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7/30/2019 Nonlinear Correlation Coefficients
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Gcrkvklb Lmldklcir Jmrrcditkml Jmchhkjkclts hrmf Pirtkid Fmfclts
Ay
Hrcg Xkmdc
MXXM Hkliljkid Zystcfs
Ilg
Givkg LiwrmjnkXkddilmvi Slkvcrskty
Xkddilmvi Zjemmd mh Ausklcss
500 Diljistcr IvclucXkddilmvi, PI 9;053 SZI
890-39;-7:1:
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]7/30/2019 Nonlinear Correlation Coefficients
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Gcrkvklb Lmldklcir Jmrrcditkml Jmchhkjkclts hrmf Pirtkid Fmfclts
Iastrijt
Rc kltrmgujc i lmldklcir jmrrcditkml jmchhkjkclt fctrkj gcrkvcg hrmf pirtkid fmfclts teit
jil ac suastktutcg hmr tec Pcirsml jmrrcditkml jmchhkjkclt kl dklcir klstiljcs is wcdd. Wec
hdcxkakdkty mhhcrcg ay pirtkid fmfclts cliadcs mrgcrcg pirtktkmls mh tec giti wecrcay
dklcir scbfclts irc ibbrcbitcg hmr il mvcridd jmrrcditkml jmchhkjkclt. Mur jmchhkjkclt
wmrns wktemut tec lccg tm pcrhmrf i dklcir trilshmrfitkml ml tec ulgcrdyklb giti, ilg
jil idsm prmvkgc i bclcrid fcisurc mh lmldklcirkty actwccl twm virkiadcs. Rc idsm
cxtclg tec ilidysks tm i fudtkpdc lmldklcir rcbrcsskml wktemut tec igvcrsc chhcjts mh
fudtkjmddklcirkty.
Ncywmrgs? Pirtkid fmfclts, Lmldklcir jmrrcditkml, Lmldklcir fudtkvirkitc ilidysks
7/30/2019 Nonlinear Correlation Coefficients
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9
9. KLWQMGSJWKMLJecl ct id. (1090) cxpdmrc tec prmadcf mh cstkfitklb i lmldklcir jmrrcditkml (Zcc
Hkburc 9). Wecy lmtc teit i bclcrkj usc stitkstkj suje is tec Pcirsml jmrrcditkml
jmchhkjkclt gmcs lmt cxkst hmr lmldklcir jmrrcditkmls. Rc kltrmgujc i bclcrkj lmldklcir
jmrrcditkml jmchhkjkclt fctrkj gcrkvcg hrmf pirtkid fmfclts teit jil ac suastktutcg hmr tec
Pcirsml jmrrcditkml jmchhkjkclt kl dklcir klstiljcs is wcdd. Wec hdcxkakdkty mhhcrcg ay
pirtkid fmfclts cliadcs mrgcrcg pirtktkmls mh tec giti wecrcay dklcir scbfclts irc
ibbrcbitcg hmr il mvcridd jmrrcditkml jmchhkjkclt.
Pirtkid fmfclts eivc tercc fikl igviltibcs? (9) lm gkstrkautkmlid issufptkml ks
rcqukrcg, (1) pirtkid fmfclts irc kltcbritcg kltm cjmlmfkjs termube cxpcjtcg utkdkty
tecmry (Emdteiuscl, 9;59 ilg Butemhh ct id., 9;;2), ilg irc kltcbritcg kltm stitkstkjs is
Xkmdc ilg Liwrmjnk (1091) hklg teit pirtkid fmfclts jil ac uscg tm gcrkvc tec JGH ilg
PGH mh ily gkstrkautkml.
Wec pipcr ks mrbilkzcg is hmddmws? Wec lcxt scjtkml wkdd jmvcr tec gcvcdmpfclt mh tec
fcisurc hmddmwcg ay i scjtkml wkte cfpkrkjid rcsudts. Lcxt, wc cxtclg tec ilidysks tm i
fudtkgkfclskmlid lmldklcir ilidysks wkte il ippdkjitkml tm lmldklcir rcbrcsskml ilidysks.
