0shulrgrjudp hvwlpdwh lv wkhuhiruh frqvlvwhqw 2e s dqg dv|pswrwlfdoo| qrupdo/ exw frqyhujhv dw d udwh vorzhu wkdq wkh xvxdo A1 Do0 (cid:9) whuqdwlyho|/ wkh yduldqfh ri _ pd| eh frqvlvwhqwo| hvwlpdwhg e| wkh frqyhqwlrqdo ROV yduldqfh hvwlpdwh iurp wkh uhjuhvvlrq lq htxdwlrq +<,1 Vrph uhfhqw olwhudwxuh kdv h{whqghg Urelqvrq*v uhvxowv1 Ghr dqg Kxuylfk +4<<<, suryhg wkh frqvlvwhqf| dqg (cid:9) dv|pswrwlf qrupdolw| ri _ iru fhuwdlq qrqqrupdo wlph vhulhv1 Yhodvfr +4<<<, suryhg (cid:9) wkh frqvlvwhqf| ri _ lq wkh fdvh 318(cid:23) _ (cid:9)4 dqg lwv dv|pswrwlf qrupdolw| lq wkh fdvh 318(cid:23) _ (cid:9)31:81 Urelqvrq +4<<8e, sursrvhgdq dowhuqdwlyh vhplsdudphwulf hvwlpdwruri _/ zklfk lv dv|pswrwlfdoo| pruh h!flhqw dqg wkh surshuwlhv ri zklfk fdq eh hvwdeolvkhg xqghu ploghu frqglwlrqv +Urelqvrq +4<<8e,/ Urelqvrq dqg Khqu| +4<<<,,1 Wklv hvwlpdwru/ (cid:20) fdoohg wkh Jdxvvldq vhplsdudphwulf +JVS, hvwlpdwru/ lv _ ’ @h}4(cid:16)? -E_(cid:28)/ zkhuh _ s -E_(cid:28) ’ *L}E(cid:129)P6 b2_UEb (cid:28)(cid:28) (cid:3) 2_P6 *L}b (cid:23) Urelqvrq +4<<8e, suryhg wkdw 6E_ (cid:9) 6 (cid:26)’(cid:129) (cid:26) (cid:26) 6 (cid:26)’(cid:129) (cid:26) 6Vwulfwo|/wkhsurrivlqUrelqvrq+4<<8d,uhtxluhgvrphriwkhyhu|orzhvwiuhtxhqflhvwrehrplw0 whg iurp wkh uhjuhvvlrq lq htxdwlrq +<,1 Vxevhtxhqwo|/ Kxuylfk/ Ghr dqg Eurgvn| +4<<;, surylghg d yhuvlrq ri wklv surri zklfk grhv qrw uhtxluh dq| vxfk wulpplqj1 ;

(cid:3)_(cid:28) $ (cid:7)Efc (cid:129)(cid:28)/ xqghu frqglwlrqv jlyhq lq wkdw sdshu1 e Wkh prghov ri vxevhfwlrqv 515 dqg 516 fdq lpso| wkdw wkh dxwrfryduldqfh ixqf0 wlrqv ri vtxduhg/ orj0vtxduhg dqg devroxwh uhwxuqv kdyh wkh vdph orqj phpru| surs0 huw| dv wkh xqghuo|lqj yrodwlolw| surfhvv1 Wklv prwlydwhv uhvhdufkhuv wr dsso| vhpl0 (cid:9) (cid:20) sdudphwulf phwkrgv vxfk dv _ dqg _ wr wkh vtxduhg/ orj0vtxduhg ru devroxwh uhwxuqv lq d elgwr hvwlpdwh wkh orqj phpru| lq wkh yrodwlolw| ghshqghqflhv zlwkrxw kdylqj wr vshfli| d frpsohwh sdudphwulf prgho1 Wkhuh lv olwwoh wkhruhwlfdo uhdvrq wr suhihu rqh yrodwlolw| phdvxuh ryhu dq| ri wkh rwkhuv1 Oredwr dqg Urelqvrq +4<<;, dqg Oredwr dqg Vdylq +4<<;, xvh vtxduhg uhwxuqv/ Judqjhu dqg Glqj +4<<9, xvh devroxwh uhwxuqv/ Euhlgw/ Fudwr dqg gh Olpd +4<<;, xvh orj0vtxduhg uhwxuqv dqg Eroohuvohy dqg Zuljkw +5333, xvh doo wkuhh ri wkhvh yrodwlolw| phdvxuhv1 Wkh irfxv ri wkh suhvhqw sdshu lv rq h{dplqlqj zklfk lv wkh dssursuldwh yrodwlolw| phdvxuh wr xvh lq sudfwlfh/ zkhq hvwlpdwlqj orqj phpru| lq wkh yrodwlolw| ri dvvhw uhwxuqv1 61 Hpslulfdo Uhvxowv zlwk X1V1 Vwrfn Pdunhw Gdwd Lq wklv vhfwlrq/ L dsso| wkh orj0shulrgrjudp uhjuhvvlrq wr yrodwlolw| phdvxuhv frq0 vwuxfwhg iurp wkh ghphdqhg frqwlqxrxvo| frpsrxqghg wrwdo uhwxuqv rq wkh ydoxh0 zhljkwhg dqg htxdo0zhljkwhg gdlo| vwrfn lqglfhv/ rewdlqhg iurp wkh Fhqwhu iru Uh0 vhdufk lq Vhfxulwlhv Sulfhv +FUVS,1 Wkh gdwd fryhuv wkh shulrg Mxo| 6 4<95 wr Gh0 fhpehu 64 4<<;/ iru d wrwdo ri <4<3 revhuydwlrqv1 <

