More Related Content Similar to A Non-Random Walk Revisited: Short- and Long-Term Memory in Asset Prices Seminte tomate brilliant_f1,_aurelius_f1,_secolo_f1,_marissa_f1,_venezia_f1,_... Seminte tomate brilliant_f1,_aurelius_f1,_secolo_f1,_marissa_f1,_venezia_f1,_... Gherghescu Gabriel
Seminte salata touareg,_alamis,_fulmaria,_stallion,_mohawk,_radja,_luberon,_f... Seminte salata touareg,_alamis,_fulmaria,_stallion,_mohawk,_radja,_luberon,_f... Gherghescu Gabriel
Similar to A Non-Random Walk Revisited: Short- and Long-Term Memory in Asset Prices (20) 1. Board of Governors of the Federal Reserve System
International Finance Discussion Papers
Number 956
November 2008
A Non-Random Walk Revisited:
Short- and Long-Term Memory in Asset Prices
by
Paul S. Eitelman
Justin T. Vitanza
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Papers (other than an acknowledgment that the writer has had access to unpublished material)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.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the
Social Science Research Network electronic library at http://www.ssrn.com/
2. A Non-Random Walk Revisited:
Short- and Long-Term Memory in Asset Prices*
Paul S. Eitelman
Justin T. Vitanza*
Abstract
In this paper, we test for short and long memory in asset prices across 44 emerging and industrialized
economies. Using methodology from Lo and MacKinlay (1988) and Lo (1991), we find that markets
with a poor Sharpe ratio are more likely to reject the random walk than better performing markets. We
also make a methodological contribution. Contrary to the Baillie (1996) criticism, our long memory
analysis suggests that the choice of a truncation lag is not as important as one might initially believe.
Tests that reject the null hypothesis tend to do so across any reasonable choice in lag.
Keywords: random walk, long-range dependence, equities, commodities, exchange rates
JEL Codes: E30, G14
*
Author notes: We appreciate the comments of Shaghil Ahmed, Brett Berger, Dale Henderson, Erik
Hjalmarsson, Andrea Raffo, and Robert Vigfusson. Eitelman and Vitanza are research assistants in the
Division of International Finance at the Federal Reserve Board. Corresponding Author: Paul Eitelman,
Mail Stop 24, Federal Reserve Board, Washington, DC 20551 USA. Email: paul.s.eitelman@frb.gov.
The views expressed in this paper are solely the responsibility of the authors and should not be interpreted
as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person
associated with the Federal Reserve System.
6. GJE =Y;A=FL E9JC=L 9DD AFGJE9LAGF ;GFL9AF= AF @AKLGJA;9D HJA;=K AK AFKL9FL9F=GMKDQ J=T=;L=
AF L@= ;MJJ=FL E9JC=L HJA;=
/@AK =Z=;LAN=DQ HJ=;DM=K L@= GHHGJLMFALQ LG =9JF 9:FGJE9D J=LMJFK
L@JGM?@ 9 LJ=F LJ9AF? 9HHJG9;@
$GO=N=J KGE= AFN=KLE=FL KLJ9L=?A=K 9J= KLADD =A;9L= LG L@=
J=K=9J;@ 9F =PHDGAL9LAGF G HJA;= LJ=FK
#AN=F L@= ;GFLAFM= MK= G L=;@FA;9D 9F9DQKAK AF SF9F;A9D
=;GFGEA;K L@= J9FGE O9DC @QHGL@=KAK =K=JN=K MJL@=J =EHAJA;9D 9F9DQKAK
J9FGE O9DC L=KL
AFA;9L=K L@= =PAKL=F;= G AFL=JL=EHGJ9D =H=F=F;= 9L KGE= ;@GK=F D9?
J=B=;LAGF G L@= J9FGE
O9DC @QHGL@=KAK AEHDA=K L@9L 9 LJ=F AF 9KK=L HJA;=K GJ E=EGJQ =PAKLK
2= E9C= LOG E9AF ;GFLJA:MLAGFK LG L@= DAL=J9LMJ=
0KAF? 9 MFAIM=DQ D9J?= 9L9K=L G ;GEEGALA=K
9F KLG;C E9JC=L AFA;=K JGE =E=J?AF? 9F AFMKLJA9D =;GFGEA=K O= 9J= 9:D= LG ;GEH9J= L@=
:=@9NAGJ G AFL=JF9LAGF9D 9KK=L HJA;=K
2= SJKL H=JGJE 9 J9FGE O9DC L=KL GF =9;@ E9JC=L GN=J
K=N=J9D D9?K
*=PL O= ;9D;MD9L= L@= .@9JH= J9LAG
J=?J=KKAGF G 9 MEEQ N9JA9:D= AFA;9LAF?
O@=L@=J GJ FGL L@= J9FGE O9DC O9K J=B=;L= GF L@= .@9JH= J9LAG J=N=9D= L@9L E9JC=LK OAL@ HGGJ=J
JAKC 7. 9BMKL= J=LMJFK 9J= EGJ= DAC=DQ LG J=B=;L L@= J9FGE O9DC @QHGL@=KAK
/@AK SFAF? KM??=KLK
L@9L ;GFLJ9JA9F AFN=KLE=FL KLJ9L=?A=K O@A;@ DGGC GJ MF=JN9DM= 9KK=LK AF =HJ=KK= E9JC=LK E9Q
GZ=J L@= HJM=FL AFN=KLGJ 9F GHHGJLMFALQ LG :=9L L@= J=LMJFK G KL9F9J =IMALQ AFA;=K
.=;GF O= L=KL GJ DGF? E=EGJQ AF 9KK=L J=LMJFK MKAF? L@= )GAS= -=K;9D= -9F?= -.
KL9LAKLA; =N=DGH= :Q (G
.GE= ;JALA;AKEK G L@AK L=KL ;AL= L@9L L@=J= AK FG GHLAE9D E=L@G
GJ ;@GGKAF? 9 LJMF;9LAGF D9?
DL@GM?@ L@AK ;JALA;AKE AK L@=GJ=LA;9DDQ N9DA L@= J=KMDLK G GMJ 9F9DQKAK
KM??=KL L@9L L@= ;@GA;= G 9 LJMF;9LAGF D9? GL=F @9K DALLD= :=9JAF? GF L@= KA?FAS;9F;= G J=KMDLK
2=
SF EAP= =NA=F;= G DGF? E=EGJQ AF AFL=JF9LAGF9D =IMALQ E9JC=LK
+ L@= 9N9F= E9JC=LK GFDQ
=FE9JC 9H9F *GJO9Q 9F .O==F =P@A:AL DGF? E=EGJQ
%F L@= 0
.
GDD9J GJ=A?F =P;@9F?=
E9JC=LK J=?AGF9D 9;LGJK 9HH=9J LG := 9L HD9Q
2= SF L@9L GMJ G L@= KAP (9LAF E=JA;9F ;MJJ=F;A=K
KLMA= AF L@AK H9H=J J?=FLAF9 J9RAD @AD= 9F GDGE:A9 K@GO DGF? E=EGJQ O@=J=9K O= 9AD
LG J=B=;L L@= FMDD @QHGL@=KAK GJ =N=JQ 9N9F;= E9JC=L ;MJJ=F;Q 9F GJ EGKL ;GMFLJA=K 9;JGKK
!E=J?AF? KA9 L@= )AD= !9KL 9F JA;9
+ L@= ;GEEGALA=K =N9DM9L= AF L@AK H9H=J GFDQ
KGQ:=9FK 9F ;9LLD= K@GO KA?FK G DGF? E=EGJQ
/@= 9L9 9J= =K;JA:= AF =L9AD AF HH=FAP
8. .quot;# /0+.5 +# .quot;2+1/ 0quot;.01.quot;
quot;AF9F;A9D LAE= K=JA=K 9F9DQKAK G;MK=K GF L@= AFL=JL=EHGJ9D =H=F=F;A=K G 9KK=L HJA;=K
!9JDQ 9KK=L
HJA;AF? EG=DK O=J= :9K= GF L@= 9KKMEHLAGFK L@9L J=LMJFK 9J= A=FLA;9DDQ 9F AF=H=F=FLDQ AKLJA: 10. FGJE9D AKLJA:MLAGF
)9F=D:JGL O9K 9EGF? L@= SJKL LG K@GO L@9L L@=
FGJE9D AKLJA:MLAGF G=K FGL 9=IM9L=DQ ;9HLMJ= L@= 9L L9ADK GJ D=HLGCMJLGKAK G J=LMJFK
!F?D=
9F GDD=JKD=N L@=F A=FLAS= L@= HJ=K=F;= G LAE= 12. LA;ALQ -$ ;D9KK G EG=DK
)9FQ KM:K=IM=FL KLMA=K @9N= KAF;= ;GFSJE= L@=K= SFAF?K 9F
L@= 9KKMEHLAGF G AA 13. FGJE9D J=LMJFK AK FGO OA=DQ J=B=;L= AF L@= DAL=J9LMJ=
/@= -9FGE 29DC $QHGL@=KAK HGKALK L@9L LG9QUK KLG;C HJA;= AK 9F MFGJ=;9KL9:D= LJ9FKGJE9 14. LAGF G ALK HJ=NAGMK N9DM=
9K= GF L@AK 9J?ME=FL )9DCA=D 9F .@9JH= ;GF;DM=
L@9L H9KKAN= DGO ;GKL AF=P MFK K@GMD GMLH=JGJE L@=AJ 9;LAN=DQ E9F9?= ;GMFL=JH9JLK :Q KGE=
MF;LAGF G L@= LJ9AF? 9EAFAKLJ9LAN= 9F E9F9?=E=FL =PH=FK=K GO=
)GJ= :JG9DQ 9FQ =ZGJL
LG GJ=;9KL 9KK=L HJA;=K L@9L GDDGO L@= J9FGE O9DC K@GMD := N9DM= 15. J9AFAF?
