• No results found

From market micro structure to macro fundamentals : is there predictability in the dollar Deutsche Mark exchange rate?

N/A
N/A
Protected

Academic year: 2020

Share "From market micro structure to macro fundamentals : is there predictability in the dollar Deutsche Mark exchange rate?"

Copied!
52
0
0

Loading.... (view fulltext now)

Full text

(1)

WORKING PAPERS SERIES

WP99-12

(2)

!"#$ %&"'() %*+"#,-)".+)."( )#

%&+"# !./0&$(/)&123

42 56("( 7"(0*+)&8*1*)9 */ )6( :#11&"

:(.)2+6( %&"' ;<+6&/=( >&)(?

!"#$%& '())*+, +,- .+%/ 0+)*",

1(,+,2(+) 32","*$&%(24 !$4$+%25 6$,&%$7

6(&8 9,(:$%4(&8 ;<4(,$44 025"")

=",-",

!"#$ %&'&()&*!+++

(3)

!

"#$%&'()$*&#

,$-. /0/&* -. '12'&*2&3 4-#$ #$& 3&#&'#-12 15 06#1*&7*&..-8& .#*6'#6*& 1* #&(/1*09 3&/&23&2'& 023 $&2'& /*&3-'#0)-9-#: -2 $-7$ 5*&;6&2': 51*&-72 &<'$027& *0#&. 3&#&*(-2&3 12 #$& %=>???@> &9&'#*12-' #*03-27 .:.#&(A B& 0*& 50'&3 4-#$ #41 -((&3-0#& /*1)9&(.C #$& '$1-'& 15 .#0#-.#-'09 #&'$2-;6& 51* #$& 0209:.-. 15 0 8&*: 90*7& .0(/9& 15 -**&7690*9: ./0'&3 30#0 023 .&'1239: #$& ;6&.#-12 15 4$-'$ &'121(-' #$&1*: #1 '099 6/12 #1 (13&9 #$& 30#0A

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email protected] ./*&03 -. 91.# 4$&2 077*&70#&3 #1 &8&2 0 30-9: )0.-. 023 $&2'& -. 9-D&9: #1 )& -**&9&802# 4$&2 0##&(/#-27 #1 (13&9 #$& 9127 *62 &;6-9-)*-6( 8096& 15 #$& &<'$027& *0#&A I-(-90*9: 2&4 -251*(0#-12 12 (0'*1 56230(&2#09. -. .-(/9: 21# 080-90)9& 12 #$& .&'123 ): .&'123 #-(& .'09& *&9&802# #1 (13&99-27 #*02.0'#-12. 30#0A J14&8&* )1#$ 0//*10'$&. /6*/1*# #1 (13&9 #$& ()*$ 623&*9:-27 30#0 023 $&2'& %KLA B& 0*& 50'&3 4-#$ 0 56230(&2#09 -..6& 15 '12.-.#&2': 023 0# .1(& .#07& $08& #1 0.D -5 #$&*& -. 02: -2#&99&'#6099: '1$&*&2# .(11#$ #*02.-#-12 )&#4&&2 #$& #41 (13&99-27 0//*10'$&.A B$-9& 4& (0: )& 4-99-27 #1 0..6(& #$0# #$&*& -.E -2 /*-2'-/9&E 0 .-279& 30#0 7&2&*0#-12 /*1'&.. 51* #$& %1990*@ %(0*D &<'$027& *0#& -# .&&(. #$0# #$&*& 4-99 21# )& 0 .-279& &'121(&#*-' (13&9 1* .-279& .#0#-.#-'09 *&/*&.&2#0#-12 15 #$0#+,- #$0# 4& 41693 402# #1 6.& 51* 099 /6*/1.&.A

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

=0*D&# (-'*1 .#*6'#6*& #$&1*: 31&. 21# -(/9: *0231( #*03-27 023 (0*D&# &T'-&2': 31&. 21# -(/9: *0231(2&.. -2 #$& %$)0"($! &<'$027& *0#& 629&.. #$& &</&'#&3 &;6-9-)*-6( &<'$027& *0#& -. '12.#02# Q.&& 51*

(4)

-2.#02'& =6..0 Q!++?SS .1 7-8&2 .:.#&(0#-' 023 4&99 &.#0)-9.$&3 -2'&2@ #-8&. 51* (0*D&# #*03&*. 023 .:.#&(0#-' 8-&4. 0. #1 4$&*& #$& &;6-9-)*-6( &<'$027& *0#& 9-&.E *&90#-8& #1 #$& '6**&2# 8096&E -# -. 21# 62*&0.120)9& #1 &</&'# #$0# 4& .$1693 U23 0 3&7*&& 15 /*&3-'#0)-9-#: -2 #$& 8&*: .$1*# *623"4$&0 .6-#0)9& '123-#-12-27 -251*(0#-12 .&# A B$-9& #*03&*. '9&0*9: $08& 3-M&*&2# 1)P&'#-8&. 0# 3-M&*&2# #-(&. #$&: 4-99 #*03& -2 3-M&*&2# (0*D&#. .6'$ 0. #$& 51*40*3 (0*D&# -5 #$&: 0*& &</9-'-#9: #0D-27 0 9127 #&*( /1.-#-12 -2 4$-'$ 56230(&2#09 -251*(0#-12 -. 9-D&9: #1 )& (1*& *&9@ &802# #$02 #$& ./1# (0*D&# .6'$ 0. %=>???@>A I1 4& (-7$# &</&'# #1 .&& 9-##9& 3-*&'# -(/0'# 15 56230(&2#09. -2 %=>???@> 30#0E &<'&/# 0# #-(&. 15 (0P1* 022162'&(&2#. 4$-'$ 41693 09914 #$& (0*D&# #1 03P6.# -#O. 8-&4 15 #$& &;6-9-)*-6( 62#-9 #$& 2&<# 2&4. 12 56230(&2#09. 0**-8&. A V2& 40: -2 4$-'$ 4& (-7$# .&& 8-&4. 15 #$& &;6-9-)*-6( *0#& )&-27 &<@ /*&..&3 -2 #$& #*02.0'#-12. 30#0 .&# '1693 )& -2 #$& .$0/&. 023 /1.-#-12. 15 #$& )-3 023 1M&* '6*8&. 0. #*03&*. #0D& 9-(-# 1*3&* /1.-#-12. 040: 5*1( #$& '6**&2# (0*D&# /*-'& -2 02#-'-/0#-12 15 #$& (0*D&# (18-27 #1@ 40*3. #$&-* 142 F&;6-9-)*-6(G 8-&4A B$&#$&* .6'$ )&$08-16* -. 3*-8&2 ): 56230(&2#09. 1* (1#-80#&3 ): 3-*&'# #*03-27 '12'&*2. 41693 .&&( #1 )& 3-T'69# -5 21# -(/1..-)9& #1 3&#&*(-2& )6# '9&0*9: 911D-27 0# #$& 40: #$& )-3 023 1M&* '6*8&. (18& 0*1623 (0P1* 022162'&(&2#. 4-99 )& -(/1*#02#A

K-8&2 #$&.& 0*76(&2#. *&70*3-27 #$& (-<#6*& 15 &'121(-' 51*'&. #$0# 0*& 9-D&9: #1 )& 0# 41*D -2 #$& (0*D&# 4& $08& 3&'-3&3 #1 031/# #$& .-(@

(5)

/9&.# 0#$&1*&#-'09 (13&99-27 .#*0#&7: 0# #$-. .#07& 4$-'$ -. #1 .-(/9: #1 -28&.#-70#& -5 #$&*& -. 02: 06#1*&7*&..-8& 3&/&23&2'& -2 #$& %=>???@> 30#0 &-#$&* 5*1( 4-#$-2 #$& #*02.0'#&3 /*-'&. #$&(.&98&. 1* (1*& 7&2@ &*099: 7-8&2 1#$&* (-'*1 (0*D&# -251*(0#-12A ,$-. 9&03. 6. #1 16* .&'@ 123 -((&3-0#& '12'&*2 4$-'$ -. 4$0# .#0#.#-'09 #&'$2-;6&. .$1693 4& &(/91: #1 '0/#6*& #&(/1*09 3&/&23&2'& -2 $-7$ 5*&;6&2': -**&7690*9: ./0'&3 #*02.0'#-12. 30#0A

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

/&*-13A

,-(& ! \Q"S

[0( #1 R0( @?A?W WAR!

R0( #1 !?0( @?A?> WA]!

!?0( #1 !>/( ?A?> [AR!

!>/( #1 > /( @?A?" "A!R

>/( #1 ]/( ?A?? WA?W

]/( #1 [/( @?A?] [A]>

[/( #1 [0( @?A!W >^?A"!

,0)9& !_ `-*.# 1*3&* 06#1'1**&90#-12 '1&T'-&2#E %023L Q!+++S

H2 4$0# 519914. 4& &</91*& #$-. '12'96.-12 56*#$&* ): '12.-3&*-27 #$& 3-T'69#-&. -2 6.-27 #$& 06#1'1**&90#-12 562'#-12 4-#$ -**&7690* 30#0 023 .677&.# #$& 6.& 15 3-M&*&2# #&'$2-;6&.E 21#0)9: #$& 4)%"63%)* -2 /*&5&*&2'& #1 #$& 06#1'1**&90#-12 562'#-12 4$&2 '12.-3&*-27 -**&7690* 30#0A

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

(6)

.&'123 1*3&* .#0#-120*: /*1'&..&.A B& #$&2 *&8-&4 .&8&*09 .#0#-.#-'09 3-T'69#-&. 4-#$ #$& 6.& 15 #$& 06#1'1**&90#-12 562'#-12 12 #&(/1*099: 077*&70#&3 30#0 )&51*& #6*2-27 #1 0//9: #$& 80*-17*0( 023 '*1.. 80*-@ 17*0( #1 #$& %=>???@> 30#0A `-2099: 4& #6*2 #1 '12.-3&* #$& -(/0'# 15 (0'*1 2&4. 12 #$& (-'*1 (0*D&# '$0*0'#&*-.#-'. 023 #$& *&#6*2 /*1@ '&.. 12 #$& &<'$027& *0#& -#.&95 #1 -28&.#-70#& F*&7-(&. 15 /*&3-'#0)-9-#:G 4-#$-2 #$& /&*-13 0. 3-.'6..&3 51* -2.#02'& ): K60*30 023 I09(12Q!++^SE J-99(02Q!++RS 023 %0''1 023 I0#'$&99 Q!++RSE 0(127.# 1#$&*.A H2 02 0/@ /&23-< 4& &</91*& #$& 6.& 15 D*-7-27 Q#$& #&*( 6.&3 -2 #$& 7&1.#0#-.#-'09 9-#&*0#6*& 51* a1/#-(09 /*&3-'#-12OS 12 .-(690#&3 023 *&09 .&*-&.A

+

"#$%*#,*) -$.$*&#.%*$/ .#' "#$%*#,*) 0.#'&1 2(#)3

$*&#,

=0#$&*12Q!+^WS -2#*136'&3 #$& '12'&/#. 15 "&'%"&("5 (')'"6&)%"'8 023 "&'%"&("5 %)&!6* ./&5'"6&( -2 #$& '12#&<# 15 #$& .#0#-.#-'09 0209:.-. 023 .6).&;6&2# /*&3-'#-12 15 (-2&*09 3&/1.-#. 4$&*& 212@.#0#-120*-#: 0/@ /&0*. #1 )& 0. '1((12/90'& 0. -# -. -2 &'121(-'.A I/0#-09 .#0#-.#-'. #*&0#. 1).&*80#-12. 0. 0*-.-27 5*1( .1(& 7&2&*09 '12#-2616. (69#-@3-(&2.-1209 '11*3-20#& .:.#&( 023 4$-9& 4& 0*& 21# -((&3-0#&9: -2#&*&.#&3 -2 #$& b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`-2099: #$& .#0#-.#-'09 /*1/&*#-&. #$& 80*-17*0( -2 #&*(. 15 U2-#& .0(/9& )-0. (0: )& .6).#02#-099: )&##&*

(7)

#$02 #$1.& 15 #$& 06#1'1**&90#-12 562'#-12A `1* 16* /6*/1.&. #$&2 #$& 80*-17*0( &20)9&. 6. #1 .-(690#02&16.9: '12.-3&* #$& 3:20(-' 3&/&2@ 3&2'& -2 #$& .&*-&. 7-8&2 0 *027& 15 .#0#-120*: 023 212@.#0#-120*: %KL. 51* 4$-'$ #$& 0'5 (0: 21# 51*(099: 3&U2&3A

B& .#0*# ): '12.-3&*-27 0 7&2&*09 .#1'$0.#-' /*1'&..

