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Análise de contágio a partir do modelo de correlação condicional constante com mudança de regime Markoviana

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FUNDAÇÃO GETÚLIO VARGAS ESCOLA DE ECONOMIA DE SÃO PAULO

PEDRO NIELSEN ROTTA

ANÁLISE DE CONTÁGIO A PARTIR DO MODELO DE CORRELAÇÃO

CONDICIONAL CONSTANTE COM MUDANÇA DE REGIME MARKOVIANA

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PEDRO NIELSEN ROTTA

ANÁLISE DE CONTÁGIO A PARTIR DO MODELO DE CORRELAÇÃO

CONDICIONAL CONSTANTE COM MUDANÇA DE REGIME MARKOVIANA

Dissertação apresentada à Escola de Economia de São Paulo da Fundação Getúlio Vargas como requisito para obtenção de título de Mestre em Economia

Campo de conhecimento: Economia

Orientador: Prof. Dr. Pedro Luiz Valls Pereira

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Rotta, Pedro Nielsen.

Análise de Contágio a partir do Modelo de Correlação Condicional Constante / Pedro Nielsen Rotta. - 2012.

48 f.

Orientador: Pedro Luiz Valls Pereira.

Dissertação (MPFE) - Escola de Economia de São Paulo.

1. Mercado financeiro - Modelos econométricos. 2. Markov, Processos de. 3. Bolsa de Valores. 4. Crise financeira. I. Pereira, P. (Pedro). II. Dissertação (MPFE) - Escola de Economia de São Paulo. III. Título.

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PEDRO NIELSEN ROTTA

ANÁLISE DE CONTÁGIO A PARTIR DO MODELO DE CORRELAÇÃO

CONDICIONAL CONSTANTE COM MUDANÇA DE REGIME MARKOVIANA

Dissertação apresentada à Escola de Economia de São Paulo da Fundação Getúlio Vargas como requisito para obtenção de título de Mestre em Economia.

Campo de conhecimento: Economia

Data de aprovação: 18/12/2012

Banca Examinadora:

Prof. Dr. Pedro Luiz Valls Pereira FGV-EESP

Prof. Dr. Marcelo Fernandes FGV-EESP

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❆●❘❆❉❊❈■▼❊◆❚❖❙

❊♠ ♣r✐♠❡✐r♦ ❧✉❣❛r✱ ❛❣r❛❞❡ç♦ ♣r♦❢✉♥❞❛♠❡♥t❡ ❛♦ ♣r♦❢❡ss♦r✱ ♠❡✉ ♦r✐❡♥t❛❞♦r✱ P❡❞r♦ ❱❛❧❧s ♣❡❧♦ ❣r❛♥❞❡ ❛♣♦✐♦ ❞❡❞✐❝❛❞♦ ❛ ❡❧❛❜♦r❛çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ❆❣r❛❞❡ç♦ t❛♠❜é♠ ❛♦s ✐♥t❡❣r❛♥t❡s ❞❛ ❜❛♥❝❛ ❡①❛♠✐♥❛❞♦r❛✱ ♣r♦❢❡ss♦r ▼❛r❝❡❧♦ ❋❡r♥❛♥❞❡s ❡ ❊♠❡rs♦♥ ▼❛rç❛❧✱ ♣❡❧❛s ✈❛❧✐♦s❛s ❝♦♥s✐❞❡r❛çõ❡s ❡ s✉❣❡stõ❡s ♣❛r❛ ❛s ♠❡❧❤♦r✐❛s ❞❛ ♣r❡s❡♥t❡ ❉✐ss❡rt❛çã♦✳ ❆✐♥❞❛ ♥♦ â♠❜✐t♦ ❞❛ ❡s❝♦❧❛ ❋●❱✲❊❊❙P✱ ❛❣r❛❞❡ç♦ ❛♦ ♣r♦❢❡ss♦r ❲❛❣♥❡r ▼♦♥t❡✐r♦ ♣❡❧❛s ✐♠♣♦rt❛♥t❡s ❝♦♥tr✐❜✉✐çõ❡s✳

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❘❊❙❯▼❖

◆❛s ú❧t✐♠❛s ❞é❝❛❞❛s✱ ❛ ❛♥á❧✐s❡ ❞♦s ♣❛❞rõ❡s ❞❡ ♣r♦♣❛❣❛çã♦ ✐♥t❡r♥❛❝✐♦♥❛❧ ❞❡ ❡✈❡♥t♦s ✜♥❛♥❝❡✐r♦s s❡ t♦r♥♦✉ ♦ t❡♠❛ ❞❡ ❣r❛♥❞❡ ♣❛rt❡ ❞♦s ❡st✉❞♦s ❛❝❛❞ê♠✐❝♦s ❢♦❝❛❞♦s ❡♠ ♠♦✲ ❞❡❧♦s ❞❡ ✈♦❧❛t✐❧✐❞❛❞❡ ♠✉❧t✐✈❛r✐❛❞♦s✳ ❉✐❛♥t❡ ❞❡st❡ ❝♦♥t❡①t♦✱ ♦❜❥❡t✐✈♦ ❝❡♥tr❛❧ ❞♦ ♣r❡s❡♥t❡ ❡st✉❞♦ é ❛✈❛❧✐❛r ♦ ❢❡♥ô♠❡♥♦ ❞❡ ❝♦♥tá❣✐♦ ✜♥❛♥❝❡✐r♦ ❡♥tr❡ r❡t♦r♥♦s ❞❡ í♥❞✐❝❡s ❞❡ ❇♦❧s❛s ❞❡ ❱❛❧♦r❡s ❞❡ ❞✐❢❡r❡♥t❡s ♣❛ís❡s ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❡❝♦♥♦♠étr✐❝❛✱ ❛♣r❡s❡♥t❛❞❛ ♦r✐❣✐♥❛❧♠❡♥t❡ ❡♠ P❡❧❧❡t✐❡r ✭✷✵✵✻✮✱ s♦❜r❡ ❛ ❞❡♥♦♠✐♥❛çã♦ ❞❡ ❘❡❣✐♠❡ ❙✇✐t❝❤✐♥❣ ❉②♥❛♠✐❝ ❈♦rr❡❧❛t✐♦♥ ✭❘❙❉❈✮✳ ❚❛❧ ♠❡t♦❞♦❧♦❣✐❛ ❡♥✈♦❧✈❡ ❛ ❝♦♠❜✐♥❛çã♦ ❞♦ ▼♦❞❡❧♦ ❞❡ ❈♦rr❡❧❛çã♦ ❈♦♥❞✐❝✐♦♥❛❧ ❈♦♥st❛♥t❡ ✭❈❈❈✮ ♣r♦♣♦st♦ ♣♦r ❇♦❧❧❡rs❧❡✈ ✭✶✾✾✵✮ ❝♦♠ ♦ ▼♦❞❡❧♦ ❞❡ ▼✉❞❛♥ç❛ ❞❡ ❘❡❣✐♠❡ ❞❡ ▼❛r❦♦✈ s✉❣❡r✐❞♦ ♣♦r ❍❛♠✐❧t♦♥ ❡ ❙✉s♠❡❧ ✭✶✾✾✹✮✳ ❋♦✐ ❢❡✐t❛ ✉♠❛ ♠♦❞✐✜❝❛çã♦ ♥♦ ♠♦❞❡❧♦ ♦r✐❣✐♥❛❧ ❘❙❉❈✱ ❛ ✐♥tr♦❞✉çã♦ ❞♦ ♠♦❞❡❧♦ ●❏❘✲●❆❘❈❍ ❢♦r♠✉❧❛❞♦ ❡♠ ●❧♦st❡♥✱ ❏❛❣❛♥♥❛t❤❛♥ ❡ ❘✉♥❦❧❡ ✭✶✾✾✸✮✱ ♥❛ ❡q✉❛çã♦ ❞❛s ✈❛r✐â♥❝✐❛s ❝♦♥❞✐❝✐♦♥❛✐s ✐♥❞✐✈✐❞✉❛✐s ❞❛s sér✐❡s ♣❛r❛ ♣❡r♠✐t✐r ❝❛♣t✉r❛r ♦s ❡❢❡✐t♦s ❛ss✐♠étr✐❝♦s ♥❛ ✈♦❧❛t✐❧✐❞❛❞❡✳ ❆ ❜❛s❡ ❞❡ ❞❛❞♦s ❢♦✐ ❝♦♥str✉í❞❛ ❝♦♠ ❛s sér✐❡s ❞✐ár✐❛s ❞❡ ❢❡❝❤❛♠❡♥t♦ ❞♦s í♥❞✐❝❡s ❞❛s ❇♦❧s❛s ❞❡ ❱❛❧♦r❡s ❞♦s ❊st❛❞♦s ❯♥✐❞♦s ✭❙P✺✵✵✮✱ ❘❡✐♥♦ ❯♥✐❞♦ ✭❋❚❙❊✶✵✵✮✱ ❇r❛s✐❧ ✭■❇❖❱❊❙P❆✮ ❡ ❈♦ré✐❛ ❞♦ ❙✉❧ ✭❑❖❙P■✮ ♣❛r❛ ♦ ♣❡rí♦❞♦ ❞❡ ✵✷✴✵✶✴✷✵✵✸ ❛té ✷✵✴✵✾✴✷✵✶✷✳ ❆♦ ❧♦♥❣♦ ❞♦ tr❛❜❛❧❤♦ ❛ ♠❡t♦✲ ❞♦❧♦❣✐❛ ✉t✐❧✐③❛❞❛ ❢♦✐ ❝♦♥❢r♦♥t❛❞❛ ❝♦♠ ♦✉tr❛s ♠❛✐s ❞✐❢✉♥❞✐❞♦s ♥❛ ❧✐t❡r❛t✉r❛✱ ❡ ♦ ♠♦❞❡❧♦ ❘❙❉❈ ❝♦♠ ❞♦✐s r❡❣✐♠❡s ❢♦✐ ❞❡✜♥✐❞♦ ❝♦♠♦ ♦ ♠❛✐s ❛♣r♦♣r✐❛❞♦ ♣❛r❛ ❛ ❛♠♦str❛ s❡❧❡❝✐♦✲ ♥❛❞❛✳ ❖ ❝♦♥❥✉♥t♦ ❞❡ r❡s✉❧t❛❞♦s ❡♥❝♦♥tr❛❞♦s ❢♦r♥❡❝❡♠ ❡✈✐❞ê♥❝✐❛s ❛ ❢❛✈♦r ❞❛ ❡①✐stê♥❝✐❛ ❞❡ ❝♦♥tá❣✐♦ ✜♥❛♥❝❡✐r♦ ❡♥tr❡ ♦s ♠❡r❝❛❞♦s ❞♦s q✉❛tr♦ ♣❛ís❡s ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❞❡✜♥✐çã♦ ❞❡ ❝♦♥✲ tá❣✐♦ ✜♥❛♥❝❡✐r♦ ❞♦ ❇❛♥❝♦ ▼✉♥❞✐❛❧ ❞❡♥♦♠✐♥❛❞❛ ❞❡ ✏♠✉✐t♦ r❡str✐t✐✈❛✑✳ ❚❛❧ ❝♦♥❝❧✉sã♦ ❞❡✈❡ s❡r ❛✈❛❧✐❛❞❛ ❝♦♠ ❝❛✉t❡❧❛ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❡①t❡♥s❛ ❞✐✈❡rs✐❞❛❞❡ ❞❡ ❞❡✜♥✐çõ❡s ❞❡ ❝♦♥tá❣✐♦ ❡①✐st❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛✳

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❆❇❙❚❘❆❈❚

❖✈❡r t❤❡ ❧❛st ❞❡❝❛❞❡s✱ t❤❡ ❛♥❛❧②s✐s ♦❢ t❤❡ tr❛♥s♠✐ss✐♦♥s ♦❢ ✐♥t❡r♥❛t✐♦♥❛❧ ✜♥❛♥❝✐❛❧ ❡✈❡♥ts ❤❛s ❜❡❝♦♠❡ t❤❡ s✉❜❥❡❝t ♦❢ ♠❛♥② ❛❝❛❞❡♠✐❝ st✉❞✐❡s ❢♦❝✉s❡❞ ♦♥ ♠✉❧t✐✈❛r✐❛t❡ ✈♦❧❛t✐✲ ❧✐t② ♠♦❞❡❧s ✈♦❧❛t✐❧✐t②✳ ❚❤❡ ❣♦❛❧ ♦❢ t❤✐s st✉❞② ✐s t♦ ❡✈❛❧✉❛t❡ t❤❡ ✜♥❛♥❝✐❛❧ ❝♦♥t❛❣✐♦♥ ❜❡t✇❡❡♥ st♦❝❦ ♠❛r❦❡t r❡t✉r♥s✳ ❚❤❡ ❡❝♦♥♦♠❡tr✐❝ ❛♣♣r♦❛❝❤ ❡♠♣❧♦②❡❞ ✇❛s ♦r✐❣✐♥❛❧❧② ♣r❡s❡♥t❡❞ ❜② P❡❧❧❡t✐❡r ✭✷✵✵✻✮✱ ♥❛♠❡❞ ❘❡❣✐♠❡ ❙✇✐t❝❤✐♥❣ ❉②♥❛♠✐❝ ❈♦rr❡❧❛t✐♦♥ ✭❘❙❉❈✮✳ ❚❤✐s ♠❡t❤♦❞♦✲ ❧♦❣② ✐♥✈♦❧✈❡s t❤❡ ❝♦♠❜✐♥❛t✐♦♥ ♦❢ ❈♦♥st❛♥t ❈♦♥❞✐t✐♦♥❛❧ ❈♦rr❡❧❛t✐♦♥ ▼♦❞❡❧ ✭❈❈❈✮ ♣r♦♣♦✲ s❡❞ ❜② ❇♦❧❧❡rs❧❡✈ ✭✶✾✾✵✮ ✇✐t❤ ▼❛r❦♦✈ ❘❡❣✐♠❡ ❙✇✐t❝❤✐♥❣ ▼♦❞❡❧ s✉❣❣❡st❡❞ ❜② ❍❛♠✐❧t♦♥ ❛♥❞ ❙✉s♠❡❧ ✭✶✾✾✹✮✳ ❆ ♠♦❞✐✜❝❛t✐♦♥ ✇❛s ♠❛❞❡ ✐♥ t❤❡ ♦r✐❣✐♥❛❧ ♠♦❞❡❧ ❘❙❉❈✱ t❤❡ ✐♥tr♦❞✉❝✲ t✐♦♥ ♦❢ t❤❡ ●❏❘✲●❆❘❈❍ ●❧♦st❡♥ ♠♦❞❡❧ ❢♦r♠✉❧❛t❡❞ ✐♥ ●❧♦st❡♥✱ ❏❛❣❛♥♥❛t❤❛♥ ❡ ❘✉♥❦❧❡ ✭✶✾✾✸✮✱ ♦♥ t❤❡ ❡q✉❛t✐♦♥ ♦❢ t❤❡ ❝♦♥❞✐t✐♦♥❛❧ ✉♥✐✈❛r✐❛t❡ ✈❛r✐❛♥❝❡s t♦ ❛❧❧♦✇ ❛s②♠♠❡tr✐❝ ❡❢✲ ❢❡❝ts ✐♥ ✈♦❧❛t✐❧✐t② ❜❡ ❝❛♣t✉r❡❞✳ ❚❤❡ ❞❛t❛❜❛s❡ ✇❛s ❜✉✐❧t ✇✐t❤ t❤❡ s❡r✐❡s ♦❢ ❞❛✐❧② ❝❧♦s✐♥❣ st♦❝❦ ♠❛r❦❡t ✐♥❞✐❝❡s ✐♥ t❤❡ ❯♥✐t❡❞ ❙t❛t❡s ✭❙P✺✵✵✮✱ ❯♥✐t❡❞ ❑✐♥❣❞♦♠ ✭❋❚❙❊✶✵✵✮✱ ❇r❛③✐❧ ✭■❇❖❱❊❙P❆✮ ❛♥❞ ❙♦✉t❤ ❑♦r❡❛ ✭❑❖❙P■✮ ❢♦r t❤❡ ♣❡r✐♦❞ ❢r♦♠ ✵✷✴✵✶✴✷✵✵✸ t♦ ✷✵✴✵✾✴✷✵✶✷✳ ❚❤r♦✉❣❤♦✉t t❤❡ ✇♦r❦ t❤❡ ♠❡t❤♦❞♦❧♦❣② ✇❛s ❝♦♠♣❛r❡❞ ✇✐t❤ ♦t❤❡rs ♠♦st ✇✐❞❡s♣r❡❛❞ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✱ ❛♥❞ t❤❡ ♠♦❞❡❧ ❘❙❉❈ ✇✐t❤ t✇♦ r❡❣✐♠❡s ✇❛s ❞❡✜♥❡❞ ❛s t❤❡ ♠♦st ❛♣♣r♦✲ ♣r✐❛t❡ ❢♦r t❤❡ s❡❧❡❝t❡❞ s❛♠♣❧❡✳ ❚❤❡ s❡t ♦❢ r❡s✉❧ts ♣r♦✈✐❞❡ ❡✈✐❞❡♥❝❡ ❢♦r t❤❡ ❡①✐st❡♥❝❡ ♦❢ ✜♥❛♥❝✐❛❧ ❝♦♥t❛❣✐♦♥ ❜❡t✇❡❡♥ ♠❛r❦❡ts ♦❢ t❤❡ ❢♦✉r ❝♦✉♥tr✐❡s ❝♦♥s✐❞❡r✐♥❣ t❤❡ ❞❡✜♥✐t✐♦♥ ♦❢ ✜♥❛♥❝✐❛❧ ❝♦♥t❛❣✐♦♥ ❢r♦♠ t❤❡ ❲♦r❧❞ ❇❛♥❦ ❝❛❧❧❡❞ ✧✈❡r② r❡str✐❝t✐✈❡✧✳ ❙✉❝❤ ❛ ❝♦♥❝❧✉s✐♦♥ s❤♦✉❧❞ ❜❡ ❡✈❛❧✉❛t❡❞ ❝❛r❡❢✉❧❧② ❝♦♥s✐❞❡r✐♥❣ t❤❡ ✇✐❞❡ ❞✐✈❡rs✐t② ♦❢ ❞❡✜♥✐t✐♦♥s ♦❢ ❝♦♥t❛❣✐♦♥ ✐♥ t❤❡ ❧✐t❡r❛t✉r❡✳

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▲✐st❛ ❞❡ ❋✐❣✉r❛s

✶ ❙ér✐❡s ❞♦s ❮♥❞✐❝❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✷ ❙ér✐❡s ❞♦s ❘❡t♦r♥♦s ❞♦s ❮♥❞✐❝❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✸ ❙ér✐❡s ❞❛s ❱❛r✐â♥❝✐❛s ❈♦♥❞✐❝✐♦♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✹ Pr♦❜❛❜✐❧✐❞❛❞❡s ❙✉❛✈✐③❛❞❛s ❝♦♠ ✷ ❘❡❣✐♠❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✺ Pr♦❜❛❜✐❧✐❞❛❞❡s ❙✉❛✈✐③❛❞❛s ❝♦♠ ✸ ❘❡❣✐♠❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✻ ❙ér✐❡s ❞♦s ◆í✈❡✐s ❡st✐♠❛❞♦s ♣❡❧♦ ▼♦❞❡❧♦ ❞❡ ◆í✈❡❧ ▲♦❝❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✼ ❍✐st♦❣r❛♠❛ ❞♦s ❘❡t♦r♥♦s ❞♦s ❮♥❞✐❝❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✼ ✽ Pr♦❜❛❜✐❧✐❞❛❞❡s ❙✉❛✈✐③❛❞❛s ❝♦♠ ✷ ❘❡❣✐♠❡s ✭❘❙❉❈✲●❆❘❈❍✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶ ✾ Pr♦❜❛❜✐❧✐❞❛❞❡s ❙✉❛✈✐③❛❞❛s ❝♦♠ ✸ ❘❡❣✐♠❡s ✭❘❙❉❈✲●❆❘❈❍✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶

▲✐st❛ ❞❡ ❚❛❜❡❧❛s

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❙✉♠ár✐♦

✶ ■♥tr♦❞✉çã♦ ✸

✷ ❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛ ✺

✷✳✶ ❉❡✜♥✐çã♦ ❞❡ ❈♦♥tá❣✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺ ✷✳✷ ❆❜♦r❞❛❣❡♥s ❊❝♦♥♦♠étr✐❝❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻

✸ ▼❡t♦❞♦❧♦❣✐❛ ✾

✸✳✶ ▼♦❞❡❧♦ ❘❙❉❈ ✭▼❙✲❈❈❈✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾ ✸✳✷ ❊st✐♠❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸

✹ ❇❛s❡ ❞❡ ❉❛❞♦s ✶✺

✹✳✶ ❉❡s❝r✐çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺ ✹✳✷ ❚r❛t❛♠❡♥t♦s ❡ ❆♥á❧✐s❡s ■♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻ ✹✳✸ ❋✐❧tr❛❣❡♠ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽

✺ ❘❡s✉❧t❛❞♦s ✷✵

✺✳✶ ▼♦❞❡❧♦ ❘❙❉❈ ✭▼❙✲❈❈❈✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✺✳✶✳✶ ❉✐str✐❜✉✐çõ❡s ▼❛r❣✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✺✳✶✳✷ ❈♦♠ ✷ ❘❡❣✐♠❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✺✳✶✳✸ ❈♦♠ ✸ ❘❡❣✐♠❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ✺✳✷ ❈♦♠♣❛r❛çã♦ ❝♦♠ ♦s ▼♦❞❡❧♦s ❈❈❈ ❡ ❉❈❈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✻ ❈♦♥❝❧✉sã♦ ✸✶

❘❡❢❡rê♥❝✐❛s ✸✺

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✶ ■♥tr♦❞✉çã♦

❆ ❣❧♦❜❛❧✐③❛çã♦✱ ❞❡sr❡❣✉❧❛♠❡♥t❛çã♦ ❡ ♦s ❛✈❛♥ç♦s t❡❝♥♦❧ó❣✐❝♦s ♠♦❞✐✜❝❛r❛♠ ❞❡ ❢♦r♠❛ ✐♥t❡♥s❛ ❛ ❡str✉t✉r❛ ❞❡ r❡❧❛çã♦ ❡♥tr❡ ♦s ♠❡r❝❛❞♦s ✜♥❛♥❝❡✐r♦s ❞❡ ❞✐❢❡r❡♥t❡s ♣❛ís❡s✳ ❊①✐st❡♠ ❡✈✐❞ê♥❝✐❛s s✉✜❝✐❡♥t❡s ❞❡ q✉❡ ♦ ❛✉♠❡♥t♦ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞❡ tr❛♥s♠✐ssã♦ ❞❛s ✐♥❢♦r♠❛çõ❡s ❢♦✐ r❡s♣♦♥sá✈❡❧ ♣♦r ♣❛r❝❡❧❛ ❡①♣r❡ss✐✈❛ ❞❛ ♠❛✐♦r ✐♥t❡❣r❛çã♦ ❡♥tr❡ ♦s ♠❡r❝❛❞♦s✳ ❉✐❛♥t❡ ❞❡st❛s ♠♦❞✐✜❝❛çõ❡s✱ s✉r❣✐r❛♠ q✉❡st✐♦♥❛♠❡♥t♦s s♦❜r❡ ❛s ❞❡s✈❛♥t❛❣❡♥s ❞❡st❡ ♣r♦❝❡ss♦✳ ❊♥tr❡ ♦s ❞✐✈❡rs♦s ❛s♣❡❝t♦s ♥❡❣❛t✐✈♦s ❛♣♦♥t❛❞♦s✱ ✉♠ ❞❡❧❡s ❞✐③ r❡s♣❡✐t♦ à ✐♥t❡♥s✐✜❝❛çã♦ ❞♦ ❢❡♥ô♠❡♥♦ ❞❡ ❝♦♥tá❣✐♦ ✜♥❛♥❝❡✐r♦ ❡ ❛s ♣❡r❞❛s ❛tr❡❧❛❞❛s ❛s ❞❡s❝♦♥t✐♥✉✐❞❛❞❡s ♥♦s ♠❡❝❛♥✐s♠♦s ❞❡ ♣r♦✲ ♣❛❣❛çã♦ ❞❡ ❝❤♦q✉❡s✳ ❖✉ s❡❥❛✱ ♦ ❡str❡✐t❛♠❡♥t♦ ❞♦ r❡❧❛❝✐♦♥❛♠❡♥t♦ ❡♥tr❡ ♦s ♠❡r❝❛❞♦s ♣♦❞❡ ❛❝❛rr❡t❛r ✉♠❛ ❡❧❡✈❛çã♦ s✐❣♥✐✜❝❛t✐✈❛ ❞❛ ✈✉❧♥❡r❛❜✐❧✐❞❛❞❡ ❞❛s ❡❝♦♥♦♠✐❛s ❢r❡♥t❡ ❛ ❝❤♦q✉❡s ✜♥❛♥❝❡✐r♦s ❡①t❡r♥♦s✳ ❆❧é♠ ❞✐ss♦✱ ♦ ❝♦♥tá❣✐♦ ✜♥❛♥❝❡✐r♦ ❞❡s♣❡rt❛ ✐♥t❡r❡ss❡ ❞❡ ✐♥✈❡st✐❣❛✲ çã♦ ♣❛r❛ ❢♦r♠✉❧❛❞♦r❡s ❞❡ ♣♦❧ít✐❝❛ ❡❝♦♥ô♠✐❝❛ ❡ ✐♥✈❡st✐❞♦r❡s ✐♥t❡r♥❛❝✐♦♥❛✐s q✉❡ ❜✉s❝❛♠ ❞✐✈❡rs✐✜❝❛çã♦ ❞❡ r✐s❝♦s✳ ❉❡st❛ ❢♦r♠❛✱ ♥❛s ú❧t✐♠❛s ❞✉❛s ❞é❝❛❞❛s✱ ❛ ❛♥á❧✐s❡ ❞♦s ♣❛❞rõ❡s ❞❡ ♣r♦♣❛❣❛çã♦ ✐♥t❡r♥❛❝✐♦♥❛❧ ❞❡ ❡✈❡♥t♦s ✜♥❛♥❝❡✐r♦s s❡ t♦r♥♦✉ ♦ t❡♠❛ ❞❡ ❣r❛♥❞❡ ♣❛rt❡ ❞♦s ❡st✉❞♦s ❛❝❛❞ê♠✐❝♦s ❢♦❝❛❞♦s ❡♠ ♠♦❞❡❧♦s ❞❡ ✈♦❧❛t✐❧✐❞❛❞❡✳