/@=J= AK ;GFKA=J9:D= =:9L= 9EGF? SF9F;A9D =;GFGEAKLK O@=L@=J L@= J9FGE O9DC @QHGL@=KAK
@GDK
!9JDQ J=K=9J;@ AFLG L@= J9FGE O9DC @QHGL@=KAK 9KKME= ;GFKL9FL NGD9LADALQ AF L@= J=KAM9D
L=JE
=;9MK= G !F?D=UK O=DD 16. G;ME=FL= =PHGKALAGF GF L@= ;GFALAGF9D NGD9LADALQ G J=LMJFK 9
J=B=;LAGF G L@= J9FGE O9DC :=;9MK= G @=L=JGK;=9KLA;ALQ AK G DALLD= AFL=J=KL
/@= EGJ= 9N9F;=
(G 9F )9;'AFD9Q @=L=JGK;=9KLA;ALQ 17. ;GFKAKL=FL E=L@GGDG?Q AK AFN9JA9FL LG -$ HJG;=KK=K
)9F=D:JGL 9DKG AK;GN=J= 9 F=O =EHAJA;9D HJGH=JLQ AF L@= LAE= K=JA=K G 9KK=L HJA;=K
DGO J=IM=F;Q H=JKAKL=FL L=EHGJ9D =H=F=F;= @=J=9L=J DGF? E=EGJQ
(GF? E=EGJQ AK ;GEEGFDQ
;@9J9;L=JAR= :Q 9 KDGO=J 20. 9EHD= /9QDGJ 9F AF? #J9F?=J 9F !F?D= GMF 9 @QH=J:GDA; J9L= G =;9Q AF L@=
9:KGDML= N9DM= G 9KK=L J=LMJFK
K HGAFL= GML AF (G DGF? 21. L=JE E=EGJQ AK LJGM:D=KGE=
:=;9MK= AL AK AF;GFKAKL=FL OAL@ L@= ;GFLAFMGMK LAE= KLG;@9KLA; HJG;=KK=K =EHDGQ= AF E9JLAF?9D=
E=L@GK GJ L@= HJA;AF? G GHLAGFK 9F MLMJ=K ;GFLJ9;LK
)9F=D:JGL 99HL= 9 HJ=NAGMKDQ
=PAKLAF? L=KL LG A=FLAQ L@= HJ=K=F;= G DGF? E=EGJQ
/@AK L=KL J=K;9D= J9F?= O9K SJKL AFLJGM;=
:Q L@= @QJGDG?AKL $9JGD $MJKL LG A=FLAQ DGF? 22. L=JE H9LL=JFK AF L@= AK;@9J?= G L@= *AD=
-AN=J
/@= J=KL G L@AK H9H=J AK GJ?9FAR= 9K GDDGOK .=;LAGF =K;JA:=K L@= E=L@GGDG?Q 9F J=KMDLK
GJ GMJ K@GJL E=EGJQ J9FGE O9DC 9F9DQKAK 9K O=DD 9K 9 AK;MKKAGF GF L@= HGO=J G GMJ ;@GK=F L=KL
KL9LAKLA;
.=;LAGF =K;JA:=K L@= E=L@GGDG?Q 9F J=KMDLK G GMJ DGF? E=EGJQ 9F9DQKAK
.=;LAGF
23. ;GF;DM=K GMJ H9H=J 9F AK;MKK=K HJ9;LA;9D 9HHDA;9LAGFK GJ GMJ SFAF?K AF SF9F;A9D =;GFGEA;K
/@=
9HH=FA;=K HJGNA= 9 EGJ= =L9AD= NA=O G GMJ 9L9 9F J=KMDLK
%+.0 quot;)+.5
quot;0%+!+(+$5
quot;AJKL O= =FGL= 9K L@= AF=P D=N=D 9L LAE= quot; 9F =SF= L@= DG? 24. HJA;= HJG;=KK DF
/@=
;GFN=FLAGF9D GJE G L@= J9FGE O9DC AK L@=F ?AN=F 9K
O@=J= AK 9F 9J:ALJ9JQ JAL H9J9E=L=J 9F AK L@= J9FGE =JJGJ L=JE
/@= KL9F9J FMDD
@QHGL@=KAK $ KLAHMD9L=K L@9L L@= =JJGJ L=JEK 9J= AF=H=F=FLDQ 9F A=FLA;9DDQ AKLJA:ML=
FGJE9D J9FGE N9JA9:D=K OAL@ ;GFKL9FL N9JA9F;= GJ
$ %%
$GO=N=J ?AN=F L@= O=DD 25. G;ME=FL= 9;L L@9L SF9F;A9D LAE= K=JA=K =NA9L= JGE FGJE9DALQ 9F
L@= EGMFLAF? =NA=F;= G NGD9LADALQ ;DMKL=JAF? K@GOF SJKL :Q !F?D= 9F GDD=JKD=N 9
J=B=;LAGF G L@= J9FGE O9DC M= LG L@=K= 9;LGJK OGMD := G DALLD= AFL=J=KL
/@=J=GJ= O= KLMQ
L@= K@GJL E=EGJQ HJG;=KK=K G GMJ N9JA9:D=K MKAF? L@= (G 9F )9;'AFD9Q N9JA9F;= J9LAG L=KL
/@AK L=KL 9KKME=K L@9L HGKK=KK=K MF;GJJ=D9L= AF;J=E=FLK :ML AL 9DDGOK GJ EGJ= ?=F=J9D GJEK
G @=L=JGK;=9KLA;ALQ 9F J=D9P=K L@= J=IMAJ=E=FL GJ #9MKKA9F AF;J=E=FLK
/@= J=KL GDDGOK 9DEGKL AJ=;LDQ JGE L@= (G 9F )9;'AFD9Q E=L@GGDG?Q
quot;GJ G:K=JN9 26. LAGFK O@=J= AK 9FQ AFL=?=J ?J=9L=J L@9F O= =SF= L@= 9KQEHLGLA; =KLAE9LGJK G
L@= E=9F 9F N9JA9F;= G J=LMJFK J=KH=;LAN=DQ
27. .== HH=FAP GJ MJL@=J =NA=F;= 9F KMEE9JQ KL9LAKLA;K KH=;AS; LG GMJ 9L9 K=L
(G 9F )9;'AFD9Q ;GFN=JL L@=AJ 9L9 JGE 9ADQ LG O==CDQ J=IM=F;Q LG EALA?9L= L@= :A9K=K AFLJGM;= :Q FGF 29. 9KC KHJ=9 9F 9KQF;@JGFGMK HJA;=K
2= =NA9L= KDA?@LDQ JGE L@=AJ E=L@G G J=IM=F;Q ;GFN=JKAGF
2= ;9D;MD9L= L@= O==CDQ J=LMJF GJ =9;@ K=JA=K 9K L@= J=LMJF JGE 2=F=K9QUK ;DGKAF? HJA;= LG L@= GDDGOAF? 2=F=K 30. 9QUK ;DGK=
% L@= GDDGOAF? 2=F=K9QUK HJA;= AK EAKKAF? O= MK= /M=K9QUK HJA;=
% /M=K9QUK HJA;= AK 9DKG EAKKAF?