I hklid gksjusskml ilg suffiry jmfpdctcs tec pipcr.
1. GCXCDMPFCLW MH LMLDKLCIQ JMQQCDIWKML FCIZSQCWec Pcirsml jmrrcditkml jmchhkjkclt ks rcprcscltcg ay
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1
ilg ks stilgirgkzcg kl tec rilbc ^-9,9V. Wec jmvirkiljc ilg stilgirg gcvkitkml jillmt
ksmditc ilg gkhhcrcltkitc tec klhmrfitkml prcsclt kl cije mh tec hmur pmsskadc rcditkmlsekps
actwccl twm virkiadcs wecrc tec tirbct ks smfc rchcrcljc pmklt?
acdmw tirbct, acdmw tirbctacdmw tirbct, iamvc tirbctiamvc tirbct, acdmw tirbctiamvc tirbct, iamvc tirbct
Rc prmpmsc i fctemg mh pirtktkmlklb tec gkstrkautkml wkte pirtkid fmfclts tm jipturc tec
klhmrfitkml hrmf cije dklcir rcditkmlsekp cfacggcg wktekl i ak- mr fudtkvirkitc
rcditkmlsekp (dklcir mr lmldklcir). Aiscg ml tec iamvc hmur rcditkmlsekps actwccl twm
virkiadcs, i jm- mr gkvcrbclt pirtkid fmfclt ks jmlstrujtcg tm quiltkhy kt.k
1.9 Jm-Pirtkid Fmfclts
( |) { }
(|) { }
wecrcrcprcsclts tec mascrvitkml U it tkfc t, rcprcsclts tec mascrvitkml [ it tkfc t,lks tec gcbrcc mh tec DPF, qks tec gcbrcc mh tec SPF, ks tec tirbct hmr jmfputklbacdmw tirbct mascrvitkmls hmr U, ilg ks tec tirbct hmr jmfputklb iamvc tirbctmascrvitkmls hmr U. Hmr skfpdkjkty wc issufc teit .
7/30/2019 Nonlinear Correlation Coefficients
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:
1.1 Gkvcrbclt Pirtkid Fmfclts
(|) { }
(|) ( { })
1.: Gchklktkml mh Xirkiadc Qcditkmlsekps?
acdmw tirbct, acdmw tirbct (|)acdmw tirbct, iamvc tirbct ||iamvc tirbct, acdmw tirbct ||iamvc tirbct, iamvc tirbct (|)
Wm ivmkg tec adult jmvirkiljc ilg stilgirg gcvkitkml gcpclgcljc mh tec Pcirsml
jmchhkjkclt, wc jil usc tec hmddmwklb lmlpirifctrkj hmrfudi kl cquitkml 3 tm gctcrfklc
tec jmrrcditkml (dklcir mr lmldklcir) actwccl twm virkiadcs.
( |)(|)( |)(|)( |)(|)( |)(|)
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7
Wec ixkmfitkj rcditkmlsekp actwccl jmrrcditkml ilg jm- mr gkvcrbclt rcturls hmddmws.
Kh tecrc ks i -9 jmrrcditkml, tecl tec rcturls actwccl tec virkiadcs wkdd idwiys ac
gkvcrbclt,
(|)(|)(|)(|)
Kh tecrc ks i pcrhcjt jmrrcditkml actwccl twm virkiadcs, tecl tecrc wkdd ac lm gkvcrbclt
rcturls,
(|)(|)(|)(|)
Kh tecrc ks zcrm jmrrcditkml actwccl twm virkiadcs, tecl tec jm- ilg gkvcrbclt rcturls wkdd
ac mh cquid hrcqucljy mr fiblktugc (gcbrcc zcrm ilg gcbrcc mlc rcspcjtkvcdy),
( |) ( |) ( |)(|)[kcdgklb i 0 rcsudt,
^(|)(|)(|)(|)V^(|)(|)(|)(|)V
7/30/2019 Nonlinear Correlation Coefficients
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3
Gcbrcc mlc jil ac suastktutcg hmr pirifctcrs lilg q, tm bclcritc jmrrcditkmls
wecrcay tec fiblktugc mh tec tirbct gcvkitkmls irc jmfpircg> teus bclcritklb i
gcpclgcljc jmchhkjkclt.