614 Wkh Prgl(cid:31)hg Orj0Vtxduhg Wudqvirupdwlrq Dq lqolhu sureohp riwhq dulvhv zkhq ghdolqj zlwk orj0vtxduhg uhwxuqv> li wkh dvvhw uhwxuqlvyhu|forvhwr}hur/wkhqwkhorj0vtxduhgwudqvirupdwlrq|lhogvdodujhqhjdwlyh qxpehu1 Vxfk dq revhuydwlrq fdq wkhq juhdwo| d(cid:30)hfw wkh uhvxowv ri vxevhtxhqw gdwd dqdo|vlv1 Lqwkh h{wuhph fdvh/ liwkh dvvhwuhwxuq lvhtxdo wr}hur/ wkhqwkh orj0vtxduhg wudqvirupdwlrq lv qrw hyhq gh(cid:31)qhg +wkrxjk wklv grhv qrw dulvh lq wkh suhvhqw frqwh{w ehfdxvh wkh uhwxuqv duh ghphdqhg,1 Ixoohu +4<<9, sursrvhg d voljkw prgl(cid:31)fdwlrq ri wkh orj0vtxduhg wudqvirupdwlrq/ zklfk grhv qrw frqyhujh wr plqxv lq(cid:31)qlw| dv wkh dujxphqwfrqyhujhvwr}hur1 Wklvvshfl(cid:31)hvwkdwwkhwudqviruphgvhulhvridvvhwuhwxuqv lv (cid:12)r2 +W ’ *L}E+2 n(cid:12)r2(cid:28)(cid:3) c +43, | | +2 n(cid:12)r2 | zkhuh r2 lv wkh vdpsoh yduldqfh ri + dqg (cid:12) lv d vpdoo frqvwdqw1 Lq wklv sdshu/ L xvh | irxu yrodwlolw| phdvxuhv= vtxduhg/ orj0vtxduhg dqg devroxwh uhwxuqv/ dqg wkh prgl(cid:31)hg orj0vtxduhg uhwxuqv/ dv gh(cid:31)qhg lq htxdwlrq +43, +zlwk(cid:12) vhw wr 3135/ iroorzlqj Ixoohu,1 615 Uhvxowv Wkh vdpsoh dxwrfruuhodwlrqv ri hdfk ri wkh irxu yrodwlolw| phdvxuhv dssolhg wr wkh htxdo0zhljkwhg uhwxuqv duh vkrzq lq Iljxuh 41 Wkh| doo h{klelw wkh vorz udwh ri ghfd| wkdw lv wkh gh(cid:31)qlqj fkdudfwhulvwlf ri d orqj phpru| prgho1 Wdeoh 4 uhsruwv wkh orj0 (cid:9) shulrgrjudp hvwlpdwh/ _/ xvlqj doo irxu yrodwlolw| phdvxuhv/ iru erwk htxdo0zhljkwhg 43

(cid:20) dqg ydoxh0zhljkwhg uhwxuqv1 Uhvxowv xvlqj wkh JVS hvwlpdwru/ _/ lqvwhdg duh jlyhq lq Wdeoh 51 Lqerwkwdeohv/ uhvxowv duhuhsruwhgiruirxufkrlfhv riwkh edqgzlgwk/ 6@83/ 433/ 483 dqg 5331 Wzr nh| wklqjv fdq eh qrwlfhg lq Wdeohv 4 dqg 51 Iluvwo|/ wkhuh lv vwurqj dqg frqvlvwhqw hylghqfh iru orqj phpru| yrodwlolw| ghshqghqflhv +_:3,1 Wkh uhvxowv duh qrw wrr vhqvlwlyh wr wkh edqgzlgwk +zklfk fdq riwhq eh dsureohp+Jhzhnh +4<<;,,/ qru duh wkh| wrr vhqvlwlyh wr wkh fkrlfh ri hvwlpdwru1 Exw vhfrqgo|/ pxfk orzhu hvwlpdwhv ri _ duh rewdlqhg zlwk vtxduhg uhwxuqv wkdq zlwk wkh rwkhu yrodwlolw| (cid:9) (cid:20) phdvxuhv1 Wklv lv wuxh dfurvv doo edqgzlgwkv/ dqg zlwk erwk _ dqg _1 Lq vrph fdvhv zlwk vtxduhg uhwxuqv/ wkh hvwlpdwh ri _ lv qrw vljql(cid:31)fdqwo| gl(cid:30)huhqw iurp }hur +dw wkh 8( ohyho,1 Phdqzkloh _ lv vljql(cid:31)fdqwo| srvlwlyh dw doo frqyhqwlrqdo vljql(cid:31)fdqfh ohyhov iru doo wkh rwkhu yrodwlolw| phdvxuhv1 71 Prqwh0Fduor Uhvxowv Wkh pdlq jrdo ri wklv sdshu lv wr frpsduh wkh surshuwlhv ri wkh vhplsdudphwulf (cid:9) (cid:20) hvwlpdwruv _ dqg _/ xvlqj wkh gl(cid:30)huhqw yrodwlolw| phdvxuhv wr ghwhuplqh zklfk duh jrrg2edg fkrlfhv dqg wr dffrxqw iru vrph ri wkh uhvxowv uhsruwhg lq Wdeoh 41 Wkhru| jlyhv xv olwwoh jxlgdqfh dv wr zklfk phdvxuh vkrxog eh xvhg/ dqg vr/ lq wklv vhfwlrq L uhsruw wkh uhvxowv ri d Prqwh0Fduor vlpxodwlrq xvlqj wkuhh gdwd jhqhudwlqj surfhvvhv/ fdoleudwhg wr wkh FUVS htxdo0zhljkwhg uhwxuqv= 44