O= MK= )GF9QUK HJA;= =L;
32. O@=J=
AK L@= 9MLG;GJJ=D9LAGF ;G=Y;A=FL =KLAE9LGJ
*GL= L@9L O@=F
KAEHDAS=K LG
L@= SJKL 37. /@= GDDGOAF? L=KL KL9LAKLA; $ AK 9KQEHLGLA;9DDQ KL9F9J FGJE9D 9F AK MK= LG =K;JA:= GMJ
=EHAJA;9D J=KMDLK AF K=;LAGF
*GL= L@9L I ;9F := AFL=JHJ=L= 9K L@= H=JAG GJ O@A;@ L@= =PAKL=F;=
G E=EGJQ AK :=AF? L=KL=
$
/@AK L=KL KL9LAKLA; AK A=9D GJ =N9DM9LAF? L@= J9FGE O9DC @QHGL@=KAK :=;9MK= AL 9;;GMFLK GJ L@=
NGD9LADALQ ;DMKL=JAF? AF@=J=FL AF 9KK=L HJA;=K
$GO=N=J KAF;= L@= =Z=;LAN= K9EHD= KAR= =;J=9K=K 9K
?=LK D9J?=J KE9DD 38. K9EHD= :A9K=K OADD KC=O L@AK KL9LAKLA; 9L KMY;A=FLDQ D9J?= D9?K (G 9F )9;'AFD9Q
quot;/1(0/
/@= J=KMDLK G GMJ J9FGE O9DC KLMQ 9J= K@GOF AF HH=FAP
/@= 9K@= GJ9F?= 9F J=
DAF=K J=HJ=K=FL 9F H=J;=FL J=B=;LAGF D=N=DK G L@= @=L=JGK;=9KLA;ALQ 43. J=N=JKAGF AF L@= LAE= K=JA=K 9L L@9L D9?
/@AK H9H=J G=K FGL 9LL=EHL LG HJGN=
=PHD9F9LGJQ 9;LGJK GJ 9FQ FGF 44. J9FGE HJG;=KK=K A=FLAS= @=J=AF AFKL=9 O= J=N=9D L@GK= 9J=9K
O@=J= MJL@=J MF9E=FL9D 9F9DQKAK K@GMD HJGN= JMALMD GJ 9;9=EA;K 9F HJ9;LALAGF=JK
=O
FGL9:D= L@=E=K =E=J?=
%F ;GEEGALQ E9JC=LK O= SF ;GEEGF LJ=FK OAL@AF ;GEEGALQ ?JGMHAF?K
!F=J?Q AL=EK
AF;DMAF? ;JM= GAD F9LMJ9D ?9K 9F @=9LAF? GAD =P@A:AL E=9F J=N=JLAF? HJA;= :=@9NAGJ
/@AK SFAF?
AK ;GFKAKL=FL OAL@ J=;=FL OGJC :Q #=E9F
K AF D=9F=Q 9F #J==F9O9Q O= 9AD LG
J=B=;L L@= J9FGE O9DC @QHGL@=KAK GJ =9;@ G L@= FAF= E=L9DK K=JA=K AF GMJ KLMQ
/@= 9?JA;MDLMJ9D
J9O E9L=JA9DK F9E=DQ ;GLLGF 9F JM::=J K@GO KA?FAS;9FL H=JKAKL=F;= AF J=LMJFK O@AD= L@= SFAK@=
9JE HJGM;LK 9J= D9J?=DQ J9FGE
.GQ:=9F HJA;=K 9J= L@= =P;=HLAGF @GO=N=J 9K L@=Q 9J= K@GOF LG
=NA9L= JGE L@= J9FGE O9DC
2= 9AD LG J=B=;L L@= J9FGE O9DC @QHGL@=KAK GJ 0
.
GJ=A?F =P;@9F?= E9JC=LK
+MJ SFAF?K 9J=
;GFKAKL=FL OAL@ (AM 9F $= O@G MK= L@= K9E= @=L=JGK;=9KLA;ALQ 47. GDD9J J9L=K =9;@ =P@A:AL HGKALAN= K=JA9D ;GJJ=D9LAGF H9JLA;MD9JDQ
GJ KE9DD N9DM=K O@=J=9K L@= J9FGE O9DC ;9FFGL := J=B=;L= GJ L@= 9F9A9F 48. 0
.
GDD9J J9L=
+L@=J FGL9:D= ;MJJ=F;A=K AF;DM= L@= MKLJ9DA9F GDD9J 9F L@= !MJG :GL@ G O@A;@ K==E LG =P@A:AL
J9FGE HJA;= :=@9NAGJ
2= 9DKG 9AD LG J=B=;L L@= J9FGE O9DC @QHGL@=KAK GJ L@= . , 9 N9DM= 49. O=A?@L= AF=P 9L
9FQ ;GFN=FLAGF9D D9?
.AEAD9JDQ O= ;9FFGL J=B=;L L@= J9FGE O9DC @QHGL@=KAK GJ E9FQ GL@=J E9BGJ
AFL=JF9LAGF9D =IMALQ E9JC=LK AF;DMAF? @AF9 L@= 0FAL= 'AF?GE quot;J9F;= #=JE9FQ %FA9 J9RAD
.OALR=JD9F .GML@ 'GJ=9 .H9AF 9F .O==F
/@AK AK ;GFKAKL=FL OAL@ L@= SFAF?K G 9EH:=DD
(G 9F )9;'AFD9Q
/@=Q ;9FFGL J=B=;L L@= J9FGE O9DC @QHGL@=KAK GJ 9 0
.
N9DM= 50. O=A?@L= AF=P
$GO=N=J L@= E9AF SFAF? G L@=AJ H9H=J AK L@9L L@=Q J=B=;L L@= J9FGE O9DC GJ
L@= -., =IM9D 51. O=A?@L= AF=P
;;GJAF?DQ L@=Q KM??=KL L@9L SJE KAR= AK 9 JANAF? 9;LGJ GJ L@=
J9FGEF=KK G ALK K=;MJALQ HJA;=
quot;JGE GMJ 9F9DQKAK AL 9HH=9JK L@9L JAKC 52. 9BMKL= J=LMJFK 9J= 9DKG
9F AFA;9LGJ G HJ=A;L9:ADALQ
quot;GJ =P9EHD= :Q GJ=JAF? E9JC=LK 9;;GJAF? LG L@=AJ .@9JH= J9LAGK
O= FGLA;= L@9L L@= K=N=F O=9C=KL =IMALQ E9JC=LK AF GMJ K9EHD= R=;@ -=HM:DA; ,@ADAHHAF=K
9H9F /@9AD9F %L9DQ 9F J?=FLAF9 9DD J=B=;L L@= J9FGE O9DC
/@AK J=KMDL AK KMHHGJL= :Q
=;GFGEA; AFLMALAGF
(GO JAKC 53. 9BMKL= J=LMJFK K@GMD =;J=9K= L@= =E9F GJ 9F9DQKL ;GN=J9?=
O@A;@ OGMD J=KMDL AF O=9C=J AFGJE9LAGF9D =Y;A=F;Q
/@= 9EH:=DD (G 9F )9;'AFD9Q SFAF?K 9J= :9K= GF 0
.
N9DM= 54. O=A?@L= AF=P 9L9 JGE L@= =FL=J
GJ -=K=9J;@ AF .=;MJALQ ,JA;=K -., 9L= MDQ LG =;=E:=J
/@= ;GFN=FLAGF9D GJE G L@= .@9JH= J9LAG AK O@=J= AK L@= JAKC 55. J== J9L=
=;9MK= G L@= K;9J;ALQ
9F AF;GFKAKL=F;Q G 9L9 GF AFL=JF9LAGF9D JAKC 58. %F quot;A?MJ=
O= K@GO 9 K;9LL=JHDGL G L@= .@9JH= J9LAG 9?9AFKL L@= E9PAEME N9DM= GN=J
9DD D9?K G L@= 9:KGDML= N9DM= G $ /@= O9K ;9D;MD9L= MKAF? L@= J=LMJF 9F KL9F9J =NA9LAGF
G J=LMJFK GN=J 9DD 9N9AD9:D= 9L9
.O==F O9K AEE=A9L=DQ AKJ=?9J= 9K 9F GMLDA=J
10
8
6
Zmax
4
2
0
0 .1 .2 .3
Sharpe Ratio
non-oil oi l
quot;A?MJ=
2= AEE=A9L=DQ FGLA;= L@9L =F=J?Q ;GEEGALA=K 9F +,! 59. E=E:=J =IMALQ E9JC=LK L=F= LG
=NA9L= JGE L@= E9BGJALQ G L@= 9L9
-=EGNAF? L@=K= HGAFLK E9?FAS=K L@= J=D9LAGFK@AH :=LO==F
JAKC 61. 6
4
Zmax
2
0
0 .05 .1 .15 .2
Sharpe Ratio
quot;A?MJ=
/9:D=
K@GOK L@= ;GJJ=D9LAGF :=LO==F L@=K= K=JA=K 9DGF? OAL@ L@= ;G=Y;A=FLK 9F L 62. KL9LAKLA;K
G 9 J=?J=KKAGF G 9 MEEQ N9JA9:D= O@A;@ AFA;9L=K O@=L@=J GJ FGL L@9L E9JC=L ;9F J=B=;L L@=
J9FGE O9DC OAL@ ;GFS=F;= 9L KGE= D9? A
=
$
GF L@=
/@GM?@ GFDQ
L@= +(. =KLAE9L=K 9J= J=HGJL= L@= J=KMDLK 9J= JG:MKL LG K=N=J9D EGAS;9LAGFK AF;DMAF? JG:MKL
KL9F9J =JJGJK 9F AL=J9LAN=DQ J=O=A?@L= D=9KL KIM9J=K OAL@ $M:=J 9F :AO=A?@L MF;LAGFK LMF=
LG =Y;A=F;Q
/9:D=
//quot;0/ +..quot;(0+* L 67. 9BMKL= E9JC=L H=JGJE9F;= 9F =Y;A=F;Q
quot;MJL@=J J=K=9J;@ AF L@AK 9J=9 OGMD DAC=DQ
HJGN= J=O9JAF?