1.7 Xksuidkzitkml mh tec Pirtktkmls Ssklb Fcils is Wirbcts?
Hkburc 9. 9stmrgcr pirtktkmlklb mh tec gkstrkautkml aiscg ml virkiadc rcditkmlsekps
wkte jm- ilg gkvcrbclt pirtkid fmfclts ml il mascrvcg lmldklcir jmrrcditkml kl i
fkjrmirriy stugy hrmf Jecl ct id. (1090).
| |
| || |
| |
[
U
7/30/2019 Nonlinear Correlation Coefficients
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8
Hkburc 1. 1lg
mrgcr pirtktkmlklb mh tec fkjrmirriy stugy aiscg ml fcils mh pirtkid
fmfclt suascts is tirbcts.
|| hurtecrpirtktkmlcg wkte lcw fcil tirbcts, ilg .
U
[
7/30/2019 Nonlinear Correlation Coefficients
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2
1.3 Gchklktkml mh Xirkiadc Zuascts?
||
|
|
|| ||
1.8 Gchklktkml mh Zuasct Fcils?
1.2 Gchkltkml mh Zuasct Pirtkid Fmfclts?
({ } { } )
({ } { })
7/30/2019 Nonlinear Correlation Coefficients
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5
({ } { })
({ } { } )
Hmr i :
rg
mrgcr ilidysks hmr cxifpdc, mlc lccgs tm tecl jmfputc tec 91 rcfiklklb
suasct pirtkid fmfclts (kl iggktkml tm tec hmur kgcltkhkcg kl cquitkmls ;-91 iamvc) usklb
tec ipprmprkitc suasct fcil tirbcts hmr cije quigrilt. Wec tmtid ifmult mh suasct fcils
wkdd ac dcss teil mr cquid tm wecrc L ks tec lufacr mh mrgcrs spcjkhkcg. kkWec cvcltuid lmrfidkzcg jmrrcditkml fctrkj ks ijjmfpdksecg ay iggklb idd JSPFs
ilg JDPFs (pmsktkvc jmrrcditkmls) ilg suatrijtklb GSPFs ilg GDPFs(lcbitkvc
jmrrcditkmls) kl tec lufcritmr, wekdc suffklb idd 98 jm- ilg gkvcrbclt pirtkid fmfclts
rcprcscltklb tec cltkrc gkstrkautkml kl tec gclmfklitmr pcr cquitkml 9: acdmw.
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;
Lufcritmr?
( Gclmfklitmr?
( (9:)
1.5 Lmldklcir Issmjkitkml?
Rc jil idsm gchklc tec ifmult mh lmldklcirkty prcsclt actwccl twm virkiadcs.
(||)(||)
(|)(|)
Cquitkml 97 gcsjrkacs tec ifmult mh lmldklcirkty prcsclt wecl tec lcbitkvc
jmrrcditkmls irc cquid kl hrcqucljy mr fiblktugc (gcpclgklb ml gcbrcc 0 mr 9
rcspcjtkvcdy) tm tec pmsktkvc jmrrcditkmls.
Recl cquids mlc, tecrc ks fixkfuf lmldklcirktyactwccl tec twm virkiadcs.Is ipprmijecs 0 mr , kt ks ipprmijeklb fixkfuf dklcirkty.