◆❡st❡ ❝♦♥t❡①t♦✱ ♦ ♦❜❥❡t✐✈♦ ❝❡♥tr❛❧ ❞♦ ♣r❡s❡♥t❡ ❡st✉❞♦ é ❛♥❛❧✐s❛r ♦ ❢❡♥ô♠❡♥♦ ❞❡ ❝♦♥✲ tá❣✐♦ ✜♥❛♥❝❡✐r♦ ❡♥tr❡ í♥❞✐❝❡s ❞❡ ❇♦❧s❛s ❞❡ ❱❛❧♦r❡s ❞❡ ❞✐❢❡r❡♥t❡s ♣❛ís❡s ❛ ♣❛rt✐r ❞❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❡❝♦♥♦♠étr✐❝❛✱ ❛♣r❡s❡♥t❛❞❛ ♦r✐❣✐♥❛❧♠❡♥t❡ ❡♠ P❡❧❧❡t✐❡r ✭✷✵✵✻✮ s♦❜r❡ ❛ ❞❡♥♦♠✐✲ ♥❛çã♦ ❞❡ ❘❡❣✐♠❡ ❙✇✐t❝❤✐♥❣ ❉②♥❛♠✐❝ ❈♦rr❡❧❛t✐♦♥ ✭❘❙❉❈✮✱ q✉❡ ❡♥✈♦❧✈❡ ❛ ❝♦♠❜✐♥❛çã♦ ❞♦ ▼♦❞❡❧♦ ❞❡ ❈♦rr❡❧❛çã♦ ❈♦♥❞✐❝✐♦♥❛❧ ❈♦♥st❛♥t❡ ✭❈❈❈✮ ♣r♦♣♦st♦ ♣♦r ❇♦❧❧❡rs❧❡✈ ✭✶✾✾✵✮ ❝♦♠ ♦ ▼♦❞❡❧♦ ❞❡ ▼✉❞❛♥ç❛ ❞❡ ❘❡❣✐♠❡ ❞❡ ▼❛r❦♦✈ s✉❣❡r✐❞♦ ♣♦r ❍❛♠✐❧t♦♥ ❡ ❙✉s♠❡❧ ✭✶✾✾✹✮✳ ❋♦✐ ❢❡✐t❛ ✉♠❛ ❛❞❛♣t❛çã♦ ♥♦ ♠♦❞❡❧♦ ♦r✐❣✐♥❛❧ ❘❙❉❈✱ q✉❡ ❝♦♥s✐st✐✉ ♥❛ ✐♥tr♦❞✉çã♦ ❞♦ ♠♦❞❡❧♦ ●❏❘✲●❆❘❈❍✱ ❢♦r♠✉❧❛❞♦ ❡♠ ●❧♦st❡♥✱ ❏❛❣❛♥♥❛t❤❛♥ ❡ ❘✉♥❦❧❡ ✭✶✾✾✸✮✱ ♥❛ ♠♦❞❡❧❛❣❡♠ ❞❛s ✈❛r✐â♥❝✐❛s ✐♥❞✐✈✐❞✉❛✐s ❞❛s sér✐❡s ♣❛r❛ ♣❡r♠✐t✐r ❝❛♣t✉r❛r ♦s ❡❢❡✐t♦s ❛ss✐♠étr✐❝♦s ♥❛ ✈♦❧❛t✐❧✐✲ ❞❛❞❡✳ ➱ r❡❧❡✈❛♥t❡ ❞❡st❛❝❛r q✉❡ ♥ã♦ ❢❛③ ♣❛rt❡ ❞♦ ❡s❝♦♣♦ ❞❡st❡ tr❛❜❛❧❤♦ ✐❞❡♥t✐✜❝❛r ♣♦ssí✈❡✐s ❝❛✉s❛s ♦✉ ❛✈❛❧✐❛r ❛s ❝♦♥s❡q✉ê♥❝✐❛s ❡❝♦♥ô♠✐❝❛s ❞♦ ❝♦♥tá❣✐♦ ✜♥❛♥❝❡✐r♦✳

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❞♦ ♠♦❞❡❧♦ ❘❙❉❈ ❝♦♠♦ ❛❧t❡r♥❛t✐✈❛ ❛♦ ❉❈❈✳ ❖ ♣r✐♠❡✐r♦ ❞✐③ r❡s♣❡✐t♦ à ❝❛♣❛❝✐❞❛❞❡ ❞♦ ▼♦❞❡❧♦ ❘❙❉❈✱ ♣♦r ✐♥❝♦r♣♦r❛r ♠✉❞❛♥ç❛s ❞❡ r❡❣✐♠❡ à s✉❛ ❞✐♥â♠✐❝❛✱ ♥ã♦ ♣r❡❝✐s❛r ❞❡✜♥✐r ❛ ♣r✐♦r✐ q✉❛✐s ♦s ♣❡rí♦❞♦s ❞❡ ❝r✐s❡s ✜♥❛♥❝❡✐r❛✳ ❊st❛ ❞❡✜♥✐çã♦ é ❢❡✐t❛ ❡♥❞♦❣❡♥❛♠❡♥t❡✱ ❞❛❞♦ q✉❡ ❛ ❝❛❞❛ ✐♥st❛♥t❡ t sã♦ ❝❛❧❝✉❧❛❞❛s ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❡st❛r ❡♠ ❝❛❞❛ r❡❣✐♠❡✳ ❖ s❡❣✉♥❞♦ ❝♦♥s✐st❡ ♥❛ ✐❞é✐❛ ❞❡ q✉❡ ♣♦ss✐✈❡❧♠❡♥t❡ ❛ ❝♦♥tr✐❜✉✐çã♦ ♣❛r❛ ❛ ❧✐t❡r❛t✉r❛ ♣♦❞❡r✐❛ s❡r ♠❛✐♦r✱ ❞❛❞♦ q✉❡ ♦ ❉❈❈ ❥á s❡ ❡♥❝♦♥tr❛ ♠✉✐t♦ ❞✐❢✉♥❞✐❞♦ ❡ ✉t✐❧✐③❛❞♦ ❡♥tr❡ ♦s t❡st❡s ❞❡ ❝♦♥tá❣✐♦ r❡❛❧✐③❛❞♦s ♥♦s ú❧t✐♠♦s ❞❡③ ❛♥♦s✳ P❛r❛ ❝♦♠♣❧❡♠❡♥t❛r ❛ ❛♥á❧✐s❡ ❞❡st❡ tr❛❜❛❧❤♦✱ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ❝♦♠♣❛r❛çã♦✱ t❛♠❜é♠ ♥♦ ❝❛♣ít✉❧♦ ✺✱ ❡♥tr❡ ♦s r❡s✉❧t❛❞♦s ❞❡ ❛♠❜♦s ♦s ♠♦❞❡❧♦s✳

❆ ❜❛s❡ ❞❡ ❞❛❞♦s ❢♦✐ ❝♦♥str✉í❞❛ ❝♦♠ ❛s sér✐❡s ❞✐ár✐❛s ❞❡ ❢❡❝❤❛♠❡♥t♦ ❞♦s ❮♥❞✐❝❡s ❞❛s ❇♦❧s❛s ❞❡ ❱❛❧♦r❡s ❞♦s ❊st❛❞♦s ❯♥✐❞♦s ✭❙P✺✵✵✮✱ ❘❡✐♥♦ ❯♥✐❞♦ ✭❋❚❙❊✶✵✵✮✱ ❇r❛s✐❧ ✭■❇❖✲ ❱❊❙P❆✮ ❡ ❈♦ré✐❛ ❞♦ ❙✉❧ ✭❑❖❙P■✮ ♣❛r❛ ♦ ♣❡rí♦❞♦ ❞❡ ✵✷✴✵✶✴✷✵✵✸ ❛té ✷✵✴✵✾✴✷✵✶✷✳ ❆ ❥✉st✐✜❝❛t✐✈❛ ♣❛r❛ ❡s❝♦❧❤❛ ❞❡st❡ ❣r✉♣♦ ❞❡ ♣❛ís❡s ❢♦✐ ❛ ✐❞é✐❛ ❞❡ t❡r ❞♦✐s r❡♣r❡s❡♥t❛♥t❡s ❞❡ r❡✲ ❣✐õ❡s ❞✐❢❡r❡♥t❡s ❞❡ ♠❡r❝❛❞♦s ❞❡s❡♥✈♦❧✈✐❞♦s ✭❆♠ér✐❝❛ ❞♦ ◆♦rt❡ ❡ ❊✉r♦♣❛✮ ❡ ❞♦✐s ❞✐❢❡r❡♥t❡s ❞❡ ♠❡r❝❛❞♦s ❡♠❡r❣❡♥t❡s ✭❆♠ér✐❝❛ ❞♦ ❙✉❧ ❡ ➪s✐❛✮✳

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✷ ❘❡✈✐sã♦ ❞❛ ▲✐t❡r❛t✉r❛

✷✳✶ ❉❡✜♥✐çã♦ ❞❡ ❈♦♥tá❣✐♦

◆❛s ú❧t✐♠❛s ❞✉❛s ❞é❝❛❞❛s✱ ❛ ❛♥á❧✐s❡ ❞❡ r✉♣t✉r❛s ❞♦ ♣❛❞rã♦ tr❛❞✐❝✐♦♥❛❧ ❞❡ ♣r♦♣❛❣❛çã♦ ✐♥t❡r♥❛❝✐♦♥❛❧ ❞❡ ❡✈❡♥t♦s ✜♥❛♥❝❡✐r♦s tr❛♥s❢♦r♠♦✉✲s❡ ❡♠ ❛❧✈♦ ❞❛ ♣r♦❞✉çã♦ ❛❝❛❞ê♠✐❝❛ ❢♦❝❛❞❛ ♥❛ ♠♦❞❡❧❛❣❡♠ ❞❡ ✈♦❧❛t✐❧✐❞❛❞❡✳ ◗✉❛s❡ q✉❡ ❛ t♦t❛❧✐❞❛❞❡ ❞❡st❡s tr❛❜❛❧❤♦s s❡ ❞❡♣❛r❛ ❝♦♠ ✉♠❛ ❞✐✜❝✉❧❞❛❞❡ ♣r✐♠ár✐❛✱ ❛ ❛✉sê♥❝✐❛ ❞❡ ✉♠❛ ❞❡✜♥✐çã♦ ❝♦♥s❡♥s✉❛❧ ❞❡ ❝♦♥tá❣✐♦ ✜♥❛♥❝❡✐r♦✳ ❯♠❛ ❡✈✐❞ê♥❝✐❛ ❞❛ ❤❡t❡r♦❣❡♥❡✐❞❛❞❡ ❞❡ ❞❡✜♥✐çõ❡s ♣♦❞❡ s❡r ✐❧✉str❛❞❛ ♣❡❧♦ ❛rt✐❣♦ ❞❡ P❡r✐❝♦❧✐ ❡ ❙❜r❛❝✐❛ ✭✷✵✵✶✮ q✉❡ s✉❣❡r✐r❛♠ ❝✐♥❝♦ ❞✐❢❡r❡♥t❡s ❞❡✜♥✐çõ❡s ❞❡ ❝♦♥tá❣✐♦✿ ❛✉♠❡♥t♦ s✐❣♥✐✜❝❛t✐✈♦ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❝r✐s❡ ❡♠ ✉♠ ♣❛ís ❝♦♥❞✐❝✐♦♥❛❧ ❛♦ ❛❝♦♥t❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ ❝r✐s❡ ❡♠ ♦✉tr♦ ♣❛ís❀ tr❛♥s❜♦r❞❛♠❡♥t♦ ✭s♣✐❧❧♦✈❡r✮ ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ❞❡ ✉♠ ♣❛ís ❡♠ ❝r✐s❡ ♣❛r❛ ♦ ♠❡r❝❛❞♦ ✜♥❛♥❝❡✐r♦ ❞❡ ♦✉tr♦s ♣❛ís❡s❀ ❛❝❡♥t✉❛❞♦ ❝r❡s❝✐♠❡♥t♦ ❞❡ ❝♦✲♠♦✈✐♠❡♥t♦s ❞❡ ♣r❡ç♦s ❡ q✉❛♥t✐❞❛❞❡s ❡♥tr❡ ♠❡r❝❛❞♦s✱ ❝♦♥❞✐❝✐♦♥❛❧ ❛♦ ❛❝♦♥t❡❝✐♠❡♥t♦ ❞❡ ✉♠❛ ❝r✐s❡ ❡♠ ✉♠ ♠❡r❝❛❞♦ ♦✉ ❣r✉♣♦ ❞❡ ♠❡r❝❛❞♦s❀ ❛❧t❡r❛çã♦ ♥♦ ❝❛♥❛❧ ❞❡ tr❛♥s♠✐ssã♦ ❞❡ ❝❤♦q✉❡s ❡♥tr❡ ♠❡r❝❛❞♦s❀ ❡①❝❡ss♦ ❞❡ ❝♦✲♠♦✈✐♠❡♥t♦s ♥ã♦ ❡①♣❧✐❝❛❞♦s ♣♦r ❢✉♥❞❛♠❡♥t♦s✳