+3quot;.
%F L@AK K=;LAGF O= =L9AD L@= J=D9LAN= HGO=J G L@= (G 9F )9;'AFD9Q @=L=JGK;=9KLA;ALQ 69. AF;J=E=FLK
+F= K@GMD =PH=;L L@9L GJ J9FGE 9KK=L HJA;= AFFGN9LAGFK :GL@ L@= @GEGK;=9KLA;
9F @=L=JGK;=9KLA; E=L@GGDG?A=K OADD 9AD LG J=B=;L L@= FMDD @QHGL@=KAK G 9 J9FGE O9DC 9F HJGM;=
N=JQ KAEAD9J J=KMDLK
+MJ KAEMD9LAGF J=KMDLK ;GFSJE L@AK
K 9F =P9EHD= O= AF;DM= L@= SJKL K9EHD=
G L@= KAEMD9LAGF AF quot;A?MJ=
quot;A?MJ=
%% 70. *GJE9D ,JG;=KK
%L AK D=KK G:NAGMK @GO L@= J9FGE O9DC L=KLK OADD :=@9N= AF L@= HJ=K=F;= G LAE= 73. N9JQAF? NGD9LADALQ 9F 9HHJGHJA9L=DQ 9ADK LG J=B=;L L@= J9FGE
O9DC O@=J=9K L@= @GEGK;=9KLA; 9DL=JF9LAN= AK :A9K= LGO9JK J=B=;LAGF
quot;A?MJ=
K@GOK L@= SJKL
K9EHD= AF GMJ KAEMD9LAGF 9F L@= J=B=;LAGF :A9K G L@= @GEGK;=9KLA; L=KL
74. quot;A?MJ=
#-$ ,JG;=KK
#-$ HJG;=KK=K GJ
)GJ= GJE9DDQ O= MK= )GFL= 9JDG KAEMD9LAGFK LG ?=F=J9L=
G L@= KAR= 9F L@=F 9HHDQ L@= @GEGK;=9KLA; 9F @=L=JGK;=9KLA; J9FGE O9DC L=KLK
LG L@= 9L9
/@= J=KMDLK GJ K=N=J9D 9J:ALJ9JQ D9?K 9J= HJ=K=FL= AF /9:D=
Table 2.3.1: Percent of GARCH(1,1) Processes Rejected
Confidence Methodology q
Level ( ) 2 4 8 16 32 64
Homoscedastic 12.41 12.35 11.57 11.08 9.85 8.12
= 95%
Heteroscedastic 5.04 5.28 5.30 4.71 4.88 4.88
Homoscedastic 4.39 4.63 4.42 4.12 3.38 3.53
= 99%
Heteroscedastic 0.83 1.07 1.35 1.41 1.58 2.03
/@= 9:GN= L9:D= ;D=9JDQ K@GOK L@9L L@= @GEGK;=9KLA; L=KL AK :A9K= LGO9JK J=B=;LAGF AF L@= HJ=K 77. ;GFKAKL=FL
L=KL :=;9MK= AL AK L@= GJ=;9KL9:ADALQ G HJA;= ;@9F?=K L@9L AK G HJAE9JQ AFL=J=KL AF J9FGE O9DC
9F9DQKAK
#-$ HJG;=KK=K 9J= OJALL=F G L@= GJE #-$ O@=J= AK L@= FME:=J G D9?K G L@= ;GFALAGF9D N9JA9F;=
9F AK L@= FME:=J G D9?K G L@= KIM9J= AFFGN9LAGFK
quot;GJ KAEHDA;ALQ O= 9KKME= L@= ;GEEGF #-$ HJG;=KK
9F L@=F =KLAE9L= L@= #-$ ;G=Y;A=FLK JGE GMJ O==CDQ . , 9L9
78. +*$ quot;)+.5
=;9MK= 9 F=O LQH= G L=KL AK F=== GJ DGF? E=EGJQ 9F9DQKAK O= KMJN=Q= L@= DAL=J9LMJ= GJ
9DL=JF9LAN=K
DL@GM?@ HGO=JMD GJ L@=GJ=LA;9D EG=DAF? 9F NGD9LADALQ 9F9DQKAK KLMA=K :9K= MHGF
L@= 9:KGDML= N9DM= G J=LMJFK A
=
AF? #J9F?=J 9F !F?D= 9F 9;GJG?F9 =L
9D
HJGNA= FG AFLMALAGF J=?9JAF? L@= AJ=;LAGF G 9 DGF? E=EGJQ ;Q;D= GFDQ ALK =PAKL=F;=
/@= J=K;9D=
J9F?= ;D9KK G L=KL KL9LAKLA;K @GO=N=J 9J= 9:D= LG AKLAF?MAK@ :=LO==F HGKALAN= KLJGF? =H=F=F;=
H=JKAKL=F;= 9F F=?9LAN= KLJGF? =H=F=F;= E=9F J=N=JKAGF
quot;0%+!+(+$5
?9AF O= =FGL= 9K L@= AF=P D=N=D 9L LAE= quot; 9F =SF= L@= ;GFLAFMGMKDQ ;GEHGMF= KAF?D=
H=JAG J=LMJF JGE quot; LG quot; 9K DF DF
/G 9NGA ;GFMKAGF OAL@ L@= FGL9LAGF JGE
GMJ J9FGE O9DC L=KL AF K=;LAGF O= =FGL= L@= LJMF;9LAGF D9? AF 9QK 9K
+MJ DGF? E=EGJQ
E=L@GGDG?Q GDDGOK =P9;LDQ JGE (G
(// ( 1./0 *!quot;(.+0 quot;/ (quot;! *$quot;
/@= ;D9KKA;9D $MJKL 85. O@=J= ! AK L@= MKM9D E9PAEME DAC=DA@GG KL9F9J =NA9LAGF =KLAE9LGJ
87. 2@=F HJGH=JDQ FGJE9DAR= L@AK KL9LAKLA; O=9CDQ ;GFN=J?=K LG L@= J9F?= G L@= JGOFA9F :JA?=
/@= ;D9KKA;9D J=K;9D= J9F?= KL9LAKLA; @GO=N=J G=K FGL AKLAF?MAK@ :=LO==F K@GJL 90. L=JE 9MLG;GJJ=D9LAGF ;G=Y;A=FLK
G H=J;=FL L@=
E=9F G E9Q := :A9K= MHO9J :Q H=J;=FL ;9MKAF? 9 J=B=;LAGF G L@= FMDD @QHGL@=KAK 9L 9FQ
;GFN=FLAGF9D KA?FAS;9F;= D=N=D
#AN=F L@AK O=9CF=KK 9F L@= K@GJL 91. L=JE 9MLGJ=?J=KKAN= HJGH=JLA=K G
GMJ 9L9 =K;JA:= AF K=;LAGF
O= K=D=;L= L@= EGAS= J=K;9D= J9F?= KL9LAKLA; (G GJ GMJ
DGF? E=EGJQ 9F9DQKAK :=;9MK= G ALK AFN9JA9F;= LG K@GJL 93. +8/ +!7quot;! quot;/ (quot;! *$quot;
/@= EGAS= J=K;9D= J9F?= KL9LAKLA; AZ=JK GFDQ AF ALK =FGEAF9LGJ LG 9;@A=N= AFN9JA9F;= LG
K@GJL E=EGJQ HJG;=KK=K
103. 9J= L@= K9EHD= N9JA9F;= 9F 9MLG;GN9JA9F;= MH LG D9?
G J=KH=;LAN=DQ
*GL= L@9L
L@= EGAS= J=K;9D= J9F?= KAEHDAS=K LG L@= ;D9KKA;9D $MJKL 104. )9F=D:JGL J=K;9D= J9F?= KL9LAKLA; AF
L@= KH=;A9D ;9K= O@=J=
E9AF ;JALA;AKE G L@= EGAS= -. AK L@9L L@=J= AK DALLD= ?MA9F;= 9:GML @GO LG K=D=;L 9F
GHLAE9D LJMF;9LAGF D9?