+4, Wkh ILVY prgho jlyhq e| htxdwlrqv +4, dqg +5,/ zkhuh (cid:5) lv dq DUILPD+4/g/3, | wlph vhulhv/ vr wkdw E(cid:129) (cid:3) @u(cid:28)E(cid:129) (cid:3) u(cid:28)_(cid:5) ’ (cid:4) dqg (cid:4) lv Jdxvvldq1 L vhw @ ’3185/ | | | _@317:8dqgj2@3144;1 Wkhvh zhuh wkh hvwlpdwhgydoxhv iurp(cid:31)wwlqj wkh ILVYprgho wr wkh FUVS htxdo0zhljkwhg uhwxuqv +dv lq vhfwlrq 6 deryh, e| wkh iuhtxhqf|0grpdlq pd{lpxp0olnholkrrg surfhgxuh ri Euhlgw/ Fudwr dqg gh Olpd +4<<;,1 L vhw j2 ’ (cid:129)/ 0 zlwkrxw orvv ri jhqhudolw|71 +5,WkhILJDUFKprghojlyhqe|htxdwlrqv+9,dqg+:,1 Lvhw/@31355/ q@31769/ (cid:24)@3163< dqg _@317:61 Wkhvh zhuh wkh hvwlpdwhg ydoxhv iurp (cid:31)wwlqj wkh ILJDUFK prgho wr wkh FUVS htxdo0zhljkwhg uhwxuqv e| pd{lpxp0olnholkrrg +dv lq Eroohuvohy dqg Plnnhovhq +4<<9,,1 +6,WkhILHJDUFKprghojlyhqe|htxdwlrqv+9,dqg+;,1 Lvhw/@03198/ w@31796/ (cid:14)@0 3147/ (cid:6)@031994/ (cid:24)@31;66 dqg _@316;51 Wkhvh zhuh wkh hvwlpdwhg ydoxhv iurp (cid:31)wwlqj wkh ILHJDUFK prgho wr wkh FUVS htxdo0zhljkwhg uhwxuqv e| pd{lpxp0olnholkrrg1 Lq hdfk prgho/ lw lv ixuwkhu vshfl(cid:31)hg wkdw 0 lv w0glvwulexwhg rq (cid:15) ghjuhhv ri iuhhgrp/ | (cid:15)@5/6/8/:/4/ vr wkdw 0 kdv (cid:15) (cid:3)(cid:129) (cid:31)qlwh prphqwv1 Wkh fdvh (cid:15) ’ 4 fruuhvsrqgv wr | qrupdolw|1 Wkh vdpsoh vl}h A lv 5(cid:129)2@73<9 ru 5(cid:129)(cid:12)@;4<5> wkh odwwhu lv d w|slfdo vdpsoh vl}h iru gdlo| X1V1 vwrfn uhwxuq gdwd1 Lq wkh ILVY prgho/ wkh Jdxvvldq DUILPD 7Fkdqjlqj (cid:30)5 dprxqwv wr pxowlso|lqj |5 ru m| m e| d frqvwdqw/ ru dgglqj d frqvwdqw wr orj+|5,> % w w w wkh orj0shulrgrjudp uhjuhvvlrq lv qxphulfdoo| lqyduldqw wr wkhvh wudqvirupdwlrqv1 45

vhulhvzhuhjhqhudwhge|wkhdojrulwkpriGdylhvdqgKduwh+4<;:,>wkhILJDUFKdqg ILHJDUFK vhulhv zhuh vlpxodwhg h{dfwo| dv ghvfulehg lq Eroohuvohy dqg Plnnhovhq +4<<9,1 Iru hdfk vlpxodwlrq/ 4333 uhsolfdwlrqv zhuh frqgxfwhg1 Uhvxowv lq zklfk wkh Prqwh0Fduor h{shulphqw lv lqvwhdg fdoleudwhg wr wkh FUVS ydoxh0zhljkwhg uhwxuqv duh vlplodu dqg duh dydlodeoh iurp wkh dxwkru rq uhtxhvw/ exw duh qrw vkrzq/ vr dv wr frqvhuyh vsdfh1 Wkh vlpxodwhg eldvhv ri wkh JSK dqg JVS hvwlpdwruv xvlqj wkh irxu gl(cid:30)huhqw yrodwlolw|phdvxuhv/lqwkhdowhuqdwlyhprghov/duhvkrzqlqIljxuhv5081 Wkhvlpxodwhg vwdqgdug ghyldwlrqv duh lq Iljxuhv 90<1 Lq doo fdvhv/ wkh eldv dqg vwdqgdug ghyldwlrq lv sorwwhg djdlqvw wkh edqgzlgwk 6/ iru ydoxhv ri 6 ehwzhhq 63 dqg 6331 Wkh nh| srlqwv wr qrwh duh= +4, Wkh hvwlpdwruv jhqhudoo| h{klelw vrph grzqzdug eldv1 Wklv lv frqvlvwhqw zlwk (cid:31)qglqjv lq d qxpehu ri rwkhu sdshuv/ lqfoxglqj Eroohuvohy dqg Zuljkw +5333,/ zkhuh vroxwlrqv wr wkh eldv xvlqj kljk iuhtxhqf| gdwd zhuh glvfxvvhg1 Lq wkh suhvhqw sdshu/ lw lv dvvxphg wkdw qr vxfk gdwd lv dydlodeoh1 Dffruglqjo|/ whpsrudo djjuhjdwlrq lv qrw dq lvvxh1 +5, Wkh fkrlfh ri yrodwlolw| phdvxuh kdv olwwoh wr gr zlwk wkh pdjqlwxgh ri wkh eldv/ surylghg wkdw wkh gdwd lv frqglwlrqdoo| Jdxvvldq +(cid:15) ’ 4,1 +6, Krzhyhu/ xvlqj vtxduhg uhwxuqv jlyhv pxfk pruh grzqzdug eldv wkdq dq| ri wkh 46

