Global Risk Aversion Spillover Dynamics and Investors’ Attention Allocation

Munich Personal RePEc Archive

Global Risk Aversion Spillover Dynamics and Investors’ Attention Allocation

Ceylan, Özcan

Istanbul Kemerburgaz University

9 May 2016

Online at https://mpra.ub.uni-muenchen.de/71320/

MPRA Paper No. 71320, posted 17 May 2016 09:15 UTC

●❧♦❜❛❧ ❘✐s❦ ❆✈❡rs✐♦♥ ❙♣✐❧❧♦✈❡r ❉②♥❛♠✐❝s ❛♥❞ ■♥✈❡st♦rs✬

❆tt❡♥t✐♦♥ ❆❧❧♦❝❛t✐♦♥

Ö③❝❛♥ ❈❡②❧❛♥

▼❛② ✾✱ ✷✵✶✻

❆❜str❛❝t

❚❤✐s ♣❛♣❡r ✐♥✈❡st✐❣❛t❡s ♠❛r❦❡t✲✇✐❞❡ r✐s❦ ❛✈❡rs✐♦♥ ✐♥ ❛♥ ✐♥t❡r♥❛t✐♦♥❛❧ s❡tt✐♥❣✳ P❛rt✐❝✉❧❛r❧②✱

t❤✐s ❡♠♣✐r✐❝❛❧ st✉❞② ❡✈❛❧✉❛t❡s r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡r ❞②♥❛♠✐❝s ❛s ❛♥ ✉♥❝❡rt❛✐♥t② tr❛♥s♠✐ss✐♦♥

♠❡❝❤❛♥✐s♠ ❢♦r t❤❡ ♣❡r✐♦❞ ✷✵✵✵✲✷✵✶✺ t♦ r❡✈❡❛❧ ✐❢ t❤❡r❡ ❤❛s ❜❡❡♥ ❛ s✐❣♥✐✜❝❛♥t ❝❤❛♥❣❡ ✐♥ t❤❡s❡

❞②♥❛♠✐❝s ✇❤❡♥ ♠❛r❦❡ts ❛r❡ ❣♦✐♥❣ t❤r♦✉❣❤ t✉r❜✉❧❡♥t ♣❡r✐♦❞s✳ ❆s ❛ ♣❧❛✉s✐❜❧❡ ♣r♦①② ❢♦r r✐s❦

❛✈❡rs✐♦♥✱ ✈❛r✐❛♥❝❡ r✐s❦ ♣r❡♠✐✉♠ ✭❱❘P✮ ✐s ❝♦♠♣✉t❡❞ t❤r♦✉❣❤ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❡①♣❡❝t❡❞

✈❛r✐❛♥❝❡s ✉♥❞❡r r✐s❦✲♥❡✉tr❛❧ ❛♥❞ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡s ❢♦r s❡✈❡♥ ♠❛r❦❡ts st✉❞✐❡❞✿ ❯♥✐t❡❞ ❙t❛t❡s✱

❯♥✐t❡❞ ❑✐♥❣❞♦♠✱ ●❡r♠❛♥②✱ ❋r❛♥❝❡✱ ◆❡t❤❡r❧❛♥❞s✱ ❙✇✐t③❡r❧❛♥❞ ❛♥❞ ❏❛♣❛♥✳ ❊✛❡❝ts ♦❢ ❛ s❤♦❝❦

t♦ ❯✳❙✳ ❱❘P ♦♥ t❤❡ ♦t❤❡r ♠❛r❦❡ts✬ ❱❘Ps ❛r❡ ❡✈❛❧✉❛t❡❞ t❤r♦✉❣❤ ●❡♥❡r❛❧✐③❡❞ ❋♦r❡❝❛st ❊rr♦r

❱❛r✐❛♥❝❡ ❉❡❝♦♠♣♦s✐t✐♦♥✳ ❘❡s✉❧ts s❤♦✇ t❤❛t r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡rs ❢r♦♠ ❯✳❙✳ t♦ ♦t❤❡r ♠❛r❦❡ts

❛r❡ str♦♥❣❡r ✇❤✐❧❡ t❤❡ ❯✳❙✳ ✐s ❣♦✐♥❣ t❤r♦✉❣❤ t✉r❜✉❧❡♥t ♣❡r✐♦❞s ❝♦♥✜r♠✐♥❣ t❤❡ ✐♥t✉✐t✐♦♥ t❤❛t

✐♥✈❡st♦rs ❛r❡ ♠♦r❡ ❢♦❝✉s❡❞ ♦♥ ✐♥❝✐❞❡♥ts ✐♥ t❤❡ t✉r❜✉❧❡♥t ♠❛r❦❡t✳ ▼❛r❦❡ts ❜❡❝♦♠❡ ♠♦r❡ ❝♦♥✲

♥❡❝t❡❞ ✐♥ t❡r♠s ♦❢ s❡♥t✐♠❡♥ts ✇❤❡♥ ❛ ❝♦✉♥tr② ✐s ✉♥❡①♣❡❝t❡❞❧② ❤✐t ❜② ❛ ♠❛❥♦r ❝r✐s✐s✱ ❧✐♠✐t✐♥❣

❞✐✈❡rs✐✜❝❛t✐♦♥ ♦♣♣♦rt✉♥✐t✐❡s✳

❏❊▲ ❈❧❛ss✐✜❝❛t✐♦♥✿ ❉✽✱ ❋✸✻✱ ●✶✹✱ ●✶✺✳

❑❡②✇♦r❞s✿ ■♥✈❡st♦r s❡♥t✐♠❡♥t✱ ❘✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡rs✱ ❱❛r✐❛♥❝❡ r✐s❦ ♣r❡♠✐✉♠✱ ●❡♥❡r❛❧✐③❡❞

❢♦r❡❝❛st ❡rr♦r ✈❛r✐❛♥❝❡ ❞❡❝♦♠♣♦s✐t✐♦♥✱ ■♥✈❡st♦rs✬ ❛tt❡♥t✐♦♥ ❛❧❧♦❝❛t✐♦♥✱ ❋✐♥❛♥❝✐❛❧ ❝r✐s❡s✳

∗■st❛♥❜✉❧ ❑❡♠❡r❜✉r❣❛③ ❯♥✐✈❡rs✐t②✱ ❊✲♠❛✐❧✿ ♦③❝❛♥✳❝❡②❧❛♥❅❦❡♠❡r❜✉r❣❛③✳❡❞✉✳tr✱ P❤♦♥❡✿ ✾✵✲✷✶✷✲✻✵✹✵✶✺✸✲✹✵✺✸✱

❋❛①✿ ✾✵✲✷✶✷✲✹✹✺✾✷✺✺✳

✶

✶ ■♥tr♦❞✉❝t✐♦♥

❋♦❧❧♦✇✐♥❣ t❤❡ ✷✵✵✼ s✉❜♣r✐♠❡ ❝r✐s✐s✱ ❡♠♣✐r✐❝❛❧ ❛♥❞ t❤❡♦r❡t✐❝❛❧ st✉❞✐❡s ♦♥ ❝♦♥t❛❣✐♦♥ ❤❛✈❡ r❡❣❛✐♥❡❞

❛tt❡♥t✐♦♥✳ ❊❛r❧② st✉❞✐❡s ❤❛✈❡ ❝♦♥❝❡✐✈❡❞ t❤❡ ❝♦♥t❛❣✐♦♥ ♣❤❡♥♦♠❡♥♦♥ ✐♥ ❛ ✈❡r② ❜r♦❛❞ s❡♥s❡✱ ❛s

❜❡✐♥❣ ❛♥② ❝r♦ss✲❝♦✉♥tr② tr❛♥s♠✐ss✐♦♥ ♦❢ s❤♦❝❦s✳ ❋✉♥❞❛♠❡♥t❛❧s✲❜❛s❡❞ ❡①♣❧❛♥❛t✐♦♥s ♦❢ ❝♦♥t❛❣✐♦♥

❞♦♠✐♥❛t❡❞ t❤✐s ❣❡♥❡r❛t✐♦♥ ♦❢ st✉❞✐❡s✳ ❙♦♠❡ ♣❛♣❡rs ❛r❣✉❡❞ t❤❛t s❤♦❝❦s ❛r❡ tr❛♥s♠✐tt❡❞ t❤r♦✉❣❤

tr❛❞❡ ❧✐♥❦s t❤❛t ❝♦♥♥❡❝t ❞✐✛❡r❡♥t ❝♦✉♥tr✐❡s ✭●❧✐❝❦ ❛♥❞ ❘♦s❡✱ ✶✾✾✾✮✱ ✇❤✐❧❡ s❡✈❡r❛❧ ♦t❤❡rs ❡♠♣❤❛s✐③❡

t❤❡ r♦❧❡ ♦❢ ✜♥❛♥❝✐❛❧ ❧✐♥❦❛❣❡s ✐♥ ♣r♦♣❛❣❛t✐♦♥ ♦❢ ❝r✐s❡s ✭❑❛♠✐♥s❦② ❛♥❞ ❘❡✐♥❤❛rt✱ ✷✵✵✵✮✳ ❆♥♦t❤❡r str❛♥❞ ♦❢ ❧✐t❡r❛t✉r❡ ❛❞♦♣t❡❞ ❛ r❡str✐❝t✐✈❡ ❞❡✜♥✐t✐♦♥✱ ❝♦♥✜♥✐♥❣ t❤❡ ❝♦♥t❛❣✐♦♥ ♣❤❡♥♦♠❡♥♦♥ t♦ ❡①❝❡s✲

s✐✈❡ ❝r♦ss✲❝♦✉♥tr② ❝♦rr❡❧❛t✐♦♥s✱ ❜❡②♦♥❞ ✇❤❛t ❝❛♥ ❜❡ ❡①♣❧❛✐♥❡❞ t❤r♦✉❣❤ tr❛❞❡ ❛♥❞ ❝r❡❞✐t ❝❤❛♥♥❡❧s✳

❇❡❤❛✈✐♦r❛❧ ❛r❣✉♠❡♥ts ❛r❡ ❡♠♣❧♦②❡❞ t♦ ❡①♣❧❛✐♥ t❤❡s❡ ❡①❝❡ss✐✈❡ ❝♦rr❡❧❛t✐♦♥s✳ ❚❤❡ r♦❧❡ ♦❢ ❛ r✐s❦ ♣r❡✲

♠✐✉♠ ❝❤❛♥♥❡❧ ✐s str❡ss❡❞ ✇✐t❤✐♥ t❤❡s❡ ❜❡❤❛✈✐♦r❛❧ ❛r❣✉♠❡♥ts✳ ❲❤❡♥ ♦♥❡ ♠❛r❦❡t ✐s ❤✐t ❜② ❛♥ ❛❞✈❡rs❡

s❤♦❝❦✱ ✐♥✈❡st♦rs✬ r✐s❦ ❛✈❡rs✐♦♥ ✐♥❝r❡❛s❡s✳ ❚❤✐s s❤✐❢t ✐♥ ✐♥✈❡st♦r s❡♥t✐♠❡♥t ❧❡❛❞s t♦ ❛♥ ✉♣✇❛r❞ ❛❞✲

❥✉st♠❡♥t ♦❢ r✐s❦ ♣r❡♠✐❛ ♦♥ ❛❧❧ r✐s❦② ❛ss❡ts ✭❑✉♠❛r ❛♥❞ P❡rs❛✉❞✱ ✷✵✵✷✮✳ ▲♦♥❣st❛✛ ✭✷✵✶✵✮ ✜♥❞s t❤❛t

♥❡❣❛t✐✈❡ s❤♦❝❦s t♦ s✉❜♣r✐♠❡ ❛ss❡t✲❜❛❝❦❡❞ ❝♦❧❧❛t❡r❛❧✐③❡❞ ❞❡❜t ♦❜❧✐❣❛t✐♦♥s ♠❛r❦❡t ❛r❡ ♣r♦♣❛❣❛t❡❞

t♦ ♦t❤❡r ♠❛r❦❡ts ♣r✐♠❛r✐❧② t❤r♦✉❣❤ t✐♠❡✲✈❛r②✐♥❣ r✐s❦ ♣r❡♠✐❛✳ ❇❛❦❡r ❡t ❛❧✳ ✭✷✵✶✷✮ s✉❣❣❡st t❤❛t

✐♥✈❡st♦r s❡♥t✐♠❡♥t ✐ts❡❧❢ ✐s ❝♦♥t❛❣✐♦✉s ❛♥❞ t❤❛t ✐♥t❡r♥❛t✐♦♥❛❧ ❝❛♣✐t❛❧ ✢♦✇s ❝♦♥st✐t✉t❡ ❛♥ ✐♠♣♦rt❛♥t

♠❡❝❤❛♥✐s♠ ❜② ✇❤✐❝❤ s❡♥t✐♠❡♥t s♣r❡❛❞s ❛❝r♦ss ♠❛r❦❡ts✳ ❆♥ ✐♥t❡r❡st✐♥❣ ♣❛♣❡r ❜② ▼♦♥❞r✐❛ ❛♥❞

◗✉✐♥t❛♥❛✲❉♦♠❡q✉❡ ✭✷✵✶✸✮ s✉❣❣❡st t❤❛t s✉❞❞❡♥ s❤✐❢ts ✐♥ ♠❛r❦❡t ❝♦♥✜❞❡♥❝❡ ❝❛✉s❡ ❝♦♥t❛❣✐♦♥✳ ❚❤❡②