!"!#" ##"$#

3&U2&3 -2 $ 0 *0231( .&# -2 c6'9-3&02 $ % ,$& 0)-9-#: #1 3*04 1).&*@ 80#-12. 5*1( 0 & 3-(&2.-1209 ./0'& -. 21# 12& #$0# 4& 2&&3 #1 &</91-# )6# 4& .$099 6.& #$& 50'# #$0# #$& 30#0 -. -23&<&3 12 #$& *&09 9-2& 0. 1/@ /1.&3 #1 0 .&# 15 *&7690*9: ./0'&3 -2#&7&*.A B& 4-99 09.1 *&5&* #1 -**&7690* ./0'&3 30#0 0. )&-27 1).&*8&3 0# /1-2#. !' #($ %) %%%%%) *# *0#$&* #$02 #$& *&7690* ./0'-27 15 1).&*80#-12. 0#!' $(#($ %) %%%%%%) *#%

,$& 4)%"63%)* -. 3&U2&3 0. #$& 80*-02'& 15 #$& 3-M&*&2'& )&#4&&2 #41 8096&. 15 #$& .#1'$0.#-' /*1'&.. .&/0*0#&3 ): .1(& /1#&2#-099: 212@ -2#&7&* 8096&3 3-.#02'& +A I6'$ -2'*&(&2# /*1'&..&. $08& )&&2 .#63@ -&3 51* (02: :&0*.E .&& d19(171*18Q!+]!SE e0791(Q""SE K&9O5023 023 f-9&2D-2 Q!+[]SA =1*& 50(-9-0* #1 &'121(&#*-'-02. 4-99 )& B$-##9& Q !+RWS 023 #$& '90..-' f12 g&6(02 Z0#-1 Q!+]!S 0/0*# 5*1( #$& *&'&2# 9-#&*0#6*& 12 #$& 6.& 15 f0*-02'& Z0#-1 .#0#-.#-'. 51* 3&#&*(-2-27 #$& /*&.@ &2'& 15 0 62-# *11# 023 -23&/&23&2'& -2 #-(& .&*-&. 30#0E .&& h1'$*02& Q!+RRSEL1#&*)0 023 I6((&*. Q!+RRSE %-&)193 Q!+R+SE Z-'$0*3.12 023 I#1'D Q!+R+SE i1 023 ='d-29&:Q!+RRSA g12& 15 #$-. (1*& *&'&2# 9-#&*0@ #6*& $0. -# .&&(. *&09-.&3 #$& 3&&/&* /1#&2#-09 1M&*&3 ): #$& 80*-17*0( -2 #$& 0209:.-. 15 -**&7690*9: ./0'&3 30#0 023 #$& /14&* 15 #$& 623&*9:-27 '12'&/#. 15 -2#*-2.-' .#0#-120*-#: 023 -2#*-2.-' *0231( 562'#-12.A

j /*1'&.. -. 3&U2&3 0. )&-27"&'%"&("5)008 (')'"6&)%8 -5

,&"!#'+"%"!#"( $ ) Q!S

023

- ./&"!#'+"%"!#"( $ *0!+" Q>S

H2 1#$&* 41*3. #$& 80*-02'& 15 #$& + -2'*&(&2# -. .-(/9: 0 562'#-12 15 + 023 21# #$& #-(& 1*-7-2A ,$& 562'#-12 0!+" -. D2142 0. #$& ($*"7 4)%"63%)*A ,$& -(/1*#02# /*1/&*#-&. 15 02 -2#*-2.-' .#0#-120*: /*1'&.. 0*& 3&U2&3 -2 #&*(. 15 #$& "&5%$*$&'(= !"!#'+"%"!#""% h1(/0*-27 #$-. 3&U2-#-12 4-#$ ($56&! 6%!$% (')'"6&)%"'8 4& 2&&3 #1 '12.-3&* )1#$ (&02 023 80*-02'& .#0#-120*-#:A

,$& /*1'&.. -.*$)& (')'"6&)%8= -5

,&"!#"( $ 1 QWS

(8)

0234)%")&5$ (')'"6&)%8E -5

2./&"!#"( $3 $4!)" Q]S

-. 4&99 3&U2&3 023 '12.#02# 023

562&"!#") "!#'+"( $4!+" Q"S

-. 129: 0 562'#-12 15 #$& 907 -2#&*809A H2 #$-. 90##&* '0.& 4& $08&

2./&"!#'+"%"!#"( $2./&"!#'+"( '2./&"!#"(%*562&"!#'+""!#"(

j..6(-27 .&'123 1*3&* .#0#-120*-#: 023 7-8&2

4!)" $2./&"!#'+"( $ 2./&"!#"( $3

4& (0: 4*-#&

0!+" $ 4!)"%4!+"

.$14-27 #$0# 099 .&'123 1*3&* .#0#-120*: /*1'&..&. 0*& -2#*-2.-'099: .#0@ #-120*:A g1#-'& #$0# 6&08 -2 #$& '0.& 15 .&'123 1*3&* .#0#-120*-#: 4-99 #$& 06#1'1**&90#-12 562'#-12 )& 4&99 3&U2&3 023 #$&*& 4-99 )& 0 .-(/9& *&90#-12 4-#$ #$& .'09&3 .&(-80*-17*0(

!!+" $ 4!+"

4!)" $ %%

0!+"

4!)"

,$& '128&*.& -. 21# #*6& $14&8&* .-2'& 0. h*&..-&Q!++RS .$14.E -5

!7 #' $ %)*) %%#-. 0 B-&2&* /*1'&.. 1).&*8&3 0#' $ %)*) %%%#$&2*0!+" $

3 + !+ $ %)*) %%%%" )6# 562!7 ) 7 " $ 3 +,-!') 8" 4$-'$ -. 21# 0 562'@

#-12 15 &'%8%& I-(-90*9: 0 5*0'#-1209 k*142-02 (1#-12 Q.&& =0239&)*1# 023 f02 g&..Q!+[RSS 4$&*&

*0!+" $9'+' 9 :))); < ;*

-. 02 -2#*-2.-'099: .#0#-120*: /*1'&.. )6# 21# .&'123 1*3&* .#0#-120*:A ,$& 80*-17*0( -. (1*& 7&2&*09 #$02 #$& 0'5 023 &20)9&. #$& .&'123 (1@ (&2# 3&/&23&2'& 15 0 4-3&* '90.. 15 #-(& .&*-&. #1 )& '$0*0'#&*-.&3A

B& '02 09.1 .&& #$0# 4$&2 #$& 80*-02'& 15 #$& /*1'&.. -. 4&99 3&U2&3

023 .,+ 4!+" $ ) .1 #$& 3&/&23&2'& -2 #$& /*1'&.. 71&. #1 N&*1 0.

#$& 907 -2#&*809 -2'*&0.&. #$&2

4!)" $ .,+ 0!+"

023 #$& 0.:(/#1#& 15 #$& .&(-80*-17*0( -. #$& 80*-02'& 15 #$& /*1'&.. 4$&2 .&'123 1*3&* .#0#-120*-#: $193.AB$&2 #$& /*1'&.. -. 21# 80*-02'&

(9)

.#0#-120*: #$& 80*-17*0( *&#0-2. -#. 6.609 -2#&*/*&#0#-12 629-D& #$& 0'5 )6# 31&. 21# #&23 #1 02 0.:(/#1#&A ,$& 06#1'180*-02'& -. 1)8-16.9: 21# 3&U2&3 -2 #$-. '0.&A %-&)193Q!+R+SE h*&..-&Q!++!S 023 k&*02Q !++]S 3-.'6.. #$& 6.& 15 #$& 80*-17*0( -2 3&#&'#-27 9127 (&(1*: 023 #$& 3-*&'# &.#-(0#-12 15 #$& J6*.# &</12&2# 5*1( 02 &.#-(0#&3 80*-17*0(A

j. 4& $08& &(/$0.-.&3 0)18& &8&2 -5 #$& /*1'&.. -. 21# 80*-02'& .#0#-120*: -# (0: 2&8&*#$&9&.. )& 0 809-3"&'%"&("5)008 (')'"6&)%8 >%65$(( 4$-'$ -. 02 "&'%"&("5)008 %)&!6* ./&5'"6& 15 1*3&*)%

`19914-27 h*&..-&Q!+RRS 4& .6//1.&

" $ !" ) " ) %%%%%%%%) " "

*&/*&.&2# 1).&*80#-12. 0# -**&7690*9: ./0'&3 #-(& /1-2#.!' #($ %%%%%%*#% ,$& -5 4& 3&U2& 02*(& (0#*-<= 4-#$ ( '+*14

%) ' ) ' ) %%%%%'

I6//1.& #$0# < -. 02 *(% 8&'#1* 15 *&09 26()&*. .0#-.5:-27= < $ ) #$&2 < -. '099&3 0 7&2&*09-.&3 -2'*&(&2# 8&'#1* 15 1*3&* Q&%%"023< " -. 0 7&2&*09-.&3 -2'*&(&2# 15 1*3&* Q&%%"%j2 -2#*-2.-' *0231( 562'#-12 15 1*3&* Q&%%" -. 3&U2&3 0. 02: /*1'&..E!" #'))#51* 4$-'$

- $ < " 8))