▼✉✐t♦s tr❛❜❛❧❤♦s ❞❡❞✐❝❛♠ ✉♠ ❡s♣❛ç♦ ♣❛r❛ ❞✐s❝✉ssã♦ ❛❝❡r❝❛ ❞❛ ❞✐st✐♥çã♦ ❡♥tr❡ ✐♥t❡r❞❡✲ ♣❡♥❞ê♥❝✐❛ ❡ ❝♦♥tá❣✐♦✳ ❊ss❛ ❧✐t❡r❛t✉r❛ ❢♦✐ r❡✈✐s❛❞❛ ♣♦r ❉♦r♥❜✉s❝❤✱ P❛r❦ ❡ ❈❧❛❡ss❡♥s ✭✷✵✵✵✮✱ ❉✉♥❣❡②✱ ❋r② ❡ ▼❛rt✐♥ ✭✷✵✵✺✮✱ P❡s❛r❛♥ ❡ P✐❝❦ ✭✷✵✵✼✮ ❡ ▼❛rç❛❧ ❡t ❛❧ ✭✷✵✶✶✮✳ ▼❛ss♦♥ ✭✶✾✾✽✮ ♣r♦♣õ❡ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❡ três ❞✐❢❡r❡♥t❡s ❝❛t❡❣♦r✐❛s✳ ❆ ♣r✐♠❡✐r❛✱ ❞❡♥♦♠✐♥❛❞❛ ♠♦♥s♦♦♥❛❧ ❡✛❡❝ts✱ s✉❣❡r❡ q✉❡ ❝r✐s❡s ✜♥❛♥❝❡✐r❛s ♣❛r❡❝❡♠ s❡r ❝♦♥t❛❣✐♦s❛s ♣♦r ❝♦♥t❛ ❞❛ ❝♦rr❡❧❛çã♦ ❡♥✲ tr❡ ❛s ✈❛r✐á✈❡✐s ♠❛❝r♦❡❝♦♥ô♠✐❝❛s ❞♦s ♣❛ís❡s✳ ◆❛ s❡❣✉♥❞❛✱ ❛s ❝r✐s❡s ✜♥❛♥❝❡✐r❛s ♣♦❞❡♠ s❡r tr❛♥s♠✐t✐❞❛s ❡♥tr❡ ♣❛ís❡s ❛tr❛✈és ❞❡ tr❛♥s❜♦r❞❛♠❡♥t♦ ✭s♣✐❧❧♦✈❡r✮✿ ✉♠❛ ❝r✐s❡ ❛❢❡t❛ ♦✉tr♦ ♣❛ís ❛tr❛✈és ❞❡ ❧✐❣❛çõ❡s ❡①t❡r♥❛s✱ t❛✐s ❝♦♠♦ ♦ ❝♦♠ér❝✐♦✳ ❊st❛s ❞✉❛s ♣r✐♠❡✐r❛s ❝❛t❡❣♦r✐❛s ✐❧✉str❛♠ s✐t✉❛çõ❡s ❞❡ ✐♥t❡r❞❡♣❡♥❞ê♥❝✐❛✳ P♦r ú❧t✐♠♦✱ ❛ t❡r❝❡✐r❛ ❝❛t❡❣♦r✐❛✱ r❡❢❡r❡♥t❡ à t❡♦✲ r✐❛ ❞♦ ✧❝♦♥tá❣✐♦ ♣✉r♦✧ ❞❡✜♥❡ q✉❡ ✉♠❛ ❝r✐s❡ ❡♠ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ♣❛ís ♣♦❞❡ ♣r♦✈♦❝❛r ✉♠❛ ❝r✐s❡ ❡♠ ♦✉tr♦ ♣❛ís s❡♠ ❛❢❡t❛r ♦s ❢✉♥❞❛♠❡♥t♦s ❡❝♦♥ô♠✐❝♦s ❡♥tr❡ ❡st❡s✳

❖ ❇❛♥❝♦ ▼✉♥❞✐❛❧✶ ♦❢❡r❡❝❡ três ❞✐❢❡r❡♥t❡s ❞❡✜♥✐çõ❡s ❞❡ ❝♦♥tá❣✐♦✿ ❛♠♣❧❛✱ r❡str✐t✐✈❛ ❡

♠✉✐t♦ r❡str✐t✐✈❛✳ ◆❛ ❞❡✜♥✐çã♦ ❛♠♣❧❛✱ ♦ ❝♦♥tá❣✐♦ é ✐❞❡♥t✐✜❝❛❞♦ ❝♦♠♦ ♦ ♣r♦❝❡ss♦ ❣❡r❛❧ ❞❡ tr❛♥s♠✐ssã♦ ❞❡ ❝❤♦q✉❡ ❡♥tr❡ ♦s ♣❛ís❡s✳ P♦❞❡♥❞♦ ♦❝♦rr❡r t❛♥t♦ ❞✉r❛♥t❡ ✧❜♦♥s✧ ❡ ✧♠❛✉s✑ ♣❡rí♦❞♦s✱ ♦✉ s❡❥❛✱ ♥ã♦ é ❛♣❡♥❛s ❛ss♦❝✐❛❞♦ ❝♦♠ ❝❤♦q✉❡s ♥❡❣❛t✐✈♦s✱ ♠❛s t❛♠❜é♠ ❝♦♠ ♣♦✲ s✐t✐✈♦s✳ P❡❧❛ ❞❡✜♥✐çã♦ r❡str✐t✐✈❛✱ ❝♦♥tá❣✐♦ é ❛ tr❛♥s♠✐ssã♦ ❞♦s ❝❤♦q✉❡s ♣❛r❛ ♦✉tr♦s ♣❛ís❡s ♦✉ ❝♦rr❡❧❛çõ❡s ❡♥tr❡ ♣❛ís❡s✱ ❛❧é♠ ❞❡ q✉❛❧q✉❡r ❡❧♦ ❢✉♥❞❛♠❡♥t❛❧ ❡♥tr❡ ♦s ♣❛ís❡s ❡ ❛❧é♠ ❞♦s ❝❤♦q✉❡s ❝♦♠✉♥s✳ ❊st❛ ❞❡✜♥✐çã♦ é ♥♦r♠❛❧♠❡♥t❡ r❡❢❡r✐❞❛ ❝♦♠♦ ♦ ❡①❝❡ss♦ ❞❡ ❝♦✲♠♦✈✐♠❡♥t♦✱

❉✐s♣♦♥í✈❡❧ ♥♦ s✐t❡ ❞♦ ❇❛♥❝♦ ▼✉♥❞✐❛❧ ❤tt♣✿✴✴✇♦r❧❞❜❛♥❦✳♦r❣✳ ❖ ❧✐♥❦ ❞✐r❡t♦ ♣❛r❛ ❛s ❞❡✜♥✐çõ❡s

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❢r❡q✉❡♥t❡♠❡♥t❡ ❡①♣❧✐❝❛❞❛ ♣❡❧♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ♠❛♥❛❞❛✳ ❆ ❞❡✜♥✐çã♦ ♠✉✐t♦ r❡str✐t✐✈❛ ❞✐③ q✉❡ ♦ ❝♦♥tá❣✐♦ ♦❝♦rr❡ q✉❛♥❞♦ ❝♦rr❡❧❛çõ❡s ❡♥tr❡ ♣❛ís❡s ❛✉♠❡♥t❛♠ ❞✉r❛♥t❡ ✧t❡♠♣♦s ❞❡ ❝r✐s❡✧ r❡❧❛t✐✈❛♠❡♥t❡ às ❝♦rr❡❧❛çõ❡s ❡♠ ✧t❡♠♣♦s tr❛♥q✉✐❧♦s✧✳ ❊st❛ ú❧t✐♠❛ ❞❡✜♥✐çã♦ ♣♦❞❡ s❡r ✐♥t❡r♣r❡t❛❞❛ ❝♦♠♦ ❛ ♠✉❞❛♥ç❛ ❞♦ ♠❡❝❛♥✐s♠♦ ❞❡ tr❛♥s♠✐ssã♦ q✉❡ ♦❝♦rr❡ ❞✉r❛♥t❡ ✉♠ ♣❡rí♦❞♦ ❞❡ t✉r❜✉❧ê♥❝✐❛✳ ❚❛♠❜é♠ é ❝♦♠✉♠❡♥t❡ ❞❡♥♦♠✐♥❛❞❛ ❞❡ s❤✐❢t✲❝♦♥t❛❣✐♦✳

❆♣ós ❛♥❛❧✐s❛r ❛ ❧✐t❡r❛t✉r❛ ❞❡s❝r✐t❛✱ ♣❛r❛ ♦ ♣r❡s❡♥t❡ ❡st✉❞♦✱ ❛ ❞❡✜♥✐çã♦ ❞❡ ❝♦♥tá❣✐♦ ❛❞♦t❛❞❛ s❡rá ❛ ♠❡s♠❛ q✉❡ ❛ ❞❡ ❋♦r❜❡s ❡ ❘✐❣♦❜♦♥ ✭✷✵✵✷✮✳ ❊st❛ ❞❡✜♥✐çã♦ é ❛ ♠❡s♠❛ q✉❡ ❛ ❞❡♥♦♠✐♥❛❞❛ ❞❡ ♠✉✐t♦ r❡str✐t✐✈❛ ♣❡❧♦ ❇❛♥❝♦ ▼✉♥❞✐❛❧✳ P♦❞❡♠♦s ❞❡✜♥✐r✱ ♣♦rt❛♥t♦✱ ❝♦♥tá❣✐♦ ❝♦♠♦ ✉♠❛ ♠✉❞❛♥ç❛ ♥♦ ♣❛❞rã♦ ❞❡ ❝♦rr❡❧❛çã♦ ❡♥tr❡ ♦s r❡t♦r♥♦s ❞♦s ❮♥❞✐❝❡s ❞❡ ❇♦❧s❛ ❞❡ ❱❛❧♦r❡s ❞❡ ❞✐❢❡r❡♥t❡s ♣❛ís❡s q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦s ♣❡rí♦❞♦s ❞❡ ❝❛❧♠❛r✐❛ ❡ ❞❡ ❝r✐s❡s ✜♥❛♥❝❡✐r❛s✳

❈♦♥s✐❞❡r❛♥❞♦ q✉❡ ♥❛ ♠❡t♦❞♦❧♦❣✐❛ ❡❝♦♥♦♠étr✐❝❛ ❛ s❡r ❛♣r❡s❡♥t❛❞❛ ♥♦ ❝❛♣ít✉❧♦ ✸ ♥ã♦ s❡rá ✉t✐❧✐③❛❞❛ ♥❡♥❤✉♠❛ ✈❛r✐á✈❡❧ ♠❛❝r♦❡❝♦♥ô♠✐❝❛ ♦✉ ❢✉♥❞❛♠❡♥t♦ ❡❝♦♥ô♠✐❝♦✱ ❡stá s❡♥❞♦ ❛ss✉♠✐❞♦ ❞❡ ❝❡rt❛ ♠❛♥❡✐r❛✱ ❝♦♠♦ ♣r❡♠✐ss❛✱ q✉❡ ❡st❡s ❢❛t♦r❡s ♦✉ ♠❡❝❛♥✐s♠♦s ♥ã♦ s❡r✐❛♠ ❝❛♣❛③❡s ❞❡ tr❛♥s♠✐t✐r ♦s ❡❢❡✐t♦s ❞❛s ❝r✐s❡s ♦❜s❡r✈❛❞❛s ❡♥tr❡ ✷✵✵✸ ❛té ✷✵✶✷ ❞❡ ❢♦r♠❛ tã♦ rá♣✐❞❛ ❡ ❛❜r✉♣t❛✳ ◆♦ ❝❛♣ít✉❧♦ ✻ ✭❈♦♥❝❧✉sã♦✮ é ❢❡✐t❛ ✉♠❛ r❡❢❡rê♥❝✐❛ ❛ ❡st❛ q✉❡stã♦✱ q✉❡ ❡stá ❞✐r❡t❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞❛ ❛ ❞✐st✐♥çã♦ ❡♥tr❡ ✐♥t❡r❞❡♣ê♥❞❡♥❝✐❛ ❡ ❝♦♥tá❣✐♦✱ ❝♦♠♦ ❢♦r♠❛ ❞❡ s✉❣❡stã♦ ❞❡ ❡①t❡♥sã♦ ❢✉t✉r❛ ❞❡st❛ ❞✐ss❡rt❛çã♦✳