❡♠♣✐r✐❝❛❧❧② ✜♥❞ t❤❛t ✇❤❡♥ ❛ r❡❣✐♦♥ ✐s ❤✐t ❜② ❛ ✜♥❛♥❝✐❛❧ ❝r✐s✐s✱ ✐♥✈❡st♦rs ♦♣t✐♠❛❧❧② r❡❧♦❝❛t❡ t❤❡✐r

❛tt❡♥t✐♦♥ t♦ t❤✐s r❡❣✐♦♥ ❛♥❞ t❤❛t t❤✐s ❛tt❡♥t✐♦♥ r❡❧♦❝❛t✐♦♥ ❧❡❛❞s t♦ ✈♦❧❛t✐❧✐t② tr❛♥s♠✐ss✐♦♥ ❢r♦♠ t❤❡

t✉r❜✉❧❡♥t r❡❣✐♦♥ t♦ t❤❡ ♦t❤❡rs✳ ❚❤❡ ❧❡ss ❛♥t✐❝✐♣❛t❡❞ t❤❡ ❝r✐s✐s ✐s✱ t❤❡ ♠♦r❡ ❢♦❝✉s❡❞ t❤❡ ✐♥✈❡st♦rs

✇♦✉❧❞ ❜❡ ♦♥ t❤❡ t✉r❜✉❧❡♥t r❡❣✐♦♥✱ ❣✐✈✐♥❣ r✐s❡ t♦ ❛ ❤✐❣❤❡r ❝♦♥t❛❣✐♦♥✳

❘❡❧❛t❡❞ t♦ t❤❡ ❛❜♦✈❡ st✉❞✐❡s ❤✐♥❣✐♥❣ ♦♥ t❤❡ r✐s❦ ♣r❡♠✐✉♠ ❝❤❛♥♥❡❧ t♦ ❡①♣❧❛✐♥ ✈♦❧❛t✐❧✐t② s♣✐❧❧♦✈❡rs✱

t❤✐s ♣❛♣❡r ✐♥✈❡st✐❣❛t❡s ♠❛r❦❡t✲✇✐❞❡ r✐s❦ ❛✈❡rs✐♦♥ ✐♥ ❛♥ ✐♥t❡r♥❛t✐♦♥❛❧ s❡tt✐♥❣✳ ❆s ❛ ♣❧❛✉s✐❜❧❡ ♣r♦①②

❢♦r r✐s❦ ❛✈❡rs✐♦♥✱ ✈❛r✐❛♥❝❡ r✐s❦ ♣r❡♠✐✉♠ ✭❱❘P✮ ✐s ❝♦♠♣✉t❡❞ t❤r♦✉❣❤ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❡①✲

♣❡❝t❡❞ ✈❛r✐❛♥❝❡s ✉♥❞❡r r✐s❦✲♥❡✉tr❛❧ ❛♥❞ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡s✳ ❚❤❡ r✐s❦✲♥❡✉tr❛❧ ♠❡❛s✉r❡s ❛r❡ r❡❛❞✐❧②

♣r♦✈✐❞❡❞ ❜② ❱■❳✲t②♣❡ ✐♠♣❧✐❡❞ ✈♦❧❛t✐❧✐t② ✐♥❞❡①❡s ❢♦r s❡✈❡♥ ♠❛r❦❡ts st✉❞✐❡❞✿ ❯♥✐t❡❞ ❙t❛t❡s✱ ❯♥✐t❡❞

❑✐♥❣❞♦♠✱ ●❡r♠❛♥②✱ ❋r❛♥❝❡✱ ◆❡t❤❡r❧❛♥❞s✱ ❙✇✐t③❡r❧❛♥❞ ❛♥❞ ❏❛♣❛♥✳ ❚❤❡ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡s ❛r❡ ❜❛s❡❞

✶

♦♥ r❛♥❣❡✲❜❛s❡❞ ✈♦❧❛t✐❧✐t✐❡s t❤❛t ❛r❡ ❝♦♠♣✉t❡❞ ✉s✐♥❣ ❞❛✐❧② st♦❝❦ ✐♥❞❡① ❞❛t❛✳ ❚❤❡ r✐s❦✲♥❡✉tr❛❧ ♠❡❛✲

s✉r❡ ♣r♦✈✐❞❡s ✉s ✇✐t❤ t❤❡ ✐♠♣❧✐❡❞ ✈♦❧❛t✐❧✐t② t❤❛t ❝❛♣t✉r❡s ✐♥✈❡st♦rs✬ ♣❡r❝❡♣t✐♦♥ ♦♥ t❤❡ ✉♥❝❡rt❛✐♥t②

❢♦r t❤❡ ✉♣❝♦♠✐♥❣ ♠♦♥t❤ ✇❤❡r❡❛s t❤❡ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡ ❣✐✈❡s t❤❡ ❡①♣❡❝t❡❞ ❧❡✈❡❧ ♦❢ ❛❝t✉❛❧ ✈♦❧❛t✐❧✐t②

❢♦r t❤❡ s❛♠❡ ♣❡r✐♦❞✳ ❚❤✐s t✐♠❡✲✈❛r②✐♥❣ r✐s❦ ❛✈❡rs✐♦♥ ✐s ❛ ♥♦t❡✇♦rt❤② ❢❛❝t♦r ❜❡❤✐♥❞ ✢✉❝t✉❛t✐♦♥s ✐♥

t❤❡ r✐s❦ ♣r❡♠✐❛✳ ■t ✐s t❤✉s ✇♦rt❤ t♦ ❛♥❛❧②③❡ r✐s❦ ♣r❡♠✐✉♠ s♣✐❧❧♦✈❡rs ❛s ❛♥ ✐♠♣♦rt❛♥t ❛s♣❡❝t r❡❧❛t❡❞

t♦ t❤❡ r✐s❦ ♣r❡♠✐✉♠ ❝❤❛♥♥❡❧✳

❚❤✐s ❡♠♣✐r✐❝❛❧ st✉❞② ❡✈❛❧✉❛t❡s r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡r ❞②♥❛♠✐❝s ❢♦r t❤❡ ♣❡r✐♦❞ ✷✵✵✵✲✷✵✶✺✳ ❚❤✐s

♣❡r✐♦❞ ✐s ❞✐✈✐❞❡❞ ✐♥t♦ ✜✈❡ s✉❜♣❡r✐♦❞s ❝♦✈❡r✐♥❣ tr❛♥q✉✐❧ ♦r t✉r❜✉❧❡♥t st❛t❡s ✐♥ t❤❡ ❯✳❙✳ ❛♥❞ ❊✉✲

r♦♣❡❛♥ ✜♥❛♥❝✐❛❧ ♠❛r❦❡ts✳ ❋♦r ❡❛❝❤ ♣❡r✐♦❞✱ r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡rs ❛r❡ st✉❞✐❡❞ ❛s ❛♥ ✉♥❝❡rt❛✐♥t② tr❛♥s♠✐ss✐♦♥ ♠❡❝❤❛♥✐s♠ t♦ r❡✈❡❛❧ ✐❢ t❤❡r❡ ❤❛s ❜❡❡♥ ❛ s✐❣♥✐✜❝❛♥t ❝❤❛♥❣❡ ✐♥ t❤❡ s♣✐❧❧♦✈❡r ❞②♥❛♠✐❝s

❡s♣❡❝✐❛❧❧② ❛r♦✉♥❞ s✉❜♣r✐♠❡ ♠♦rt❣❛❣❡ ❝r✐s✐s✳ ❊✛❡❝ts ♦❢ ❛ s❤♦❝❦ t♦ ❯✳❙✳ ❱❘P ♦♥ t❤❡ ♦t❤❡r ♠❛r❦❡ts✬

❱❘Ps ❛r❡ ❡✈❛❧✉❛t❡❞ t❤r♦✉❣❤ ●❡♥❡r❛❧✐③❡❞ ❋♦r❡❝❛st ❊rr♦r ❱❛r✐❛♥❝❡ ❉❡❝♦♠♣♦s✐t✐♦♥ ✭●❋❊❱❉✮ ❞❡✲

✈❡❧♦♣❡❞ ❜② P❡s❛r❛♥ ❛♥❞ ❙❤✐♥ ✭✶✾✾✽✮✳ ❘❡s✉❧ts s❤♦✇ t❤❛t r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡rs ❢r♦♠ ❯✳❙✳ t♦ ♦t❤❡r

♠❛r❦❡ts ❛r❡ str♦♥❣❡r ✇❤✐❧❡ t❤❡ ❯✳❙✳ ✐s ❣♦✐♥❣ t❤r♦✉❣❤ t✉r❜✉❧❡♥t ♣❡r✐♦❞s ❝♦♥✜r♠✐♥❣ t❤❡ ✐♥t✉✐t✐♦♥ t❤❛t

✐♥✈❡st♦rs ❛r❡ ♠♦r❡ ❢♦❝✉s❡❞ ♦♥ ✐♥❝✐❞❡♥ts ✐♥ t❤❡ t✉r❜✉❧❡♥t ♠❛r❦❡t✳ ▼❛r❦❡ts ❜❡❝♦♠❡ ♠♦r❡ ❝♦♥♥❡❝t❡❞

✐♥ t❡r♠s ♦❢ s❡♥t✐♠❡♥ts ✇❤❡♥ ❛ ❝♦✉♥tr② ✐s ✉♥❡①♣❡❝t❡❞❧② ❤✐t ❜② ❛ ♠❛❥♦r ❝r✐s✐s✱ ❧✐♠✐t✐♥❣ ❞✐✈❡rs✐✜❝❛t✐♦♥

♦♣♣♦rt✉♥✐t✐❡s ✇❤❡♥ ✐♥✈❡st♦rs ❛r❡ ♠♦st ✐♥ ♥❡❡❞ ♦❢ t❤❡ ❣❛✐♥s st❡♠♠✐♥❣ ❢r♦♠ ❞✐✈❡rs✐✜❝❛t✐♦♥✳

❚❤❡ r❡♠❛✐♥❞❡r ♦❢ t❤❡ ♣❛♣❡r ✐s ❛s ❢♦❧❧♦✇s✿ ❚❤❡ s❡❝♦♥❞ s❡❝t✐♦♥ ✐♥tr♦❞✉❝❡s t❤❡ ❝♦♥str✉❝t✐♦♥

♦❢ ✈♦❧❛t✐❧✐t② ♠❡❛s✉r❡s✳ ❘❛♥❣❡✲❜❛s❡❞ ✈♦❧❛t✐❧✐t✐❡s✱ ♣❤②s✐❝❛❧ ❛♥❞ r✐s❦✲♥❡✉tr❛❧ ♠❡❛s✉r❡s ♦❢ ❡①♣❡❝t❡❞

♠❡❛s✉r❡s t❤❛t ❛r❡ ✉s❡❞ t♦ ❡st✐♠❛t❡ ❱❘Ps ❛s ❛ ♣r♦①② ❢♦r ♠❛r❦❡t✲✇✐❞❡ r✐s❦ ❛✈❡rs✐♦♥ ❧❡✈❡❧s ❛r❡

s❤♦rt❧② ❞✐s❝✉ss❡❞ ❤❡r❡✳ ❉❛t❛ ✉s❡❞ ❢♦r t❤❡ ❛♥❛❧②s✐s ✐s ❣✐✈❡♥ ✐♥ t❤❡ t❤✐r❞ s❡❝t✐♦♥✳ ❚❤❡ ❢♦✉rt❤ s❡❝t✐♦♥

♣r❡s❡♥ts t❤❡ ❡♠♣✐r✐❝❛❧ ♠❡t❤♦❞♦❧♦❣② ❞✐s❝✉ss❡s t❤❡ ❡♠♣✐r✐❝❛❧ r❡s✉❧ts✳ ❚❤❡ ✜❢t❤ s❡❝t✐♦♥ ❝♦♥❝❧✉❞❡s✳

✷ ❘❛♥❣❡✲❇❛s❡❞ ❱♦❧❛t✐❧✐t② ❛♥❞ ❱❛r✐❛♥❝❡ ❘✐s❦ Pr❡♠✐❛

✷✳✶ ❘❛♥❣❡✲❇❛s❡❞ ❱♦❧❛t✐❧✐t✐❡s

■♥ t❤❡ ❧✐t❡r❛t✉r❡ s❡✈❡r❛❧ ✈♦❧❛t✐❧✐t② ❡st✐♠❛t♦rs ❛r❡ ❡♠♣❧♦②❡❞ r❛♥❣✐♥❣ ❢r♦♠ t❤❡ ❝❧❛ss✐❝❛❧ ❝❧♦s❡✲t♦✲

❝❧♦s❡ ❡st✐♠❛t♦r ❜❛s❡❞ ♦♥ ❞❛✐❧② r❡t✉r♥s t♦ r❡❛❧✐③❡❞ ✈♦❧❛t✐❧✐t✐❡s ❞❡r✐✈❡❞ ❢r♦♠ ✐♥tr❛❞❛② ♣r✐❝❡s✳ ❲❤✐❧❡