rwkhu wkuhh yrodwlolw| phdvxuhv/ li wkh gdwd lv frqglwlrqdoo| ohswrnxuwlf1 Wklv lv wuxh lq wkh ILVY/ ILJDUFK dqg ILHJDUFK prghov1 Vtxduhg uhwxuqv jlyh wkh zruvw eldv hyhq iru (cid:15) ’ . +qrw yhu| khdy| wdlov,1 Wkh eldv xvlqj vtxduhg uhwxuqv frqwlqxhv wr zruvhq dv (cid:15) idoov/ dqg lv hqruprxv iru (cid:15) ’ 2 ru (cid:15) ’ (cid:12)1 Wkh rwkhu yrodwlolw| phdvxuhv |lhog frpsdudeoh eldv dqg vkrz olwwoh whqghqf| wr ehfrph pruh eldvhg dv wkh wdlo wklfnqhvv lqfuhdvhv/ h{fhsw wkdw xvlqj devroxwh uhwxuqv jlyhv pruh eldv wkdq orj0vtxduhg ru prgl(cid:31)hg orj0vtxduhg uhwxuqv li (cid:15) ’ 2 +d udwkhu h{wuhph vshfl(cid:31)fdwlrq,1 Hyhq zlwk (cid:15) ’ 2/ dowkrxjk wkh eldv xvlqj devroxwh uhwxuqv lv odujh/ lw lv vxevwdqwldoo| vpdoohu wkdq wkh eldv xvlqj vtxduhg uhwxuqv1 (cid:9) (cid:20) +7, Wkh fkrlfh ri hvwlpdwru +_ ru _, dqg wkh vdpsoh vl}h erwk kdyh olwwoh wr gr zlwk wkh pdjqlwxgh ri wkh eldv1 Lq wkh ILVY dqg ILHJDUFK prghov/ lqfuhdvlqj wkh edqgzlgwk pdnhv wkh eldv vrphzkdw zruvh1 +8, Wkh vwdqgdug ghyldwlrq ri wkh hvwlpdwruv lv qrw juhdwo| d(cid:30)hfwhg e| wkh fkrlfh ri yrodwlolw| phdvxuh/ exw lv w|slfdoo| vrphzkdw kljkhu xvlqj vtxduhg uhwxuqv/ h{fhsw lq wkh fdvh (cid:15) ’ 21 Ryhudoo/ lq wkhvh vlpxodwlrqv/ wkhuh lv olwwoh gl(cid:30)huhqfh ehwzhhq wkh shuirupdqfh ri wkh vhplsdudphwulf hvwlpdwruv ri _ xvlqj dowhuqdwlyh yrodwlolw| phdvxuhv/ h{fhsw wkdw ohvv uholdeoh uhvxowv duh rewdlqhg zlwk wkh vtxduhg uhwxuqv +srlqw +7,,1 Wklv revhuydwlrq lv wkh pdlq irfxv ri wklv sdshu dqg lv frqvlvwhqw zlwk wkh hpslulfdo uhvxowv ri wkh 47

suhylrxvvhfwlrq1 Lwlvfohduwkdwdvvhwuhwxuqvkdyhkhdy|wdlov/ dqgshukdsvhyhqkdyh lq(cid:31)qlwh nxuwrvlv +Oruhwdq dqg Skloolsv +4<<7,,1 Yrodwlolw| foxvwhulqj zlwk frqglwlrqdo Jdxvvldqlw| fdq dffrxqw iru vrph ri wklv ohswrnxuwrvlv/ exw lw lv zlgho| djuhhg wkdw 0 | pxvw kdyh khdylhu wdlov wr dssur{lpdwh wkh dfwxdo wdlo ehkdylru ri vwrfn pdunhw dqg h{fkdqjhudwhuhwxuqv+vhhh1j1 Eroohuvohy +4<;:,/ Eroohuvohy/ HqjohdqgQhovrq+4<<7,/ Iulgpdq dqg Kduulv +4<<;,/ Jdoodqw/ Kvlhk dqg Wdxfkhq +4<<:,/ Jhzhnh +4<<;, dqg Olhvhqihog dqg Mxqj +4<<:,8,1 Zkloh 0 lv xqolnho| wr eh w0glvwulexwhg rq 5 ghjuhhv | ri iuhhgrp/ lw vhhpv yhu| uhdvrqdeoh wr wklqn ri lw dv ehlqj w0glvwulexwhg rq : ru 8 +ru hyhq ihzhu, ghjuhhv ri iuhhgrp1 Dffruglqjo|/ wkh grzqzdug eldv xvlqj vtxduhg uhwxuqv irxqg lq wkhvh vlpxodwlrqv fdq eh h{shfwhg wr eh dq hpslulfdoo| uhohydqw skhqrphqrq1 Vr/ vtxduhg uhwxuqv vkrxog qrw eh xvhg dv wkh yrodwlolw| phdvxuh lq wkh orj0shulrgrjudp uhjuhvvlrq hvwlpdwlrq ri orqj phpru| yrodwlolw| ghshqghqflhv1 Lq wkh ILVY/ ILJDUFK dqg ILHJDUFK prghov/ li wkh 6wk prphqw ri 0 lv | lq(cid:31)qlwh/ wkhq wkh 6wk xqfrqglwlrqdo prphqw ri + pxvw dovr eh lq(cid:31)qlwh1 Gdylv dqg | Plnrvfk +4<<;, vkrz wkdw wkh vdpsoh dxwrfruuhodwlrq ixqfwlrq ri d jhqhudo vwdwlrqdu| lq(cid:31)qlwh yduldqfh surfhvv kdv d udqgrp olplw1 Wkh| dovr vkrz wkdw wkh vdpsoh dxwr0 fruuhodwlrq ixqfwlrq ri d jhqhudo vwdwlrqdu| surfhvv zlwk (cid:31)qlwh yduldqfh exw lq(cid:31)qlwh 8Iru h{dpsoh/ Iulgpdq dqg Kduulv +4<<;, dqg Olhvhqihog dqg Mxqj +4<<:, erwk frqvlghu wkh sdudphwulf hvwlpdwlrq ri d vkruw phpru| dxwruhjuhvvlyh vwrfkdvwlf yrodwlolw| prgho/ e| vlpxodwhg pd{lpxpolnholkrrg/doorzlqjirufrqglwlrqdoqrqqrupdolw|1 Erwksdshuv(cid:31)qghylghqfhrivljql(cid:31)fdqw frqglwlrqdo qrqqrupdolw| lq vwrfn uhwxuqv1 48

irxuwk prphqw frqyhujhv wr lwv srsxodwlrq frxqwhusduw/ exw dw d udwh vorzhu wkdq wkh xvxdo A(cid:129)*2 udwh1 Wkh qrqvwdqgdug dv|pswrwlfv ri vdpsoh dxwrfruuhodwlrq ixqfwlrqv ri khdy|0wdlohg surfhvvhv duh uhohydqw wr wkh uhvxowv L (cid:31)qg lq wkhvh Prqwh0Fduor vlp0 xodwlrqv1 Li wkh irxuwk prphqw ri 0 lv (cid:31)qlwh/ exw lwv hljkwk prphqw lv lq(cid:31)qlwh/ wkhq | +2 pxvw kdyh dq lq(cid:31)qlwh irxuwk prphqw/ exw m+ m pd| kdyh d (cid:31)qlwh irxuwk prphqw1 | | Vlploduo|/ li 0 kdv (cid:31)qlwh yduldqfh exw dq lq(cid:31)qlwh irxuwk prphqw/ wkhq +2 pxvw kdyh | | lq(cid:31)qlwh yduldqfh/ exw m+ mpd| kdyh (cid:31)qlwh yduldqfh1 Wkh vtxduhg uhwxuqv duh prvw | olnho| wr eh pruh yxoqhudeoh wr wkh gl!fxowlhv wkdw dulvh zlwk khdy|0wdlohg yduldeohv1 D srvvleoh lqwxlwlrq iru wkh grzqzdug eldv zkhq xvlqj vtxduhg uhwxuqv zlwk frqglwlrqdoo| ohswrnxuwlf gdwd lv dv iroorzv91 Wkh ghqrplqdwru ri wkh vdpsoh dxwr0 fruuhodwlrq ri m+ mR zloo lqyroyh h{wuhpho| odujh whupv li + grhv qrw kdyh 2R (cid:31)qlwh | | prphqwv1 Phdqzkloh/ wkh qxphudwru ri wkh vdpsoh dxwrfruuhodwlrq dw odj (cid:26) zloo lqyroyh odujh whupv rqo| li m+ mR dqg m+ mR duh erwk odujh1 Khqfh wkh vdpsoh dxwrfru0 | |3(cid:26) uhodwlrqv ri m+ mR vkulqn wrzdugv }hur dqg wkh dvvrfldwhg vhplsdudphwulf hvwlpdwru ri | _ lv eldvhg grzqzdugv1 Wklv sureohp lv zruvh iru vtxduhg uhwxuqv wkdq iru devroxwh uhwxuqv/ ehfdxvh devroxwh uhwxuqv zloo dozd|v kdyh pruh (cid:31)qlwh prphqwv wkdq vtxduhg uhwxuqv1 9L dp judwhixo wr dq dqrq|prxv uhihuhh iru vxjjhvwlqj wklv lqwxlwlrq1 49

81 Frqfoxvlrq Uhvhdufkhuv xvh d ydulhw| ri yrodwlolw| phdvxuhv wr hvwlpdwh wkh orqj phpru| sdudph0 whu lq wkh yrodwlolw| ri dvvhw uhwxuqv1 Iru gdlo| X1V1 vwrfn uhwxuqv/ xvlqj vtxduhg uhwxuqv jlyhv wkh orzhvw hvwlpdwhv1 Lq Prqwh0Fduor vlpxodwlrqv/ L kdyh irxqg wkdw xvlqj vtxduhg uhwxuqv fdxvhv d odujh grzqzdug eldv/ li wkh uhwxuqv duh vx!flhqwo| ohswrnxuwlf/ frqglwlrqdo rq wkh yrodwlolw| surfhvv1 Vlqfh frqglwlrqdo ohswrnxuwrvlv lv d zlgho| dffhswhg surshuw| ri dvvhw uhwxuqv/ L frqfoxgh wkdw uhvhdufkhuv vkrxog dyrlg xvlqj vtxduhg uhwxuqv dv wkh yrodwlolw| phdvxuh lq vhplsdudphwulf hvwlpdwlrq ri orqj phpru| yrodwlolw| ghshqghqflhv1 