-. .&'123 1*3&* .#0#-120*: 51* 02: !' #($ %%%%%%*# 023 02: 7&2&*09-.&3 -2'*&(&2# 8&'#1*E < 15 1*3&* Q&%%"% g1#-'& #$0# 4-#$ *&7690*9: ./0'&3 30#0 #$& U*.# 3-M&*&2'& #*02.51*(0#-12 /*18-3&. #$& 4&-7$#. 51* #$& 7&2@ &*09-.&3 -2'*&(&2# /*1'&.. 023 #$-. '02 214 )& 7&2&*09-.&3 #1 -**&7690*9: ./0'&3 30#0A B$0# -. &M&'#-8&9: 0'$-&8&3 -2 #$& -**&7690*9: ./0'&3 30#0 '0.& 0)18& -. #$0# 0 /0*#-'690* 4&-7$#&3 '1()-20#-12 15 #$& 1).&*80#-12. E 7-8&2 ): #$& 7&2&*09-.&3 -2'*&(&2# 8&'#1*E 7&2&*0#&. 0 .&'123 1*3&* .#0@ #-120*: /*1'&..A ,$& 7&2&*09-.&3 -2'*&(&2# 8&'#1* 022-$-90#&. )1#$ #$& 212.#0#-120*: (&02 Q/19:21(-09. -2 #-(&S 023 .#1'$0.#-' #*&23.A ,$& /0*099&9. 4-#$ -2#&7*0#&3 /*1'&..&. 0*& '9&0* 023 #$& -2#*-2.-' *0231( 562'#-12 -3&0 0//&0*. #1 )& (1*& 7&2&*09 023 0//9-'0)9& #1 -**&7690*9: ./0'&3 30#0A X.-27 *&.69#. 5*1( K&9O5023 023 f-9&2D-2 Q!+[]SE =0#$@ &*12Q!+^WS .$14&3 #$0# 02: -2#*-2.-' /*1'&.. 15 1*3&*& /1'&..&. 0 3$&7 $%)0"($! 564)%")&5$ *)'%"? >!+" # + " ? .6'$ #$0# 7-8&2 30#0 " 023 7&2&*09-.&3 -2'*&(&2# 8&'#1*.E< 0232! 15 1*3&* &%%S

@62!< ") 2 "" $ < 2 >!' %' "

(10)

,$-. *&.69# '02 )& 6.&3 4$&2 '12.-3&*-27 /*&3-'#-12 3-*&'#9: 5*1( #$& .&'123 (1(&2# .#*6'#6*& 15 #$&.& -2#*-2-.'099: .#0#-120*: /*1'&..&. Q.&& 0//&23-< WSA

4

567 8($&)&%%79.$*&# 2(#)$*&# :*$6 "%%7;(9.% <=3

,7%>.$*&#,

B& 214 #6*2 #1 '12.-3&* #$& 6.& 15 #$& 06#1'1**&90#-12 562'#-12 -2 (&0@ .6*-27 #$& 3&/&23&2'& -2 02 -**&7690*9: ./0'&3 #-(& .&*-&.A ,$& 1)8-16. /*1)9&( -. #$0# #$& &0.: -2#&*/*&#0#-12 15 06#1'1**&90#-12 562'#-12. 12 *&7690*9: ./0'&3 30#0 -. 91.# 0. 4& (18& #1 -**&7690*9: ./0'&3 30#0A K-8&2 *&7690* 30#0 4& '02 '09'690#& 3-*&'#9: #$& &M&'# 15 0 .$1'D #130: 12 .1(& 80*-0)9&+ 30:. 0$&03A J14&8&* 4$&2 4& $08& -**&7690* 30#0 4& 91.& #$& 20#6*09 #-(& .'09& 023 09#$167$ 4& '02 '1(/6#& 06#1'1**&90#-12. -2 #$& 21*(09 40: 4& '0221# &0.-9: -2#&*/*&# #$& *&.69#. 023 4-99 21# D214E 51* -2.#02'&E 4$&#$&* 0 .$1'D 4-99 *&0'$ -#. $095 9-5& -2 #$& 2&<# (-26#& 1* -2 #$& 2&<# 30:A V/&*0#-1209 #-(& 06#1'1**&90#-12 4-99 $08& 3-M&*&2# -(/9-'0#-12. -2 #&*(. 15 '09&230* #-(& 3&/&23-27 12 #$& #-(& 15 30: 1* .#0#& 15 #$& (0*D&# 023 -# -. 3-T'69# -5 21# -(/1..-)9& #1 6.& 1/&*0#-1209 #-(& 06#1'1**&90#-12. 12 #$& '91'D #-(& .'09&A

,$-. -..6& $0. )&&2 '12.-3&*&3 ): \6&216-99& Q!+"RSEk*-99-27&* Q!+^>S 023 h90*D Q!+^"S 0(127.# 1#$&*.A j6#1'1**&90#-12. '1(/6#&3 -2 -**&76@ 90* 1/&*0#-1209 #-(& 4-99 )& 4&-7$#&3 08&*07&. 15 #$& 06#1'1**&90#-12. 12 0 *&7690* .'09&A ,$&*& 0*& #41 40:. 51*40*3C #$& U*.# 023 ): 50* #$& (1.# '1((12 -. .-(/9: #1 077*&70#& #$& -**&7690* 30#0 -2#1 U<&3 -2#&*809. 023 #$& .&'123 -. #1 6.& .1(& 51*( 15 #-(& 3&51*(0#-12 #*02.51*(0#-12 #1 &<#*0'# 0 *&7690* 0'5 5*1( #$& -**&7690* 0'5A B& 2&&3 #1 &(/$0.-.& $&*& #$0# 4& 0*& 21# 3&09-27 4-#$ 02 623&*9:-27 '12#-2616. #-(& /*1'&.. )6# 0 3-.'*&#& /1-2# /*1'&.. .1 #$& 09#&*20#-8& 15 #*&0#-27 #$& *&09-.&3 30#0 0. -**&7690* 1).&*80#-12. 12 02 623&*9:-27 3-M6.-12 /*1'&.. -. 21# 12& 4& 4-.$ #1 &</91-#A

H5 4& 4*-#& #$& .#0230*3 06#1'180*-02'& &.#-(0#1* Q 0..6(-27 0 N&*1 (&02 51* #$& (1(&2#S 0.

4 !A" $ %

*%A "!'""!' "

)0.&3 12 #$& 1).&*8&3 )6# -**&7690* 30#0"!' ") #$&2 h90*DQ!+^"S .$14. #$0# #$-. &.#-(0#1* -. 0 (&02 .;60*& '12.-.#&2# &.#-(0#1* 15

,&4 !A"( $ 4!2"&B !2"

(11)

4$&*& #$& 3-.#*-)6#-12 562'#-12B !/'"15 #$& 1/&*0#-1209 #-(& -2#&*809.

!' %'"/*18-3&. 0 4&-7$#-27 12 #$& #*6& 06#1'180*-02'& 562'#-12 E4!2"%

I1 -2 /*-2'-/9& -5 #$& 3-.#*-)6#-12 15 #$& 36*0#-12.E!' %' " 40. D2142 4& '1693 41*D )0'D 5*1( #$-. &</*&..-12 #1 02 &.#-(0#& 15 #$& 623&*9:-27 06#1'180*-02'& .#*6'#6*&A

4?!

5*17 @7A&%1.$*&#

,$& -3&0 )&$-23 #-(& 3&51*(0#-12 -. #1 '12.#*6'# 0 .6-#0)9& #*02.51*@ (0#-12 15 '91'D #-(& -2#1 &'121(-' #-(& .1 #$0# &0'$ -2#&*809 15 '91'D #-(& '0/#6*&. #$& .0(& ;602#-#: 15 -251*(0#-12 0)16# #$& 623&*9:-27 .#1'$0.#-' /*1'&..A k*-99-27&* Q!+^>S /*1/1.&3 02 &.#-(0#1* -2 4$-'$ $& 6.&3 #$& 1).&*8&3 -2#&*809. )&#4&&2 #$& 1).&*80#-12.E2 )#1 &.#-(0#& #$& 06#1'180*-02'& 562'#-12 51* #$& .#0#-120*: /1-2# /*1'&.. 4$-'$ 7&2&*@ 0#&. #$& -2#&*809. 4$-'$ '1693 #$&2 )& 6.&3 #1 -(/*18& #$& &.#-(0#& 15 #$& 06#1'180*-02'& 562'#-12 15 #$& 623&*9:-27 #*02.0'#-12.A ,$-. &.#-@ (0#1* -. *&90#-8&9: -2&T'-&2# 0. #$& 1).&*80#-12. 0*& 21# *&90#&3 #1 #$& 1/&*0#-1209 #-(& 70/ )&#4&&2 #$&(A h90*D /*1/1.&3 02 &.#-(0#1* )0.&3 12 ./&'-5:-27 0 /1-..12 /*1'&.. 4$-'$ &M&'#-8&9: (0//&3 1/&*0#-1209 #-(& #1 '91'D #-(& 023 &20)9&3 3-*&'# &.#-(0#-12 15 0 '12#-2616. jZQ!" (13&9 5*1( #$& -**&7690* 30#0A K$:.&9.E K16*-&*16< 023 Y0.-0DEQ!++[S $08& 0//*10'$&3 #$& /*1)9&( -2 0 .-(-90* 40: ): '12.#*6'#-27 0 #*02.@ 51*(0#-12 #$0# &M&'#-8&9: 0##&(/#. #1 #*02.90#& 02 -**&7690* .0(/9& -2 '91'D #-(& -2#1 0 *&7690* ./0'&3 .0(/9& -2 &'121(-' #-(&A ,$&: 0*& -2#&*&.#&3 -2 (&0.6*-27 #$& 06#1'180*-02'& .#*6'#6*& -2 &'121(-' #-(& 023 41*D 5*1( 0'5 '09'690#&3 12 077*&70#&3 '91'D #-(& #1 -(/9: #$& 0'5 -2 &'121(-' #-(&A H2 /0*#-'690*E 7-8&2 .1(& 3-*&'#-27 /*1'&..E7) #$0# 0..1'-0#&. '91'D #-(& 4-#$ &'121(-' #-(&

7 #'" * %+7 "?

023 #$0# #$& /*1'&.. 15 -2#&*&.# -. &8198-27 -2 &'121(-' #-(& 0.

= #C"? %+= "?

4& (0: -236'& #$& /*1'&.. 1).&*8&3 -2 '91'D #-(&' " *): '12.-3&*-27

= $= ,7 $=

K-8&2 02 0..6(/#-12 *&70*3-27 #$& 20#6*& 15 #$& #-(& 3&51*(0#-12 /*1'&..E 7E 51* -2.#02'& -5 8196(& (&0.6*-27 -251*(0#-12 b14E 3&#&*@ (-2&. #$& 40: -2 4$-'$ #$& 20#6*09 #-(& .'09& '02 )& .#*&#'$&3 023 '12#*0'#&3E 4& '02 '12.-3&* #41 06#1'1**&917*0(. -2 #&*(. 15 '91'D #-(&

(12)

023 02 -**&7690* ./0'&3 -2#*-2.-' #-(&A ,$& 06#1'1**&917*0( -2 02 -**&76@ 90*9: ./0'&3 30#0 .&# (0: #$&2 )& '1(/6#&3 #$*167$ 0 D&*2&9 .(11#$-27 /*1'&36*&A ,41 3-M&*&2# D&*2&9. 4&*& 6.&3 ): K$:.&9.E K16*-&*16< 023 Y0.-0D #1 &.#-(0#& #$& 0'5O. 51* 30-9: *&#6*2. 12 #$& geIc 4-#$ #*03-27 8196(& 6.&3 0. 0 3-*&'#-27 /*1'&..A

907 I#0230*3 0'5 K06..-02 D&*2&9 k1623&3 D&*2&9

? !A?? !A? !A?