✷

r❡❛❧✐③❡❞ ✈♦❧❛t✐❧✐t② ♠❡❛s✉r❡s ♣r♦✈✐❞❡ ♠♦r❡ ❛❝❝✉r❛t❡ ✈♦❧❛t✐❧✐t② ❡st✐♠❛t❡s✱ ❞❛✐❧② ❞❛t❛ ❜❛s❡❞ ✈♦❧❛t✐❧✐t②

❡st✐♠❛t♦rs ❛r❡ st✐❧❧ ❜❡✐♥❣ ✇✐❞❡❧② ✉s❡❞ ❛s ✐t ♠❛② ❜❡ ❤❛r❞ ✭♦r ✐♠♣♦ss✐❜❧❡ ✐♥ s♦♠❡ ❝❛s❡s✮ t♦ ♦❜t❛✐♥

✐♥tr❛❞❛② ❞❛t❛✳ ❘❛♥❣❡✲❜❛s❡❞ ✈♦❧❛t✐❧✐t② ❡st✐♠❛t♦rs ♣r♦✈✐❞❡ ❛♥ ✐♥t❡r♠❡❞✐❛t❡ s♦❧✉t✐♦♥ t♦ t❤✐s ❞✐❧❡♠♠❛✳

❲❡ ❞♦ ♥♦t ♥❡❡❞ ✐♥tr❛❞❛② ❞❛t❛ t♦ ❡st✐♠❛t❡ r❛♥❣❡✲❜❛s❡❞ ✈♦❧❛t✐❧✐t✐❡s✱ ❛♥❞ r❛♥❣❡✲❜❛s❡❞ ✈♦❧❛t✐❧✐t✐❡s ❛r❡

❢❛r ❜❡tt❡r ❡st✐♠❛t♦rs ♦❢ ✈♦❧❛t✐❧✐t✐❡s ✇❤❡♥ ❝♦♠♣❛r❡❞ t♦ t❤❡ ❝❧♦s❡✲t♦✲❝❧♦s❡ ❡st✐♠❛t♦r✳

●❛r♠❛♥ ❛♥❞ ❑❧❛ss ✭✶✾✽✵✮ ♣r♦♣♦s❡❞ ❛ ✈♦❧❛t✐❧✐t② ❡st✐♠❛t♦r ❜❛s❡❞ ♦♥ t❤❡ ♦♣❡♥✐♥❣✱ ❝❧♦s✐♥❣✱ ❤✐❣❤❡st

❛♥❞ ❧♦✇❡st ♣r✐❝❡s ✐♥❢♦r♠❛t✐♦♥✳ ❆s t❤❡ ✐♥tr❛❞❛② ❤✐❣❤✲❧♦✇ ♣r✐❝❡ r❛♥❣❡ ♣r♦✈✐❞❡s ❛❞❞✐t✐♦♥❛❧ ✐♥❢♦r♠❛t✐♦♥

r❡❣❛r❞✐♥❣ ✈♦❧❛t✐❧✐t②✱ ●❛r♠❛♥✲❑❧❛ss ❡st✐♠❛t♦r ❝♦♥st✐t✉t❡ ❛ ♠♦r❡ ❡✣❝✐❡♥t ❡st✐♠❛t♦r t❤❛♥ t❤❡ ❝❧♦s❡✲

t♦✲❝❧♦s❡ ❡st✐♠❛t♦r t❤❛t ✐s ❜❛s❡❞ ♦♥ t✇♦ ❛r❜✐tr❛r② ♣♦✐♥ts ✐♥ ♣r✐❝❡ s❡r✐❡s✳ ●❛r♠❛♥ ❛♥❞ ❑❧❛ss s✉❣❣❡st t❤❡ ❢♦❧❧♦✇✐♥❣ ❡st✐♠❛t♦r t❤❛t ♠❛② ❜❡ ❛♣♣❧✐❡❞ t♦ ❝♦♠♣✉t❡ ❞❛✐❧② ✈♦❧❛t✐❧✐t✐❡s✿

σ_t= s

0.5

log H_t

L_t 2

−[2 log 2−1]

log

C_t O_t

2

x100 ✭✶✮

✇❤❡r❡ O_t ✐s t❤❡ ♦♣❡♥✐♥❣ ♣r✐❝❡✱ C_t ✐s t❤❡ ❝❧♦s✐♥❣ ♣r✐❝❡✱ H_t ✐s t❤❡ ❤✐❣❤❡st ♣r✐❝❡ ❛♥❞L_t ✐s t❤❡ ❧♦✇❡st

♣r✐❝❡ ♦❢ t❤❡ t^th tr❛❞✐♥❣ ❞❛②✳

✷✳✷ ❱❛r✐❛♥❝❡ ❘✐s❦ Pr❡♠✐❛

■♥✈❡st♦rs ❞♦ ♥♦t ♦♥❧② r❡q✉✐r❡ ❝♦♠♣❡♥s❛t✐♦♥ ❢♦r ✈♦❧❛t✐❧✐t② ♦❢ r❡t✉r♥s✳ ■t ✐s ♥♦✇ ✇❡❧❧ ❡st❛❜❧✐s❤❡❞

t❤❛t ✐♥✈❡st♦rs ❞❡♠❛♥❞ ❛❞❞✐t✐♦♥❛❧ ❝♦♠♣❡♥s❛t✐♦♥ ❢♦r r✐s❦ ✇❤❡♥ t❤❡② ♣❡r❝❡✐✈❡ t❤❛t t❤❡ ❞❛♥❣❡r ♦❢

❜✐❣ s❤♦❝❦s t♦ t❤❡ st❛t❡ ♦❢ t❤❡ ❡❝♦♥♦♠② ✐s ❤✐❣❤^✶✳ ❱❘P ✐s t❤❡ ❝♦♠♣❡♥s❛t✐♦♥ ❢♦r ✈❛r✐❛♥❝❡ r✐s❦ t❤❛t st❡♠s ❢r♦♠ t❤❡ r❛♥❞♦♠♥❡ss ♦❢ r❡t✉r♥ ✈❛r✐❛♥❝❡s✳ ■t ✐s s❤♦✇♥ t♦ ❜❡ ♣r♦❝②❝❧✐❝❛❧✱ ✐♥❝r❡❛s✐♥❣ ✐♥ ♠❛r❦❡t

❞♦✇♥t✉r♥s t❤❛t ❛r❡ ❝❤❛r❛❝t❡r✐③❡❞ ❜② ❤✐❣❤ ✈♦❧❛t✐❧✐t② ❛♥❞ ❤✐❣❤ r✐s❦ ❛✈❡rs✐♦♥✳ ❆s s✉❝❤✱ ✐t ✐s ✉s❡❞ t♦

❝❛♣t✉r❡ ✐♥✈❡st♦rs✬ ❛tt✐t✉❞❡s t♦✇❛r❞ ✉♥❝❡rt❛✐♥t② ✭❇♦❧❧❡rs❧❡✈ ❡t ❛❧✳✱ ✷✵✶✶❀ ❇❛❦s❤✐ ❛♥❞ ▼❛❞❛♥✱ ✷✵✵✻✮✳

■❢ ❡st✐♠❛t❡❞ ❛♣♣r♦♣r✐❛t❡❧②✱ ❱❘P ♠❛② ❝♦♥st✐t✉t❡ ❛ ❣♦♦❞ ♣r♦①② ❢♦r t❤❡ r✐s❦ ❛✈❡rs✐♦♥✳

❱❘P ✐s ❞❡✜♥❡❞ ❛s t❤❡ ❞✐✛❡r❡♥❝❡ ✐♥ ❡①♣❡❝t❡❞ ✈❛r✐❛♥❝❡s ✉♥❞❡r r✐s❦✲♥❡✉tr❛❧ ❛♥❞ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡s

♦✈❡r t❤❡ [t, t+n] t✐♠❡ ✐♥t❡r✈❛❧^✷✿

✶❙❡❡✱ ❢♦r ❡①❛♠♣❧❡✱ ❇♦❧❧❡rs❧❡✈ ❡t ❛❧✳✱ ✷✵✵✾❀ ❉r❡❝❤s❧❡r ❛♥❞ ❨❛r♦♥✱ ✷✵✶✶

✷❙❡❡✱ ❢♦r ❡①❛♠♣❧❡✱ ❉❡♠❡t❡r✜ ❡t ❛❧✳✱ ✶✾✾✾❀ ❇r✐tt❡♥✲❏♦♥❡s ❛♥❞ ◆❡✉❜❡r❣❡r✱ ✷✵✵✵❀ ❏✐❛♥❣ ❛♥❞ ❚✐❛♥✱ ✷✵✵✺❀ ❈❛rr ❛♥❞

❲✉✱ ✷✵✵✽

✸

V RP_t,t+n= E^P(V art,t+n | F^t)−E^Q(V art,t+n | F^t) ✭✷✮

✇❤❡r❡ E^P(·) ❛♥❞ E^Q(·)❞❡♥♦t❡ t❤❡ t✐♠❡ t ❡①♣❡❝t❛t✐♦♥ ♦♣❡r❛t♦r ✉♥❞❡r t❤❡ ♣❤②s✐❝❛❧ ❛♥❞ r✐s❦✲♥❡✉tr❛❧

♠❡❛s✉r❡s r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡s❡ ♠❡❛s✉r❡s ❛r❡ ♥♦t ❞✐r❡❝t❧② ♦❜s❡r✈❛❜❧❡✳ ❙❡✈❡r❛❧ ♠❡t❤♦❞s ❤❛✈❡ ❜❡❡♥

❞❡✈❡❧♦♣❡❞ t♦ ❛♣♣r♦①✐♠❛t❡ t❤❡♠✳

❚♦ ♠❛❦❡ t❤❡ ❞✐str✐❜✉t✐♦♥ ❝❧♦s❡r t♦ ♥♦r♠❛❧✐t② V RP_t,t+n ♠❛② ❜❡ ❡①♣r❡ss❡❞ ✐♥ ✐ts ❧♦❣❛r✐t❤♠✐❝

❢♦r♠✿

log (V RPt,t+n) = log E^P(V art,t+n| F^t)

−log E^Q(V art,t+n| F^t)

✭✸✮

❚❤❡ r✐s❦✲♥❡✉tr❛❧ ❡①♣❡❝t❛t✐♦♥ ♦❢ t❤❡ ❢✉t✉r❡ ✈❛r✐❛♥❝❡ E^Q

✐♥ t❤❡ ❛❜♦✈❡ ❡q✉❛t✐♦♥ ✐s ♠❡❛s✉r❡❞

❜❛s❡❞ ♦♥ ♦♣t✐♦♥ ♣r✐❝❡s✱ ❛s ❛ ✇❡✐❣❤t❡❞ ❛✈❡r❛❣❡✱ ♦r ✐♥t❡❣r❛❧✱ ♦❢ ❛ ❝♦♥t✐♥✉✉♠ ♦❢ ❛ ✜①❡❞ ♥✲♠❛t✉r✐t②

♦♣t✐♦♥s✿

E^Q_t(V ar_t,t+n) = IV^∗_t,t+n∆= 2 Z ^∞

0

C(t+n, K)−C(t, K)

K² dK ✭✹✮

✇❤❡r❡C(t, K)❞❡♥♦t❡s t❤❡ ♣r✐❝❡ ♦❢ ❛ ❊✉r♦♣❡❛♥ ❝❛❧❧ ♦♣t✐♦♥ ♠❛t✉r✐♥❣ ❛t t✐♠❡t ✇✐t❤ str✐❦❡ ♣r✐❝❡ K✳

❚❤❡ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡ E^P

✐s ❛♣♣r♦①✐♠❛t❡❞ t❤r♦✉❣❤ ✉s✐♥❣ r❡❛❧✐③❡❞ ✈❛r✐❛♥❝❡ ♠❡❛s✉r❡s t❤❛t ❛r❡

❞❡r✐✈❡❞ ❢r♦♠ t❤❡ ✉♥❞❡r❧②✐♥❣ s❡❝✉r✐t② ♣r✐❝❡s✳ ▼❡t❤♦❞s ✉s❡❞ t♦ ❝♦♠♣✉t❡ t❤❡ ♣❤②s✐❝❛❧ ❡①♣❡❝t❛t✐♦♥

✈❛r② ✐♥ ♣r❛❝t✐❝❡✳ ❲❤✐❧❡ ❈❛rr ❛♥❞ ❲✉ ✭✷✵✵✽✮ ✉s❡ s✐♠♣❧② t❤❡ ❡①✲♣♦st ❢♦r✇❛r❞ r❡❛❧✐③❡❞ ✈❛r✐❛♥❝❡

t♦ s✉❜st✐t✉t❡ ❢♦r t❤❡ ❡①♣❡❝t❡❞ r❡t✉r♥ ✈❛r✐❛♥❝❡ ❉r❡❝❤s❧❡r ❛♥❞ ❨❛r♦♥ ✭✷✵✶✶✮ ✉s❡ ❧❛❣❣❡❞ ✐♠♣❧✐❡❞

❛♥❞ r❡❛❧✐③❡❞ ✈❛r✐❛♥❝❡s t♦ ❢♦r❡❝❛st ✐t✳ ❚♦❞♦r♦✈ ✭✷✵✵✾✮ ❡st✐♠❛t❡s t❤❡ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡ ✐♥ ❛ s❡♠✐✲