Uhihuhqfhv Dqghuvhq/ W1J1 dqg W1 Eroohuvohy +4<<:,= Khwhurjhqhrxv Lqirupdwlrq Duulydov dqg Uhwxuq Yrodwlolw| G|qdplfv= Xqfryhulqj wkh Orqj Uxq lq Kljk Iuhtxhqf| Uhwxuqv/ Mrxuqdo ri Ilqdqfh/ 85/ ss1<:8043381 Edloolh/ U1W1 +4<<9,= Orqj Phpru| Surfhvvhv dqg Iudfwlrqdo Lqwhjudwlrq lq Hfrqr0 phwulfv/ Mrxuqdo ri Hfrqrphwulfv/ :6/ ss1808<1 Edloolh/ U1W1/ W1 Eroohuvohy dqg K1R1 Plnnhovhq +4<<9,= Iudfwlrqdoo| Lqwhjudwhg Jhq0 hudol}hg Dxwruhjuhvvlyh Frqglwlrqdo Khwhurvnhgdvwlflw|/ Mrxuqdo ri Hfrqrphwulfv/ :7/ ss160631 Eodfn/ I1 +4<:9,= Vwxglhv ri Vwrfn Sulfh Yrodwlolw| Fkdqjhv/ Surfhhglqjv iurp wkh Dphulfdq Vwdwlvwlfdo Dvvrfldwlrq/ Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv Vhfwlrq/ ss14::0 4;41 Eroohuvohy/ W1 +4<;:,= D Frqglwlrqdo Khwhurvnhgdvwlf Wlph Vhulhv Prgho iru Vshfxod0 wlyh Sulfhv dqg Udwhv ri Uhwxuq/ Uhylhz ri Hfrqrplfv dqg Vwdwlvwlfv/ 9</ ss1875087:1 Eroohuvohy/ W1/ U1I1 Hqjoh dqg G1E1 Qhovrq +4<<7,= DUFK Prghov lq Kdqgerrn ri Hfrqrphwulfv/ Yro 7/ +U1I1 Hqjoh dqg G1O1 PfIdgghq/ hgv1,/ Hovhylhu/ Dpvwhugdp1 Eroohuvohy/ W1 dqg K1R1 Plnnhovhq +4<<9,= Prgholqj dqg Sulflqj Orqj Phpru| lq Vwrfn Pdunhw Yrodwlolw|/ Mrxuqdo ri Hfrqrphwulfv/ :6/ ss148404;71 4:

Eroohuvohy/ W1 dqg M1K1 Zuljkw +5333,= Vhplsdudphwulf Hvwlpdwlrq ri Orqj Phpru| Yrodwlolw| Ghshqghqflhv= Wkh Uroh ri Kljk Iuhtxhqf| Gdwd/Mrxuqdo ri Hfrqrphwulfv/ <;/ ss1;404391 Euhlgw/ I1M1/ Q1 Fudwr dqg S1 gh Olpd +4<<;,= Wkh Ghwhfwlrq dqg Hvwlpdwlrq ri Orqj Phpru| lq Vwrfkdvwlf Yrodwlolw|/ Mrxuqdo ri Hfrqrphwulfv/ ;6/ ss1658067;1 Gdfrurjqd/ P1P1/ X1D1 P oohu/ U1M1 Qdjohu/ U1E1 Rovhq dqg R1Y1 Slfwhw +4<<6,= D Jhrjudsklfdo Prgho iru wkh Gdlo| dqg Zhhno| Vhdvrqdo Yrodwlolw| lq wkh Iruhljq H{fkdqjh Pdunhw/ Mrxuqdo ri Lqwhuqdwlrqdo Prqh| dqg Ilqdqfh/ 45/ ss1746076;1 Gdylhv/ U1E1 dqg G1V1 Kduwh +4<;:,= Whvwv iru Kxuvw H(cid:30)hfw/ Elrphwulnd/ :7/ ss1 <80 4351 Gdylv/ U1D1 dqg W1 Plnrvfk +4<<;,= Wkh Vdpsoh Dxwrfruuhodwlrqv ri Khdy|0Wdlohg Surfhvvhv zlwk Dssolfdwlrqv wr DUFK/ Dqqdov ri Vwdwlvwlfv/ 59/ ss1537<053;31 Ghr/ U1V1 dqg F1P1 Kxuylfk +4<<<,= Rq wkh Orj Shulrgrjudp Uhjuhvvlrq Hvwlpdwru riwkh Phpru| Sdudphwhulq Orqj Phpru| Vwrfkdvwlf Yrodwlolw| Prghov/ xqsxeolvkhg pdqxvfulsw/ Qhz \run Xqlyhuvlw|1 Glqj/ ]1/ F1Z1M1 Judqjhu dqg U1I1 Hqjoh +4<<6,= D Orqj Phpru| Surshuw| ri Vwrfn Uhwxuqv dqg d Qhz Prgho/ Mrxuqdo ri Hpslulfdo Ilqdqfh/ 4/ ss1;604391 Hqjoh/ U1I1 +4<;5,= Dxwruhjuhvvlyh Frqglwlrqdo Khwhurvnhgdvwlflw| zlwk Hvwlpdwhv ri wkh Yduldqfh ri XN Lq dwlrq/ Hfrqrphwulfd/ 83/ ss1<;:0433:1 Idpd/ H1I1 +4<98,= Wkh Ehkdylru ri Vwrfn Pdunhw Sulfhv/ Mrxuqdo ri Exvlqhvv/ 6;/ ss16704381 Iulgpdq/P1dqgO1Kduulv+4<<;,=DPd{lpxpOlnholkrrgDssurdfkiruQrq0Jdxvvldq VwrfkdvwlfYrodwlolw|Prghov/Mrxuqdo riExvlqhvvdqgHfrqrplfVwdwlvwlfv/49/ss15;70 5<41 Ixoohu/ Z1 D1 +4<<9,= Lqwurgxfwlrq wr Vwdwlvwlfdo Wlph Vhulhv/ Zloh|/ Qhz \run1 Jdoodqw/ D1U1/ G1 Kvlhk dqg J1 Wdxfkhq +4<<:,= Hvwlpdwlrq