✷✳✷ ❆❜♦r❞❛❣❡♥s ❊❝♦♥♦♠étr✐❝❛s

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♣❛r❛ ❞❡st❛❝❛r ❛s ♣r✐♥❝✐♣❛✐s s❡♠❡❧❤❛♥ç❛s ❡ ❞✐❢❡r❡♥ç❛s ❡♥tr❡ ❛s ❞✐✈❡rs❛s ❛❜♦r❞❛❣❡♥s✳

❆♦s ♣♦✉❝♦s ❛s ♠❡t♦❞♦❧♦❣✐❛s ❝♦♥✈❡r❣✐r❛♠ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❞❡ ❤❡t❡r♦❝❡❞❛st✐❝✐❞❛❞❡ ❝♦♥✲ ❞✐❝✐♦♥❛❧✱ ❛♣ós ♦s tr❛❜❛❧❤♦s s❡♠✐♥❛✐s ❞❡ ❊♥❣❧❡ ✭✶✾✽✷✮ ❡ ❇♦❧❧❡rs❧❡✈ ✭✶✾✽✻✮✳ ❚❛✐s ♠♦❞❡❧♦s ❢♦r❛♠✱ ❡♠ ♣♦✉❝♦ t❡♠♣♦✱ ❣❡♥❡r❛❧✐③❛❞♦s ♣❛r❛ ♦ ♠✉♥❞♦ ♠✉❧t✐✈❛r✐❛❞♦ ♣♦r ❞✉❛s ♣r✐♥❝✐♣❛✐s ❢♦r✲ ♠✉❧❛çõ❡s✳ ❯♠❛ ❞❛s ❢♦r♠✉❧❛çõ❡s ❢♦✐ ♦ ♠♦❞❡❧♦ ❱❊❈ ❡♠ q✉❡ ❇♦❧❧❡rs❧❡✈✱ ❊♥❣❧❡ ❡ ❲♦♦❧❞r✐❞❣❡ ✭✶✾✽✽✮ ❡st❡♥❞❡r❛♠ ♦ ♠♦❞❡❧♦ ●❆❘❈❍✲▼ ♣❛r❛ ♦ ❝♦♥t❡①t♦ ♠✉❧t✐✈❛r✐❛❞♦ ✉s❛♥❞♦ ♦ ♦♣❡r❛❞♦r ❱❊❈❍✳ ❆ ♦✉tr❛ ❢♦r♠✉❧❛çã♦ ❢♦✐ ♦ ♠♦❞❡❧♦ ❇❊❑❑ ❞❡s❡♥✈♦❧✈✐❞♦ ♣♦r ❊♥❣❧❡ ❡ ❑r♦♥❡r ✭✶✾✾✺✮✳ ❆ ❞❡♥♦♠✐♥❛çã♦ ❇❊❑❑ r❡❢❡r❡✲s❡ ❛s ✐♥✐❝✐❛✐s ❞♦ ♥♦♠❡ ❞❡ ❝❛❞❛ ✉♠ ❞♦s s❡✉s ❛✉t♦r❡s ❇❛❜❛✱ ❊♥❣❧❡✱ ❑r❛❢t ❡ ❑r♦♥❡r✳

❖s ♠♦❞❡❧♦s ●❆❘❈❍ ♠✉❧t✐✈❛r✐❛❞♦s ❛tr❛ír❛♠ ❝♦♥s✐❞❡rá✈❡❧ ✐♥t❡r❡ss❡ ❞❛❞❛ ❛ s✉❛ ❛♣❧✐✲ ❝❛çã♦ ❞✐r❡t❛ t❛♥t♦ ❡♠ ♣❡sq✉✐s❛s ❡❝♦♥ô♠✐❝❛s q✉❛♥t♦ ✜♥❛♥❝❡✐r❛s✳ ◆♦ ❡♥t❛♥t♦✱ ❛ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❞❡ ♣r♦❜❧❡♠❛s s✉r❣✐✉ q✉❛♥❞♦ ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞♦s ♠♦❞❡❧♦s ●❆❘❈❍ ♠✉❧t✐✈❛r✐❛❞♦s ❞❡ ❣r❛♥❞❡ ❞✐♠❡♥sã♦ ❞❡✈✐❞♦ à ❝♦♠♣❧❡①✐❞❛❞❡ ❞♦s ♣r♦❝❡❞✐♠❡♥t♦s ❝♦♠♣✉t❛❝✐♦♥❛✐s ♣❛r❛ ❡st✐✲ ♠❛t✐✈❛ ❞♦s ♣❛râ♠❡tr♦s ❞❡❝♦rr❡♥t❡s ❞♦ ❡❧❡✈❛❞♦ ♥ú♠❡r♦ ❞❡ ❝♦❡✜❝✐❡♥t❡s✳ ❚❛✐s ❞✐✜❝✉❧❞❛❞❡s ❡st✐♠✉❧❛r❛♠ ❞✐✈❡rs♦s ❡st✉❞♦s ❛❝❛❞ê♠✐❝♦s ❛ ❛♣r❡s❡♥t❛r❡♠ ❛♣❡r❢❡✐ç♦❛♠❡♥t♦s ❡ ❛❧t❡r♥❛t✐✈❛s ❛♦s ♠♦❞❡❧♦s ●❆❘❈❍ ♠✉❧t✐✈❛r✐❛❞♦s tr❛❞✐❝✐♦♥❛✐s✳

❯♠ ❞♦s ♠♦❞❡❧♦s ♠❛✐s ❞✐ss❡♠✐♥❛❞♦s ❞❡ ✈♦❧❛t✐❧✐❞❛❞❡ ♠✉❧t✐✈❛r✐❛❞❛ é ❝❡rt❛♠❡♥t❡ ♦ ▼♦❞❡❧♦ ❞❡ ❈♦rr❡❧❛çã♦ ❈♦♥❞✐❝✐♦♥❛❧ ❈♦♥st❛♥t❡ ✭❈❈❈✮ ❞❡ ❇♦❧❧❡rs❧❡✈ ✭✶✾✾✵✮✱ ❡♠ q✉❡ ❛s ❝♦✈❛r✐â♥❝✐❛s ❞❡ ✉♠ ✈❡t♦r ❞❡ r❡t♦r♥♦s sã♦ ❞❡❝♦♠♣♦st♦s ❡♠ ✈❛r✐â♥❝✐❛s ❡ ❝♦rr❡❧❛çõ❡s✳ ❆ ❤✐♣ót❡s❡ ❝❡♥tr❛❧ ♥❡st❡ ♠♦❞❡❧♦ é q✉❡ ❛s ❝♦rr❡❧❛çõ❡s ❝♦♥❞✐❝✐♦♥❛✐s sã♦ ❝♦♥st❛♥t❡s ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦✳ ❆ ❣r❛♥❞❡ ✈❛♥t❛❣❡♠ é q✉❡ ♦ ❈❈❈ ❛♣r❡s❡♥t❛ ❛ ✢❡①✐❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ●❆❘❈❍ ✉♥✐✈❛r✐❛❞♦✱ ♠❛s ♥ã♦ ❛ ❝♦♠♣❧❡①✐❞❛❞❡ ❞❡ ✉♠ ●❆❘❈❍ ♠✉❧t✐✈❛r✐❛❞♦ tr❛❞✐❝✐♦♥❛❧✳ ❊♥❣❧❡ ✭✷✵✵✷✮ ❡ ❚s❡ ❡ ❚s✉✐ ✭✷✵✵✷✮ ❛♣r❡s❡♥t❛r❛♠ ✉♠❛ ❡①t❡♥sã♦ ❛♦ ♠♦❞❡❧♦ ❈❈❈ q✉❡ ✉t✐❧✐③❛ ❛ ♠❡s♠❛ ❞❡❝♦♠♣♦s✐çã♦ ❞❛ ♠❛tr✐③ ❞❡ ✈❛r✐â♥❝✐❛✱ ♣♦ré♠ ❡♠ ✈❡③ ❞❡ ❛ss✉♠✐r ❝♦rr❡❧❛çõ❡s ❝♦♥st❛♥t❡s✱ ♦s ❛✉t♦r❡s ♣r♦♣õ❡♠ ✉♠❛ ❞✐♥â♠✐❝❛ ❞♦ t✐♣♦ ●❆❘❈❍ ♣❛r❛ ❛s ♠❛tr✐③❡s ❞❡ ❝♦rr❡❧❛çã♦✳ ❚❛✐s ♠♦❞❡❧♦s✱ ❞❡♥♦♠✐♥❛❞♦s ❞❡ ❈♦rr❡❧❛çã♦ ❈♦♥❞✐❝✐♦♥❛❧ ❉✐♥â♠✐❝❛ ✭❉❈❈✮ ♣♦ss✉❡♠ ❡st❛❜✐❧✐❞❛❞❡ ♥✉♠ér✐❝❛ ❛té ♣❛r❛ ❣r❛♥❞❡s ❞✐♠❡♥sõ❡s✱ ❞❛❞♦ q✉❡✱ ❛ss✐♠ ❝♦♠♦ ♦ ❈❈❈✱ ♣♦❞❡ s❡r ❛♣❧✐❝❛❞♦ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ❞❡ ❡st✐♠❛çã♦ ❡♠ ❞✉❛s ❡t❛♣❛s✳ ❆ ♣r✐♥❝✐♣❛❧ ✈❛♥t❛❣❡♠ ❞♦s ♠♦❞❡❧♦s ❈❈❈ ❡ ❉❈❈ s♦❜r❡ ♦s ♠♦❞❡❧♦s ❞❛ ❝❧❛ss❡ ❇❊❑❑ ♦✉ ❱❊❈ é ❛ ♣❛r❝✐♠ô♥✐❛ ♥❛ ♣❛r❛♠❡tr✐③❛çã♦✱ ♦ q✉❡ ♣❡r♠✐t❡ ✉❧tr❛♣❛ss❛r ❛s ❜❛rr❡✐r❛s ❞❡ ❞✐♠❡♥s✐♦♥❛♠❡♥t♦ ♣❛r❛ ❝❛s♦s s✉♣❡r✐♦r❡s ❛♦ ❜✐✈❛r✐❛❞♦✳ ❊♥tr❡ ♦s tr❛❜❛❧❤♦s q✉❡ ✉t✐❧✐③❛r❛♠ ❡st❡s ♠♦❞❡❧♦s ❞❡ ✈♦❧❛t✐❧✐❞❛❞❡ ♠✉❧t✐✈❛r✐❛❞❛ ♣❛r❛ ✐♥✈❡st✐❣❛çã♦ ❞❡ ❝♦♥tá❣✐♦ ❡stã♦✿ ▲♦♠❜❛r❞✐ ❡t ❛❧ ✭✷✵✵✹✮✱ ▼❛rç❛❧ ❡ ❱❛❧❧s P❡r❡✐r❛ ✭✷✵✵✽✮ ❡ ❋✐❧❧❡t✐✱ ❍♦tt❛ ❡ ❩❡✈❛❧❧♦s ✭✷✵✵✽✮✳