% AK ;@GK=F LGG KE9DD KA?FAS;9FL 9MLG;GN9JA9F;=K E9Q := A?FGJ= L@MK
:A9KAF? L@= KL9LAKLA;
DKG A AK LGG D9J?= J=D9LAN= LG L@= K9EHD= KAR= (G 9F )9;'AFD9Q
K@GO L@9L L@= SFAL= 106. =H=F=FL
O@=J= AK L@= ?J=9L=KL AFL=?=J D=KK L@9F GJ =IM9D LG 9F
AK L@= SJKL 107. GJ=J 9MLG;GJJ=D9LAGF
;G=Y;A=FL
2= K@GO L@= FJ=OK 9L9 =H=F=FL AF K=;LAGF
:=DGO 9 :JG9=J J9F?= G
UK 9J= ?J9H@= AF HH=FAP
DL@GM?@ O= J=HGJL L@= FJ=OK AF L@AK H9H=J AL @9K FGL :==F
HJGN=F LG := 9F GHLAE9D E=L@G GJ K=D=;LAF? 9F FG CFGOF E=L@G ;MJJ=FLDQ =PAKLK
%F =L=JEAFAF? L@= KA?FAS;9F;= G GMJ J=KMDLK AL ;9F := K@GOF L@9L L@= EGAS= J=K;9D= J9F?=
KL9LAKLA; ;GFN=J?=K LG L@= J9F?= G L@= JGOFA9F :JA?=
quot;GDDGOAF? JGE /@=GJ=E
G (G L@= ;MEMD9LAN= AKLJA:MLAGF MF;LAGF quot; GJ L@=
110. L9AD= L=KL ;9F := G:L9AF= JGE L@= 9:GN= =IM9LAGF L@= EGKL ;GEEGFDQ
MK= N9DM=K 9J= K@GOF AF /9:D=
/9:D=
JALA;9D 19DM=K G L@= AKLJA:MLAGF 112. #
quot;A?MJ=
MEMD9LAN= AKLJA:MLAGF quot;MF;LAGF G L@= )GAS= -.
quot;/1(0/
/@= J=KMDLK G GMJ DGF? E=EGJQ 9F9DQKAK 9J= K@GOF AF =L9AD AF HH=FAP
?9AF L@= 9K@=
GJ9F?= 9F J= DAF=K J=HJ=K=FL 9F H=J;=FL J=B=;LAGF D=N=DK G L@= EGAS= J=K;9D= J9F?= @Q 116. KMDLK G GMJ EGAS= J=K;9D= 9F9DQKAK MKAF? FJ=OKU 9L9 117. =H=F=FL
2= SF DALLD= =NA=F;= GJ DGF? 119. L=JE 9MLG;GJJ=D9LAGFK G MH LG LJ9AF? 9QK 9HHJGPAE9L=DQ GF= Q=9J L@= FMDD @QHGL@=KAK
G FG DGF? L=JE =H=F=F;= ;9FFGL := J=B=;L= GJ G L@= =IMALQ E9JC=LK KLMA=
JALA;AKEK
D=NA= 9?9AFKL L@= EGAS= J=K;9D= J9F?= :Q 9ADDA= GJ =P9EHD= ;AL= L@9L
9 E9BGJ HJ9;LA;9D AY;MDLQ ;GF;=JFK L@= ;@GA;= G 9F @GO LG AKLAF?MAK@ := 120. LO==F K@GJL J9F?= =H=F=F;A=K 9F DGF? J9F?= =H=F=F;A=K
+MJ ?J9H@A;9D J=KMDLK AF HH=FAP G FGL KMHHGJL L@AK ;D9AE
2= 9AD LG J=B=;L L@= FMDD @Q 121. HGL@=KAK 9L *- AFL=?=J D9? GJ L@= 0FAL= .L9L=K 0FAL= 'AF?GE 9F E9FQ GL@=J =E=J?AF? 9F
AFMKLJA9DAR= =IMALQ E9JC=LK
quot;MJL@=JEGJ= GMJ SFAF?K 9J= D9J?=DQ ;GFKAKL=FL OAL@ GL@=J 9F9DQK=K
G L@= 0
.
(G 9F ?DG:9D @GO =L
9D =IMALQ E9JC=LK
%F L@= GJ=A?F =P;@9F?= E9JC=LK O= SF ?J=9L AKH9JALQ AF L@= DGF? E=EGJQ =NA=F;= :=LO==F
=E=J?AF? 9F AFMKLJA9DAR= =;GFGEA=K
GFLJ9JQ LG )MDDA?9F O= SF FG =NA=F;= G DGF?
E=EGJQ AF L@= :AD9L=J9D LJ9= G 0
.
GDD9JK OAL@ GL@=J 9N9F;= E9JC=L ;MJJ=F;A=K
DAC=DQ J=9KGF
GJ L@AK AKH9JALQ AK )MDDA?9FUK MK= G EGFL@DQ 9N=J9?=K AFKL=9 G HGAFL 9L9 O@A;@ E9Q :A9K J=KMDLK
AF L@= HJ=K=F;= G K@GJL 122. L=JE =H=F=;= AF L@= 9ADQ 9L9
2= J=B=;L L@= FMDD @QHGL@=KAK GJ E9FQ
=E=J?AF? =;GFGEA=K @GO=N=J H9JLA;MD9JDQ AF (9LAF E=JA;9
2= SF N=JQ DALLD= =NA=F;= G DGF? E=EGJQ AF EGKL ;GEEGALQ E9JC=LK
$GO=N=J GJJ9RR9
=L
9D
GMF J9;L9D J=LMJFK AF L@= MLMJ=K E9JC=LK GJ KGQ:=9FK O@=9L G9LK 9F ;GJF
2=
KAEAD9JDQ GMF DGF? E=EGJQ AF L@= KHGL J=LMJFK G L@= KGQ:=9FK E9JC=L
K AF (G O@=F J=HGJLAF? J=KMDLK GJ L@= 9L9 123. =H=F=FL
O= J=HD9;= L@= *=O=Q 9F 2=KL
9MLG;GJJ=D9LAGF O=A?@LK AF =IM9LAGF OAL@ L@GK= KM??=KL= :Q FJ=OK
J=B=;LAGF G L@= FMDD @QHGL@=KAK G=K FGL HJ=;AK=DQ AEHDQ L@9L DGF? E=EGJQ AK HJ=K=FL :ML L@9L L@= KLG;@9KLA;
HJG;=KK G=K FGL KAEMDL9F=GMKDQ K9LAKQ 9DD G L@= @QHGL@=KAK ;GFALAGFK AF (G
)MDDA?9F MK=K EGFL@DQ 9L9 JGE L@= quot;==J9D -=K=JN= 9FC G .L
(GMAK
124. Equity Indices Foreign Exchange
Country * V( *) * V( *) Commodity * V( *)
Argentina 4 1.50 2 1.91* Crude Oil 0 0.95
Brazil 5 1.31 3 1.89* Gasoline 1 1.06
Chile 14 1.75 3 1.88* Natural Gas 0 0.92
Colombia 7 1.62 0 1.91* Heating Oil 3 1.02
Mexico 7 1.38 0 1.00 Copper 4 1.28
Peru 11 2.31** 2 1.41 Aluminum 2 1.26
Venezuela 8 1.25 --- --- Lead 4 1.26
China 2 1.38 --- --- Nickel 1 1.30
Hong Kong 4 1.37 --- --- Tin 4 1.54
Indonesia 12 1.66 6 1.46 Zinc 0 1.47
India 6 1.45 9 2.12** Gold 3 1.03
South Korea 6 1.88* 7 1.95* Platinum 2 1.39
Malaysia 8 1.50 1 1.35 Silver 2 1.00
Philippines 9 1.37 5 1.67 Cotton 2 1.58
Russia 7 1.66 8 2.00* Rubber 13 1.21
Singapore 9 1.48 5 1.34 Corn 0 1.65
Taiwan 5 1.50 --- --- Wheat 5 1.19
Thailand 7 1.79 4 1.57 Soybeans 1 2.08*
Israel 1 0.98 2 2.05* Cattle 2 0.72**
Kuwait 1 1.85 --- --- Cocoa 2 0.90
Nigeria 15 1.21 12 1.23 Coffee 0 1.25
Saudi Arabia 2 2.20** --- --- Sugar 4 1.57
South Africa 4 1.43 1 2.01*
Turkey 4 1.47 5 1.36
UAE 2 2.16** --- ---
Australia 7 1.36 3 1.30
Belgium 8 1.85 --- ---
Canada 9 0.99 2 1.64
Czech Republic 5 1.86 1 1.71
Denmark 3 2.02* --- ---
European Union --- --- 0 1.51
France 2 1.54 --- ---
Germany 1 1.58 --- ---
Hungary 5 1.39 --- ---
Italy 11 1.61 --- ---
Japan 7 1.95* 3 1.23
Netherlands 0 1.40 --- ---
Norway 1 2.12** 0 1.43
New Zealand 5 1.00 2 1.45
Poland 6 1.32 3 1.79
Sweden 1 1.93* 0 1.48
Spain 2 1.63 --- ---
Switzerland 2 1.48 2 1.38
UK 2 1.18 4 1.44
US 5 1.57 --- ---
* and ** denote significance at the 95 and 99 percent confidence levels, respectively
/9:D=
-=KMDLK G L@= )GAS= -. /=KL GJ +HLAE9D (9?