♣❛r❛♠❡tr✐❝ ❢r❛♠❡✇♦r❦✳ ❇♦❧❧❡rs❧❡✈ ❡t ❛❧✳ ✭✷✵✵✾✮ ✉s❡ ❛ ♠✉❧t✐❢r❡q✉❡♥❝② ❛✉t♦r❡❣r❡ss✐♦♥ ✇✐t❤ ♠✉❧t✐♣❧❡

❧❛❣s ❛♥❞ ❩❤♦✉ ✭✷✵✶✵✮ ✉s❡s ❛ s✐♠♣❧❡ ❛✉t♦r❡❣r❡ss✐♦♥ ✇✐t❤ t✇❡❧✈❡ ❧❛❣s t♦ ❡st✐♠❛t❡ t❤❡ ♦❜❥❡❝t✐✈❡

❡①♣❡❝t❛t✐♦♥ ♦❢ t❤❡ r❡t✉r♥ ✈❛r✐❛♥❝❡✳

■♥ t❤✐s ♣❛♣❡r✱ t❤❡ ❡①♣❡❝t❡❞ ✈❛r✐❛♥❝❡ ✉♥❞❡r t❤❡ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡ ✐s ❡st✐♠❛t❡❞ t❤r♦✉❣❤ ❛ ❍❡t✲

❡r♦❣❡♥❡♦✉s ❆✉t♦r❡❣r❡ss✐✈❡ ✭❍❆❘✮ ♠♦❞❡❧ t❤❛t ✐s ♣r♦♣♦s❡❞ ❜② ❈♦rs✐ ✭✷✵✵✾✮✳ ❚❤❡ ❍❆❘ ♠♦❞❡❧

✐s ❛ str❛✐❣❤t❢♦r✇❛r❞ ✉♥❢♦❧❞✐♥❣ ♦❢ ❍❡t❡r♦❣❡♥❡♦✉s ❆✉t♦r❡❣r❡ss✐✈❡ ❈♦♥❞✐t✐♦♥❛❧ ❍❡t❡r♦s❝❡❞❛st✐❝✐t②

✭❍❆❘❈❍✮ ♠♦❞❡❧s ❛♥❛❧②s❡❞ ❡❛r❧✐❡r ✐♥ ▼ü❧❧❡r ❡t ❛❧✳ ✭✶✾✾✼✮✳ ❆♥ ❍❆❘ ♠♦❞❡❧ ❝❛♥ ❜❡ s♣❡❝✐✜❡❞

✹

❛s ❛ ♠✉❧t✐✲❝♦♠♣♦♥❡♥t ✈❛r✐❛♥❝❡ ♠♦❞❡❧ ✐♥ ✇❤✐❝❤ t❤❡ ❝♦♥❞✐t✐♦♥❛❧ ✈❛r✐❛♥❝❡ ✐s ♣❛r❛♠❡tr✐③❡❞ ❛s ❛ s✉♠

♦❢ ✈❛r✐❛♥❝❡ ❝♦♠♣♦♥❡♥ts ♦✈❡r ❞✐✛❡r❡♥t ❤♦r✐③♦♥s✳ ■♥ ✐ts s✐♠♣❧❡st ❢♦r♠✱ ❛♥ ❍❆❘ ♠♦❞❡❧ ✐s ❡st✐♠❛t❡❞

t❤r♦✉❣❤ t❤❡ s✉♠ ♦❢ ❞❛✐❧②✱ ✇❡❡❦❧② ❛♥❞ ♠♦♥t❤❧② ✈❛r✐❛♥❝❡s

σ²_t =β_Dσ²_t−1+β_Wσ_t²_−5:t−1+β_Mσ_t²_−22:t−1 ✭✺✮

✇❤❡r❡

σ²_t+1−k:t= 1 k

k

X

j=1

σ_t²−j

❛♥❞ ✇❤❡r❡ t❤❡ ❝♦❡✣❝✐❡♥ts β_D✱ β_W✱β_M ❛r❡ ❞❡t❡r♠✐♥❡❞ t❤r♦✉❣❤ ❛♥ ❖▲❙ ❡st✐♠❛t✐♦♥✳

●✐✈❡♥ t❤❛t t❤❡ ❧♦❣❛r✐t❤♠✐❝ ❞❛✐❧② ✈❛r✐❛♥❝❡s ❛r❡ ❛♣♣r♦①✐♠❛t❡❧② ✉♥❝♦♥❞✐t✐♦♥❛❧❧② ♥♦r♠❛❧❧② ❞✐s✲

tr✐❜✉t❡❞✱ ❊q✉❛t✐♦♥ 5 ✐s ❡①♣r❡ss❡❞ ✐♥ ✐ts ❧♦❣❛r✐t❤♠✐❝ ❢♦r♠ ❢♦❧❧♦✇✐♥❣ ❆♥❞❡rs❡♥ ❡t ❛❧✳ ✭✷✵✵✼✮✿

log σ_t²

=β_Dlog σ_t²₋₁

+β_W log σ²_t−5:t−1

+β_Mlog σ_t²_−22:t−1

✭✻✮

✇❤❡r❡

log(σ_t+1−² _k:t) = 1 k

k

X

j=1

log(σ²_t−j)

✸ ❉❛t❛

■♥ t❤✐s ♣❛♣❡r ❱❘P s❡r✐❡s ❛r❡ ❝♦♠♣✉t❡❞ ❢♦r ✶✺ ②❡❛rs✱ ❢r♦♠ ❋❡❜r✉❛r② ✷✵✵✵ t♦ ❋❡❜r✉❛r② ✷✵✶✺✱ ❢♦r s❡✈❡♥

♠❛r❦❡ts st✉❞✐❡❞✿ ❯♥✐t❡❞ ❙t❛t❡s✱ ❯♥✐t❡❞ ❑✐♥❣❞♦♠✱ ●❡r♠❛♥②✱ ❋r❛♥❝❡✱ ◆❡t❤❡r❧❛♥❞s✱ ❙✇✐t③❡r❧❛♥❞

❛♥❞ ❏❛♣❛♥✳ ❆s ♠❡♥t✐♦♥❡❞ ❛❜♦✈❡✱ ❡st✐♠❛t✐♦♥ ♦❢ t❤❡ ❱❘P s❡r✐❡s t❤❛t ■ ❡♠♣❧♦② t♦ ❛♣♣r♦①✐♠❛t❡

r✐s❦ ❛✈❡rs✐♦♥ ❧❡✈❡❧s ❢♦r ❡❛❝❤ ♠❛r❦❡t ✐s ❜❛s❡❞ ♦♥ r✐s❦✲♥❡✉tr❛❧ ❛♥❞ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡s ♦❢ ❢✉t✉r❡ ✐♥❞❡①

✈♦❧❛t✐❧✐t✐❡s✳

❚❤❡ r✐s❦✲♥❡✉tr❛❧ ♠❡❛s✉r❡s✱ t❤❡ ♦♣t✐♦♥s✲✐♠♣❧✐❡❞ ✈♦❧❛t✐❧✐t✐❡s✱ ❛r❡ r❡❛❞✐❧② ♣r♦✈✐❞❡❞ ❜② ❉❛t❛str❡❛♠✳

■♠♣❧✐❡❞ ✈♦❧❛t✐❧✐t② s❡r✐❡s ❛r❡ ❝♦♠♣✉t❡❞ ❜❛s❡❞ ♦♥ ✐♥❞❡① ♦♣t✐♦♥s ❝♦✈❡r✐♥❣ ♦✉t✲♦❢✲t❤❡✲♠♦♥❡② str✐❦❡

♣r✐❝❡s ❢♦r ♥❡❛r ❛♥❞ ♥❡①t✲t❡r♠ ♠❛t✉r✐t✐❡s ❢♦❧❧♦✇✐♥❣ t❤❡ ✇✐❞❡❧② ✉s❡❞ ❱■❳ ♠❡t❤♦❞♦❧♦❣② ♦❢ t❤❡ ❈❤✐❝❛❣♦

✺

❇♦❛r❞ ♦❢ ❖♣t✐♦♥s ❊①❝❤❛♥❣❡ ^✸✳ ❚❤✐s ♠♦❞❡❧✲❢r❡❡ ✐♠♣❧✐❡❞ ✈♦❧❛t✐❧✐t② ✐s ♣r♦✈❡♥ t♦ ❜❡ ❛ ❜❡tt❡r ❛♣♣r♦①✲

✐♠❛t✐♦♥ t♦ t❤❡ ♦♥❡ ♠♦♥t❤ ❛❤❡❛❞ r✐s❦✲♥❡✉tr❛❧ ❡①♣❡❝t❛t✐♦♥ ♦❢ t❤❡ ✐♥t❡❣r❛t❡❞ ✈♦❧❛t✐❧✐t② t❤❛♥ t❤❡

❇❧❛❝❦✲❙❝❤♦❧❡s ✐♠♣❧✐❡❞ ✈♦❧❛t✐❧✐t②✳ ■♠♣❧✐❡❞ ✈♦❧❛t✐❧✐t② s❡r✐❡s ✇❡r❡ ♣r♦✈✐❞❡❞ ✐♥ ❛♥♥✉❛❧✐③❡❞ ♠❡❛s✉r❡s✳

■♥ ♦r❞❡r t♦ ♦❜t❛✐♥ ❞❛✐❧② ❡st✐♠❛t❡s✱ ✐♠♣❧✐❡❞ ✈♦❧❛t✐❧✐t② ♠❡❛s✉r❡s ❛r❡ ❞✐✈✐❞❡❞ ❜② √

365✳ ❚❤❡ ❞❛✐❧②✲

st❛♥❞❛r❞✐③❡❞ ❡st✐♠❛t❡s ♦❢ t❤❡ ❡①♣❡❝t❡❞ ♦♥❡✲♠♦♥t❤ ❛❤❡❛❞ ✈♦❧❛t✐❧✐t② ✉♥❞❡r t❤❡ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡ ❛r❡

♦❜t❛✐♥❡❞ ❜❛s❡❞ ♦♥ t❤❡ ❧♦❣❛r✐t❤♠✐❝ ❍❆❘ ♠♦❞❡❧ ❣✐✈❡♥ ✐♥ ❊q✉❛t✐♦♥ ✻✳

❏❛♣❛♥❡s❡ ♠❛r❦❡t ✐s ❝❧♦s❡❞ ❜❡❢♦r❡ t❤❡ ♦t❤❡r ♠❛r❦❡ts ❛r❡ ♦♣❡♥❡❞✳ ❉❛t❛ ✐s ❛❞❥✉st❡❞ t♦ ❝♦♣❡ ✇✐t❤

t❤✐s ✐ss✉❡✿ ❢♦r t❤❡ ❡st✐♠❛t✐♦♥✱ ❏❛♣❛♥❡s❡ ♠❛r❦❡t ❞❛t❛ ✐s ❧❡❞ ❜② ♦♥❡ ❞❛②✳

❙✉♠♠❛r② st❛t✐st✐❝s ♦❢ t❤❡ ❝♦♥str✉❝t❡❞ ✈♦❧❛t✐❧✐t② s❡r✐❡s ❢♦r ❡❛❝❤ ♠❛r❦❡t ❛r❡ ♣r♦✈✐❞❡❞ ✐♥ ❚❛❜❧❡ ✶✳

❋♦r ❛❧❧ ♦❢ t❤❡ ✜♥❛♥❝✐❛❧ ♠❛r❦❡ts✱ ❛❦✐♥ t♦ t❤❡ ❡♠♣✐r✐❝❛❧ ❧✐t❡r❛t✉r❡✱ r✐s❦✲♥❡✉tr❛❧ ♠❡❛s✉r❡s ❛r❡ ❤✐❣❤❡r t❤❛♥ t❤❡ ♣❤②s✐❝❛❧ ♠❡❛s✉r❡s ♦❢ ❡①♣❡❝t❡❞ ✈♦❧❛t✐❧✐t② ❞✉r✐♥❣ ❛❧♠♦st ❛❧❧ t❤❡ ♣❡r✐♦❞✳ ❱❘P s❡r✐❡s ❤❛✈❡

t❤✉s ♥❡❣❛t✐✈❡ ✈❛❧✉❡s✳ ❚♦ r❡♣r❡s❡♥t t❤❡ ❧❡✈❡❧ ♦❢ r✐s❦ ❛✈❡rs✐♦♥✱ t❤❡s❡ s❡r✐❡s ❛r❡ ♠✉❧t✐♣❧✐❡❞ ❜② −1✳

▲♦❣❛r✐t❤♠✐❝ ♠❡❛s✉r❡s ♦❢ r✐s❦ ❛✈❡rs✐♦♥ ❧❡✈❡❧s ❛r❡ ❢❛✐r❧② ❝❧♦s❡ t♦ ♥♦r♠❛❧✐t②✱ ❛❧t❤♦✉❣❤ s♦♠❡ ♦❢ t❤❡

s❡r✐❡s ❛r❡ s❧✐❣❤t❧② r✐❣❤t s❦❡✇❡❞ ❛♥❞ ❧❡♣t♦❦✉rt✐❝✳

❋✐❣✉r❡ ✶ s❤♦✇s r✐s❦ ❛✈❡rs✐♦♥ s❡r✐❡s ✉s❡❞ ✐♥ t❤❡ ❡st✐♠❛t✐♦♥✳ ❉❛t❛ ❝♦✈❡rs ✜✈❡ s✉❜♣❡r✐♦❞s ♦❢ ❛❧t❡r✲