?A>" @ A+[ A+R+

?A^" @ A^! A?>

! @?A?^ ?A""[ @?A?"[[

!A" @ ?A>+ @?A?>

> @?A?W ?A!>[ @?A?>

,0)9& >_ Y0.-0DE K$:.&9. 023 K16*-&*16< ,-(& 3&51*(&3 D&*2&9 0'5O.

,$& 907. 51* #$& .#0230*3 0'5 0*& )0.&3 12 #$& 30-9: 1).&*80#-12. 023 51* #$& D&*2&9 06#1'1**&90#-12. 907 D '1**&./123. #1 C $ DE E 4$&*& E -. #$& 08&*07& 30-9: #*03-27 8196(&A ,$-. 0//*10'$ 41*D. -2 #$& 1//1.-#& 3-*&'#-12 5*1( #$0# 4& 0*& -2#&*&.#&3 -2E -&A -# 0##&(/#. #1 (18& 5*1( 02 077*&70#&3 30-9: 0'5 #1 #$& 623&*9:-27 -**&7690*9: ./0'&3 06#1'1**&90#-12 .#*6'#6*&A g&8&*@#$&@9&.. -# -. .#*-D-27 5*1( #$& #0)9& Q>S $14 #$& 30-9: 0'5 '02 7-8& ;6-#& 0 3-M&*&2# -(/*&..-12 15 #$& 623&*9:-27 06#1'180*-02'& .#*6'#6*& -2 *&09 #-(& 5*1( #$& #-(& 3&51*(&3 0'5O. 4-#$ #$& 30-9: 0'5 -23-'0#-27 *&90#-8&9: 9-##9& #-(& 3&/&23&2'& 4$-9& )1#$ #-(& 3&51*(&3 0'5O. .$14 .-72-U'02# 06#1*&7&..-8& .#*6'#6*&A

H# -. '9&0*9: -(/1*#02#E 7-8&2 #$&.& *&.69#.E #1 *&'172-.& #$& .-72-U'02# &M&'# #&(/1*09 077*&70#-12 /1#&2#-099: $0. 12 #$& (&0.6*&(&2# 15 #$& 06#1*&7*&..-8& .#*6'#6*&A ,$& '*-#-'09 62'&*#0-2#: -2 #$-. /*1'&.. 9-&. -2 #$& '$1-'& 15 #-(& 3&51*(0#-12 #*02.51*(0#-12A H# -. 09.1;6-#& 0//0*&2# #$0# #$& #41 3-M&*&2# D&*2&9 '$1-'&. 3&9-8&* ;6-#& 3-M&*&2# &.#-(0#&3 06#1'1**&917*0(. 0# ./&'-U' 3-.'*&#& 907.A

4?+

07;(9.%9/ -.1B97' 8($&)&%%79.$*&#

i&# 6. 214 '12.-3&* #$& -..6& 15 4$-'$ 8096& #1 #0D& 0. *&/*&.&2#0#-8& 51* 02 077*&70#&3 -2#&*809A ,$& 3-M&*&2# U*.# 1*3&* 06#1*&7*&..-8& '1&T@ '-&2#. #$0# '1693 )& 3*042 5*1( 16* %=>???@> 30#0 .&# 4-#$ #*02.0'#-12. 077*&70#&3 -2#1 >? .&'123 -2#&*809. ): .&9&'#-27 3-M&*&2# *&/*&.&2#0#-8& 8096&. -. .$142 -2 #$& 519914-27 #0)9&A ,$& #41 U76*&. )&914 `-7Q!S 023 `-7Q>S .$14 $14 #$& '$1-'& 0M&'#. #$& .6**170#& #-(& /0#$ '*&0#&3 51* #$& 077*&70#&3 .&*-&.A H5 #$& *-7$# $023 8096& -. 6.&3 #$&2 #$0# 8096& 4-99 )& #$& 8096& 0..6(&3 51* #$& 077*&70#&3 .&*-&.E .$142 4-#$ #$& '-*9@ '&.E 62#-9 #$& 2&<# #*02.0'#-12 1''6*.E .-(-90*9: 4-#$ #$& 9&5# $023 8096&A

(13)

Right interpolation

absz[1:10]

pricez[1:10]

517500 518000 518500 519000 519500

1

.7

5

2

0

1

.7

5

3

0

1

.7

5

4

0

1

.7

5

5

0

`-76*& !_

,$& .19-3 9-2& -2 #$& 7*0/$. /*18-3&. #$& 9-2&0* -2#&*/190#-12 8096& 4$-'$ 0..6(&. #$0# #$&*& 4-99 )& #*02.0'#-12. '12#-2616.9: 18&* 02: -2#&*809 )&#4&&2 0'#609 #*02.0'#-12.A

,$& 3-M&*&2# #-(& /0#$. -(/9-&3 0M&'# #$& &.#-(0#&3 U*.# 1*3&* 06@ #1'1**&90#-12 '1&T'-&2#. 0. .$142 -2 #0)9& QWS

`-76*&.

,-(& L&*-13 CD "E5 0D "E5 C"E "E5 @7F3E

?@>] @?A>> @?A>] ?A?W

!R@[ @?A>R @?A]! ?A!> ?A>+

[@R @?A?+ @?A!? ?A?! @?A!"

R@!? @?A!R @?A!> @?A!+ @?A!]

!?@!> @?A!" @?A?^ @?A?W @?AWR

!>@!] @?A!R @?A!> @?A!! ?A?W

!]@![ @?A!R @?A!! @?A?R @?A??

![@!R @?A?R @?A?[ ?A>W ?A?"

,0)9& W_ `-*.# V*3&* jh` h1&T'-&2#. 51* f0*-16. H2#&*/190#-12 =&#$13. 023 %& Y127 023 g-P(02

,$-. #0)9& .$14. '9&0*9: $14 -25&*&2'& *&70*3-27 #$& &<-.#&2'& 15 06@ #1*&7*&..-8& .#*6'#6*& '1693 )& .&*-16.9: 0M&'#&3 ): 0 /0*#-'690* '$1-'& 15 *&/*&.&2#0#-8& &9&(&2# -2 #$& 077*&70#&3 -2#&*809 A B& 09.1 21#& #$&

(14)

Left interpolation

absz[1:10]

pricez[1:10]

517500 518000 518500 519000 519500

1

.7

5

2

0

1

.7

5

3

0

1

.7

5

4

0

1

.7

5

5

0

`-76*& >_

*03-'099: 3-M&*&2# )&$08-16* 3-./90:&3 ): #$& %&Yg (&#$13 -2 #$-. '1(@ /0*-.12 023 .$14. $14 .&2.-#-8& &8&2 0 '12.-.#&2# -2#&*/190#-12 (&#$13 4-99 )& #1 #$&.& 0..6(/#-12. 12 .&9&'#-27 *&/*&.&2#0#-8& 8096&. -5 4& .&&D #1 077*&70#& #$& 30#0 -2#1 *&7690* -2#&*809.A

K-8&2 #$&.& 0()-76-#-&. 023 #$& 3-M&*&2# &.#-(0#&. 15 06#1*&7*&.@ .-8& .#*6'#6*& #$0# '1693 )& 7&2&*0#&3 ): 3-M&*&2# '$1-'&. 15 #-(& 3&@ 51*(0#-12 #*02.51*(0#-12E -2#&*/190#-12 (&#$13 1* *&/*&.&2#0#-8& 8096& -2 077*&70#&3 -2#&*809 4& $08& '$1.&2 21# #1 51'6. 12 #$& 06#1'1**&90@ #-12 562'#-12 -2 16* 0209:.-.A H2.#&03 4& $08& 3&'-3&3 #1 &</91*& #$& 3-*&'# 6.& 15 #$& 80*-17*0( #1 (&0.6*& 06#1*&7*&..-8& .#*6'#6*& -2 #$& -**&7690*9: ./0'&3 .0(/9& 15 #*02.0'#-12 12 #$& %1990*@%(0*D &<'$027& *0#&A

G

567 H.%*&;%.1 .#' I%&,, H.%*&;%.1 :*$6 "%%7;3

(9.%9/ <=,7%>7' @.$.

X23&* #$& -2#*-2.-' .#0#-120*-#: 0..6(/#-12 #$& '90..-' 80*-17*0( &.#-@ (0#1* Q 3&U2&3 $&*& 51* #$& (1(&2# 12 *&7690*9: ./0'&3 30#0S -. 7-8&2 ):

0

0!+" $ %

*!*%+" !D %D"

(15)

023 -. 62)-0.&3A ,$& 62)-0.&32&.. 519914. .-2'& '*-#-'099: #$-. &.#-(0#1* 129: 6.&. 3-M&*&2'&. 15 #$& 30#0 023 .-2'& -# 31&. 21# *&;6-*& &.#-(0#&. 15 #$& (&02 629-D& #$& 06#1'1**&90#-12A B& 4-99 6.& 0 .(11#$&3 8&*.-12 15 #$& 80*-17*0( &.#-(0#&3 0# 3-M&*&2# 907.+

0

0!+" $ %

* %

&F!+"& !D!#"%D!# "" Q[S

4$&*& #$& .6( -. 18&*F!+"- !!() A" ##%# $+#023&F!+"&-. #$& 26(@

)&* 15 3-.#-2'# &9&(&2#. -2F!+"% H2 /*-2'-/9& 4& '1693 .-(/9: '09'690#& #$& 8096& 15 00!+" 51* &8&*:+ #$0# 1''6*. -2 #$& 30#0 E )6# 4& '$11.& #1 6.&+ #3&U2&3 12 0 *&7690* 7*-3A `-*.# 4& '12.#*6'# 0 #19&*02'& 4-2314 0*1623 &0'$ -2'*&(&2#E+) .1 #$0# 099 /0-*. .0#-.5:-27