125. +* (1/+*
/@AK H9H=J HJ=K=FLK 9F =PL=FKAN= 9F9DQKAK G K@GJL 128. F9LAGF9D SF9F;A9D 9L9
/@= J9FGE O9DC K=;LAGF 9LL=EHLK LG 9FKO=J L@= IM=KLAGF ;9F 9KK=L HJA;=K
:= GJ=;9KL= :9K= GF @AKLGJA;9D HJA;= AFGJE9LAGF 9DGF= 0KAF? 9 @=L=JGK;=9KLA;ALQ 129. ;GFKAKL=FL
L=KL O= ;GF;DM= L@9L SF9F;A9D 9L9 9J= :JG9DQ MFHJ=A;L9:D= OAL@ 9 =O FGL9:D= =P;=HLAGFK
quot;AJKL
=F=J?Q HJA;=K =P@A:AL E=9F 132. GJE9F;= 9J= EGJ= DAC=DQ L@= J=B=;L L@= J9FGE O9DC
2= =PH=;L L@9L HJGDGF?= O=9C H=JGJE9F;=
AF L@=K= E9JC=LK @9K =L=JJ= 9F9DQKL ;GN=J9?= J=KMDLAF? AF J=D9LAN=DQ DGO AFGJE9LAGF9D =Y;A=F;Q
/@AK A=9 AK ;GFKAKL=FL OAL@ ;GFLJ9JA9F AFN=KLE=FL KLJ9L=?A=K O@A;@ K==C LG =9JF HGKALAN= 9:FGJE9D
J=LMJFK AF =HJ=KK= E9JC=LK
)M;@ G L@= =EHAJA;9D DAL=J9LMJ= GF DGF? E=EGJQ ;GF;=JFK L@= J9L= G =;9Q AF L@= 9MLG;GJJ=D9LAGF
G NGD9LADALQ
DL@GM?@ AEHGJL9FL GJ 9HHDA;9LAGFK AF JAKC E9F9?=E=FL GHLAGFK 9F GL@=J =JAN9LAN=
E9JC=LK DGF? E=EGJQ AF NGD9LADALQ G=K FGL HJGNA= AFLMALAGF J=?9JAF? L@= AJ=;LAGF G L@= ;Q;D=
AF J=LMJFK
2@=F $MJKL K=L GML LG A=FLAQ DGF? E=EGJQ H9LL=JFK AF L@= *AD= -AN=J GJ
=P9EHD= @= O9K FGL ;GF;=JF= OAL@ A=FLAQAF? NGD9LADALQ AF K=AE=FL AK;@9J?= :ML L@= HJ=A;LAGF
G TGG HGKALAN= 9F JGM?@L F=?9LAN= ;Q;D=K LG AEHJGN= JAN=J E9F9?=E=FL AF L@= =DL9
2= 9J=
;GF;=JF= OAL@ KAEAD9J IM=KLAGFK AF 9KK=L HJA;AF?
9F O= A=FLAQ DGF? L=JE ;Q;D=K AF 9KK=L HJA;=K
LG =9JF =P;=KK J=LMJFK 2= 9LL=EHL LG 9FKO=J L@AK IM=KLAGF NA9 9 EG=JFAR9LAGF G $MJKLUK L=KL
L@= EGAS= J=K;9D= J9F?= KL9LAKLA; 9F AF SF9F;A9D 9KK=L J=LMJFK O= SF N=JQ DALLD= =NA=F;= G
DGF? E=EGJQ ;Q;D=K
/@= EGKL HJGEAKAF? 9J=9 GJ MJL@=J DGF? E=EGJQ J=K=9J;@ 9HH=9JK LG := L@=
:AD9L=J9D =P;@9F?= G 0
.
GDD9JK OAL@ L@= ;MJJ=F;A=K G (9LAF E=JA;9F =;GFGEA=K
136. 67 9ADDA= -
/
(GF? )=EGJQ ,JG;=KK=K 9F quot;J9;LAGF9D %FL=?J9LAGF AF !;GFGE=LJA;K
$)#! $ 138. 67 9ADDA= -
/
GDD=JKD=N /
9F )ACC=DK=F $
+
quot;J9;LAGF9DDQ %FL=?J9L= #=F=J9DAR=
MLGJ=?J=KKAN= GFALAGF9D $=L=JGKC=9KLA;ALQ $)#! $ 141. -MF /J=FK AF L@= -=D9LAN= ,JA;= G ,JAE9JQ
GEEGALA=K 9F AF L@= /=JEK G /J9= G =N=DGHAF? GMFLJA=K ,$ 143. 67 GDD=JKD=N /
#=F=J9DAR= MLGJ=?J=KKAN= GFALAGF9D $=L=JGKC=9KLA;ALQ $)#! $
145. 67 9DN=L (
quot;AK@=J
9F )9F=D:JGL
)MDLAJ9;L9D )G=D G KK=L -=LMJFK
$+!'
$)#($# ')''$# %'
67 9EH:=DD
4
(G
2
9F )9;'AFD9Q
146. $#$quot;(' $
##! ('
*=O =JK=JQ ,JAF;=LGF 0FAN=JKALQ ,J=KK
67 9F9J=DD9 #
9F ,GDD9J .
'
!Y;A=F;Q G GEEGALQ quot;MLMJ=K 1=;LGJ MLGJ= 148. 67 @GO '
1
,9F )
9F .9C9FG -
+F L@= (GF? 150. /=JE =H=F=F;=
AF .LG;C ,JA;=K !NA=F;= JGE %FL=JF9LAGF9D .LG;C )9JC=LK *+ $ )#(((*
##
# $)#(# 151. 67 GJ9RR9 )
)9DDA9JAK #
*9J=DDA
.=9J;@AF? GJ J9;L9D KLJM;LMJ= AF 9?JA;MDLMJ9D
MLMJ=K E9JC=LK
$)#! $
)()' ('
X
67 9;GJG?F9 )
)
)[DD=J 0
*9?D=J -
+DK=F -
9F ,A;L=L +
1
#=G?J9H@A;9D )G=D GJ L@= 9ADQ 9F 2==CDQ .=9KGF9D 1GD9LADALQ AF L@= quot;GJ=A?F !P;@9F?=
)9JC=L $)#! $ #(#($#! $#- #
## 152. 67 A;C=Q
9F quot;MDD=J 2
MLGJ=?J=KKAN= /AE= .=JA=K OAL@ 9 0FAL -GGL $)#!
$ ( quot;# (('(! ''$($#
153. 67 AF? 5
#J9F?=J
2
9F !F?D= -
quot;
(GF? )=EGJQ ,JGH=JLQ G .LG;C
-=LMJFK 9F 9 *=O )G=D $)#! $ 155. 67 !F?D= -
quot;
MLGJ=?J=KKAN= GFALAGF9D $=L=JGK;=9KLA;ALQ OAL@ !KLAE9L=K G L@= 19JA 158. 67 #=E9F $
)=9F -=N=JKAGF N=JKMK -9FGE 29DC AF +AD 9F *9LMJ9D #9K ,JA;=K
*#' # (quot;(!
## AJC@9MK=J GKLGF
67 $MJKL $
!
(GF? 163. ,#
'(($#'
67 (AM
4
9F $=
19JA9F;= 164. -9LAG /=KL G -9FGE 29DCK AF quot;GJ=A?F !P;@9F?=
-9L=K $)#! $
##
165. 67 (G
2
(GF? /=JE )=EGJQ AF .LG;C )9JC=L ,JA;=K 167. 67 (G
2
9F )9;'AFD9Q
.LG;C )9JC=L ,JA;=K G *GL quot;GDDGO -9FGE 29DCK
!NA=F;= JGE 9 .AEHD= .H=;AS;9LAGF /=KL *+ $
##! ()' 168. 67 (G
2
9F )9;'AFD9Q
/@= .AR= 9F ,GO=J G L@= 19JA9F;= -9LAG /=KL AF quot;AFAL=
.9EHD=K )GFL= 9JDG %FN=KLA?9LAGF $)#! $ 170. 67 )9DCA=D
#
#$quot; ! $+# !! (( *=O 4GJC 2
2
*GJLGF 9F
GEH9FQ
67 )9F=D:JGL
/@= 19JA9LAGF G =JL9AF .H=;MD9LAN= ,JA;=K $)#! $ )'#'' 171. 67 )9F=D:JGL
2@=F 9F ,JA;= := J:ALJ9?= !Y;A=FLDQ (AEAL LG L@= 19DAALQ
G L@= -9FGE 29DC 9F )9JLAF?9D= )G=DK *+ $ 173. 67 )9F=D:JGL
.L9LAKLA;9D )=L@GGDG?Q GJ *GFH=JAGA; Q;D=K quot;JGE L@= GN9JA9F;=
LG -. F9DQKAK ##!' $ 175. 67 )MDDA?9F -
quot;
quot;J9;L9D F9DQKAK G quot;GJ=A?F !P;@9F?= )9JC=LK #(#($#! *#'
# 177. 67 *=O=Q 2
'
9F 2=KL '
.AEHD= ,GKALAN= =SFAL= $=L=JGK;=9KLA;ALQ 9F
MLG;GJJ=D9LAGF GFKAKL=FL GN9JA9F;= )9LJAP 179. 67 -G:=JLK $
.L9LAKLA;9D N=JKMK DAFA;9D ,J=A;LAGF G L@= .LG;C )9JC=L
#( $
' # )(- ' 0FAN=JKALQ G @A;9?G
67 .@9JH= 2
quot;
/@= JAL@E=LA; G ;LAN= )9F9?=E=FL
##! #!-'(' $)#!