7/30/2019 Nonlinear Correlation Coefficients
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90
-5
-8
-7
-10
1
7
8
5
-7 -: -1 -9 0 9 1 : 7[
U
-5
-8
-7
-1
0
1
7
8
5
-7 -: -1 -9 0 9 1 : 7
[
U
:. CFPKQKJID CXKGCLJC?Wekrg mrgcr gcbrcc mlc pirtktkmls irc semwl ilg jidjuditcg. Wec 9
stmrgcr pirtktkml ks
tec tekjn rcg dklc (pcr Hkburc 9), tec 1lg
mrgcr pirtktkml ks tec tekl rcg dklc (pcr Hkburc 1)
ilg tec :rg
mrgcr pirtktkml ks tec gmttcg adijn dklc.
Dklcir Cquidktkcs?kkk, kv
Pcirsml 9.0
9.0 0
Hkburc :. Dklcir pmsktkvc rcditkmlsekp
actwccl twm virkiadcs (U, [).
Pcirsml -9.0
-9.0
Hkburc 7. Dklcir klvcrsc rcditkmlsekp
actwccl twm virkiadcs (U, [).
7/30/2019 Nonlinear Correlation Coefficients
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99
0
1
7
8
5
90
-7 -: -1 -9 0 9 1 : 7
[
U
0
90000
10000
:0000
70000
30000
80000
20000
50000
;0000
900000
0 30 900 930 100 130 :00 :30
[
U
Lmldklcir Gkhhcrcljcs?
hmr pmsktkvc UPcirsml 0.;85
0.;;; 0.0009
Hkburc 3. Lmldklcir pmsktkvc rcditkmlsekp
actwccl twm virkiadcs (U, [).
(pmsktkvc sncw)
Pcirsml -0.008
0.9:3 0.735
Hkburc 8. Lmldklcir rcditkmlsekp actwccl
twm virkiadcs (U, [).
7/30/2019 Nonlinear Correlation Coefficients
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91
0
9C+17
1C+17
:C+17
7C+17
3C+17
8C+17
2C+17
0 30 900 930 100 130 :00 :30
[
U
110
170
180
150
:00
:10
:70
:80
330 800 830 200 230 500
[
U
Is tec cxpmlcltkid huljtkml kljrciscs kl fiblktugc, wc ijtuiddy hklg kt tm rctikl kts
dklcir rcditkmlsekp
Pcirsml 0.881
0.;;8 0.0009
Hkburc 2. Lmldklcir pmsktkvc rcditkmlsekp
actwccl twm virkiadcs (U, [).
Ilg i jmfpdctcdy lmldklcir jdustcrcg gitisct, wecrc jmchhkjkclt wckbetklb guc tm
pirtktkml mjjupiljy ks cxcfpdkhkcg.
Pcirsml -0.815
-0.00;2 9.01
Hkburc 5. Lmldklcir rcditkmlsekp actwccl
twm virkiadcs (U, [).
7/30/2019 Nonlinear Correlation Coefficients
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9:
7. FSDWKGKFCLZKMLID LMLDKLCIQ ILID[ZKZ?
Wm hklg tec 9stmrgcr ibbrcbitc jmrrcditkml hmr fmrc teil twm gkfclskmls, tec fctemg
ks skfkdir tm weit wis oust prcscltcg. Klstcig mh jm- ilg gkvcrbclt pirtkid fmfclts, wc
irc bmklb tm suastktutc jm- ilg gkvcrbclt pirtkid fmfclt fitrkjcskltm cquitkml 3. I l x
lfitrkx hmr cije mh tec kltcrijtkmls (JDPF, GDPF, GSPF ilg JSPF) pcr Xkmdc ilg
Liwrmjnk (1091), jil ac jmlstrujtcg ilg trcitcg ilidmbmusdy tm tec gkrcjt pirtkid fmfclt
jmfputitkml.