&# %# %+& .'6G

0*& 51623 023

F!+"- !!() A" #&# %# %+& .'6G#

h9&0*9: 4& '02 129: *&9-0)9: &.#-(0#& #$& 80*-17*0( 0# 907. 51* 4$-'$ 4& $08& &2167$ 1).&*80#-12. 023 .1 4& 6.& 0 '6# 1M *69& E .-(-90* #1 #$0# .677&.#&3 -2 h*&..-&Q!++!SE #$0#F!+")1)%B& $08& 09.1 &</&*-(&2#&3 4-#$ 3-M&*&2# .(11#$-27 *69&. .6'$ 0. 6.-27 0 U<&3 26()&* 15 2&-7$@ )16*. 023 #$& *&.69#. 0*& 21# 3*0(0#-'099: 3-M&*&2# 5*1( #$1.& *&/1*#&3 )&914A =1*& .1/$-.#-'0#&3 80*-0)9& )0234-3#$ D&*2&9 023 *1)6.# &.#-@ (0#1*. 15 #$& 80*-17*0( '1693 )& '12.-3&*&3E 4$-'$ 4& 4-99 &</91*& -2 #$& 56#6*&A

j. 02 &<0(/9& U76*&QWS .$14. #$& -**&7690* 80*-17*0( &.#-(0#&3 12 #$& %=>???@> 30#0 18&* 12& 30: )&#4&&2 ![A?? 023 !RA?? 6.-27 .#&/. 15 >? .&'123. 023 ! .&'123 023 0 #19&*02'& 15 )%)* .&'123. 51* )1#$A ,$& $1*-N12#09 0<-. .$14. #$& 907 -2#&*809 -2 .&'123.A B& '02 .&& #$0# 0. #$& -2#&*809 )&'1(&. 90*7& #$&*& 0*& 9&.. 1).&*80#-12. -2 )1#$ 80*-17*0(. )6# (1*& &0.-9: -2 #$& >? .&'123 80*-17*0(A g1#& #$0# #$& #*02.0'#-12. -2 %=>???@> 0*& *&'1*3&3 12 0 12& $623*&3#$ 15 0 .&'123 #-(& .'09&A ,$&*& -. 21 -2#&*/190#-12 1* '$1-'& 15 *&/*&.&2#0#-8& 8096& -28198&3 -2 #$&.& '09'690#-12. )&:123 #$& 08&*07-27 -(/9-&3 -2 6.-27 0 51*( 15 .(11#$-27 &.#-(0#1*A,$& 08&*07& -. #:/-'099: #0D&2 18&* .&8&*09 #$16.023 1).&*80#-12. 0# &0'$ 907A B$&*& -2.6T'-&2# 1).&*80#-12. &<-.# #$& 80*-17*0( -. .-(/9: 21# '1(/6#&3 0# #$0# 8096&A k0.-'099: #$& .0(& /0##&*2 -. .&&2 51* #$& #41 80*-17*0(.

(16)

lag

Variogram

0 200 400 600 800

0

.0

0

.0

5

0

.1

0

0

.1

5

0

.2

0

0

.2

5

1 and 20 Second Variogram Estimates: Hours 16 to 18

`-76*& W_

G?!

@*,)%*1*#.$*#; J%&)7,,7, :*$6 $67 H.%*&;%.1

,$& )0.-' 80*-17*0( 4& 4-99 41*D 4-#$ 7-8&2 -2 &;60#-12 [E 023 4& 4-99 '1(/0*& #$& &.#-(0#&3 8&*.-12 4-#$ #$& 3-.#*-)6#-12. 15 #$& 80*-17*0( 623&* 3-M&*&2# /*1'&..&.A ,$&*& -. .1(& 0.:(/#1#-' #$&1*: 080-90)9&A H2 /0*#-'690* i1 023 =0'd-290: Q!+RRS 3&*-8& #$& 3-.#*-)6#-12 51* 0 .'09&3 8&*.-12 15 #$& 80*-17*0(E ?!+" $-!+"H-!%" 4$&*& -!+" $ 00!+"A X23&* .#0230*3 21*(09-N0#-12 #$& *&.69#-27 #&.# .#0#-.#-' -. 3-.#*6)6#&3 .#0230*3 21*(09A J14&8&*E 0. d1*(&23- 023 =&76-*& Q!+ S 3&(12.#*0#& #$& U2-#& .0(/9& 3-.#*-)6#-12 15 .6'$ 80*-17*0(. '02 )& .&*-16.9: .D&4&3E (0D-27 #$& .:((&#*-' 0.:(/#1#-' 3-.#*-)6#-12 9&.. 6.&569A B& #$&*&51*& /*1'&&3 ): 6.-27 .-(690#&3 3-.#*-)6#-12.A H2 1*3&* #1 50'-9-#0#& &0.: '1(/0*-.12 15 #$& /91#. 4& 6.& 0 .-(/9& .'09&3 80*-17*0(00!+"H00!+ "% + -. #$& (-2-(6( 907 4& 3-.#02'& 4& 4-99 &.#-(0#& #$& 80*-17*0( 51*A I1E 51* &<0(/9& -5 4& 6.& 0 >? .&'123 -2#&*809E #$&2+ -. >?A

H2 #$& 519914-27 /91#E U76*&Q]S 4& /*18-3& 0 .-(690#-12 4$&*& #$& 30.$&3 9-2&. 0*& &.#-(0#&3 21*(09-.&3 80*-17*0(. 51* #41 06#1*&7*&.@ .-8& /*1'&..&. #17&#$&* 4-#$ #$& .-(690#&3 &(/-*-'09 3-.#*-)6#-12. Q +^A" 023 >A" /&*'&2#-9&.S 51* #$& 62-# *11#A B& '02 .&& #$0# #$& '0.& 4-#$ 02 jZ /0*0(&#&* ! 15 )%23 '0221# )& 3-.#-276-.$&3 5*1( 0 62-# *11# 12 #$-. )0.-. 0# #$& +"l 9&8&9 )6# ! $ )%4 -. '9&0*9: .&&2 #1 )& .-72-U@ '02#9: 3-M&*&2# 5*1( 0 62-# *11#A ,$& &(/-*-'09 3-.#*-)6#-12 -. .&&2 #1 )& .D&4&3E 3&(12.#*0#-27 #$& 6.&5692&.. 15 6.-27 .-(690#&3 3-.#*-)6#-12. 4-#$ 9-(-#&3 .0(/9& .-N&.A `-76*& " .$14. #$& &(/-*-'09 3-.#*-)6#-12 5*1(

(17)

0 10 20 30 40 50

0

2

0

4

0

6

0

8

0

1

0

0

Unit Root Empirical Distribution

lag

Variogram Estimate

`-76*& ]_ ,$& &(/-*-'09 3-.#*-)6#-12 51* #$& 80*-17*0( 51* 0 62-# *11# /*1'&..A ,$& #41 31##&3 9-2&. .$14 #$& (&02 80*-17*0( 18&* 0 .-(690#-12 51* jZQ!S /*1'&..&. 4-#$ /0*0(&#&* ?A+" Q6//&* 9-2&S 023 ?ARA

021#$&* .-(690#-12 .#63: 4$&*& #$& 30#0 -. .-(/9: #$& 3-M&*&2'&. 5*1( #$& 62-# *11* /*1'&..E -A&A -A-A3A 21*(09 &**1*.A B& 4-99 6.& #$&.& #:/&. 15 .-(690#&3 3-.#*-)6#-12. #1 #&.# $:/1#$&.&. 0)16# #$& `m 30#0 90#&*A

,$& h*1..@ 80*-17*0(E 4$-'$ -. 6.&569 -2 &</91*-27 '*1.. #&(/1@ *09 3&/&23&2'&E -. 3&U2&3 51* 0 8&'#1* 15 -2#*-2.-'099: .#0#-120*: /*1@ '&..&. !!!#"5 !" !#") " !#"%%%%%" !#""# 3&U2&3 12 #$& '12#-2616. 1).&*@ 80#-12 ./0'&

0.

*0 !+" $2./!"!#'+"%" !#"" +"?

I-(-90* &.#-(0#1*. 51* #$& '*1.. 80*-17*0( 0. 3&.'*-)&3 51* #$& 80*-17*0( 0)18& $08& )&&2 6.&3 -2 #$& '09'690#-12. *&/1*#&3 )&914A `-76*&Q[S .$14. #$& '*1.. 80*-17*0( )&#4&&&2 #41 .&*-&. 7&2&*0#&3 5*1( #$& 519@ 914-27 .-(690#&3 /*1'&..&.C

I!'"/F!))%"

J!'" $%)%4I!'%%)" 'K!'"

K!'"/F!))%"

(18)

0 10 20 30 40 50

0.0

0.5

1.0

1.5

2.0

Independence Empirical Distribution

lag

Variogram Estimate

`-76*& "_ ,$& &(/-*-'09 3-.#*-)6#-12 51* #$& 80*-17*0( 51* -A-A3 gQ?E!S &**1*.A ,$& 31##&3 9-2& .$14 #$& (&02 80*-17*0( 18&* 0 .-(690#-12 51* jZQ!S /*1'&..&. 4-#$ /0*0(&#&* ?A>

Index

upperquant

0 20 40 60 80 100

0

.0

0

.5

1

.0

1

.5

Cross Variogram Null Distribution and Example of a Correlated Series

`-76*& [_

(19)

,$& '09'690#&3 '*1..@80*-17*0( -. 21*(09-.&3 0. 0)18& #1 #0D& #$& 8096& 15 62-#: 12 N&*1 '*1..@'180*-02'&A ,$& 236 '12U3&2'& -2#&*809. -2 #$-. '0.& 0*& '09'690#&3 ): )11#.#*0/ (&#$13. 623&* -23&/&23&2# *&.0(/9-27 :-&93-27 02 0//*1<-(0#& (&#$13 51* -23-'0#-27 -2#&*3&/&23&2'&A g1#& #$0# #$-. &(/-*-'09 3-.#*-)6#-12 -. #$& .0(& 0. #$0# 15 #$& 80*-17*0( (&0.6*&-27 3&/&23&2'& 4-#$-2 0 .-279& -A-A3A /*1'&..A

G?+

-.1B9*#; J%&B7%$*7, &A $67 H.%*&;%.1 .#' $67

8)A?

,$& .0(/9& 06#1'180*-02'& '02 )& $1/9&..9: )-0.&3 4$&2 #$& /*1'&.. -. 21# (&02 .#0#-120*: 023 #$& 06#1'180*-02'& -#.&95 -. 21# &8&2 3&U2&3 4$&2 #$& /*1'&.. -. 21# 80*-02'& .#0#-120*:A ,$& .#0230*3 06#1'180*-@ 02'& &.#-(0#& -. 7-8&2 ):

0

4!+" $ !*%+" !D %D7"!D %D7"

023 #$& (0P1* /*1)9&( 4-#$ #$& 6.& 15 #$& 0'5 -2 /*0'#-'& -. #$& 2&&3 #1 &.#-(0#& #$& (&02 15 #$& /*1'&..A H# -. 4&99 D2142 #$0# #$& 80*-02'& 15 #$& .0(/9& (&02 51* '1**&90#&3 30#0 -. 21#3 H* 023 -2 '12.&;6&2'& 0

4!+" 4-99 )& )-0.&3 -2 U2-#& .0(/9&.E .&& `699&* Q!+^[E / >W[SA c8&2 -5

21# &</9-'-#9: *&09-.&3 0 #*&23 Q7D S -. -(/9-'-#9: &.#-(0#&3 #$*167$ #$& (&02 023 #$& 0'5 -. '09'690#&3 6.-27 #$& &M&'#-8& *&.-3609. !D %D7"% I-2'& #$& *&.-3609. 0*& 9-2&0*9: *&90#&3 #$*167$ !D %D7" $ ) E &8&2 -5 #$& !D# 0*& -23&/&23&2# #$& *&.-3609. !D %D7# 4-99 )& 2&70#-8&9: '1**&90#&3 023 0 U2-#& .0(/9& )-0. -236'&3 -2 #$& &.#-(0#&3 0'5A H23&&3 #$& (1*& /*12162'&3 #$& 06#1'180*-0#-12 #$& (1*& /*12162'&3 #$& )-0. 0. .$142 51* -2.#02'& ): g&4)193 023 j7-0D917916Q!++WS -2 #$& '0.& 15 5*0'#-1209 21-.&A

,$& .0(/9-27 /*1/&*#-&. 1540!+" $08& )&&2 3-.'6..&3 023 '1(/0*&3 4-#$ #$1.& 15 #$& 80*-17*0( ): h*&..-& 023 K*123120Q!++>S 023 J0.9&## Q!++^SA ,$&.& *&.69#. .$14 #$0# #$& '90..-'09 80*-17*0( 7-8&2 0)18&E -. 62)-0.&3 4$&2 #$& /*1'&.. -. 129: (&02 .#0#-120*: 023 0 20#6*09 09#&*20#-8& &.#-(0#1* 129: $0. 0 .(099 )-0. 4$&2 #$& /*1'&.. &8&2 4$&2 #$& /*1'&.. -. 2&-#$&* (&02 21* 80*-02'& .#0#-120*:A ,$& 09#&*20#-8& &.#-(0#1*E 4$-'$ -. #$& .0(/9& 80*-02'& 15 #$& 3-M&*&2'&. 4$&*&00!+" -. #$& 08&*07& 15 #$&-* .;60*&.E -. 7-8&2 ): J0.9&## 0.