181. ,,quot;*!4 0
,,quot;*!4 -105 *! quot;/
9ADQ =IMALQ AF=P 9L9 GJ =9;@ ;GMFLJQ O=J= GOFDG9= JGE DGGE:=J?
2= GOFDG9= L@=
S=DK VHP8D9KLW D9KL HJA;= 9F V=IQ8D9KL8HK8?JGKKW ANA=FK H=J K@9J= LG ;J=9L= 9 LGL9D J=LMJF
K=JA=K 9;;GJAF? LG L@= MF9E=FL9D J=D9LAGFK@AH
2= AFALA9DAR= L@= SJKL G:K=JN9LAGF G L@= LGL9D J=LMJF AF=P LG =IM9D L@= :9KA; AF=P D=N=D
!IM9LAGF O9K L@=F MK= LG ;GFKLJM;L L@= LGL9D J=LMJF AF=P K=JA=K 9K L@= KME G L@= ANA=F
9F ;9HAL9D ?9AFK QA=DK J=KH=;LAN=DQ O@=J= 9J= ANA=FK H=J K@9J=
=;9MK= GMJ DGGE:=J?
GOFDG9 HJG?J9E GFDQ HJGNA= LOG =;AE9D HD9;=K 9F AFA;=K 9J= ;9D;MD9L= OAL@ 9F 9J:ALJ9JQ
:9K= A
=
LAE= K=JA=K G ;GMFLJA=K =PH=JA=F;AF? =PLJ9GJAF9JQ ?JGOL@ GJ ;JAK=K O=J=
LJMF;9L= LG 9NGA JGMFAF? =JJGJK
quot;GJ =P9EHD= 9L L@= :=?AFFAF? G L@= 9L9K=L KGE= ;GMFLJA=K
DAC= ,=JM @9 AF=P N9DM=K 9L GJ F=9J V
W
-=LMJFK ;9D;MD9L= GF KM;@ DGO HJA;= D=N=DK O=J=
AF@=J=FLDQ MF=SF= GJ =PLJ=E=DQ NGD9LAD= 9F L@MK FGL J=HJ=K=FL9LAN= G L@= @AKLGJA;9D J=;GJ
K 9
JMD= 183. L@ME: O= ;GJJ=;L= GJ L@AK :Q =DAEAF9LAF? L@= SJKL quot; G:K=JN9LAGFK O@=J= D=9NAF?
9 J=KAM9D JGMFAF? =JJGJ FG ?J=9L=J L@9F
GMFLJQ /A;C=J =K;JAHLAGF .9EHD= EEQQ
0* )quot;.
- J?=FLAF9 )- )=JN9D %F=P 185. ( @AD= %#, %,. .LG;C %F=P 188. ,! ,=JM %#1( ,=JM (AE9 #=F=J9D %F=P 192. GMFLJQ /A;C=J =K;JAHLAGF .9EHD= EEQQ
% %FGF=KA9 % 9C9JL9 .LG;C %F=P 193. %* %FA9 .!*.!3 .=FK=P .LG;C %F=P 204. '2 'MO9AL '2.!% 3 'MO9AL .! 0FO=A?@= %F=P 211. 0 0! quot;)#% M:9A #=F=J9D .LG;C %F=P 215. 9F99 .,/.3 . , /GJGFLG .LG;C %F=P 217. * =FE9JC '3 +)3 GH=F@9?=F 222. 9H9F /,3 /+,%3 .LG;C %F=P 227. GMFLJQ /A;C=J =K;JAHLAGF .9EHD= EEQQ
,( ,GD9F 2%# 2.! 2%# %F=P 228. . .O==F .2.)quot;quot;- Z9JKN9JD=F .LG;C %F=P 234. ,,quot;*!4 +))+!0quot;/
/@= ;GEEGALQ 9L9 9J= 9ADQ ;DGKAF? HJA;=K AF L@= KHGL E9JC=L
-M::=J HJA;= 9L9 AK JGE
DGGE:=J? 9F 9DD GL@=J ;GEEGALA=K 9J= JGE L@= GEEGALQ -=K=9J;@ MJ=9M quot;AF9D )9JC=LK
9L9:9K=
.GMJ;=
GEEGALQ =K;JAHLAGF .9EHD= EEQQ
*quot;.$5
JM= +AD *4)!3 2=KL /=P9K %FL=JE=A9L= ;JM= GAD 235. MK@AF? +'
*9LMJ9D #9K *4)!3 *9LMJ9D ?9K $=FJQ $M: 237. #9KGDAF= *4)!3 #9KGDAF= MFD=9= J=?MD9J 240. GHH=J *4)!3+)!3 GHH=J @A?@ ?J9= K;J9H OAJ= 246. /AF 0.#. /AF KLJ9A?@LK ;GEHGKAL= 247. 5AF; )) 5AF; HJAE= O=KL=JF GE=KLA; 248. *4)!3 AK L@= *=O 4GJC )=J;9FLAD= !P;@9F?= +)!3 AK L@= GEEGALQ !P;@9F?= ()! AK L@= (GFGF )=L9D
!P;@9F?= 0.#. AK L@= 0
.
#=GDG?A;9D .MJN=Q )) AK L@= E=JA;9F )=L9D )9JC=L 0. AK L@= 0
.
=H9JLE=FL
G ?JA;MDLMJ= )- AK L@= )9D9QKA9F -M::=J G9J +/ AK L@= @A;9?G G9J G /J9= '+/ AK L@= '9FK9K
ALQ G9J G /J9= )! AK L@= @A;9?G )=J;9FLAD= !P;@9F?= 9F *4+/ AK L@= *=O 4GJC G9J G /J9=
249. GEEGALQ .GMJ;= =K;JAHLAGF .9EHD= EEQQ
$. 1(01.quot;
9LLD= )! (AN= ;9LLD= ;@GA;= 9N=J9?= 251. GZ== 0. GZ== J9RADA9F 256. .M?9J *4+/ .M?9J OGJD J9O 257. 2@=9L '+/ 2@=9L @9J OAFL=J 258. ,,quot;*!4 +.quot;$* 4 %*$quot; 0quot;/
*GEAF9D :AD9L=J9D =P;@9F?= J9L=K 9J= AF MFALK G GJ=A?F ;MJJ=F;Q H=J 0
.
GDD9J
/@= 9L9
GJ MKLJ9DA9 J9RAD 9F99 =FE9JC L@= !MJGH=9F )GF=L9JQ 0FAGF %FA9 9H9F )9D9QKA9
)=PA;G *=O 5=9D9F *GJO9Q .AF?9HGJ= .GML@ JA;9 .GML@ 'GJ=9 .O==F .OALR=JD9F /9AO9F
/@9AD9F 9F L@= 0FAL= 'AF?GE 9J= L@= ,) J9L=K JGE L@= quot;==J9D -=K=JN= 9FC G *=O 4GJC
DD GL@=J =P;@9F?= J9L= 9L9 9J= ;DGKAF? HJA;=K JGE DGGE:=J?
GMFLJA=K ;MJJ=FLDQ =EHDGQAF? 9
SP= GJ H=??= =P;@9F?= J9L= J=?AE= 9J= A?FGJ= AF L@AK KLMQ :=;9MK= ;9D;MD9LAGFK G L=EHGJ9D
=H=F=F;= 9J= E=9FAF?D=KK MF=J SP= HJA;=K
MJJ=F;Q ;D9KKAS;9LAGFK 9J= 9K =SF= AF L@=
%)quot; FFM9D -=HGJL GF !P;@9F?= JJ9F?=E=FLK 9F !P;@9F?= -=KLJA;LAGFK
GMFLJQ MJJ=F;Q D9KKAS;9LAGF .9EHD= EEQQ
0* )quot;.