♥❛t✐♥❣ ✈♦❧❛t✐❧✐t② ❛♥❞ r✐s❦ ❛✈❡rs✐♦♥ ❧❡✈❡❧s✳ ❚❤❡ ✜rst ♣❡r✐♦❞ s♣❛♥s ❢r♦♠ ❋❡❜r✉❛r② ✷✵✵✵ t♦ ❙❡♣t❡♠❜❡r

✷✵✵✸ ❛♥❞ ✐t ✐s ❞♦♠✐♥❛t❡❞ ❜② t❤❡ ♥❡❣❛t✐✈❡ ❝♦♥s❡q✉❡♥❝❡s ♦❢ t❤❡ ❞♦t✲❝♦♠ ❜✉❜❜❧❡ ❜✉rst ❛♥❞ t❤❡ ✾✴✶✶

❛tt❛❝❦s ✐♥ t❤❡ ❯♥✐t❡❞ ❙t❛t❡s✳ ❆ r❡❧❛t✐✈❡❧② st❛❜❧❡ ♣❡r✐♦❞ ❢♦❧❧♦✇s ❢r♦♠ ❖❝t♦❜❡r ✷✵✵✸ t♦ ❏✉❧② ✷✵✵✼✳

❚❤❡ ♠♦st ✐♥t❡r❡st✐♥❣ ♣❡r✐♦❞s st❛rt ❜② ❆✉❣✉st ✷✵✵✼ ❛♥❞ ❝♦♥❝❡r♥ t❤❡ r❡❝❡♥t ✜♥❛♥❝✐❛❧ ❝r✐s✐s✳ ❉✉r✐♥❣

t❤❡ s❡❝♦♥❞ ❤❛❧❢ ♦❢ ✷✵✵✼✱ ♥❡❣❛t✐✈❡ ❡✛❡❝ts ♦❢ t❤❡ ❞❡❝❧✐♥❡ ✐♥ ❤♦✉s✐♥❣ ♣r✐❝❡s st❛rt❡❞ t♦ ❜❡ ❢❡❧t ✐♥ t❤❡

♦✈❡r❛❧❧ ❯✳❙✳ ❡❝♦♥♦♠②✱ ❛♥❞ t❤✐s ❧❡❞ t♦ ❛ ♣❛♥✐❝ ✐♥ t❤❡ st♦❝❦ ❛♥❞ ❢♦r❡✐❣♥ ❡①❝❤❛♥❣❡ ♠❛r❦❡ts ❜② t❤❡ ❜❡✲

❣✐♥♥✐♥❣ ♦❢ ✷✵✵✽✳ ❲✐t❤ t❤❡ ❝♦❧❧❛♣s❡ ♦❢ ▲❡❤♠❛♥ ❇r♦t❤❡rs ✐♥ ❙❡♣t❡♠❜❡r ✷✵✵✽✱ t❤❡ ❝r✐s✐s ✐s r❡♠❛r❦❛❜❧②

❞❡❡♣❡♥❡❞✱ ❛♥❞ ✐t ❣❛✐♥❡❞ ❛ ❣❧♦❜❛❧ ❝❤❛r❛❝t❡r t❤r♦✉❣❤ ❛ ❞r❛st✐❝ ❞❡❝r❡❛s❡ ✐♥ ❣❧♦❜❛❧ ❧✐q✉✐❞✐t② ❜② t❤❡

✜rst ❤❛❧❢ ♦❢ ✷✵✵✾✳ ❇❡t✇❡❡♥ ❏❛♥✉❛r② ✷✵✶✵ ❛♥❞ ❏✉❧② ✷✵✶✷✱ ❊✉r♦♣❡❛♥ ❙♦✈❡r❡✐❣♥ ❉❡❜t ❈r✐s✐s tr♦✉❜❧❡❞

❡s♣❡❝✐❛❧❧② t❤❡ ❊✉r♦✲❛r❡❛ ❝♦✉♥tr✐❡s✳ ❚❤❡ ❧❛st ♣❡r✐♦❞ st❛rts ❜② ❆✉❣✉st ✷✵✶✷ ❛♥❞ ✐t ✐s ❝❤❛r❛❝t❡r✐③❡❞

❜② r❡❧❛t✐✈❡ st❛❜✐❧✐t②✳

✸❚❤✐s ♠❡t❤♦❞ ✐s ❞❡✈❡❧♦♣❡❞ ❜② ❉❡♠❡t❡r✜ ❡t ❛❧✳ ✭✶✾✾✾✮✳

✻

✹ ❊♠♣✐r✐❝❛❧ ❙tr❛t❡❣② ❛♥❞ ❘❡s✉❧ts

❚❤❡ ❡♠♣✐r✐❝❛❧ ❛♥❛❧②s✐s ✐s ❜❛s❡❞ ♦♥ ●❋❊❱❉ t❤❛t ✐s ♦❜t❛✐♥❡❞ t❤r♦✉❣❤ ❛ ❱❡❝t♦r ❆✉t♦r❡❣r❡ss✐✈❡ ❱❆❘✮

♠♦❞❡❧ ❢♦r♠✉❧❛t❡❞ ❛s ❢♦❧❧♦✇s✿

X_t =

p

X

p=1

ΦpX_t−p+ǫ_t ✭✼✮

✇❤❡r❡ Y_t✱ Y_t−1✱✳✳✳✱ Y_t−p ❛r❡ (8×1) ✈❡❝t♦rs ❝♦♥t❛✐♥✐♥❣ ❧♦❣❛r✐t❤♠✐❝ ♠❡❛s✉r❡s ♦❢ ❱❘Ps ♦❢ t❤❡ s❡✈❡♥

♠❛r❦❡ts st✉❞✐❡❞ ❛s ❡st✐♠❛t❡❞ t❤r♦✉❣❤ ❊q✉❛t✐♦♥ ✸✱ ♣ ✐s t❤❡ ❱❆❘ ♦r❞❡r✱ P hi1✱ P hi2✱✳✳✳✱ P hi_p ❛r❡

(8×8)♠❛tr✐❝❡s ❝♦♥t❛✐♥✐♥❣ t❤❡ ❱❆❘ ♣❛r❛♠❡t❡rs t♦ ❜❡ ❡st✐♠❛t❡❞✱ ❛♥❞ǫ_t✐s ❛ ✈❡❝t♦r ♦❢ ✐♥♥♦✈❛t✐♦♥s✳

■♥ t❤❡ ❡♠♣✐r✐❝❛❧ ❛♥❛❧②s✐s✱ ❱❆❘ ♦r❞❡rs ❛r❡ ❞❡t❡r♠✐♥❡❞ ❜❛s❡❞ ♦♥ ❆❦❛✐❦❡ ■♥❢♦r♠❛t✐♦♥ ❈r✐t❡r✐♦♥✳

❖♥❝❡ t❤❡ ❝♦✈❛r✐❛♥❝❡ st❛t✐♦♥❛r✐t② ❝♦♥❞✐t✐♦♥ ✐s s❛t✐s✜❡❞ t❤❡ ❛❜♦✈❡ ❱❆❘ ♠♦❞❡❧ ❝❛♥ ❜❡ r❡✇r✐tt❡♥

✐♥ ❛♥ ✐♥✜♥✐t❡ ♦r❞❡r ♠♦✈✐♥❣ ❛✈❡r❛❣❡ r❡♣r❡s❡♥t❛t✐♦♥✿

X_t=

∞

X

j=0

Ψjǫ_t−j ✭✽✮

✇❤❡r❡ t❤❡ (8×8) ♠♦✈✐♥❣ ❛✈❡r❛❣❡ ❝♦❡✣❝✐❡♥t ♠❛tr✐❝❡s✱ Ψj ♦❜❡② t❤❡ r❡❝✉rs✐♦♥ Ψj = Φ1Ψj−1 + Φ2Ψj−2, ...+ ΦpΨj−p ✇✐t❤ Ψ0 ❛♥ ✐❞❡♥t✐t② ♠❛tr✐①✳

❚❤❡s❡ ♠♦✈✐♥❣ ❛✈❡r❛❣❡ ❝♦❡✣❝✐❡♥ts ❛r❡ ✉s❡❞ t♦ ❣❡♥❡r❛t❡ ✐♠♣✉❧s❡ r❡s♣♦♥s❡ ❢✉♥❝t✐♦♥s ✭■❘❋✮ ❛♥❞

❢♦r❡❝❛st ❡rr♦r ✈❛r✐❛♥❝❡ ❞❡❝♦♠♣♦s✐t✐♦♥s ✭❋❊❱❉✮ t♦ st✉❞② t❤❡ ✐♠♣❛❝t ♦❢ ❛ ❤②♣♦t❤❡t✐❝❛❧ s❤♦❝❦ ♦♥

t❤❡ ❞②♥❛♠✐❝s ♦❢ t❤❡ s②st❡♠✳ ❲❤❡♥ ❱❆❘ ✐♥♥♦✈❛t✐♦♥s ❛r❡ ❝♦♥t❡♠♣♦r❛♥❡♦✉s❧② ❝♦rr❡❧❛t❡❞ ❈❤♦❧❡s❦②

❢❛❝t♦r✐③❛t✐♦♥ ✐s ❣❡♥❡r❛❧❧② ❡♠♣❧♦②❡❞ t♦ ♦❜t❛✐♥ ♦rt❤♦❣♦♥❛❧✐③❡❞ ✐♥♥♦✈❛t✐♦♥s✳ ❍♦✇❡✈❡r✱ ✐♥ t❤✐s ❝❛s❡✱

■❘❋ ❛♥❞ ❋❊❱❉ r❡s✉❧ts ❤✐❣❤❧② ❞❡♣❡♥❞ ♦♥ t❤❡ ♦r❞❡r✐♥❣ ♦❢ t❤❡ ✈❛r✐❛❜❧❡s✳ P❡s❛r❛♥ ❛♥❞ ❙❤✐♥ ✭✶✾✾✽✮

♣r♦♣♦s❡s ❛ s♦❧✉t✐♦♥ t♦ t❤✐s ♣r♦❜❧❡♠ t❤r♦✉❣❤ ●❡♥❡r❛❧✐③❡❞ ❱❆❘ ❢r❛♠❡✇♦r❦ t❤❛t ❛❧❧♦✇s ❝♦rr❡❧❛t❡❞

s❤♦❝❦s✳ ■♥ t❤✐s ❢r❛♠❡✇♦r❦ ●❡♥❡r❛❧✐③❡❞ ■❘❋ ✐s ❞❡✜♥❡❞ ❛s ❢♦❧❧♦✇s✿

GIRF_i(h) =√

σ_iiΨhΣei ✭✾✮

✇❤❡r❡Σ ✐s t❤❡ ✈❛r✐❛♥❝❡✲❝♦✈❛r✐❛♥❝❡ ♠❛tr✐① ♦❢ r❡s✐❞✉❛❧s✱ ❛♥❞e_i ✐s t❤❡ s❡❧❡❝t✐♦♥ ✈❡❝t♦r ✇✐t❤ ♦♥❡ ❛t ❛

♣♦s✐t✐♦♥i❛♥❞ ③❡r♦s ♦t❤❡r✇✐s❡✳ ❚❤❡ ●■❘❋ t❤✉s ❞❡✜♥❡❞ ❛❧❧♦✇s ✉s t♦ ❛ss❡ss t❤❡ ❡✛❡❝t ♦❢ ♦♥❡ st❛♥❞❛r❞

✼

❡rr♦r s❤♦❝❦ t♦ t❤❡ i^th ❡q✉❛t✐♦♥ ❛t t✐♠❡ t ♦♥ ❡①♣❡❝t❡❞ ✈❛❧✉❡s ♦❢ ✈❡❝t♦r X ❛t ❤♦r✐③♦♥ t+h✳ ❚❤❡

❝♦rr❡s♣♦♥❞✐♥❣ ●❋❊❱❉ ❝❛♣t✉r❡s t❤❡ s❤❛r❡ ♦❢ t❤❡ ❤✲st❡♣ ❛❤❡❛❞ ❢♦r❡❝❛st ❡rr♦r ✈❛r✐❛♥❝❡ ♦❢ ✈❛r✐❛❜❧❡ j

✇❤✐❝❤ ✐s ❞✉❡ t♦ t❤❡ ✐♥♥♦✈❛t✐♦♥s ✐♥ ✈❛r✐❛❜❧❡ i✿

GF EV D_j,i(h) = σ_jj⁻¹Ph

h=0 e^′_jΨhΣei

²

Ph

h=0e^′_jΨhΣΨ^′_he_j ✭✶✵✮

●❋❊❱❉s ❛r❡ ❡st✐♠❛t❡❞ ❢♦r ❡❛❝❤ ♦❢ t❤❡ ✜✈❡ s✉❜♣❡r✐♦❞s ❞❡s❝r✐❜❡❞ ✐♥ t❤❡ ❞❛t❛ s❡❝t✐♦♥✳ ❆❧❧ t❤❡

●■❘❋s ❛r❡ ❢✉❧❧② st❛❜✐❧✐③❡❞ ❛t ✸✵ ❧❛❣s✳ ❚❤✉s✱ ●❋❊❱❉s ❛r❡ ❡st✐♠❛t❡❞ ❢♦r ✸✵ ❞❛②s ❤♦r✐③♦♥✳ ❆s t❤❡

s❤♦❝❦s ❛r❡ ♥♦t ♦rt❤♦❣♦♥❛❧✐③❡❞✱ ❢♦r❡❝❛st ❡rr♦r ✈❛r✐❛♥❝❡ ❞❡❝♦♠♣♦s✐t✐♦♥s ❢♦r ❡❛❝❤ r❡s♣♦♥s❡ ✈❛r✐❛❜❧❡