8

0!+" $ %

*!*%+%%" !& %&7"

4$&*& & $D %D

(20)

K

567 @.$. -7$L 07($7%, @M+NNN3+

,$& %=>???@> &9&'#*12-' 3&09-27 .:.#&( /*18-3&. 0 '12#-2616. 06'#-12 (0*D&# 51* 3&09&*. 5*1( (0P1* )02D. -2 4$-'$ *)%@$' 023 0"*"' 1*3&*. -2/6# ): /0*#-'-/02#. 0*& (0#'$&3 06#1(0#-'099: ): #$& .:.#&( 4-#$ #$& 1*3&*. 15 1#$&*.A ,$& 30#0 .&# 40. (03& 080-90)9& #1 6. 5*1( Z&6#&*. 8-0 #$& `=K 023 /*18-3&. 0 3-*&'# 5&&3 5*1( #$& .:.#&( .$14-27 #$& /90'&(&2# 15 1*3&*.E #$&-* /*-'& 023 8196(& 023 &20)9-27 #$& .#*6'#6*& 15 #$& 1*3&* )11D Q4$-'$ -. 21# 080-90)9& -2 *&09 #-(& #1 #$& 3&09&*. 6.-27 #$& .:.#&(S #1 )& '09'690#&3A %&09&*. 6.-27 #$& .:.#&( '02 1).&*8& 129: #$& )&.# '6**&2# )[email protected] ./*&03 023 8196(&.A j 5699&* 0209:.-. 15 $14 #$& *04 30#0 40. #*02.51*(&3 -2#1 0 6.0)9& 30#0 .&# 51* 0209:.-. -. 3&.'*-)&3 -2 0//&23-< !A ,$& 30#0 6.&3 '18&*. 099 %1990*n%= #*03&. 12 %=>???@> 18&* #$& 4&&D [#$@!?#$ V'#1)&* !++^A X29-D& #$& V9.&2 `m%m 30#0 .&# 4$-'$ -. 3*042 5*1( #$& Z&6#&*. `m /07& 023 .$14. -23-'0#-8& ;61#&. Q )-3 @0.D 038&*#-.-27S *0#$&* #$02 #*02.0'#-12. #$& 30#0 4& $08& *&/*&.&2#. *&09 #*02.0'#-12. 12 4$0# 214 *&/*&.&2#. .1(& ]? #1 "?l 15 #$& (0*D&#A

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no #1 !A^^%=noA ,$& 08@ &*07& 8196(& 15 #$& 1*3&*. 40.>A>RW (-99-12 023 #$& 8196(& 15 #*03&. *027&3 5*1( ! (-99-12 #1 W? 4-#$ 0 (&02 15 !AR![A ,1#09 8196(& 15 #*02.0'#-12. 40. 0)16# o[? )-99-12E ^?E]?[ 1*3&*. 4&*& '02'&99&3 )&51*& )&-27 0'#&3 6/12 023 WRE>W+ 4&*& *&(18&3 /0*#-099: U99&3A j (0*D&# &(690#-12 /*17*0((& 40. 4*-##&2 #1 &<#*0'# #$& #*02.0'#-12. 30#0 5*1( #$& 5699 30#0 .&# A `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

(21)

600000 700000 800000 900000

1.

73000002

1.

74000001

1.

75000000

1.

75999999

Filtered Series 6.00am-6.00 pm blocks each day

seconds

s

pot

`-76*& ^_

.:.#&( )6# 1M&* #$& 519914-27 &</9020#-12. 51* #$&-* /*&.&2'&C #$&: (0: 0*-.& 4$&2 0 #*03&* $0. 9&5# 0 9-(-# 1*3&* -2 #$& .:.#&( 023 51*71##&2 0)16# -# 023 -# .6).&;6&2#9: 7&#. $-#E 1* 09#&*20#-8&9: 0 #*03&* .-(/9: 2&&3. #1 #*03& 0. 0 '6.#1(&* 3&(023. -# 1* 2&0* #$& &23 15 #$& 30: 0 #*03&* $0. #1 '91.& 16# #$&-* /1.-#-12 023 P6.# #0D&. 4$0# &8&* /*-'& $& '02 7&# -((&3-0#&9:A I-2'& 4& 0*& 21# -2#&*&.#&3 -2 .6'$ )&$08-16* 0# #$& (1(&2# 4& .-(/9: #11D #$&.& 1).&*80#-12. 16# 15 #$& .&*-&.A

B$0# -. (6'$ (1*& -2/1*#02# 51* 16* /6*/1.&. -. #1 *&'172-.& #$& -(/0'# 15 (0'*1@&'121(-' 2&4. 12 #$& (0*D&# 36*-27 #$& 4&&DA ,$& 7&2&*09 .-#60#-12 36*-27 #$& 4&&D '02 )& 3&.'*-)&3 0. 62'&*#0-2#: *&@ 90#-27 #1 #&2.-12 -2 #$& K695 023 #$& /*1./&'#. 51* c6*1/&02 =12&#0*: X2-12A ,$& H#09-02 718&*2(&2# 5&99 12 ,$6*.30: Q+n!?n+^S 15 #$-. 4&&D 0. -# 50-9&3 #1 .&'6*& 0 '1(/*1(-.& 4-#$ -#. '1((62-.# '109-#-12 /0*#@ 2&* 12 #$& /*1/1.&3 )637&#p 0-(&3 0# .0#-.5:-27 #$& =00.#*-'$# '*-#&*-0A Z0#$&* (1*& .-72-U'02# 51* #$& &8196#-12 15 #$& %1990* %(0*D &<'$027& *0#& 40. #$& 62'&*#0-2#: .6**1623-27 #$& k623&.)02DO. *&/1 *0#&A V2 #$& .0(& 30: 0. #$& H#09-02 K18&*2(&2# 5&99 #$-. '&2#*09 *0#& 40. -2@ '*&0.&3 ): W? )0.-. /1-2#. 51* #$& U*.# #-(& -2 U8& :&0*.A ,$& #-(-27 40. 0 .6*/*-.& 023 #$& &M&'# 40. 3*0(0#-'E 0# 9&0.# 12 #$& #-(& .'09& 15 U76*&Q^SA ,$& `-202'-09 ,-(&. 15 #$0# 4&&D -23-'0#&. .6).#02#-09 ./&'690#-12 .6**1623-27 .6'$ 02 -2'*&0.& 023 4$&2 -# 41693 1''6*A H2 50'# ./&'690#-12 0//0*&2#9: &<-.#&3 #$0# .6'$ 02 022162'&(&2# 41693 )& (03& 12 #$& ,6&.30: Q^n!?n+^S )6# #$& k623&.)02D 9&5# #$& *0#& 62'$027&3 12 #$0# 30:A ,$&*& -. 0 '9&0* 0//*&'-0#-12 15 #$& %= -2 02@

(22)

Quantity

Price

5 10 15 20

1

.7

5

0

1

.7

5

2

1

.7

5

4

1

.7

5

6

A Snapshot of the Order Book

`-76*& R_ I0(/9& k-3 023 VM&* h6*8&.

#-'-/0#-12 15 0 $-7$&* *&/1 *0#& 6/ #1 #$& #-(& 15 022162'&(&2# 12 #$& ^#$ 4$-'$ -. 6241623 .9149: 36*-27 #$& 05#&*2112 #*03-27A B& 0209:.& #$& (0*D&# 0*1623 #$&.& #41 &8&2#. -2 #$& 90.# .&'#-12 15 #$& /0/&*A

I1(& .#:9-.&3 50'#. 15 #$& #*02.0'#-12. /*-'&. 023 *&#6*2. 0*& *&@ /1*#&3 -2 #$& 519914-27 U76*&.A ,:/-'09 )-3 023 1M&* '6*8&. 0*& .$142 -2 U76*&QRS 4-#$ 9-(-# 1*3&*. /90'&3 -2 #$& .:.#&( 0# /0*#-'690* /*-'&. 023 51* /0*#-'690* ;602#-#-&. .$142 12 #$& 8&*#-'09 023 $1*-N12#09 0<&. *&./&'#-8&9:A ,$& -2.-3& ./*&03 -2 #$-. /0*#-'690* '0.& -. *&90#-8&9: 20*@ *14 )6# -# '02 80*: .-72-U'02#9: 36*-27 #$& 30: 0. .$142 -2 U76*&Q+S 4$&*& #$& $1*-N12#09 0<-. -. -2 W? (-26#& -2#&*809. 5*1( [A??0(A ,$&*& -. 0 ./-D& 0# #$& (-339& 15 #$& 30:E #$167$ 4& .677&.# 90#&* #$-. -. -2 50'# 3*-8&2 ): #$& &8&2#. 12 12& 30:E #$& +#$ V'#1)&*A

B& $08& 09.1 '12.#*6'#&3 .1(& (&0.6*&. 15 3&/#$ 023 9-;6-3-#: -2 #$& (0*D&#A ,$& 3&/#$ (&0.6*& -. .-(/9: #$& .6( 15 099 1*3&*. -2 #$& 1*3&* )11D 12 )1#$ #$& 3&(023 023 .6//9: .-3&A ,$-. 7-8&. 6. #$& #1#09 8196(& 080-90)9& 12 &0'$ .-3& 15 #$& (0*D&#A j. 0 (&0.6*& 15 9-;6-3-#: 4& $08& &.#-(0#&3 #$& .91/&. 15 )1#$ #$& )-3 023 #$& 1M&* '6*8&. 91'099: #1 #$& (0*D&# /*-'& 023 6.&3 #$&-* 08&*07& 0. 0 (&0.6*& 15 9-;6-3-#:A ,$& '6*8&. 0*& -2 50'# 15#&2 2129-2&0* 023 09.1 4& U23 #$0# .1(&#-(&. #$&*& 0*& 0 5&4 1*3&*. .-##-27 -2 #$& .:.#&( #$0# 0*& 0# ;6-#& 1M (0*D&# /*-'&.A B& .-(/9: '12.-3&* 0 9-2&0* 0//*1<-(0#-12 #1 #$& U*.# /0*# 15

(23)

Spread: 30 Minute Means, 6-18

Index

Spread

15 20 25 30

0 .0 0 0 2 0 .0 0 0 4 0 .0 0 0 6 0 .0 0 0 8 0 .0 0 1 0 0 .0 0 1 2 `-76*& +_

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`-76*&Q!?S /*18-3&. .1(& -23-'0#-12 15 $14 #$& 08&*07& .91/& Q18&* #$& 4&&DS 15 #$& )-3 '6*8& '$027&. #$*167$ #$& 30: Q-2 W? (-26#& -2#&*809.SA g1# .6*/*-.-279: #$&*& .&&(. #1 )& 0 X .$0/& 4-#$ #$& 3&(023 7&##-27 (1*& &90.#-' Q.$09914&* .91/&S 36*-27 #$& )6.: /0*# 15 #$& 30:A ,$& 1M&* '6*8& $0. 0 .-(-90* -2#*0@30: /0##&*2A j. 0 (&0.6*& 15 8190#-9-#: 4& .$14 #$& 0).196#& *&#6*2 36*-27 #$& 30: -2 U76*&Q!!SA V#$&* .&0.1209 Q1* 3-6*209S /0##&*2. $08& )&&2 31'6(&2##&3 ): %02-&99.12 023 L0:2& Q!+++SA ,$&.& /0##&*2. '12U*( 7&2&*09 /0##&*2. *&7690*9: 1).&*8&3 -2 .6'$ #*02.0'#-12. 30#0A

O

P1B*%*).9 07,(9$,

O?!