- J?=FLAF9 ,=KG )9F9?= quot;DG9L 259. 5 J9RAD -=9D %F=H=F=FL quot;DG9L 260. ( @AD= ,=KG %F=H=F=FL quot;DG9L 263. ,! ,=JM *M=NG .GD )9F9?= quot;DG9L 264. +F L@= )9JC=LK quot;GJ=A?F !P;@9F?= K=;LAGF G L@= quot;-*4 O=:KAL= @LLHOOO
FQ
J:
GJ?E9JC=LKPJ9L=KFGGF
;E
265. GMFLJQ MJJ=F;Q D9KKAS;9LAGF .9EHD= EEQQ
)quot;.$*$ /
% %FGF=KA9 -MHA9@ )9F9?= quot;DG9L 266. %* %FA9 -MH== )9F9?= quot;DG9L 278. 9F99 GDD9J %F=H=F=FL quot;DG9L 281. 9H9F 4=F %F=H=F=FL quot;DG9L 285. . .O==F 'JGF9 %F=H=F=FL quot;DG9L 288. MKLJA9 =D?AME quot;AFD9F quot;J9F;= #=JE9FQ #J==;= %J=D9F %L9DQ (MP=E:GMJ? L@= *=L@=JD9FK ,GJLM?9D 9F
.H9AF H9JLA;AH9L= AF L@= !MJGH=9F )GF=L9JQ 0FAGF
/@= !MJGH=9F =FLJ9D 9FC E9Q AFL=JN=F= LG KEGGL@ TM;LM9LAGFK
AF L@= =MJG =P;@9F?= J9L=
289. ,,quot;*!4 1)).5 00/0 /
,,quot;*!4 -105 *! quot;/
Sample Standard Excess Jarque-Bera
Size Mean Deviation Skewness Kurtosis Statistic
Country
Argentina 1940 0.051 2.18 0.17 5.41 2377.82**
Brazil 2879 0.120 2.01 0.61 16.31 32072.80**
Chile 4358 0.069 0.78 0.16 3.82 2666.04**
Colombia 1528 0.167 1.51 -0.06 14.38 13165.80**
Mexico 4644 0.106 1.57 -0.09 5.68 6253.92**
Peru 3866 0.127 1.46 0.22 6.70 7259.93**
Venezuela 3224 0.133 1.82 -0.13 13.38 24045.15**
China 3121 0.060 1.84 0.55 21.33 59297.77**
Hong Kong 9042 0.057 1.85 -0.37 12.39 58083.83**
Indonesia 5795 0.059 1.57 4.00 97.61 2316205.03**
India 5639 0.051 1.59 -0.06 4.61 5005.44**
Korea 6620 0.043 1.62 -0.16 4.59 5847.42**
Malaysia 7316 0.036 1.40 -0.61 32.44 321301.57**
Philippines 5079 0.027 1.67 0.10 9.49 19048.88**
Russia 2995 0.078 2.70 -0.42 6.50 5357.90**
Singapore 7951 0.036 1.21 -1.32 34.04 386172.07**
Taiwan 8165 0.046 1.76 -0.23 3.77 4903.65**
Thailand 4803 0.029 1.70 0.02 6.23 7773.66**
Israel 2301 0.063 1.74 -0.17 3.70 1325.61**
Kuwait 736 0.228 1.27 -0.50 5.97 1122.54**
Nigeria 2186 0.081 0.86 -0.98 15.52 22303.69**
Saudi Arabia 2025 0.063 1.62 -0.94 15.32 20113.67**
South Africa 3054 0.050 1.20 -0.74 7.86 8144.32**
Turkey 4403 0.163 2.93 0.02 3.48 2220.95**
UAE 627 0.252 2.31 0.14 3.94 408.59**
Australia 6978 0.036 0.95 -4.53 127.01 4714368.66**
Belgium 4679 0.030 0.89 0.05 7.11 9847.77**
Canada 7602 0.035 0.85 -0.99 13.53 59242.83**
Czech Republic 3218 0.014 1.21 -0.22 3.09 1307.13**
Denmark 2975 0.043 0.94 -0.51 2.55 933.22**
France 4234 0.030 1.14 -0.21 3.45 2130.20**
Germany 4965 0.038 1.30 -0.56 6.98 10339.31**
Hungary 4163 0.074 1.60 -0.79 13.69 32927.86**
Italy 8545 0.027 1.26 -0.46 5.22 10001.44**
Japan 9027 0.017 1.04 -0.52 11.62 51222.52**
Netherlands 6275 0.035 1.28 -0.32 8.22 17771.00**
Norway 2981 0.037 1.19 -0.53 3.38 1560.75**
New Zealand 3902 0.041 0.80 0.00 8.70 12299.44**
Poland 3348 0.053 1.90 -0.17 7.36 7572.63**
Sweden 1995 -0.004 1.41 -0.11 2.42 490.24**
Spain 3641 0.045 1.17 -0.36 3.22 1649.38**
Switzerland 4824 0.029 1.13 -0.52 7.03 10142.03**
UK 5864 0.033 0.96 -0.81 11.71 34140.18**
US 9317 0.040 0.99 -1.43 34.83 474220.14**
* and ** represent significance at the 95 and 99 percent confidence levels, respectively
290. ,,quot;*!4 +))+!0quot;/
Sample Standard Excess Jarque-Bera
Size Mean Deviation Skewness Kurtosis Statistic
Commodity
Crude Oil 5630 0.016 2.45 -1.22 18.93 85435.26**
Gasoline 1086 0.090 2.96 -0.15 7.08 2271.70**
Natural Gas 3405 0.080 4.89 0.70 24.74 87144.91**
Heating Oil 1086 0.114 2.33 0.26 1.06 63.64**
Copper 1086 0.109 1.99 -0.50 3.10 480.71**
Aluminum 1114 0.074 1.45 -0.25 2.11 219.03**
Lead 1087 0.109 2.03 -0.37 5.89 1597.30**
Nickel 1114 0.117 2.65 -0.35 3.32 535.69**
Tin 1097 0.111 1.69 -0.40 3.79 685.51**
Zinc 1097 0.079 2.00 -0.50 2.60 356.57**
Gold 1166 0.078 1.11 -0.57 2.58 385.74**
Platinum 1097 0.086 1.25 -0.02 5.48 1372.32**
Silver 1164 0.104 2.04 -1.41 9.79 5032.06**
Cotton 1087 0.017 1.73 0.29 11.91 6433.98**
Rubber 1548 0.088 0.87 -0.28 2.48 416.12**
Corn 1537 0.059 1.76 0.15 1.23 103.49**
Wheat 1092 0.088 2.28 -0.49 64.15 187269.43**
Soybeans 1090 0.057 1.75 -0.82 4.35 983.71**
Cattle 1108 0.022 1.43 0.24 3.64 622.91**
Cocoa 1086 0.044 1.73 -0.24 3.39 530.14**
Coffee 1085 0.084 1.98 0.30 4.31 857.82**
Sugar 1086 0.071 1.91 -0.13 2.27 236.46**
* and ** represent significance at the 95 and 99 percent confidence levels, respectively
291. ,,quot;*!4 +.quot;$* 4 %*$quot; 0quot;/
Sample Standard Excess Jarque-Bera
Size Mean Deviation Skewness Kurtosis Statistic
Country
1544 0.030 1.15 3.18 102.82 682741.37**
Argentina
2218 -0.004 1.07 0.54 13.98 18173.92**
Brazil
2175 -0.007 0.54 0.07 2.14 414.97**
Chile
2163 -0.003 0.53 0.06 6.49 3803.08**
Colombia
2808 0.010 0.51 0.87 8.19 8195.30**
Mexico
543 0.049 0.30 -0.01 8.73 1726.16**
Peru
2695 0.036 1.85 1.71 36.17 148223.94**
Indonesia
8477 0.017 0.47 4.71 129.04 5912848.31**
India
6427 0.003 0.58 3.45 158.07 6704119.60**
Korea
638 -0.027 0.25 -0.05 3.24 279.5911**
Malaysia
2561 0.001 0.56 -7.75 218.71 5130106.64**
Philippines
2355 0.002 0.37 1.98 75.65 563129.97**
Russia
6571 -0.008 0.33 -0.80 15.94 70261.65**
Singapore
2587 -0.002 0.73 -0.51 15.62 26420.83**
Thailand
3819 0.010 0.43 1.47 25.24 102758.53**
Israel
2263 0.011 1.47 0.27 16.27 24986.60**
Nigeria
8933 0.028 0.83 1.93 53.89 1086480.52**
South Africa
1832 0.018 1.24 1.43 23.55 42949.21**
Turkey
8015 0.002 0.62 4.62 128.27 5523084.78**
Australia
8977 -0.001 0.32 -0.01 3.82 5445.18**
Canada
3122 -0.016 0.69 0.53 8.09 8663.15**
Czech Republic
2226 -0.013 0.58 -0.02 0.85 67.46**
European Union
8963 -0.013 0.62 -0.41 5.94 13425.10**
Japan
8967 -0.004 0.59 0.36 7.98 24018.13**
Norway
8949 0.002 0.67 2.72 66.20 1644907.54**
New Zealand
3049 -0.006 0.64 0.28 2.82 1049.42**
Poland
8967 -0.002 0.59 1.02 19.68 146297.76**
Sweden
8969 -0.016 0.71 0.01 3.77 5317.29**
Switzerland
8969 0.001 0.57 0.14 4.20 6608.25**
UK
* and ** represent significance at the 95 and 99 percent confidence levels, respectively