❞♦ ♥♦t ♥❡❝❡ss❛r✐❧② s✉♠ t♦ ♦♥❡✳ ■♥ ♦r❞❡r t♦ ♠❛❦❡ t❤❡ r❡s✉❧ts ❝♦♠♣❛r❛❜❧❡✱ t❤❡ s✉♠s ♦❢ ❝♦♥tr✐❜✉t✐♦♥s

♦❢ ✐♠♣✉❧s❡ ✈❛r✐❛❜❧❡s t♦ t❤❡ ✈❛r✐❛♥❝❡ ♦❢ ❢♦r❡❝❛st ❡rr♦r ♦❢ ❡❛❝❤ r❡s♣♦♥s❡ ✈❛r✐❛❜❧❡ ❛r❡ ♥♦r♠❛❧✐③❡❞ t♦

♦♥❡✳

▼❛✐♥ ❡♠♣✐r✐❝❛❧ r❡s✉❧ts ❛r❡ r❡♣♦rt❡❞ ✐♥ ❚❛❜❧❡ ✷✱ ❚❛❜❧❡ ✸✱ ❋✐❣✉r❡ ✷✱ ❛♥❞ ❋✐❣✉r❡ ✸✳ ❚❛❜❧❡ ✷ ❛♥❞

❋✐❣✉r❡ ✷ ❝♦♥t❛✐♥ t❤❡ ♣❡r❝❡♥t❛❣❡ ❝♦♥tr✐❜✉t✐♦♥s ♦❢ r✐s❦ ❛✈❡rs✐♦♥ ♦❢ t❤❡ ❯✳❙✳ ♠❛r❦❡t ✭❛s r❡♣r❡s❡♥t❡❞

❜② t❤❡ ✲❧♦❣ ♦❢ ❱❘P ♦❢ t❤❡ ❙&P ✺✵✵✮ t♦ t❤❡ ✈❛r✐❛♥❝❡s ♦❢ ❢♦r❡❝❛st ❡rr♦r ♦❢ ❡❛❝❤ ♦❢ t❤❡ ♦t❤❡r ✜♥❛♥❝✐❛❧

♠❛r❦❡ts✳ P❡r✐♦❞s ♦♥❡ t♦ ✜✈❡ ❤❡❛❞✐♥❣ t❤❡ ❝♦❧✉♠♥s ♦❢ t❤❡ t❛❜❧❡ st❛♥❞ ❢♦r t❤❡ s✉❜♣❡r✐♦❞s ♦❢ t❤❡

❞❛t❛ s❛♠♣❧❡✳ ❚❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡rs ❢r♦♠ ❯✳❙✳ t♦ ♦t❤❡r ♠❛r❦❡ts ✐s ❧♦✇❡r ✐♥

t❤❡ s❡❝♦♥❞ ♣❡r✐♦❞ ✇❤❡♥ ❝♦♠♣❛r❡❞ t♦ t❤❡ ✜rst ♣❡r✐♦❞ ✇❤✐❝❤ ♠❛r❦❡❞ ❜② ❛ ✜♥❛♥❝✐❛❧ t✉r❜✉❧❡♥❝❡ ❞✉❡

t♦ t❤❡ ❞♦t✲❝♦♠ ❜✉❜❜❧❡ ❜✉rst✳ ❆❧❧ t❤❡ ♠❛r❦❡ts s❡❡♠ t♦ ❜❡ ❢♦❝✉s❡❞ ♦♥ t❤❡ ❯✳❙✳ ♠❛r❦❡t ✇✐t❤ t❤❡

s✉❜♣r✐♠❡ ❝r✐s✐s✿ ❡①❝❡♣t ❢♦r ❏❛♣❛♥✱ t❤❡ ✇❡✐❣❤ts ♦❢ t❤❡ r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡r ❡✛❡❝ts ❢r♦♠ ❯✳❙✳ ❛r❡

♠♦r❡ t❤❛♥ ❞♦✉❜❧❡❞ ✭❡✈❡♥ tr✐♣❧❡❞✮ ✐♥ t❤❡ t❤✐r❞ ♣❡r✐♦❞✱ ❝♦♠♣❛r❡❞ t♦ t❤❡ s❡❝♦♥❞ ♣❡r✐♦❞✳ ❚❤❡s❡ ❤✐❣❤

❧❡✈❡❧s ♦❢ ✇❡✐❣❤ts ❛r❡ s✉st❛✐♥❡❞ ✐♥ t❤❡ ❢♦❧❧♦✇✐♥❣ ♣❡r✐♦❞s✳

❆♥♦t❤❡r ✐♥t❡r❡st✐♥❣ r❡❣✉❧❛r✐t② ✐s ♣r❡s❡♥t❡❞ ✐♥ ❚❛❜❧❡ ✸ ❛♥❞ ❋✐❣✉r❡ ✸✳ ❙❤❛r❡s ♦❢ ❢♦r❡❝❛st ❡rr♦r

✈❛r✐❛♥❝❡s ❞✉❡ t♦ s❤♦❝❦s t♦ ❡❛❝❤ ♠❛r❦❡t ✐ts❡❧❢ ❛r❡ ♣r♦✈✐❞❡❞ ❤❡r❡✳ ❋♦r ❛❧❧ ♦❢ t❤❡ ♠❛r❦❡ts✱ t❤❡r❡ ✐s ❛ s✉❜st❛♥t✐❛❧ ❞❡❝r❡❛s❡ ✐♥ t❤❡ ✐♠♣♦rt❛♥❝❡ ♦❢ t❤❡ ♦✇♥ s❤♦❝❦s ✐♥ ●❋❊❱❉s ✐♥ t❤❡ t❤✐r❞ ♣❡r✐♦❞ ✇❤✐❝❤ ✐s

♠❛r❦❡❞ ❜② t❤❡ ♦✉t❜r❡❛❦ ♦❢ t❤❡ s✉❜♣r✐♠❡ ❝r✐s✐s ✐♥ ❯✳❙✳ ❛❢t❡r ❛ ❧♦♥❣ ♣❡r✐♦❞ ♦❢ tr❛♥q✉✐❧✐t②✳ ❲✐t❤ t❤❡

❝r✐s✐s✱ ❛❧❧ t❤❡ ♠❛r❦❡ts ❜❡❝♦♠❡ ♠♦r❡ ♣r♦♥❡ t♦ r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡rs ❢r♦♠ ♦t❤❡r ♠❛r❦❡ts✱ ♣♦ss✐❜❧②

❜❡❝❛✉s❡ ✐♥✈❡st♦rs ❛❧❧♦❝❛t❡ ♠♦r❡ ❛tt❡♥t✐♦♥ ❛♥❞ ❜❡❝♦♠❡ ♠♦r❡ s❡♥s✐t✐✈❡ t♦ ✇❤❛t ✐s ❣♦✐♥❣ ♦♥ ✐♥ ❛❧❧

♦✈❡r t❤❡ ✇♦r❧❞✳ ❚❤❛t ✐s t♦ s❛②✱ ♠❛r❦❡ts ❜❡❝♦♠❡ ♠♦r❡ ❝♦♥♥❡❝t❡❞ ✐♥ t❡r♠s ♦❢ s❡♥t✐♠❡♥ts ✇❤❡♥ ❛

✽

❝♦✉♥tr② ✐s ✉♥❡①♣❡❝t❡❞❧② ❤✐t ❜② ❛ ♠❛❥♦r ❝r✐s✐s✳ ❇② t❤❡ ❡♥❞ ♦❢ t❤❡ s✉❜♣r✐♠❡ ❝r✐s✐s✱ ✐♥✈❡st♦rs ✐♥

❏❛♣❛♥ ❛r❡ tr❛♥q✉✐❧✐③❡❞ ❢❛st✿ ♣r❡✲❝r✐s✐s ❧❡✈❡❧s ❛r❡ ❛tt❛✐♥❡❞ ❜② t❤❡ ❢♦✉rt❤ ♣❡r✐♦❞ ✐♥ ❏❛♣❛♥✳ ❖t❤❡r

♠❛r❦❡ts s✉✛❡r ❢r♦♠ t❤❡ ♥❡❣❛t✐✈❡ ❡✛❡❝ts ♦❢ t❤❡ ❊✉r♦♣❡❛♥ s♦✈❡r❡✐❣♥ ❞❡❜t ❝r✐s✐s ✐♥ t❤❡ ❢♦✉rt❤ ♣❡r✐♦❞✳

❆✈❡rt❡❞ ✐♥✈❡st♦rs ✐♥ t❤❡s❡ ♠❛r❦❡ts ❝♦♥t✐♥✉❡ t♦ ❛❧❧♦❝❛t❡ ♠♦r❡ ❛tt❡♥t✐♦♥ t♦ t❤❡ r❡st ♦❢ t❤❡ ✇♦r❧❞✳ ❚❤❡

♥❡❣❛t✐✈❡ ❡✛❡❝ts ♦❢ t❤❡ ❞❡❜t ❝r✐s✐s ❝♦♥t✐♥✉❡ t♦ ❤♦❧❞ ♠♦r❡ ♦r ❧❡ss ❡✈❡♥ ✐♥ t❤❡ ✜❢t❤ ♣❡r✐♦❞ ❢♦r ❊✉r♦✲

③♦♥❡ ❝♦✉♥tr✐❡s ✇❤✐❧❡ ♣r❡✲s✉❜♣r✐♠❡ ❝r✐s✐s ❧❡✈❡❧s ❛r❡ ❛tt❛✐♥❡❞ ✐♥ t❤❡ ❯✳❑✳ ❛♥❞ ❙✇✐t③❡r❧❛♥❞✳ ❏❛♣❛♥

✐s st❛❜✐❧✐③❡❞ ❢❛st❡r t❤❛♥ t❤❡ ❯✳❑✳ ❛♥❞ ❙✇✐t③❡r❧❛♥❞✱ ♣♦ss✐❜❧② ❜❡❝❛✉s❡ t❤❡ ❯✳❑ ❛♥❞ ❙✇✐t③❡r❧❛♥❞ ❛r❡

♠♦r❡ ❝❧♦s❡❧② ❝♦♥♥❡❝t❡❞ t♦ ❊✉r♦✲③♦♥❡ ❝♦✉♥tr✐❡s✳

✺ ❈♦♥❝❧✉s✐♦♥

■♥ t❤✐s ♣❛♣❡r✱ r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡r ❞②♥❛♠✐❝s ✐s st✉❞✐❡❞ ❢♦r s❡✈❡♥ ✜♥❛♥❝✐❛❧ ♠❛r❦❡ts ❢r♦♠ ✷✵✵✵

t♦ ✷✵✶✺ t❤r♦✉❣❤ ❛ ●❡♥❡r❛❧✐③❡❞ ❋♦r❡❝❛st ❊rr♦r ❱❛r✐❛♥❝❡ ❉❡❝♦♠♣♦s✐t✐♦♥ ❛♥❛❧②s✐s✳ ❉❛t❛ s❛♠♣❧❡ ✐s

❞✐✈✐❞❡❞ ✐♥t♦ ✜✈❡ s✉❜♣❡r✐♦❞s ❝♦✈❡r✐♥❣ tr❛♥q✉✐❧ ♦r t✉r❜✉❧❡♥t st❛t❡s ✐♥ t❤❡ ❯✳❙✳ ♠❛r❦❡t✳ ■t ✐s ❢♦✉♥❞ t❤❛t r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡rs ❢r♦♠ ❯✳❙✳ t♦ ♦t❤❡r ♠❛r❦❡ts ❣❡t ♠✉❝❤ str♦♥❣❡r st❛rt✐♥❣ ❢r♦♠ t❤❡ t❤✐r❞ ♣❡r✐♦❞

✇❤✐❧❡ t❤❡ ❯✳❙✳ ✐s ❣♦✐♥❣ t❤r♦✉❣❤ t✉r❜✉❧❡♥t ♣❡r✐♦❞s ❝♦♥✜r♠✐♥❣ t❤❡ ✐♥t✉✐t✐♦♥ t❤❛t ✐♥✈❡st♦rs s❤✐❢t t❤❡✐r

❛tt❡♥t✐♦♥ ♦♥ ✐♥❝✐❞❡♥ts ✐♥ t❤❡ t✉r❜✉❧❡♥t ♠❛r❦❡t✳ ❘❡s✉❧ts ❛❧s♦ s❤♦✇ t❤❛t✱ ✇✐t❤ t❤❡ ♦✉t❜r❡❛❦ ♦❢ t❤❡

s✉❜♣r✐♠❡ ❝r✐s✐s ✐♥ ❯✳❙✳✱ ❛❧❧ t❤❡ ♠❛r❦❡ts ❜❡❝♦♠❡ ♠♦r❡ ♣r♦♥❡ t♦ r✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡rs ❢r♦♠ t❤❡ ♦t❤❡r