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❜❛s❡ ♣❛r❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❛ ♣r❡s❡♥t❡ ❞✐ss❡rt❛çã♦✳ ❯♠❛ ❡①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ❘❙❉❈ t❡♠ ♦r✐✲ ❣❡♠ ♥♦ tr❛❜❛❧❤♦ ❞❡ ❇✐❧❧✐♦ ❡ ❈❛♣♦r✐♥ ✭✷✵✵✺✮✳ ❊st❡ ❡st✉❞♦ ❡❧❛❜♦r❛ ❛ ❝♦♥str✉çã♦ t❡ór✐❝❛ ❞❛ ❝♦♠❜✐♥❛çã♦ ❞♦ ♠♦❞❡❧♦ ❞❡ ♠✉❞❛♥ç❛ ❞❡ r❡❣✐♠❡ ❝♦♠ ♦ ♠♦❞❡❧♦ ❉❈❈✱ s♦❜r❡ ❛ ❞❡♥♦♠✐♥❛çã♦ ▼❙✲❉❈❈✱ ♣❡r♠✐t✐♥❞♦ q✉❡ t❛♥t♦ ❛ ❝♦rr❡❧❛çã♦ ✐♥❝♦♥❞✐❝✐♦♥❛❧ ❝♦♠♦ s❡✉s r❡s♣❡❝t✐✈♦s ♣❛râ♠❡✲ tr♦s s❡❥❛♠ ❝♦♥❞✉③✐❞♦s ♣♦r ✉♠ ❝♦♠♣♦♥❡♥t❡ ♥ã♦ ♦❜s❡r✈á✈❡❧ ❝❛r❛❝t❡r✐③❛❞♦ ♣❡❧❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈✳ ❖s ❛✉t♦r❡s r❡❛❧✐③❛♠ ✉♠❛ ❛♥á❧✐s❡ ❡♠♣ír✐❝❛ ❞♦ ❢❡♥ô♠❡♥♦ ❞❡ ❝♦♥tá❣✐♦ ❝♦♠♣❛r❛♥❞♦ ♦s r❡s✉❧t❛❞♦s ❝♦♠ ❛s tr❛❞✐❝✐♦♥❛✐s r❡♣r❡s❡♥t❛çõ❡s ❈❈❈ ❡ ❉❈❈✳

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✸ ▼❡t♦❞♦❧♦❣✐❛

✸✳✶ ▼♦❞❡❧♦ ❘❙❉❈ ✭▼❙✲❈❈❈✮

❆ ♠❡t♦❞♦❧♦❣✐❛ ❝❡♥tr❛❧ ❞❡st❡ ❡st✉❞♦ ❢♦✐ ❜❛s❡❛❞❛ ♥♦ ♠♦❞❡❧♦ ❘❡❣✐♠❡ ❙✇✐t❝❤✐♥❣ ❉②♥❛♠✐❝ ❈♦rr❡❧❛t✐♦♥ ✭❘❙❉❈✮ ♣r♦♣♦st♦ ♣♦r P❡❧❧❡t✐❡r ✭✷✵✵✻✮✳ ❚r❛t❛✲s❡ ❞❛ ❝♦♠❜✐♥❛çã♦ ❞♦ ▼♦❞❡❧♦ ❞❡ ❈♦rr❡❧❛çã♦ ❈♦♥❞✐❝✐♦♥❛❧ ❈♦♥st❛♥t❡ ✭❈❈❈✮ ❛♣r❡s❡♥t❛❞♦ ♣♦r ❇♦❧❧❡rs❧❡✈ ✭✶✾✾✵✮ ❝♦♠ ♦ ▼♦❞❡❧♦ ❞❡ ▼✉❞❛♥ç❛ ❞❡ ❘❡❣✐♠❡ ❞❡ ▼❛r❦♦✈ s✉❣❡r✐❞♦ ♣♦r ❍❛♠✐❧t♦♥ ❡ ❙✉s♠❡❧ ✭✶✾✾✹✮✳ ❋♦✐ ❢❡✐t❛ ❛♣❡♥❛s ✉♠❛ ♠♦❞✐✜❝❛çã♦ ♥♦ ♠♦❞❡❧♦ ♦r✐❣✐♥❛❧ ❘❙❉❈✱ ❛ ✐♥tr♦❞✉çã♦ ❞♦ ♠♦❞❡❧♦ ●❏❘✲ ●❆❘❈❍✷ ♥❛ ♠♦❞❡❧❛❣❡♠ ❞❛s ✈❛r✐â♥❝✐❛s ✐♥❞✐✈✐❞✉❛✐s ❞❛s sér✐❡s✳ ❊st❡ ♠♦❞❡❧♦ ❢♦✐ ❢♦r♠✉❧❛❞♦

♥♦ ❛rt✐❣♦ ❞❡ ●❧♦st❡♥✱ ❏❛❣❛♥♥❛t❤❛♥ ❡ ❘✉♥❦❧❡ ✭✶✾✾✸✮ ❡ ♣❡r♠✐t❡ ❛ ✐♥tr♦❞✉çã♦ ❞❡ ❡❢❡✐t♦s ❛ss✐♠étr✐❝♦s ♥❛ ✈♦❧❛t✐❧✐❞❛❞❡✳

◆♦ ♠♦❞❡❧♦ ❈❈❈ ❞❡ ❇♦❧❧❡rs❧❡✈ ✭✶✾✾✵✮✱ ❛s ❝♦✈❛r✐â♥❝✐❛s ❝♦♥❞✐❝✐♦♥❛✐s sã♦ ♣❛r❛♠❡tr✐③❛❞❛s ❞❡ ♠♦❞♦ ❛ s❡r❡♠ ♣r♦♣♦r❝✐♦♥❛✐s ❛♦ ♣r♦❞✉t♦ ❞♦s ❞❡s✈✐♦s✲♣❛❞rã♦ ❝♦rr❡s♣♦♥❞❡♥t❡s✳ ❖✉ s❡❥❛✱ ❛s ❝♦✈❛r✐â♥❝✐❛s ❞❡ ✉♠ ✈❡t♦r ❞❡ r❡t♦r♥♦s sã♦ ❞❡❝♦♠♣♦st♦s ❡♠ ❞❡s✈✐♦s✲♣❛❞rã♦ ❡ ❝♦rr❡❧❛çõ❡s✳ ❉❡st❛ ❢♦r♠❛✱ ♦ ♣r♦❝❡ss❛♠❡♥t♦ ❝♦♠♣✉t❛❝✐♦♥❛❧ ❡①✐❣✐❞♦ ♣❛r❛ ❡st✐♠❛çã♦ ❢♦✐ r❡❞✉③✐❞♦ ❡ ❛ ✐♠✲ ♣♦s✐çã♦ ❞❛s ❝♦♥❞✐çõ❡s ♥❡❝❡ssár✐❛s ♣❛r❛ ❛ss❡❣✉r❛r q✉❡ ❛ ♠❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ s❡❥❛ ♣♦s✐t✐✈❛ s❡♠✐❞❡✜♥✐❞❛ s❡ t♦r♥♦✉ ♠❛✐s s✐♠♣❧❡s✳ P♦ré♠✱ ✉♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s ❤✐♣ót❡s❡s ❞❡st❡ ♠♦❞❡❧♦ é q✉❡ ❛s ❝♦rr❡❧❛çõ❡s ❝♦♥❞✐❝✐♦♥❛✐s sã♦ ❝♦♥st❛♥t❡s ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ❡ t❛❧ ♣r❡♠✐ss❛ ♥❡♠ s❡♠♣r❡ é s✉♣♦rt❛❞❛ ♣❡❧♦s ❞❛❞♦s ❝♦♥❢♦r♠❡ ❊♥❣❧❡ ❡ ❙❤❡♣♣❛r❞ ✭✷✵✵✶✮✳

❉✐❛♥t❡ ❞❡st❛ r❡str✐çã♦✱ P❡❧❧❡t✐❡r ✭✷✵✵✻✮ ♣r♦♣ôs ✉♠ ♥♦✈♦ ♠♦❞❡❧♦ ❞❡ ✈♦❧❛t✐❧✐❞❛❞❡ ♠✉❧t✐✲ ✈❛r✐❛❞♦ ✭❘❙❉❈✮✳ ❆ ❡str✉t✉r❛ ❞❡st❡ ♠♦❞❡❧♦ t❛♠❜é♠ ✐♥❝♦r♣♦r❛ ❛ ❞❡❝♦♠♣♦s✐çã♦ ❞❛s ❝♦✈❛r✐✲ â♥❝✐❛s ❡♠ ❞❡s✈✐♦s✲♣❛❞rã♦ ❡ ❝♦rr❡❧❛çõ❡s✱ ❝♦♥t✉❞♦ ❛s ❝♦rr❡❧❛çõ❡s ♣♦ss✉❡♠ ❛❧❣✉♠ ❞✐♥❛♠✐s♠♦✳ ❆ ♠❛tr✐③ ❞❡ ❝♦rr❡❧❛çã♦ s❡❣✉❡ ✉♠ ♠♦❞❡❧♦ ❞❡ ♠✉❞❛♥ç❛ ❞❡ r❡❣✐♠❡ ❡✱ ♣♦rt❛♥t♦✱ ♣❡r♠❛♥❡❝❡ ❝♦♥st❛♥t❡ ❞❡♥tr♦ ❞❡ ✉♠ ♠❡s♠♦ r❡❣✐♠❡✱ ♠❛s é ❞✐❢❡r❡♥t❡ ❡♥tr❡ ♦s r❡❣✐♠❡s✳ ❆s tr❛♥s✐çõ❡s ❡♥tr❡ ♦s r❡❣✐♠❡s sã♦ ❣♦✈❡r♥❛❞❛s ♣♦r ✉♠❛ ❝❛❞❡✐❛ ❞❡ ▼❛r❦♦✈✳ ❉❡ ✉♠❛ ❢♦r♠❛ r❡s✉♠✐❞❛✱ ♦ ♠♦❞❡❧♦ ❈❈❈ ♣♦❞❡ s❡r ❝♦♥s✐❞❡r❛❞♦ ✉♠ ❝❛s♦ ❡s♣❡❝✐❛❧ ❞♦ ❘❙❉❈✱ ❡♠ q✉❡ ♦ ♥ú♠❡r♦ ❞❡ r❡❣✐♠❡s é ✐❣✉❛❧ ❛ ✶✳

❯♠❛ ♠❡t♦❞♦❧♦❣✐❛ ❛❧t❡r♥❛t✐✈❛ ❛ ❡s❝♦❧❤✐❞❛ ♥♦ ♣r❡s❡♥t❡ ❡st✉❞♦ ♣♦❞❡r✐❛ s❡r ♦ ▼♦❞❡❧♦ ❞❡ ❈♦rr❡❧❛çã♦ ❈♦♥❞✐❝✐♦♥❛❧ ❉✐♥â♠✐❝❛ ✭❉❈❈✮ ❛♣r❡s❡♥t❛❞♦ ♣♦r ❊♥❣❧❡ ✭✷✵✵✷✮ ❡ ❚s❡ ❚s✉✐ ✭✷✵✵✷✮ q✉❡ ✉t✐❧✐③❛ ❛ ♠❡s♠❛ ❞❡❝♦♠♣♦s✐çã♦ ❞❛ ♠❛tr✐③ ❞❡ ✈❛r✐â♥❝✐❛ ❞❡ ❇♦❧❧❡rs❧❡✈ ✭✶✾✾✵✮✱ ♠❛s ❡♠ ✈❡③ ❞❡ ❛ss✉♠✐r ❝♦rr❡❧❛çõ❡s ❝♦♥st❛♥t❡s✱ ♦s ❛✉t♦r❡s ♣r♦♣õ❡♠ q✉❡ ❡st❛s s❡❥❛♠ ❝❛r❛❝t❡r✐③❛❞❛s ❞❡ ❛❝♦r❞♦ ❝♦♠ ✉♠❛ ❞✐♥â♠✐❝❛ ❞♦ t✐♣♦ ●❆❘❈❍✳ ❙❡❣✉♥❞♦ P❡❧❧❡t✐❡r✱ é r❛③♦á✈❡❧ q✉❡st✐♦♥❛r

❊♠ P❡❧❧❡t✐❡r ✭✷✵✵✻✮✱ ❛ ♠♦❞❡❧❛❣❡♠ ❞❛s ✈❛r✐â♥❝✐❛s ✐♥❞✐✈✐❞✉❛✐s ❢♦✐ ❢❡✐t❛ ❝♦♠ ❛ ❡s♣❡❝✐✜❝❛çã♦ ❆❘▼❆❈❍

(17)

✶✵

s❡ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞♦ t✐♣♦ ●❆❘❈❍ ♣❛r❛ ❛s ❝♦rr❡❧❛çõ❡s s❡r✐❛ ❛ ♠❛✐s ❛♣r♦♣r✐❛❞❛✱ ♣♦✐s ❛ ❞✐♥â♠✐❝❛ ❞❡ ✉♠❛ ❝♦rr❡❧❛çã♦ ♣♦❞❡ s❡r ✐♥tr✐♥s❡❝❛♠❡♥t❡ ❞✐❢❡r❡♥t❡ ❞♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❡ ✉♠❛ ❝♦✈❛r✐â♥❝✐❛ ♣❡❧♦ ❢❛t♦✱ ♣♦r ❡①❡♠♣❧♦✱ ❞❛ ❝♦rr❡❧❛çã♦ t❡r ❧✐♠✐t❡s ✐♥❢❡r✐♦r ❡ s✉♣❡r✐♦r✱ ❡♥q✉❛♥t♦ ✉♠❛ ❝♦✈❛r✐â♥❝✐❛ ♥ã♦✳ ❖✉tr❛ q✉❡stã♦ ❞✐③ r❡s♣❡✐t♦ à ❡❧❡✈❛❞❛ ♣❡rs✐stê♥❝✐❛ ❞♦s ♠♦❞❡❧♦s ❞❛ ❢❛♠í❧✐❛ ●❆❘❈❍✳ ❉✐❡❜♦❧❞ ✭✶✾✽✻✮ ❛✈❛❧✐❛ q✉❡ ❡st❛ ❛❧t❛ ♣❡rs✐stê♥❝✐❛ ♣♦❞❡ s❡r ♣r♦✈♦❝❛❞❛ ♣❡❧❛ ♥ã♦ ♦❜s❡r✈❛çã♦ ❞❛ ♠✉❞❛♥ç❛ ❞❛ ✈♦❧❛t✐❧✐❞❛❞❡ ♥ã♦ ❝♦♥❞✐❝✐♦♥❛❧✳ ◆♦ ❝❛♣ít✉❧♦ ✺ ✭❘❡s✉❧t❛❞♦s✮ é r❡❛❧✐③❛❞♦ ✉♠ ❡①❡r❝í❝✐♦ ❝♦♠ ❞✉♠♠✐❡s ♣❛r❛ ♦❢❡r❡❝❡r ❡✈✐❞ê♥❝✐❛s s♦❜r❡ ❡st❛ q✉❡stã♦ ❞❛ ♣❡rs✐stê♥❝✐❛✳