[kcdgklb,
(98)
Recrcay tec hklid rcsudt wkdd ac il cquid skzcg l xlfitrkx,
Wm gcrkvc tec mvcridd jmrrcditkml, wc lccg tm stcrkdkzc tec fikl gkibmlid mh 9s (wekje
irc scdh-jmrrcditkmls) wkte tec hmddmwklb hmrfudi,
7/30/2019 Nonlinear Correlation Coefficients
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97
Ibikl, kh tec virkiadcs irc idd acdmw mr iamvc teckr rcspcjtkvc tirbcts it tkfc t, tec JDPF
ilg JSPF fitrkjcs rcspcjtkvcdy wkdd jipturc teit klhmrfitkml. Kh tec virkiadcs irc k.k.g.,
tec dkncdkemmg teit mlc virkiadc wmudg gkvcrbc it tkfc t kljrciscs is lkljrciscs, rcgujklb
.Hurtecr mrgcr pirtktkml ilidysks jil ac trilsditcg tm tec fudtkgkfclskmlid ay jrcitklb
fitrkjcs hmr cije mh tec kgcltkhkcg suascts hmr idd mh tec virkiadcs.
7.9 Lmldklcir Qcbrcsskml Ilidysks?
Wec tirbct fcils hrmf wekje tec hmur pirtkid fmfclt fitrkjcs irc jidjuditcg idsm
scrvc is tec aisks hmr i lmldklcir rcbrcsskml. Ay pdmttklb idd mh tec fcil kltcrscjtkmls, tec
dklcir scbfclts wkdd hkt tec ulgcrdyklb, lmlpirifctrkjiddy. Wec kljrciscg mrgcr mh
pmrtkmlklb wkdd bclcritc fmrc kltcrscjtklb pmklts (fixkfuf mh ) hmr i fmrcbriludir ilidysks. Acdmw ks il cxifpdc wkte :
rgmrgcr pirtktkmlklb, bclcritklb i hkt tm tec
dklcir giti.
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93
-5
-8
-7
-1
0
1
7
8
5
-7 -: -1 -9 0 9 1 : 7
[
U
1lg mrgcr JSPF
Jmmrgklitcs
(9) ,(y9)
:rg mrgcr JSPF
Jmmrgklitcs
(
9') ,(y9')
Hkburc ;. Lmlpirifctrkj rcbrcsskml pmklts hmr i dklcir rcditkmlsekp actwccl (U, [).
Rc jil idsm pcrhmrf teks ml lmldklcir rcditkmlsekps. Acdmw ks il cxifpdc wkte :rg
mrgcr pirtktkmlklb, bclcritklb i hkt tm il cxpmlcltkid rcditkmlsekp actwccl tec virkiadcs.
7/30/2019 Nonlinear Correlation Coefficients
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98
0
9
1
:
7
38
2
5
;
90
-7 -: -1 -9 0 9 1 : 7
[
U
Hkburc 90. Lmlpirifctrkj rcbrcsskml pmklts hmr i lmldklcir rcditkmlsekp actwccl
(U, [).
Bclcritklb i fudtkpdc virkiadc lmldklcir rcbrcsskml ilidysks rcqukrcs jrcitklb i
syltectkj virkiadc. Weks virkiadc, U* ks tec wckbetcg ivcribc mh idd mh tec cxpdilitmry
virkiadcs. Wec wckbetklb ks tec lmldklcir jmrrcditkml gcrkvcg hrmf tec l x l fitrkx wecrc
tec cxpdilitmry virkiadcs irc ml tec sifc rmw is tec gcpclgclt virkiadc wekje wkdd eivc
i 9.0 scdh-jmrrcditkml. Weus, il cxpdilitmry virkiadc wktemut gcpclgcljc (zcrm
jmrrcditkml) tm tec gcpclgclt virkiadc wkdd ac cxjdugcg hrmf jmlskgcritkml.