♠❛r❦❡ts✳ ▼❛r❦❡ts ❜❡❝♦♠❡ ♠♦r❡ ❝♦♥♥❡❝t❡❞ ✐♥ t❡r♠s ♦❢ s❡♥t✐♠❡♥ts ✇❤❡♥ ❛ ❝♦✉♥tr② ✐s ✉♥❡①♣❡❝t❡❞❧②

❤✐t ❜② ❛ ♠❛❥♦r ❝r✐s✐s✱ ❧✐♠✐t✐♥❣ ❞✐✈❡rs✐✜❝❛t✐♦♥ ♦♣♣♦rt✉♥✐t✐❡s ✇❤❡♥ ✐♥✈❡st♦rs ❛r❡ ♠♦st ✐♥ ♥❡❡❞ ♦❢

t❤❡ ❣❛✐♥s st❡♠♠✐♥❣ ❢r♦♠ ❞✐✈❡rs✐✜❝❛t✐♦♥✳ ❋✉rt❤❡r ✐♥t❡r❡st✐♥❣ r❡s✉❧ts ❛r❡ ♦❜t❛✐♥❡❞ ❝♦♥❝❡r♥✐♥❣ t❤❡

❊✉r♦♣❡❛♥ s♦✈❡r❡✐❣♥ ❞❡❜t ❝r✐s✐s✳ ❚❤❡ ❞❡❜t ❝r✐s✐s ❤❛s ♦♥❧② r❡❣✐♦♥❛❧ ❡✛❡❝ts ♦♥ ✐♥✈❡st♦rs ✇✐t❤ ❏❛♣❛♥

r❡♠❛✐♥❡❞ ✉♥❛✛❡❝t❡❞✳ ❚❤❡ ♥❡❣❛t✐✈❡ ❡✛❡❝ts ♦❢ ❞❡❜t ❝r✐s✐s ♦♥ ✐♥✈❡st♦rs✬ ❛tt❡♥t✐♦♥ ❛❧❧♦❝❛t✐♦♥ ❧❛st

❧♦♥❣❡r ❢♦r ❊✉r♦✲③♦♥❡ ❝♦✉♥tr✐❡s t❤❛♥ ❢♦r t❤❡ ❯✳❑✳ ❛♥❞ ❙✇✐t③❡r❧❛♥❞✳ ❚❤✐s s❤♦✇s t❤❛t ✐♥✈❡st♦rs✬ ❢♦❝✉s

✐s ❞❡t❡r♠✐♥❡❞ ❜② ❛ ❝♦♠♣❧❡① ❛♠❛❧❣❛♠ ♦❢ ❢✉♥❞❛♠❡♥t❛❧ ❛♥❞ s❡♥t✐♠❡♥t❛❧ ❢❛❝t♦rs✳

✾

❘❡❢❡r❡♥❝❡s

❆♥❞❡rs❡♥ ❚✱ ❇♦❧❧❡rs❧❡✈ ❚ ❛♥❞ ❉✐❡❜♦❧❞ ❋❳✳ ✷✵✵✼✳ ❘♦✉❣❤✐♥❣ ✐t ✉♣✿ ✐♥❝❧✉❞✐♥❣ ❥✉♠♣ ❝♦♠♣♦♥❡♥ts ✐♥

♠❡❛s✉r✐♥❣✱ ♠♦❞❡❧✐♥❣ ❛♥❞ ❢♦r❡❝❛st✐♥❣ ❛ss❡t r❡t✉r♥ ✈♦❧❛t✐❧✐t②✳ ❘❡✈✐❡✇ ♦❢ ❊❝♦♥♦♠✐❝s ❛♥❞ ❙t❛t✐st✐❝s

✽✾✿ ✼✵✶✲✼✷✵✳

❇❛❦❡r ▼✱ ❲✉r❣❧❡r ❏ ❛♥❞ ❨✉ ❨✳ ✷✵✶✷✳ ●❧♦❜❛❧✱ ❧♦❝❛❧✱ ❛♥❞ ❝♦♥t❛❣✐♦✉s ✐♥✈❡st♦r s❡♥t✐♠❡♥t✳ ❏♦✉r♥❛❧

♦❢ ❋✐♥❛♥❝✐❛❧ ❊❝♦♥♦♠✐❝s ✶✵✹✿ ✷✼✷✲✷✽✼✳

❇❛❦s❤✐ ● ❛♥❞ ▼❛❞❛♥ ❉✳ ✷✵✵✻✳ ❆ t❤❡♦r② ♦❢ ✈♦❧❛t✐❧✐t② s♣r❡❛❞s✳ ▼❛♥❛❣❡♠❡♥t ❙❝✐❡♥❝❡ ✺✷✿ ✶✾✹✺✲

✶✾✺✻✳

❇♦❧❧❡rs❧❡✈ ❚✱ ❚❛✉❝❤❡♥ ● ❛♥❞ ❩❤♦✉ ❍✳ ✷✵✵✾✳ ❊①♣❡❝t❡❞ st♦❝❦ r❡t✉r♥s ❛♥❞ ✈❛r✐❛♥❝❡ r✐s❦ ♣r❡♠✐❛✳

❘❡✈✐❡✇ ♦❢ ❋✐♥❛♥❝✐❛❧ ❙t✉❞✐❡s ✷✷✿ ✹✹✻✸✲✹✹✾✷✳

❇♦❧❧❡rs❧❡✈ ❚✱ ●✐❜s♦♥ ▼ ❛♥❞ ❩❤♦✉ ❍✳ ✷✵✶✶✳ ❉②♥❛♠✐❝ ❡st✐♠❛t✐♦♥ ♦❢ ✈♦❧❛t✐❧✐t② r✐s❦ ♣r❡♠✐❛ ❛♥❞ ✐♥✲

✈❡st♦r r✐s❦ ❛✈❡rs✐♦♥ ❢r♦♠ ♦♣t✐♦♥✲✐♠♣❧✐❡❞ ❛♥❞ r❡❛❧✐③❡❞ ✈♦❧❛t✐❧✐t✐❡s✳ ❏♦✉r♥❛❧ ♦❢ ❊❝♦♥♦♠❡tr✐❝s ✶✻✵✭✶✮✿

✷✸✺✲✷✹✺✳

❇r✐tt❡♥✲❏♦♥❡s ▼ ❛♥❞ ◆❡✉❜❡r❣❡r ❆✳ ✷✵✵✵✳ ❖♣t✐♦♥ ♣r✐❝❡s✱ ✐♠♣❧✐❡❞ ♣r✐❝❡ ♣r♦❝❡ss❡s✱ ❛♥❞ st♦❝❤❛st✐❝

✈♦❧❛t✐❧✐t②✳ ❏♦✉r♥❛❧ ♦❢ ❋✐♥❛♥❝❡ ✺✺✭✷✮✿ ✽✸✾✲✽✻✻✳

❈❛rr P ❛♥❞ ❲✉ ▲✳ ✷✵✵✽✳ ❱❛r✐❛♥❝❡ r✐s❦ ♣r❡♠✐❛✳ ❘❡✈✐❡✇ ♦❢ ❋✐♥❛♥❝✐❛❧ ❙t✉❞✐❡s ✷✷✿ ✶✸✶✶✲✶✸✹✶✳

❈♦rs✐ ❋✳ ✷✵✵✾✳ ❆ s✐♠♣❧❡ ❛♣♣r♦①✐♠❛t❡ ❧♦♥❣✲♠❡♠♦r② ♠♦❞❡❧ ♦❢ r❡❛❧✐③❡❞ ✈♦❧❛t✐❧✐t②✳ ❏♦✉r♥❛❧ ♦❢

❋✐♥❛♥❝✐❛❧ ❊❝♦♥♦♠❡tr✐❝s ✼✭✷✮✿ ✶✼✹✲✶✾✻✳

❉❡♠❡t❡r✜ ❑✱ ❉❡r♠❛♥ ❊✱ ❑❛♠❛❧ ▼ ❛♥❞ ❩♦✉ ❏✳ ✶✾✾✾✳ ❆ ❣✉✐❞❡ t♦ ✈♦❧❛t✐❧✐t② ❛♥❞ ✈❛r✐❛♥❝❡ s✇❛♣s✳

❏♦✉r♥❛❧ ♦❢ ❉❡r✐✈❛t✐✈❡s ✻✿ ✾✲✸✷✳

❉r❡❝❤s❧❡r ■ ❛♥❞ ❨❛r♦♥ ❆✳ ✷✵✶✶✳ ❲❤❛t✬s ✈♦❧ ❣♦t t♦ ❞♦ ✇✐t❤ ✐t❄ ❘❡✈✐❡✇ ♦❢ ❋✐♥❛♥❝✐❛❧ ❙t✉❞✐❡s

✷✹✭✶✮✿ ✶✲✹✺✳

●❧✐❝❦ ❘ ❛♥❞ ❘♦s❡ ❆✳ ✶✾✾✾✳ ❈♦♥t❛❣✐♦♥ ❛♥❞ tr❛❞❡✿ ❲❤② ❛r❡ ❝✉rr❡♥❝② ❝r✐s❡s r❡❣✐♦♥❛❧❄ ❏♦✉r♥❛❧

♦❢ ■♥t❡r♥❛t✐♦♥❛❧ ▼♦♥❡② ❛♥❞ ❋✐♥❛♥❝❡ ✶✽✿ ✻✵✸✲✻✶✼✳

❏✐❛♥❣ ● ❛♥❞ ❚✐❛♥ ❨✳ ✷✵✵✺✳ ▼♦❞❡❧✲❢r❡❡ ✐♠♣❧✐❡❞ ✈♦❧❛t✐❧✐t② ❛♥❞ ✐ts ✐♥❢♦r♠❛t✐♦♥ ❝♦♥t❡♥t✳ ❘❡✈✐❡✇

♦❢ ❋✐♥❛♥❝✐❛❧ ❙t✉❞✐❡s ✶✽✿ ✶✸✵✺✲✶✸✹✷✳

❑❛♠✐♥s❦② ● ❛♥❞ ❘❡✐♥❤❛rt ❈✳ ✷✵✵✵✳ ❖♥ ❝r✐s❡s✱ ❝♦♥t❛❣✐♦♥✱ ❛♥❞ ❝♦♥❢✉s✐♦♥✳ ❏♦✉r♥❛❧ ♦❢ ■♥t❡r♥❛✲

t✐♦♥❛❧ ❊❝♦♥♦♠✐❝s ✺✶✿ ✶✹✺✲✶✻✽✳

✶✵

❑✉♠❛r ▼ ❛♥❞ ❆✈✐♥❛s❤ P✳ ✷✵✵✷✳ P✉r❡ ❝♦♥t❛❣✐♦♥ ❛♥❞ ✐♥✈❡st♦rs✬ s❤✐❢t✐♥❣ r✐s❦ ❛♣♣❡t✐t❡✿ ❛♥❛❧②t✐❝❛❧

✐ss✉❡s ❛♥❞ ❡♠♣✐r✐❝❛❧ ❡✈✐❞❡♥❝❡✳ ■♥t❡r♥❛t✐♦♥❛❧ ❋✐♥❛♥❝❡ ✺✭✸✮✿ ✹✵✶✲✹✷✻✳

▲♦♥❣st❛✛ ❋❆✳ ✷✵✶✵✳ ❚❤❡ s✉❜♣r✐♠❡ ❝r❡❞✐t ❝r✐s✐s ❛♥❞ ❝♦♥t❛❣✐♦♥ ✐♥ ✜♥❛♥❝✐❛❧ ♠❛r❦❡ts✳ ❏♦✉r♥❛❧ ♦❢

❋✐♥❛♥❝✐❛❧ ❊❝♦♥♦♠✐❝s ✾✼✭✸✮✿ ✹✸✻✲✹✺✵✳

▼♦♥❞r✐❛ ❏ ❛♥❞ ◗✉✐♥t❛♥❛✲❉♦♠❡q✉❡ ❈✳ ✷✵✶✸✳ ❋✐♥❛♥❝✐❛❧ ❝♦♥t❛❣✐♦♥ ❛♥❞ ❛tt❡♥t✐♦♥ ❛❧❧♦❝❛t✐♦♥✳

❊❝♦♥♦♠✐❝ ❏♦✉r♥❛❧ ✶✷✸✭✺✻✽✮✿ ✹✷✾✲✹✺✹✳

▼ü❧❧❡r ❯❆✱ ❉❛❝♦r♦❣♥❛ ▼▼✱ ❉❛✈é ❘❉✱ ❖❧s❡♥ ❘❇✱ P✉❝t❡t ❖❱ ❛♥❞ ✈♦♥ ❲❡✐③sä❝❦❡r ❏✳ ✶✾✾✼✳

❱♦❧❛t✐❧✐t✐❡s ♦❢ ❞✐✛❡r❡♥t t✐♠❡ r❡s♦❧✉t✐♦♥s✿ ❛♥❛❧②③✐♥❣ t❤❡ ❞②♥❛♠✐❝s ♦❢ ♠❛r❦❡t ❝♦♠♣♦♥❡♥ts✳ ❏♦✉r♥❛❧

♦❢ ❊♠♣✐r✐❝❛❧ ❋✐♥❛♥❝❡ ✹✿ ✷✶✸✲✷✸✾✳

P❡s❛r❛♥ ❍▼ ❛♥❞ ❙❤✐♥ ❨✳ ✶✾✾✽✳ ●❡♥❡r❛❧✐③❡❞ ✐♠♣✉❧s❡ r❡s♣♦♥s❡ ❛♥❛❧②s✐s ✐♥ ❧✐♥❡❛r ♠✉❧t✐✈❛r✐❛t❡