H.%*&;%.1

(24)

Bid Slope: 30 Minute Means, 6-18

Index

Bid Slope

15 20 25 30

0 .0 0 0 1 0 .0 0 0 2 0 .0 0 0 3 0 .0 0 0 4 `-76*& !?_

Intra-Day Absolute Returns: Filtered Series

Index

0 10 20 30 40

(25)

10 20

0

2

4

6

8

1

0

1

2

Variogram for 1 second Increments: Hours 6 to 8

`-76*& !>_

B& 0//9-&3 #$& .'09&3 80*-17*0( #1 #$& %=>???@> 30#0 .&# ): ./9-##-27 #$& 30: -2#1 > $16* -2#&*809. 0. 4& (-7$# &</&'# .1(& 3-M&*-27 /0##&*2. 15 3&/&23&2'& #$*167$ #$& 30:A B& 6.&3 0 907 -2#&*809 15 ! .&'123. 023 0 #19&*02'& 4-2314 15 ?A! .&'123.A k&'06.& 15 #$& 3&2.-#: 15 #$& 30#0E #$-. (&02. #$0# &8&2 4$-'$ .6'$ 0 .(099 #19&*02'& 4-2314 4& 0*& 6.-27 #$16.023. 15 /0-*. 15 1).&80#-12. 51* &0'$ 907 -2#&*809A B& *&/1*# 0 .&@ 9&'#-12 15 *&.69#. 4$&*& 4& .$14 236 '12U3&2'& -2#&*809. '12.#*6'#&3 -2 #$& 519914-27 40:A B& *&#0-2 #$& .0(& #-(&@.'09& 0. -2 #$& 0'#609 -A&A

# ) # ) # ) %%%# ))6# 16* .6**170#& /*-'& .&*-&. 0*& 7&2&*0#&3 ): .-(690#-27

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

(26)

10 20

0

5

1

0

1

5

Variogram for 1 second Increments: Hours 8 to 10

`-76*& !W_

10 20

0

1

0

2

0

3

0

4

0

Variogram for 1 second Increments: Hours 10 to 12

`-76*& !]_

(27)

10 20

0

.0

0

.5

1

.0

1

.5

2

.0

Autocovariance for 1 second increments: Hours 6 to 8

`-76*& !"_

3:20(-'. A g&<# 4& '12.-3&*&3 4$0# D-23 15 -25&*&2'&. 4& (-7$# (0D& -5 4& 911D&3 0# 02 06#1'180*-02'& )0.&3 (&0.6*& 15 3&/&23&2'& -2.#&03 15 #$& 80*-17*0(A B& &.#-(0#&3 #$& .0(/9& 06#1'180*-02'& -2 #$& .0(& 40: 0. #$& 80*-17*0( Q6.-27 0 #19&*02'& 4-2314 0*1623 &0'$ 907 -2'*&@ (&2#+) 023 21*(09-N-27 ):L!%"SE 023 09.1 7&2&*0#&3 '12U3&2'& )023. -2 #$& .0(& 40:A `-76*&. !"E ![ 023 !^ .$14 #$& *&./&'#-8& /91#.A H2@ #&*&.#-279: 4& 31 21# .&& #$& *&P&'#-12 15 #$& 62-# *11# $:/1#$&.-. 8-0 #$& 06#1'180*-02'&E .677&.#-27 #$& 80*-17*0( -. -2 50'# 62'18&*-27 .1(& 3&8-0#-12 5*1( 62-# *11# )&$08-16* #$0# #$& 06#1'180*-02'& -. 21# /-'D@ -27 6/ A ,$&.& 80*-17*0(. 0*& 911D-27 0# 8&*: .$1*# #&*( 3&/&23&2'&E -# 41693 )& 15 7*&0# -2#&*&.# #1 911D 0# 9127&* #&*( 3&/&23&2'-&. 023 -2 /0*#-'690* $14 #$& 0//0*&2# 3&/&23&2': /0##&*2. 80*: 623&* 077*&70@ #-12A B& D214 51* &<0(/9& #$0# -# -. $0*3 #1 *&P&'# 0 62-# *11# -2 #$& &<'$027& *0#& 0# #$& 30-9: 9&8&9E023 4& '12P&'#6*& #$0# #$& #&(/1*09 3&@ /&23&2'& Q0. (&0.6*&3 ): )1#$ #$& 06#1'180*-02'& 023 #$& 80*-17*0(S 80*-&. 0. 4& 077*&70#& 6/ #1 914&* 5*&;6&2'-&.A

(28)

10 20

0

.0

0

.5

1

.0

1

.5

2

.0

Autocovariance for 1 second increments: Hours 8 to 10

`-76*& ![_

10 20

0

.0

0

.5

1

.0

1

.5

2

.0

Autocovariance for 1 second increments: Hours 10 to 12

`-76*& !^_

(29)

lag

Variogram Estimate

0 500 1000 1500

0

.6

0

.8

1

.0

1

.2

1

.4

Volume(t) to Returns(t+h)

`-76*& !R_

O?+

I%&,, H.%*&;%.1

`-76*&. !R #1 >? *&/1*#. #$& '*1.. 80*-17*0( )&#4&&2 #$*&& (-'*1 80*-@ 0)9&. 023 *&#6*2.A ,$& *&#6*2. .&*-&. -. .-(/9: #$& 3-M&*&2'&. -2 #$& '12.&'6#-8& Q917S /*-'&.E .1 #$&.& 31 21# '1**&./123 #1 #$& *&#6*2 18&* #$& .0(& #-(& -2#&*809E )6# -2.#&03 0*& )&.# #$167$# 15 0. #$& -2'*&(&2@ #09 /*-'& /*1'&..A ,$&.& '*1.. 80*-17*0(. 0*& &.#-(0#&3 12 #$& (0-2 30: .&7(&2#E )&#4&&2 [j= 023 !RL=A ,$& '12U3&2'& )023. 0*& 7&2&*0#&3 ): .0(/9-27 5*1( *&/90'&(&2# 5*1( #$& 1*-7-209 .&*-&.E #$&*&51*& /*18-3@ -27 0 2699 15 -23&/&23&2'& )&#4&&2 #$& #41 .&*-&.A `1* 099 #$*&& 80*-0)9&. #$&*& .&&(. #1 )& &8-3&2'& #$0# &0'$ 80*-0)9&. 0M&'#. 56#6*& *&#6*2. 51* 0 .$1*# /&*-13A ,$-. 4& 6.&3 0 907 -2#&*809 6.&3 51* #$& &.#-(0#-12 40. >? .&'123.E 023 #$& <@0<-. 12 #$& 7*0/$ 7-8&. #$& 907. -2 .&'123.A B& '02 .&& #$0# 8196(& 0//&0*. #1 $08& 02 &M&'# 12 *&#6*2. 51* 6/ #1 !?? .&'@ 123. 0$&03A i-;6-3-#: 0//&0*. (1.# 4&0D9: *&90#&3E 129: P6.# )*&0D-27 16# 15 #$& +"l '12U3&2'& )023. 51* 0)16# [? .&'123.A

,$&.& 80*-17*0(. 023 '*1.. 80*-17*0( *&.69#. .&&( #1 1M&* '9&0* -23-'0#-12 15 #&(/1*09 .#*6'#6*& 023 $&2'& /*&3-'#0)-9-#: -2 %=>???@ >E #$167$ '9&0*9: 4& 0*& #09D-27 0)16# 8&*: .$1*# #&*( 3&/&23&2'&A B$&#$&* 0 #*03&* '1693 &</91-# #$&.& 3&/&23&2'-&. -. 62'&*#0-2A h&*@ #0-29: 0 #*03&* '1693 21# '09'690#& #$& (-'*1.#*6'#6*09 80*-0)9&. -2 *&09 #-(& 0. 4& $08&E )6# #1 #$& &<#&2# #$0# 9-;6-3-#: -. 3&#&*(-2-.#-'099:

(30)

lag

Variogram Estimate

0 500 1000 1500

0

.6

0

.8

1

.0

1

.2

1

.4

Spread(t) to Returns(t+h)

`-76*& !+_

lag

Variogram Estimate

0 500 1000 1500

0

.6

0

.8

1

.0

1

.2

1

.4

Liquidity(t) to Returns(t+h)

`-76*& >?_

(31)

/*&3-'#0)9& Q12 #-(& 15 30: 51* &<0(/9&S #$&*& (0: )& .1(& .'1/& 51* &</91-#-27 #$& 50'# #$0# .$1*# #&*( 3&/&23&2'-&. (0: 80*: #$*167$ #$& 30:A V2& (-7$# 09.1 #*: 023 '12.#*6'# *&09 #-(& 80*-0)9&. #$0# (-7$# 7-8& .1(& -23-'0#-12 15 #$& 3&/#$ 15 #$& (0*D&#E 9-D& #$& 26()&* 15 #*02.0'@ #-12. -2 #$& 90.#*.&'123.E 1* #$& 8196(& 080-90)9& 0# #$& ./*&03 /*-'&.A V5 '16*.& #*03&*. #$&(.&98&. $08& 0 5&&9 51* #$& 3&/#$ 15 #$& (0*D&#E 023 (0: -2 50'# #$*167$16# #$& 30: &2#&* 9-(-# 1*3&*. 0# 1M@(0*D&# /*-'&. -2 1*3&* #1 7607& #$& 3&/#$A