() ( )
Ilg tec lmldklcir fudtkpdc rcbrcsskml jil ac pcrhmrfcg kl nklg tm tec twm virkiadc
cxifpdc iamvc wkte fcils mh [, U* is kltcrscjtkml pmklts. Weks ks skfkdir tm i
7/30/2019 Nonlinear Correlation Coefficients
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92
lmlpirifctrkj dmjid fcils rcbrcsskml mldy tec lufacr mh fcils eis tm ac i hijtmr mh 7
guc tm tec hmur pirtkid fmfclt fitrkjcs pcr cije ilidysks.
Hkburc 99 acdmw ks tec lmldklcir jmrrcditkml fitrkx ilg tec suascquclt wckbetklbs hmr
tec fudtkpdc virkiadc lmldklcir rcbrcsskml usklb ZP[ is tec gcpclgclt virkiadc wkte WDW,
BDG, HUC, ilg BZB is cxpdilitmry virkiadcs.v Wec giti klvmdvcg 900 gikdy
mascrvitkmls hrmf 3/5/91 termube ;/12/91 hmr idd virkiadcs. Is semwl kl Xkmdc ilg
Liwrmjnk (1091) pirtkid fmfclts isyfptmtkjiddy jmlvcrbc tm tec irci mh tec huljtkml,
ilg stiakdkzc wkte ipprmxkfitcdy 900 mascrvitkmls.
Lmldklcir Jmrrcditkml Fitrkx
ZP[ WDW BDG HUC BZB
ZP[ 9.00 0.01 -0.98 -0.03 0.93
WDW 0.01 9.00 0.02 -0.33 -0.28
BDG -0.98 0.02 9.00 0.50 0.80
HUC -0.03 -0.33 0.50 9.00 0.27
BZB 0.93 -0.28 0.80 0.27 9.00
Hkburc 99. Lmldklcir jmrrcditkml fitrkx hmr 3 virkiadcs (ZP[, WDW, BDG,
HUC, BZB). Ekbedkbetcg rmw ksmditcs tec jmchhkjkclts hmr cquitkml 95.
Kl teks cxifpdc pcr cquitkml 95 mur ibbrcbitcg cxpdilitmry virkiadc ks,
Rkte tec fudtkgkfclskmlid ibbrcbitc jmrrcditkml is fcisurcg pcr cquitkml 92,
7/30/2019 Nonlinear Correlation Coefficients
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95
Ibikl, tecrc irc lm fudtkjmddklcirkty kssucs wkte tec cxpdilitmry virkiadcs, kt skfpdy
gmcs lmt fittcr kh tecy irc jmrrcditcg mr lmt. Acdmw kl hkburc 9: ks tec bripe mh teks
ilidysks wkte mur :rg
mrgcr hkt vcrsus tec 8te
mrgcr pmdylmfkid bclcritcg hrmf Cxjcd.
Wec suf mh squircs mh rcskguids ks rcgujcg ay 22% wecl kljrcisklb tec spcjkhkjitkml
hrmf i 1lg
mrgcr tm i :rg
mrgcr lmldklcir jmrrcditkml ilidysks (.072;3 tm .099 rcspcjtkvcdy).
Hkburc 91. Mur :rg
mrgcr hkt hmr i sklc wivc huljtkml mh U ilg Cxjcds 8te
mrgcr pmdylmfkid hkt wkte cquitkml.
y 6 0.0003x8- 0.0933x3+ 0.93:5x7- 0.3;02x:+ 0.391:x1+ 0.2512x
+ 0.0933
Q 6 0.;;22
-9.3
-9
-0.3
0
0.3
9
9.3
0 1 7 8 5 90 91
[
U
Zklc Rivc Huljtkml
Zcrkcs9
U
[
Qcbrcsskml
7/30/2019 Nonlinear Correlation Coefficients
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9;
Hkburc 9:. Mur :rgmrgcr hkt hmr il ulgctcrfklcg huljtkml mh U* ilg Cxjcds
8te
mrgcr pmdylmfkid hkt wkte cquitkml usklb tec ulgcrdyklb giti hrmf Hkburc
99.