❆❧é♠ ❞♦s ♣♦♥t♦s ❧❡✈❛♥t❛❞♦s✱ ❝♦♥❢♦r♠❡ t❛♠❜é♠ ❡①♣♦st♦ ♥❛ ✐♥tr♦❞✉çã♦✱ sã♦ ❞♦✐s ♦s ❛s♣❡❝t♦s ❢✉♥❞❛♠❡♥t❛✐s ♣❛r❛ ❡s❝♦❧❤❛ ❞♦ ♠♦❞❡❧♦ ❘❙❉❈ ❡♠ ✈❡③ ❞♦ ❉❈❈✳ ❖ ♣r✐♠❡✐r♦ ❡stá r❡❧❛❝✐♦♥❛❞♦ à ❝❛♣❛❝✐❞❛❞❡ ❞♦ ▼♦❞❡❧♦ ❘❙❉❈ ✐♥❝♦r♣♦r❛r ♠✉❞❛♥ç❛s ❞❡ r❡❣✐♠❡ à s✉❛ ❞✐♥â✲ ♠✐❝❛✱ ♦ q✉❡ ♣♦ss✐❜✐❧✐t❛ ♥ã♦ ♣r❡❝✐s❛r ❞❡✜♥✐r ❛ ♣r✐♦r✐ q✉❛✐s ♦s ❢❛s❡s ❞❡ ✐♥st❛❜✐❧✐❞❛❞❡ ✜♥❛♥✲ ❝❡✐r❛✳ ❊st❛ ❞❡✜♥✐çã♦ é ❢❡✐t❛ ❡♥❞♦❣❡♥❛♠❡♥t❡✱ ❞❛❞♦ q✉❡ ❛ ❝❛❞❛ ✐♥st❛♥t❡ t sã♦ ❝❛❧❝✉❧❛❞❛s ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❞❡ ❡st❛r ❡♠ ❝❛❞❛ r❡❣✐♠❡✳ ❖ s❡❣✉♥❞♦ ❡♥✈♦❧✈❡ ❛ ✐❞é✐❛ ❞❡ q✉❡ ♣♦ss✐✈❡❧✲ ♠❡♥t❡ ❛ ❝♦♥tr✐❜✉✐çã♦ ♣❛r❛ ❛ ❧✐t❡r❛t✉r❛ ♣♦❞❡r✐❛ s❡r ♠❛✐♦r✱ ❞❛❞♦ q✉❡ ♦ ❉❈❈ ❥á s❡ ❡♥❝♦♥tr❛ ♠✉✐t♦ ❞✐❢✉♥❞✐❞♦ ❡ ✉t✐❧✐③❛❞♦ ❡♥tr❡ ♦s t❡st❡s ❞❡ ❝♦♥tá❣✐♦ r❡❛❧✐③❛❞♦s ♥♦s ú❧t✐♠♦s ❞❡③ ❛♥♦s✳ P❛r❛ ❝♦♠♣❧❡♠❡♥t❛r ❛ ❛♥á❧✐s❡ ❞❡st❡ tr❛❜❛❧❤♦✱ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ ❝♦♠♣❛r❛çã♦✱ t❛♠❜é♠ ♥♦ ❝❛♣ít✉❧♦ ✺✱ ❡♥tr❡ ♦s r❡s✉❧t❛❞♦s ❞❡ ❛♠❜♦s ♦s ♠♦❞❡❧♦s✳

❙❡❣✉✐♥❞♦ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❛♣r❡s❡♥t❛❞❛ ❡♠ P❡❧❧❡t✐❡r ✭✷✵✵✻✮✱ ✉♠ ♣r♦❝❡ss♦ ✜❧tr❛❞♦ Yt ❝♦♠

❑ ✈❛r✐á✈❡✐s ♣♦❞❡ s❡r r❡♣r❡s❡♥t❛❞♦ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

Yt=H

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t Ut ✭✶✮

s❡♥❞♦ Ut ✉♠ ♣r♦❝❡ss♦ ✐♥❞❡♣❡♥❞❡♥t❡ ❡ ✐❞❡♥t✐❝❛♠❡♥t❡ ❞✐str✐❜✉í❞♦ ✭✵✱Ik ✮✳ ❆ ♠❛tr✐③ ❞❡

❝♦✈❛r✐â♥❝✐❛ ✈❛r✐❛♥t❡ ♥♦ t❡♠♣♦ Ht ♣♦❞❡ s❡r ❞❡❝♦♠♣♦st❛ ❡♠✿

Ht =StΓtSt ✭✷✮

s❡♥❞♦ St ✉♠❛ ♠❛tr✐③ ❞✐❛❣♦♥❛❧ ❝♦♠♣♦st❛ ♣❡❧♦s ❞❡s✈✐♦s✲♣❛❞rã♦ smt ❝♦♠ ♠❂✶✱✳✳✳✱❦ ❡ Γt

❛ ♠❛tr✐③ ❞❡ ❝♦rr❡❧❛çõ❡s✳

St=

      

s1t 0 0 · · · 0

0 s2t 0 · · · 0

✳✳✳ ✳✳✳ ✳✳✳

0 · · · 0 ✳✳✳ 0

0 · · · 0 0 s❦t

(18)

✶✶

❈❛❞❛ ✈❛r✐â♥❝✐❛ s2mt é ♠♦❞❡❧❛❞❛ ♣♦r ✉♠ ●❆❘❈❍ ✉♥✐✈❛r✐❛❞♦✳ ◆♦ ♣r❡s❡♥t❡ ❡st✉❞♦✱

❞✐❢❡r❡♥t❡♠❡♥t❡ ❞❡ P❡❧❧❡t✐❡r✱ s❡rá ✉t✐❧✐③❛❞♦ ♦ ●❏❘✲●❆❘❈❍ ♣❛r❛ ❝❛♣t✉r❛r ❛ ❛ss✐♠❡tr✐❛ ♥❡❣❛t✐✈❛✱ ❝♦♥❢♦r♠❡ ❛❜❛✐①♦✿

s2mt =ω+

q

X

i=1

αiǫ2t−i+ q

X

z=1

γzǫ2t−zI(ǫt−z) + p

X

j=1

βjs2t−j ✭✹✮

I(ǫt−z) =

(

1, s❡ǫt−z <0

0, ❝❛s♦ ❝♦♥trár✐♦ ✭✺✮

❆ ✐♥tr♦❞✉çã♦ ♥♦ ♠♦❞❡❧♦ ❞❛ ❞✐♥â♠✐❝❛ ❞❡ ♠✉❞❛♥ç❛ ❞❡ r❡❣✐♠❡ ♠❛r❦♦✈✐❛♥❛ é ❢❡✐t❛ ♥❛ ♠❛tr✐③ ❞❡ ❝♦rr❡❧❛çã♦✳ P♦rt❛♥t♦✱ Γt ❛ss✉♠❡ ❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

Γn =

      

1 ρ12 ρ13 · · · ρ1k

ρ21 1 ρ23 · · · ρ2k

ρ31 ρ32 ✳✳✳ ✳✳✳

✳✳✳ ✳✳✳ ✳✳✳ ρk−1k

ρ❦✶ ρ❦✷ · · · ρ❦❦−1 1

       ✭✻✮

Γt = N

X

n=1

I{∆t=n}Γn ✭✼✮

♦♥❞❡∆té ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ✐♥❞❡♣❡♥❞❡♥t❡ ❞❡ Utq✉❡ é ❞❡✜♥✐❞❛ ❝♦♠♦ ✉♠❛ ✈❛r✐á✈❡❧

❞❡ ❡st❛❞♦✳ ❊st❛ ✈❛r✐á✈❡❧ ❞❡ ❡st❛❞♦ s❡❣✉❡ ✉♠ ♣r♦❝❡ss♦ ❞❡ ▼❛r❦♦✈ ❞❡ ♣r✐♠❡✐r❛ ♦r❞❡♠ ❡ ♣♦❞❡ ❛ss✉♠✐r ❛♣❡♥❛s ✈❛❧♦r❡s ✐♥t❡✐r♦s ④✶✱✳✳✳✱◆⑥✳ ❊st❛ r❡♣r❡s❡♥t❛çã♦ ❞❡Γt♠♦str❛ ✉♠❛ ♦✉tr❛

✈❛♥t❛❣❡♠ ❞♦ ♠♦❞❡❧♦ ❘❙❉❈✳ ◆❛ ❢❛s❡ ❞❡ ❡st✐♠❛çã♦✱ ❛ ♠❛tr✐③ ❞❡ ❝♦rr❡❧❛çã♦ Γt✱ ❝♦♠♦ ✉♠

t♦❞♦✱ ♣♦❞❡ t❡r ❛♣❡♥❛s ◆ ❞✐❢❡r❡♥t❡s ❝♦♥✜❣✉r❛çõ❡s ❡✱ ❝♦♥s❡q✉❡♥t❡♠❡♥t❡✱ ♥❡❝❡ss✐❞❛❞❡ ❞❡ s❡r ✐♥✈❡rt✐❞❛ ❛♣❡♥❛s ◆ ✈❡③❡s✱ ❡♥q✉❛♥t♦ ♥♦ ♠♦❞❡❧♦ ❉❈❈ ❛ ♠❛tr✐③ ❞❡ ❝♦rr❡❧❛çã♦ t❡♠ q✉❡ s❡r ✐♥✈❡rt✐❞❛ ❛ ❝❛❞❛ ♦❜s❡r✈❛çã♦✳ ◗✉❛♥❞♦ tr❛❜❛❧❤❛♠♦s ❝♦♠ ✉♠ ♠❛✐♦r ♥ú♠❡r♦ ❞❡ sér✐❡s✱ ❡st❛ ♣♦❞❡ s❡r ✉♠❛ ✈❛❧✐♦s❛ ✈❛♥t❛❣❡♠ ❡♠ t❡r♠♦s ❞❡ ✐♠♣❧❡♠❡♥t❛çã♦ ❝♦♠♣✉t❛❝✐♦♥❛❧✳

❆ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ∆t ❛ss✉♠✐r ✉♠ ✈❛❧♦r ❥ ✈❛r✐á✈❡❧ é ❞❛❞❛ ❛♣❡♥❛s ❡♠ ❢✉♥çã♦ ❞♦ ✈❛❧♦r

❞❡ ∆t ❡♠ ∆t−1✳

P(∆t=j|∆t−1 =i) =p✐❥ ✭✽✮

(19)

✶✷

p✐✶+p✐✷+✳✳✳+p✐◆ = 1 ✭✾✮

❆s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❛ss♦❝✐❛❞❛s ❛ ❝❛❞❛ r❡❣✐♠❡ ♣♦❞❡♠ s❡r r❡♣r❡s❡♥t❛❞❛s ♣♦r ✉♠ ♠❛tr✐③ ✭◆ ① ◆✮ ✉s✉❛❧♠❡♥t❡ ❞❡♥♦♠✐♥❛❞❛ ❝♦♠♦ ♠❛tr✐③ ❞❡ tr❛♥s✐çã♦✿

Π =     

p11 p12 ✳✳✳ p1N

p21 p22 ✳✳✳ p2N

✳✳✳ ✳✳✳ ✳✳✳ ✳✳✳

p◆✶ p◆✷ ✳✳✳ p◆◆

    