ri Vwrfkdvwlf Yrodwlolw| Prghov zlwk Gldjqrvwlfv/ Mrxuqdo ri Hfrqrphwulfv/ ;4/ ss148<04<51 Jhzhnh/M1+4<<;,=FrpphqwrqUhdodqgVsxulrxvOrqj0Phpru|SurshuwlhvriVwrfn0 Pdunhw Gdwd +e| L1 Oredwr dqg Q1H1 Vdylq,/ Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv/ 49/ ss159<05:41 Jhzhnh/ M1 dqg V1 Sruwhu0Kxgdn +4<;6,= Wkh Hvwlpdwlrq dqg Dssolfdwlrq ri Orqj Phpru| Wlph Vhulhv Prghov/ Mrxuqdo ri Wlph Vhulhv Dqdo|vlv/ 7/ ss1554056:1 Judqjhu/ F1Z1M1 dqg ]1 Glqj +4<<9,= Ydulhwlhv ri Orqj Phpru| Prghov/ Mrxuqdo ri Hfrqrphwulfv/ :6/ ss1940::1 Judqjhu/F1Z1M1dqgU1 Mr|hx{+4<;3,=DqLqwurgxfwlrqwrOrqjPhpru|WlphVhulhv Prghov dqg Iudfwlrqdo Gl(cid:30)huhqflqj/ Mrxuqdo ri Wlph Vhulhv Dqdo|vlv/ 4/ ss14805<1 Krvnlqj/ M1U1P1 +4<;4,= Iudfwlrqdo Gl(cid:30)huhqflqj/ Elrphwulnd/ 9;/ ss149804:91 Kxuylfk/ F1P1/ U1V1 Ghr dqg M1 Eurgvn| +4<<;,= Wkh Phdq Vtxduh Huuru ri Jhzhnh dqg Sruwhu0Kxgdn*v Hvwlpdwru ri wkh Phpru| Sdudphwhu ri d Orqj Phpru| Wlph Vhulhv/ Mrxuqdo ri Wlph Vhulhv Dqdo|vlv/ 4</ ss14<0791 4;

Olhvhqihog/ U1 dqg U1F1 Mxqj +4<<:,= Vwrfkdvwlf Yrodwlolw| Prghov= Frqglwlrqdo Qru0 pdolw|yhuvxvKhdy|0WdlohgGlvwulexwlrqv/xqsxeolvkhgpdqxvfulsw/Xqlyhuvlw|riW elq0 jhq1 Oredwr/ L1 dqg S1P1 Urelqvrq +4<<;,= D Qrqsdudphwulf Whvw iru L+3,/ Uhylhz ri Hfrqrplf Vwxglhv/ 98/ ss17:807<81 Oredwr/ L dqg Q1H1 Vdylq +4<<;,= Uhdo dqg Vsxulrxv Orqj Phpru| Surshuwlhv ri Vwrfn0Pdunhw Gdwd/ Mrxuqdo ri Exvlqhvv dqg Hfrqrplf Vwdwlvwlfv/ 49/ ss1594059;1 Oruhwdq/P1dqgS1F1E1Skloolsv+4<<7,=WhvwlqjwkhFryduldqfhVwdwlrqdulw|riKhdy|0 WdlohgWlphVhulhv=DqRyhuylhzriwkhWkhru|zlwkDssolfdwlrqvwrVhyhudoIlqdqfldo Gdwdvhwv/ Mrxuqdo ri Hpslulfdo Ilqdqfh/ 4/ ss1544057;1 Pdqghoeurw/ E1 +4<:4,= Zkhq Fdq Sulfh Eh Duelwudjhg H!flhqwo|B D Olplw wr wkh Ydolglw| ri wkh Udqgrp Zdon dqg Pduwlqjdoh Prghov/ Uhylhz ri Hfrqrplfv dqg Vwdwlvwlfv/ 86/ ss155805691 Qhovrq/ G1E1 +4<<4,= Frqglwlrqdo Khwhurvnhgdvwlflw| lq Dvvhw Uhwxuqv= D Qhz Ds0 surdfk/ Hfrqrphwulfd/ 8</ ss167:06:31 Urelqvrq/ S1P1 +4<<4,= Whvwlqj iru Vwurqj Vhuldo Fruuhodwlrq dqg G|qdplf Frqgl0 wlrqdo Khwhurvnhgdvwlflw| lq Pxowlsoh Uhjuhvvlrq/ Mrxuqdo ri Hfrqrphwulfv/ 7:/ ss19:0 ;71 Urelqvrq/ S1P1 +4<<7,= Wlph Vhulhv zlwk Vwurqj Ghshqghqfh/ lq Dgydqfhv lq Hfrqr0 phwulfv/ Vl{wk Zruog Frqjuhvv +F1D1 Vlpv/ hg1,/ Fdpeulgjh Xqlyhuvlw| Suhvv/ Fdp0 eulgjh1 Urelqvrq/ S1P1 +4<<8d,= Orj0Shulrgrjudp Uhjuhvvlrq iru Wlph Vhulhv zlwk Orqj Udqjh Ghshqghqfh/ Dqqdov ri Vwdwlvwlfv/ 56/ ss1437;043:51 Urelqvrq/ S1P1 +4<<8e,= JdxvvldqVhplsdudphwulf HvwlpdwlrqriOrqjUdqjhGhshq0 ghqfh/ Dqqdov ri Vwdwlvwlfv/ 56/ ss14963049941 Urelqvrq/ S1P1 +4<<<,= Wkh Phpru| ri Vwrfkdvwlf Yrodwlolw| Prghov/ xqsxeolvkhg pdqxvfulsw/ Orqgrq Vfkrro ri Hfrqrplfv1 Urelqvrq/ S1P1 dqg P1 Khqu| +4<<<,= Orqj dqg Vkruw Phpru| Frqglwlrqdo Khw0 hurvnhgdvwlflw| lq Hvwlpdwlqj wkh Phpru| Sdudphwhu ri Ohyhov/ Hfrqrphwulf Wkhru|/ 48/ ss15<<06691 Wd|oru/ V1M1 +4<<7,= Prgholqj Vwrfkdvwlf Yrodwlolw|/ Pdwkhpdwlfdo Ilqdqfh/ 7/ ss14;60 5371 Yhodvfr/ F1 +4<<<,= Qrq0Vwdwlrqdu| Orj0Shulrgrjudp Uhjuhvvlrq/ Mrxuqdo ri Hfrqr0 phwulfv/ <4/ ss165806:41 4<