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10
3. GKZJSZZKML ILG ZSFFIQ[?
Wecrc ks lm irbufclt is tm wey tec pirtktkml jillmt ac hurtecr spcjkhkcg L tkfcs,
udtkfitcdy ykcdgklb i lufacr mh scbfclts. Wec pirtkid fmfclts irc gkrcjtjmfputitkmls, oust is mtecr stitkstkjs suje is fcils ilg virkiljcs. Wec mavkmus aclchkt ks
tec iakdkty tm pirsc weit wis rchcrrcg tm is lmksc kltm vidkg klhmrfitkml. Guc tm tec hijt
teit klgkvkguid mascrvitkmls irc wckbetcg ay , tec lufacr mh mascrvitkmls kl cijescbfclt wkdd wckbe tec scbfclt ijjmrgklbdy> teus ihhkrfklb mutdkcr mascrvitkml stitus hmr
suje klstiljcs wecrc i scbfclt eis fklkfid mjjupiljy.
Wec purpmsc mh teks pipcr wis tm put hmrte i lmlpirifctrkj, lmldklcir jmrrcditkml
fctrkj wecrc Jecl ct id. (1090) lmtc, tecrc ks lm jmffmldy usc stitkstkj quiltkhyklb
lmldklcir jmrrcditkml teit jil hklg i skfkdirdy bclcrkj usc is Pcirsmls jmrrcditkml
jmchhkjkclt hmr quiltkhyklb dklcir jmrrcditkml. Mur dklcir suf mh tec wckbetcg fkjrm gmcs
klgccg jipturc tec ibbrcbitc jmrrcditkml. Aut, uldknc Pcirsmls sklbdc jmrrcditkml
jmchhkjkclt, wc idsm bclcritc tec klhmrfitkml lcjcssiry tm rcjmlstrujt tec rcditkmlsekp
hrmf tec klgkvkguid pirtkid fmfclt fitrkjcs. Is hmr i gkrcjt pmdkjy stitcfclt rcsudtklb
hrmf tec lmldklcir rcbrcsskml ilidysks> kt wmudg eivc tm issufc tec hmrf mh i jmlgktkmlid
cquitkml wecrcay cije dklcir scbfclt ks gchklcg hmr i spcjkhkj rilbc mh tec cxpdilitmry
virkiadc(s).
7/30/2019 Nonlinear Correlation Coefficients
23/24
7/30/2019 Nonlinear Correlation Coefficients
24/24
11
Clglmtcs?
kLcwtml prmvcg tec kltcbrid mh i pmklt kl i jmltklumus gkstrkautkml tm ac cquid tm zcrm.
kkKh lm giti cxksts kl i suasct, lm fcil ks jidjuditcg.
kkkWec emrkzmltid dklc is kl tec cquitkml
(pmklt prmaiakdkty) ykcdgs i 0 jmrrcditkml
hmr amte Pcirsmls jmrrcditkml ilg mur fctrkj.kv
Kt semudg ac lmtcg teit hmr lmrfidkzcg giti suje is dmb rcturls mr bcmfctrkj rcturls, tec
lmrfidkzitkml jmlstilt (0 mr 9 rcspcjtkvc tm tec rcturl hmrfit fcltkmlcg) semudg ac uscgritecr teil is tec tirbct tm gctcrfklc gcpclgcljc.vIdd virkiadcs kl tec rcbrcsskml irc cxjeilbc trigcg hulgs (CWHs) teit trigc kl SZ
firncts? ZP[ ks tec Z&P 300 CWH, WDW ks tec Airjdiys 10+ ycir Wrcisury Amlg CWH,BDG ks tec Bmdg Wrust CWH, HUC ks tec Curm Jurrcljy CWH, ilg BZB ks tec Z&P BZJK
Jmffmgkty Klgcx CWH.