Q

07;*17, &A J%7'*)$.=*9*$/ .,,&)*.$7' :*$6 M.)%&

P>7#$,R

`-2099: 4& *&#6*2 #1 #$& -..6& *0-.&3 -2 #$& -2#*136'#-12 4$-'$ 40. #$& ;6&.#-12 15 $14 (-'*1 023 (0'*1 (13&9. 15 #$& &<'$027& *0#& (0: )& *0@ #-1209-.&3A H2 /0*#-'690* 4& 402# #1 '12.-3&* 4$0# -(/0'# (0'*1 &8&2#. $08& $03 12 #$& (-'*1 .#*6'#6*& 15 #$& (0*D&#E 4$0# /&*.-.#&2'& &<-.#. 023 4$&#$&* 0 7*&0#&* 3&7*&& 15 /*&3-'#0)-9-#: '02 )& 51623 0*1623 .6'$ &8&2#.A H2 16* 12& 4&&D .0(/9& 4& 0*& 51*#620#& #1 U23 #41 .6'$ &8&2#.C 12 #$& ^n!?n+^ #$& 02#-'/0#&3 )6# 62U99&3 (0*D&# ./&'690#-12 15 0 *&@ /*1 *0#& -2'*&0.& ): #$& k623&.)02D 023 #$&2 12 #$& +n!?n+^ 4$&2 #$& *&/1 *0#& 40. -2 50'# -2'*&0.&3 ): W? )0.-. /1-2#. 51* #$& U*.# #-(& -2 U8& :&0*.A Z&7-(&. 15 /*&3-'#0)-9-#: $08& )&&2 51623 -2 0 26()&* 15 &0*@ 9-&* .#63-&. -2'963-27 16* 142 /*&8-16. 41*DE K60*30 023 I09(12Q!++^S 023 J-99(02Q!++RS 023 4& )&9-&8& #$& .0(& -3&0. 4-99 $193 12 #$& #*02.@ 0'#-12. #-(& .'09&A H2 #$-. &0*9-&* 41*D 4& $08& &(/$0.-.&3 #$0# #$& 3&8&91/(&2# 15 .&8&*09 91'09 (13&9. 4-#$ 3-.#-2'# *&7-(&. 15 )&$08-16* -. 0 (1*& /*1U#0)9& *16#& #1 519914 #$02 02: 0##&(/# #1 '12.*6'# 0 '1(@ /9&< 791)09 (13&9 #$0# 0##&(/#. #1 0''162# 51* .&8&*09 3-M&*&2# (13&. 15 )&$08-16*A K&2&*099: #$& .#63: 15 .6'$ #*02.-#-12. -. '1256.&3 ): #&(/1*09 077*&70#-12 15 #$& 30#0 )6# 4-#$ #$& '6**&2# 30#0 .&# 4& $08& (0*D&# -251*(0#-12 3142 #1 #$& $623*&3#$ 15 0 .&'123A

`-76*&Q>!S .$14. #$& (18&(&2# #$& &<'$027& *0#& 18&* #$& 30: 15 ^n!?n+^E #$& ./*&03 18&* #$& .0(& /&*-13 023 #$& )-3 023 1M&* .91/&.A B& &</&'# #$&.& .91/&. #1 )&'1(& 8&*: .&2.-#-8& 0. #*03&*. 51*( 3-M&*@ -27 8-&4. *&70*3-27 #$& 56#6*& &;6-9-)*-6( &<'$027& *0#&A `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

(32)

15 #$& )-3 '6*8& -2'*&0.&. 4$-9& #$& 1M&* '6*8& b0##&2. 16#.A ,$&*& -. '12.-3&*0)9: (1*& 62'&*#0-2#: 12 #$& 1M&* .-3& 15 #$& (0*D&# /*-1* #1 #$& &8&2# #$02 -((&3-0#&9: 05#&*40*3.A

,$& -2'*&0.& 15 #$& *&/*1 *0#& 12 +n!?n+^ '9&0*9: $03 02 -((&3-0#& -(/0'# 12 #$& (0*D&# 4$-'$ 0//&0*. #1 $08& )&&2 90*7&9: 62&</&'#&3 0. '02 )& .&&2 5*1( U76*&Q>>SA H# 09.1 .&&(. #1 $08& #0D&2 #$& (0*D&# (6'$ 9127&*E .&8&*09 $16*. -2 50'# #1 3-7&.# #$& 2&4. 023 #1 U23 0 2&4 &;6-9-)*-6( #$02 .677&.#&3 -2 #$& .6*8&: ): h$&627E h$-2 023 =0*.$Q!+++SA H# 41693 .&&( #1 )& '9&0* 5*1( #$& .6)/02&9. -2 `-76*&Q>>S #$0# #$& *&/1 022162'&(&2# 9&3 #1 02 -((&3-0#& 0//*&'-0#-12 15 #$& %=0*D 023 02 -((&3-0#& .6).#02#-09 4-3&2-27 15 #$& ./*&03 023 070-2 0 3*0(0#-' -2'*&0.& 0# #$& #-(& 15 #$& 022162'&(2# 12 #$& .91/& 15 #$& 1M&* '6*8& 4-#$ 9-##9& 1* 21 '$027& -2 #$& )-3 .91/&A,$& ;6&.#-12 214 0*-.&. 15 4$&#$&* 1* 21# #$&*& -. 02: -2'*&0.&3 /*&3-'#0)-9-#:E #1 )& 51623 -((&3-0#&9: 05#&* #$& &8&2#A `-76*&.Q>WSEQ>"S 023 Q>]S .$14 #$& '*1.. 80*-17*0( *&.69#. 51* +n!?n+^ )&#4&&2 #$& (-'*1 80*-0)9&. 023 56#6*& *&#6*2.A B& '02 .&& -((&3-0#&9: #$0# #$&*& -. (6'$ .#*127&* *&P&'#-12 15 -23&/&23&2'& )&#4&&2 #$&.& 80*-0)9&. 12 #$-. 30:E #$&2 #$&*& 40. 18&* #$& 4$19& 4&&DA H2 /0*#-'690* #$&*& -. 214 '9&0* &8-3&2'& 15 3&/&23&2'& )&#4&&2 #$& 9-;6-3-#: 80*-0)9& 023 56#6*& *&#6*2.A j/0*# 5*1( #$& .$1*# #&*( 3&/&23&2'& #$0# 90.# 5*1( )&#4&&2 ! 023 > (-26#&.E #$&*& 09.1 0//&0*. #1 )& .1(& &8-3&2'& 15 (1*& 9127 #&*( 3&/&23&2'& Q#$& ./*&03 -2 /0*#-'690*S 4-#$ 9127&* 907 &.#-(0#&. 15 #$& '*1.. 80*-17*0( 5099-27 16#.-3& #$& '12U3&2'& )023.A

I1E -# 0//&0*. #$0# 12 #$& +#$ #$&*& -. .1(&4$0# (1*& 3&/&23&2'& )&#4&&2 #$& (-'*1 80*-0)9&. 023 56#6*& *&#6*2.A `-2099: 4& 0.D 0 .-(/9& ;6&.#-12 15 #$& 30#0A H. #$-. 3&/&23&2'& 1).&*8&3 #$*167$16# #$& 30:E 1* 0. 4& .6./&'#E 05#&* #$& k623&.)02D 022162'&(&2# #0D&. /90'& 023 #$& (0*D&# 03P6.#. #1 #$& 2&4 &;6-9-)*-6( &<'$027& *0#&q B& ./9-# #$& 30: -2#1 0 /*& 023 0 /1.# 022162'&(&2# .&7(&2#E 023 *&.#-(0#&3 #$& '*1.. 80*-17*0(.A `-76*&. >[ #1 W! '12U*( 16* -2#6-#-12A B& '02O# *&P&'# #$& 2699 15 -23&/&23&2'& /*&@022162'&(&2#E )6# '9&0*9: '02 31 .1 /1.#@022162'&(&2#A

S

I&#)9(,*&#

V2 #$& )0.-. 15 #$& *&.69#. /*&.&2#&3 0)18& 4& U23 -# 8&*: 3-T'69# #1 )&9-&8& #$0# #$&*& -. 21 /*&3-'#0)-9-#: -2 #$& %1990*n%(0*D #*02.0'#-12. 30#0 -2 %=>???@>A B& 5&&9 #$& 50'# #$0# 4& U23 #$-. *&.69# -. -2 /0*# 36& #1 #$& '$1-'& 15 .#0#-.#-'09 #&'$2-;6& 023 #$-. &</&*-&2'& 9&03. 6. #1 .677&.# #$0# #$& 80*-17*0( (0: /*18-3& 0 )&##&* #119 #1 &</91*& #$& -..6& 15 U23-27 .#*6'#6*& -2 -**&7690*9: ./0'&3 30#0 *0#$&* #$02 .#0230*3 06#1'1**&917*0( 0209:.-.A ,$& 2&<# .#07& 15 #$-. *&.&0*'$ (0: )& #1

(33)

Seconds

Price

630000 640000 650000 660000 670000

1

.7

4

5

1

.7

5

5

Exchange Rate

Seconds

Spread

630000 640000 650000 660000 670000

0

.0

0

.0

0

1

5

Spread

Seconds

Bid Slope

630000 640000 650000 660000 670000

-0

.0

0

0

8

-0

.0

0

0

2

Bid Slope

Seconds

Offer Slope

630000 640000 650000 660000 670000

0

.0

0

.0

0

1

0

Offer Slope

`-76*& >!_ ,$& =-'*1 f0*-0)9&. 12 #$& ^#$ V'#1)&* !++^

(34)

Seconds

Price

800000 810000 820000 830000 840000

1

.7

3

5

1

.7

5

0

Exchange Rate

Seconds

Spread

800000 810000 820000 830000 840000

0

.0

0

.0

0

3

0

.0

0

6

Spread

Seconds

Bid Slope

800000 810000 820000 830000 840000

-0

.0

0

1

4

-0

.0

0

0

4

Bid Slope

Seconds

Offer Slope

800000 810000 820000 830000 840000

0

.0

0

.0

0

1

0

Offer Slope

`-76*& >>_ ,$& =-'*1 f0*-0)9&. 12 #$& +#$ V'#1)&* !++^

(35)

lag

Variogram Estimate

0 200 400 600 800

0

.6

0

.8

1

.0

1

.2

1

.4

1

.6

1

.8

Liquidity(t) to Returns(t+h) 9th October 1997

`-76*& >W_

lag

Variogram Estimate

0 200 400 600 800

0

.6

0

.8

1

.0

1

.2

1

.4

1

.6

1

.8

Spread(t) to Returns(t+h) 9th October 1997

`-76*& >]_

References

Related documents

Cloud computing has had a significant influence on the development of smart cities, affecting the 

Chapter 7, “ Innovation Management at AIT Department Digital Safety &amp; Security” , summarizes the gate based designed innovation management process for the R&amp;D

Nash equilibrium rates of play are calculated which depend on move costs and the threshold of resources required for the attacker to gain any benefit.. A major downside of the

On the other hand, efficiency of the device in power absorption, energy capturing, energy extraction and energy exchange were optimised by using the biomimetic design

Be-cause of that, we would like to propose a solution which engages our previous prediction method [4] and convex optimization tech-nique to reduce the energy

Although there are problems in dataset integration, querying and reasoning and the management of uncertainty, as an illustration we focus on exploring semantic web technologies can

 More positive illness models are associated with better personal recovery in bipolar disorder, over and above mood symptoms..  Recovery-focused therapy should focus on