Wdeoh 4 Orj0Shulrgrjudp Hvwlpdwhv ri Orqj Phpru| lq wkh Yrodwlolw| ri X1V1 Vwrfn Uhwxuqv +Vwdqgdug Huuruv lq Sduhqwkhvhv, Yrodwlolw| Phdvxuh p@83 p@433 p@483 p@533 Vtxduhg YZ uhwxuqv 3146; 31494 3148; 31465 +31387, +31367, +31359, +31354, Orj0Vtxduhg YZ uhwxuqv 318:; 31758 3173: 31777 +313<9, +31399, +3137;, +31375, POVT YZ uhwxuqv 318;5 31789 3176: 3179: +31437, +3139;, +31383, +31378, Devroxwh YZ uhwxuqv 316;< 31735 3175: 31744 +313;5, +31398, +31383, +31375, Vtxduhg HZ uhwxuqv 31399 313<5 31447 31444 +3139<, +31383, +3136;, +31364, Orj0Vtxduhg HZ uhwxuqv 3173< 31686 316<7 316;; +313<6, +31396, +31387, +3137:, POVT HZ uhwxuqv 31757 31666 316;5 316:< +313<9, +31397, +31385, +31379, Devroxwh HZ uhwxuqv 31644 31567 3164< 31673 +313<6, +3138;, +31383, +3137:, Qrwhv= Wklv wdeoh uhsruwv wkh orj0shulrgrjudp hvwlpdwhv ri wkh orqj phpru| sdudphwhu lq irxu phdvxuhv ri wkh yrodwlolw| ri ydoxh zhljkwhg +YZ, dqg htxdo zhljkwhg +HZ, vwrfn uhwxuqv1 Wkhvh uhwxuqv duh wkh ghphdqhg/ wrwdo frqwlqxrxvo| frpsrxqghg lqgh{ uhwxuqv/ iurp FUVS1 Wkh vwdqgdug huuruv duh wkh frqyhqwlrqdo dv|pswrwlf vwdqgdug huuruv +Urelqvrq +4<<8d,,1 Wkh gdwd lv gdlo|/ fryhulqj wkh shulrg Mxo| 6 4<95 wr Ghfhpehu 64 4<<;/ iru d wrwdo ri <4<3 revhuydwlrqv1 Wkh uhwxuqv odehoohg POVT kdyh ehhq wudqviruphg e| wkh prgl(cid:15)hg orj0vtxduhg wudqvirupdwlrq/ dv lq htxdwlrq +43,1 Wkh edqgzlgwk sdudphwhu lv p1

Wdeoh 5 Jdxvvldq Vhplsdudphwulf Hvwlpdwhv ri Orqj Phpru| lq wkh Yrodwlolw| ri X1V1 Vwrfn Uhwxuqv +Vwdqgdug Huuruv lq Sduhqwkhvhv, Yrodwlolw| Phdvxuh p@83 p@433 p@483 p@533 Vtxduhg YZ uhwxuqv 3145< 3149: 314:4 3147< +313:4, +31383, +31374, +31368, Orj0Vtxduhg YZ uhwxuqv 317<6 31756 31769 3178: +313:4, +31383, +31374, +31368, POVT YZ uhwxuqv 317<4 31775 31795 317:7 +313:4, +31383, +31374, +31368, Devroxwh YZ uhwxuqv 3169< 31733 3176; 31759 +313:4, +31383, +31374, +31368, Vtxduhg HZ uhwxuqv 313:: 313;< 31456 3145: +313:4, +31383, +31374, +31368, Orj0Vtxduhg HZ uhwxuqv 31684 31667 316:; 31699 +313:4, +31383, +31374, +31368, POVT HZ uhwxuqv 316:3 31669 316;7 316:3 +313:4, +31383, +31374, +31368, Devroxwh HZ uhwxuqv 315<3 31583 31646 31637 +313:4, +31383, +31374, +31368, Qrwhv= Wklv wdeoh uhsruwv wkh Jdxvvldq vhplsdudphwulf hvwlpdwru +Urelqvrq +4<<8e,, ri wkh orqj phpru| sdudphwhulqirxuphdvxuhvriwkhyrodwlolw|riydoxhzhljkwhg+YZ,dqghtxdozhljkwhg+HZ,vwrfnuhwxuqv1 Wkhvh uhwxuqv duh wkh ghphdqhg/ wrwdo frqwlqxrxvo| frpsrxqghg lqgh{ uhwxuqv/ iurp FUVS1 Wkh gdwd lv gdlo|/ fryhulqj wkh shulrg Mxo| 6 4<95 wr Ghfhpehu 64 4<<;/ iru d wrwdo ri <4<3 revhuydwlrqv1 Wkh uhwxuqv odehoohg POVT kdyh ehhq wudqviruphg e| wkh prgl(cid:15)hg orj0vtxduhg wudqvirupdwlrq/ dv lq htxdwlrq +43,1 Wkh edqgzlgwk sdudphwhu lv p1