♠♦❞❡❧s✳ ❊❝♦♥♦♠✐❝s ▲❡tt❡rs ✺✽✿ ✶✼✲✷✾✳

❚♦❞♦r♦✈ ❱✳ ✷✵✵✾✳ ❱❛r✐❛♥❝❡ r✐s❦ ♣r❡♠✐✉♠ ❞②♥❛♠✐❝s✿ t❤❡ r♦❧❡ ♦❢ ❥✉♠♣s✳ ❘❡✈✐❡✇ ♦❢ ❋✐♥❛♥❝✐❛❧

❙t✉❞✐❡s ✷✸✭✶✮✿ ✸✹✺✲✸✽✸✳

❩❤♦✉ ❍✳ ✷✵✶✵✳ ❱❛r✐❛♥❝❡ r✐s❦ ♣r❡♠✐❛✱ ❛ss❡t ♣r❡❞✐❝t❛❜✐❧✐t② ♣✉③③❧❡s✱ ❛♥❞ ♠❛❝r♦❡❝♦♥♦♠✐❝ ✉♥❝❡r✲

t❛✐♥t②✳ ❋❡❞❡r❛❧ ❘❡s❡r✈❡ ❇♦❛r❞ ❲♦r❦✐♥❣ P❛♣❡r✳

✶✶

❚❛❜❧❡ ✶✿ ❉❡s❝r✐♣t✐✈❡ ❙t❛t✐st✐❝s

▼❛r❦❡t ❙❡r✐❡s ▼❡❛♥ ▼❡❞✐❛♥ ▼✐♥ ▼❛① ❙t❞✳ ❉❡✈✳ ❙❦❡✇♥❡ss ❊①❝✳ ❑✉rt✳

❧♦❣(E^P) ✲✵✳✸✻✽✵ ✲✵✳✹✷✽✻ ✲✶✳✷✽✺✻ ✶✳✶✻✸✶ ✵✳✹✵✹✷ ✵✳✼✵✷✶ ✵✳✸✺✵✺

❯✳❙✳ ❧♦❣(E^Q) ✵✳✵✶✺✾ ✲✵✳✵✶✷✾ ✲✵✳✻✺✽✹ ✶✳✹✹✷✽ ✵✳✸✼✵✹ ✵✳✻✶✶✷ ✵✳✷✸✼✻

✲❧♦❣✭❱❘P✮ ✵✳✸✽✸✾ ✵✳✸✼✻✻ ✲✵✳✶✼✾✶ ✶✳✵✶✸✼ ✵✳✶✺✻✺ ✵✳✷✺✷✽ ✵✳✸✼✹✹

❧♦❣(E^P) ✲✵✳✷✾✼✻ ✲✵✳✸✹✵✷ ✲✶✳✶✻✼✻ ✶✳✵✺✹✾ ✵✳✸✾✼✾ ✵✳✺✶✶✸ ✲✵✳✶✹✺✶

❯✳❑✳ ❧♦❣(E^Q) ✲✵✳✵✵✼✺ ✲✵✳✵✸✺✼ ✲✵✳✼✹✶✽ ✶✳✸✼✹✼ ✵✳✸✼✽✹ ✵✳✺✽✺✹ ✵✳✵✷✽✸

✲❧♦❣✭❱❘P✮ ✵✳✷✾✵✶ ✵✳✷✽✽✽ ✲✵✳✶✹✶✶ ✵✳✼✶✷✽ ✵✳✶✷✼✺ ✲✵✳✵✶✶✵ ✵✳✵✸✵✽

❧♦❣(E^P) ✲✵✳✵✽✷✹ ✲✵✳✶✶✸✹ ✲✵✳✾✺✸✼ ✶✳✶✼✹✺ ✵✳✹✵✾✺ ✵✳✹✼✻✷ ✲✵✳✷✾✺✷

●❡r♠❛♥② ❧♦❣(E^Q) ✵✳✶✼✾✹ ✵✳✶✷✶✻ ✲✵✳✹✾✹✻ ✶✳✹✼✶✼ ✵✳✸✺✼✸ ✵✳✼✺✼✹ ✵✳✶✽✻✹

✲❧♦❣✭❱❘P✮ ✵✳✷✻✶✾ ✵✳✷✻✶✾ ✲✵✳✶✾✽✽ ✵✳✼✻✺✼ ✵✳✶✹✵✽ ✵✳✵✻✽✻ ✵✳✶✶✺✹

❧♦❣(E^P) ✲✵✳✶✹✼✷ ✲✵✳✶✻✺✸ ✲✵✳✾✻✷✻ ✶✳✵✺✹✵ ✵✳✸✼✾✻ ✵✳✸✻✹✸ ✲✵✳✸✼✸✹

❋r❛♥❝❡ ❧♦❣(E^Q) ✵✳✶✹✸✻ ✵✳✶✶✽✷ ✲✵✳✼✷✻✷ ✶✳✹✵✼✹ ✵✳✸✹✽✵ ✵✳✺✺✹✻ ✵✳✶✷✸✹

✲❧♦❣✭❱❘P✮ ✵✳✷✾✵✽ ✵✳✷✾✵✽ ✲✵✳✶✾✸✺ ✵✳✼✻✷✽ ✵✳✶✸✹✼ ✲✵✳✵✸✷✾ ✵✳✶✻✼✼

❧♦❣(E^P) ✲✵✳✷✸✹✸ ✲✵✳✷✽✺✽ ✲✶✳✶✶✽✽ ✶✳✵✷✶✹ ✵✳✹✶✽✾ ✵✳✺✼✽✽ ✲✵✳✶✼✻✼

◆❡t❤❡r❧❛♥❞s ❧♦❣(E^Q) ✵✳✶✷✶✻ ✵✳✵✺✽✾ ✲✶✳✶✾✼✸ ✶✳✹✹✼✷ ✵✳✸✾✻✹ ✵✳✼✶✽✵ ✵✳✵✹✾✶

✲❧♦❣✭❱❘P✮ ✵✳✸✺✻✵ ✵✳✸✺✸✸ ✲✵✳✻✽✾✹ ✵✳✾✹✷✸ ✵✳✶✹✷✻ ✲✵✳✵✸✽✻ ✵✳✼✾✶✷

❧♦❣(E^P) ✲✵✳✸✼✵✵ ✲✵✳✹✼✶✸ ✲✶✳✶✺✼✻ ✵✳✾✻✾✸ ✵✳✸✾✷✾ ✵✳✽✸✷✹ ✵✳✷✸✸✾

❙✇✐t③❡r❧❛♥❞ ❧♦❣(E^Q) ✲✵✳✵✶✼✼ ✲✵✳✶✵✷✻ ✲✵✳✽✺✷✺ ✶✳✺✷✼✼ ✵✳✸✾✾✽ ✵✳✾✸✷✹ ✵✳✻✾✷✹

✲❧♦❣✭❱❘P✮ ✵✳✸✺✷✸ ✵✳✸✹✹✷ ✲✵✳✶✺✷✼ ✶✳✵✽✶✾ ✵✳✶✻✷✺ ✵✳✸✹✹✷ ✵✳✺✽✼✵

❧♦❣(E^P) ✲✵✳✷✻✻✻ ✲✵✳✷✼✻✷ ✲✶✳✶✷✹✻ ✵✳✾✹✼✼ ✵✳✸✵✽✷ ✵✳✷✹✼✹ ✵✳✹✻✵✽

❏❛♣❛♥ ❧♦❣(E^Q) ✵✳✷✻✹✹ ✵✳✷✺✺✹ ✵✳✺✵✺✾ ✶✳✺✻✺✽ ✵✳✷✾✹✺ ✵✳✽✸✷✵ ✶✳✼✺✾✻

✲❧♦❣✭❱❘P✮ ✵✳✺✸✶✶ ✵✳✺✷✹✵ ✲✵✳✸✷✷✼ ✶✳✸✶✽✻ ✵✳✶✽✵✽ ✵✳✶✾✻✽ ✵✳✷✹✵✶

✶✷

❚❛❜❧❡ ✷✿ ❘✐s❦ ❛✈❡rs✐♦♥ s♣✐❧❧♦✈❡rs ❢r♦♠ ❯✳❙✳ t♦ ♦t❤❡r ♠❛r❦❡ts

●❡♥❡r❛❧✐③❡❞ ❋♦r❡❝❛st ❊rr♦r ❱❛r✐❛♥❝❡ ❉✐str✐❜✉t✐♦♥s ❛r❡ ❣✐✈❡♥ ❢♦r r❡s♣♦♥❞✐♥❣ ❝♦✉♥tr✐❡s ❢♦r ❡❛❝❤ ♦❢

t❤❡ ✜✈❡ ♣❡r✐♦❞s✳

P❡r✐♦❞ ✶✿ ❉♦t✲❝♦♠ ❜✉❜❜❧❡ ❜✉rst ❛♥❞ ✾✴✶✶ ❛tt❛❝❦s✳

P❡r✐♦❞ ✷✿ ❘❡❧❛t✐✈❡❧② st❛❜❧❡ ♣❡r✐♦❞✳

P❡r✐♦❞ ✸✿ ❙✉❜♣r✐♠❡ ❝r✐s✐s ❛♥❞ ▲❡❤♠❛♥ ❇r♦t❤❡rs ❜❛♥❦r✉♣t❝②✳

P❡r✐♦❞ ✹✿ ❊✉r♦♣❡❛♥ s♦✈❡r❡✐❣♥ ❞❡❜t ❝r✐s✐s✳

P❡r✐♦❞ ✺✿ ❘❡❧❛t✐✈❡❧② st❛❜❧❡ ♣❡r✐♦❞✳

P❡r✐♦❞ ✶ P❡r✐♦❞ ✷ P❡r✐♦❞ ✸ P❡r✐♦❞ ✹ P❡r✐♦❞ ✺

❯✳❑✳ ✭❋❚❙❊✮ ✵✳✶✵✻✼ ✵✳✵✹✸✵ ✵✳✶✷✽✼ ✵✳✶✷✵✹ ✵✳✶✻✶✼

●❡r♠❛♥② ✭❉❆❳✮ ✵✳✵✻✾✽ ✵✳✵✺✶✺ ✵✳✶✹✼✷ ✵✳✶✷✽✺ ✵✳✶✶✷✵

❋r❛♥❝❡ ✭❈❆❈✮ ✵✳✵✺✵✵ ✵✳✵✸✾✹ ✵✳✶✸✺✻ ✵✳✵✽✻✸ ✵✳✶✵✷✾

◆❡t❤❡r❧❛♥❞s ✭❆❊❳✮ ✵✳✵✹✼✷ ✵✳✵✸✽✻ ✵✳✶✹✷✹ ✵✳✵✾✺✷ ✵✳✵✾✸✶

❙✇✐t③❡r❧❛♥❞ ✭❙▼■✮ ✵✳✵✶✾✽ ✵✳✵✶✺✽ ✵✳✵✻✷✹ ✵✳✵✼✹✽ ✵✳✵✽✶✽

❏❛♣❛♥ ✭◆■❑❑❊■✮ ✵✳✵✾✺✾ ✵✳✵✷✼✻ ✵✳✵✸✺✶ ✵✳✵✸✺✻ ✵✳✵✺✺✹

❚❛❜❧❡ ✸✿ ●❡♥❡r❛❧✐③❡❞ ❋♦r❡❝❛st ❊rr♦r ❱❛r✐❛♥❝❡ ❉✐str✐❜✉t✐♦♥s ❞✉❡ t♦ ♦✇♥ s❤♦❝❦s P❡r✐♦❞ ✶ P❡r✐♦❞ ✷ P❡r✐♦❞ ✸ P❡r✐♦❞ ✹ P❡r✐♦❞ ✺

❯✳❑✳ ✭❋❚❙❊✮ ✵✳✸✾✶✾ ✵✳✹✶✻✸ ✵✳✷✻✾✺ ✵✳✸✶✸✾ ✵✳✹✶✼✶

●❡r♠❛♥② ✭❉❆❳✮ ✵✳✹✸✾✶ ✵✳✸✾✵✷ ✵✳✸✶✶✽ ✵✳✷✾✶✻ ✵✳✸✺✼✽

❋r❛♥❝❡ ✭❈❆❈✮ ✵✳✹✻✺✾ ✵✳✸✹✵✼ ✵✳✷✼✺✷ ✵✳✸✵✾✷ ✵✳✷✽✹✻

◆❡t❤❡r❧❛♥❞s ✭❆❊❳✮ ✵✳✹✾✵✽ ✵✳✹✻✶✼ ✵✳✸✸✼✽ ✵✳✷✾✵✽ ✵✳✸✹✾✽

❙✇✐t③❡r❧❛♥❞ ✭❙▼■✮ ✵✳✻✼✽✻ ✵✳✻✶✾✵ ✵✳✺✵✵✷ ✵✳✹✾✵✶ ✵✳✻✷✼✸

❏❛♣❛♥ ✭◆■❑❑❊■✮ ✵✳✼✾✶✻ ✵✳✾✶✻✷ ✵✳✼✵✼✼ ✵✳✽✾✵✸ ✵✳✾✵✷✾

✶✸