✭✶✵✮

❖ ♠♦❞❡❧♦ ❞❡ ♠✉❞❛♥ç❛ ❞❡ r❡❣✐♠❡ ♣❡r♠✐t❡ ❝❛❧❝✉❧❛r ❛ ❞✉r❛çã♦ ❉ ❡s♣❡r❛❞❛ ❡♠ ❝❛❞❛ r❡❣✐♠❡✳ ❚r❛t❛✲s❡ ❞❛ ❞✉r❛çã♦ ♠é❞✐❛ ❞❡ ❝❛❞❛ r❡❣✐♠❡ ❝♦♥❞✐❝✐♦♥❛❧ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❡st❛r ❡♠ ✉♠ r❡❣✐♠❡ ❡s♣❡❝í✜❝♦✳ ❆ ❞❡r✐✈❛çã♦ ❞❛ ❢ór♠✉❧❛ ✜♥❛❧ ❞❡ ❊✭❉✮ ♣♦❞❡ s❡r ♦❜t✐❞❛ ♣♦r✿

D= 1,s❡∆t=j ❡ ∆=6 j; P[D= 1] = (1−p❥❥)

D= 2,s❡∆t= ∆t+1 =j ❡∆=6 j; P[D= 2] =p❥❥(1−p❥❥)

D = 3,s❡∆t= ∆t+1 = ∆t+2 =j ❡∆t+3 6=j; P[D= 3] =p2❥❥(1−p❥❥)

E(D) =P∞

j=1jP[D=j] =P (∆t+1 6=j|∆t=j) + 2P [∆t+1 =j,∆t+2 6=j|∆t =j] +✳✳✳

E(D) = (1−p❥❥) + 2p❥❥(1−p❥❥) + 3p2

❥❥(1−p❥❥) +✳✳✳

E(D) = 1

(1−p❥❥) ✭✶✶✮

❖✉tr❛ r✐❝❛ ✐♥❢♦r♠❛çã♦ q✉❡ ♣♦❞❡ s❡r ❡①tr❛í❞❛ ❞♦ ♠♦❞❡❧♦ é ❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❡r❣ó❞✐❝❛ ❞❡ ❝❛❞❛ r❡❣✐♠❡✳ ■st♦ é✱ ❛s ♣r♦❜❛❜✐❧✐❞❛❞❡s ❛ss♦❝✐❛❞❛s ❛ ❝❛❞❛ ❡st❛❞♦ ♥♦ ❡q✉✐❧í❜r✐♦✳ ❆ ♦❜t❡♥çã♦ ♣♦❞❡ s❡r ❢❡✐t❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿

(20)

✶✸         π1 π2 . . . πk         = Π         π1 π2 . . . πk         ✭✶✷✮ n X i=1

πi = 1 ✭✶✸✮

πi ≥0

✸✳✷ ❊st✐♠❛çã♦

❊♠ t❡♦r✐❛✱ ❛ ❡st✐♠❛çã♦ ❞♦ ♠♦❞❡❧♦ ❘❙❉❈ ♣♦❞❡ s❡r r❡❛❧✐③❛❞❛ t❛♥t♦ ❡♠ ✉♠❛ q✉❛♥t♦ ❡♠ ❞✉❛s ❡t❛♣❛s✳ ❈♦♥❢♦r♠❡ P❡❧❧❡t✐❡r ✭✷✵✵✻✮✱ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ❡♠ ✉♠❛ ❡t❛♣❛ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ ♣r✐♥❝✐♣❛❧ ♠❛①✐♠✐①❛r ❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♣♦r ♠❡✐♦ ❞♦ ❝á❧❝✉❧♦ ❞❛ s❡❣✉✐♥t❡ ❡①♣r❡ssã♦✿

◗▲(θ;Y) =

T

X

t=1

logfYt|Yt−1

✭✶✹✮

❡♠ q✉❡ Yt−1 = {Yt−1, Yt−2,✳✳✳} ❡ θ ♦ ✈❡t♦r t♦t❛❧ ❞❡ ♣❛râ♠❡tr♦s✳ ❖ ❝á❧❝✉❧♦ é ❢❡✐t♦

✉t✐❧✐③❛♥❞♦ ♦ ✜❧tr♦ ❞❡ ❍❛♠✐❧t♦♥ ❛♣r❡s❡♥t❛❞♦ ❡♠ ❍❛♠✐❧t♦♥ ✭✶✾✽✾✮✱ ♣♦✐s ❛ ✈❛r✐á✈❡❧ ❞❡ ❡st❛❞♦ ∆t é ✉♠ ❝♦♠♣♦♥❡♥t❡ ♥ã♦ ♦❜s❡r✈❛❞♦✳ ▼❛s✱ q✉❛♥❞♦ tr❛❜❛❧❤❛♠♦s ❝♦♠ ✉♠ ♥ú♠❡r♦ ♠❛✐♦r

❞❡ sér✐❡s✱ ♦ ♣r♦❝❡❞✐♠❡♥t♦ ❡♠ ✉♠❛ ❡t❛♣❛✱ ❞❡✈✐❞♦ ❛♦ ❡❧❡✈❛❞♦ ♥ú♠❡r♦ ❞❡ ♣❛râ♠❡tr♦s ❛ s❡r❡♠ ❡st✐♠❛❞♦s✱ s❡ t♦r♥❛ ♠✉✐t♦ ❝♦♠♣❧❡①♦✳ P♦rt❛♥t♦✱ ♣❛r❛ ♦ ♣r❡s❡♥t❡ ❡st✉❞♦ ❛♣❡♥❛s s❡rá ❛♣❧✐❝❛❞❛ ❛ té❝♥✐❝❛ ❞❡ ❡st✐♠❛çã♦ ❡♠ ❞✉❛s ❡t❛♣❛s✳

❙❡❣✉✐♥❞♦ P❡❧❧❡t✐❡r ✭✷✵✵✻✮✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ❡s♣❛ç♦ t♦t❛❧ ❞❡ ♣❛râ♠❡tr♦s θ✱ é ♣♦ssí✈❡❧

s❡♣❛rá✲❧♦ ♥♦s ❡s♣❛ç♦θ1✱ r❡❢❡r❡♥t❡ ❛♦s ♣❛râ♠❡tr♦s ❞♦s ♠♦❞❡❧♦s ❞❡ ✈♦❧❛t✐❧✐❞❛❞❡ ✉♥✐✈❛r✐❛❞♦s

♣❛r❛ ❛s ❞✐str✐❜✉✐çõ❡s ♠❛r❣✐♥❛✐s✱ ❡ θ2✱ r❡❢❡r❡♥t❡ ❛♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❞❡ ❝♦rr❡❧❛çã♦✳

❉❡♥♦t❛♥❞♦ QL1 ❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦ ❡s♣❛ç♦ ❞❡ ♣❛râ♠❡tr♦s θ1 ❡ QL2 ❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛

(21)

✶✹

◗▲1(θ1;Y) = −

1 2

T

X

t=1

❑❧♦❣(2π) + 2 log (|St|) +U

tUt

✭✶✺✮

◗▲2(θ2;Y, θ1) = −

1 2

T

X

t=1

❑❧♦❣(2π) + 2 log (|Γt|) +U

tΓ−

1

T Ut

✭✶✻✮

❆ ✈❡r♦ss✐♠✐❧❤❛♥ç❛QL1♣♦ss✉✐ ❞✉❛s ✐♠♣♦rt❛♥t❡s ❝❛r❛❝t❡ríst✐❝❛s✳ Pr✐♠❡✐r❛♠❡♥t❡✱ tr❛t❛✲

s❡ ❞❛ s♦♠❛ ❞❡ ❑ ❧♦❣✲✈❡r♦ss✐♠✐❧❤❛♥ç❛s ✉♥✐✈❛r✐❛❞❛s ❡✱ ♣♦rt❛♥t♦✱ ❡q✉✐✈❛❧❡ ❛ ♠❛①✐♠✐③❛r ❝❛❞❛ ❧♦❣✲✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✉♥✐✈❛r✐❛❞❛ s❡♣❛r❛❞❛♠❡♥t❡✳ ❊♠ s❡❣✉♥❞♦ ❧✉❣❛r✱ ♦ ❝á❧❝✉❧♦ ❞❡ ❝❛❞❛ ❧♦❣✲ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ é s✐♠♣❧❡s✱ ✈✐st♦ q✉❡ ♥ã♦ ❡♥✈♦❧✈❡ ♦ ✉s♦ ❞♦ ✜❧tr♦ ❞❡ ❍❛♠✐❧t♦♥✳

❆ ♠❛①✐♠✐③❛çã♦ ❞❡QL2✱ ❞✐❢❡r❡♥t❡♠❡♥t❡ ❞❡QL1✱ ❡①✐❣❡ ❛ ❛♣❧✐❝❛çã♦ ♦ ✜❧tr♦ ❞❡ ❍❛♠✐❧t♦♥✱

♣♦✐s ❛ ✈❛r✐á✈❡❧ ❞❡ ❡st❛❞♦ ∆t é ✉♠ ❝♦♠♣♦♥❡♥t❡ ♥ã♦ ♦❜s❡r✈❛❞♦ ❝♦♥❢♦r♠❡ ❥á ♠❡♥❝✐♦♥❛❞♦✳

❈♦♠♦ ♦ ♥ú♠❡r♦ ❞❡ ♣❛râ♠❡tr♦s ♥♦ ♠♦❞❡❧♦ ❞❡ ❝♦rr❡❧❛çã♦ ❝r❡s❝❡ ❞❡ ❢♦r♠❛ q✉❛❞rát✐❝❛ ❝♦♠ ♦ ♥ú♠❡r♦ ❞❡ sér✐❡s ❡♥✈♦❧✈✐❞❛s✱ ♣❛r❛ ♦s ❝❛s♦s ❡♠ q✉❡ Γt t❡♠ ❡❧❡✈❛❞❛ ❞✐♠❡♥sã♦✱ ✐st♦ é✱

✉♠ ❣r❛♥❞❡ ♥ú♠❡r♦ ❞❡ sér✐❡s✱ ❛ ♠❛①✐♠✐③❛çã♦ ❞✐r❡t❛ ❞❡ QL2 ♣♦❞❡ ♥ã♦ s❡r s✐♠♣❧❡s✳ P❛r❛

(22)

✶✺

✹ ❇❛s❡ ❞❡ ❉❛❞♦s

✹✳✶ ❉❡s❝r✐çã♦

❆ ❝♦♥str✉çã♦ ❞❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❡♥✈♦❧✈❡✉ ❛ ❝♦❧❡t❛✸ ❞❛s sér✐❡s ❞✐ár✐❛s ❞❡ ❢❡❝❤❛♠❡♥t♦ ❞♦s

❮♥❞✐❝❡s ❞❛s ❇♦❧s❛s ❞❡ ❱❛❧♦r❡s ❞♦s ❊st❛❞♦s ❯♥✐❞♦s ✭❙P✺✵✵✮✱ ❘❡✐♥♦ ❯♥✐❞♦ ✭❋❚❙❊✶✵✵✮✱ ❇r❛s✐❧ ✭■❇❖❱❊❙P❆✮ ❡ ❈♦ré✐❛ ❞♦ ❙✉❧ ✭❑❖❙P■✮ ♣❛r❛ ♦ ♣❡rí♦❞♦ ❞❡ ✵✷✴✵✶✴✷✵✵✸ ❛té ✷✵✴✵✾✴✷✵✶✷✳ ❆ ❥✉st✐✜❝❛t✐✈❛ ♣❛r❛ ❡s❝♦❧❤❛ ❞❡st❡ ❣r✉♣♦ ❞❡ ♣❛ís❡s ❢♦✐ ❛ ✐❞é✐❛ ❞❡ t❡r ❞♦✐s r❡♣r❡s❡♥t❛♥t❡s ❞❡ r❡❣✐õ❡s ❞✐❢❡r❡♥t❡s ❞❡ ♠❡r❝❛❞♦s ❞❡s❡♥✈♦❧✈✐❞♦s ✭❆♠ér✐❝❛ ❞♦ ◆♦rt❡ ❡ ❊✉r♦♣❛✮ ❡ ❞♦✐s ❞✐❢❡r❡♥t❡s ❞❡ ♠❡r❝❛❞♦s ❡♠❡r❣❡♥t❡s ✭❆♠ér✐❝❛ ❞♦ ❙✉❧ ❡ ➪s✐❛✮✳ ◗✉❛♥t♦ à ❞❡✜♥✐çã♦ ❞❛ ❛♠♦str❛✱ ❛ ✐♥t❡♥çã♦ ❢♦✐ s❡❧❡❝✐♦♥❛r ✉♠ ❤✐stór✐❝♦ ❞❡ ✐♥❢♦r♠❛çã♦ ❡①t❡♥s♦ ❝♦♠ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ✶✵ ❛♥♦s✱ ♦ q✉❡ t♦t❛❧✐③♦✉ ✷✺✸✻ ♦❜s❡r✈❛çõ❡s ♣❛r❛ ❝❛❞❛ sér✐❡✱ q✉❡ ❢♦ss❡ ❝❛r❛❝t❡r✐③❛❞♦ ♣❡❧❛ ♣r❡s❡♥ç❛ ❞❡ ❡✈❡♥t♦s ❞❡ ❝r✐s❡ ✜♥❛♥❝❡✐r❛✳ ❙♦❜r❡ ❡ss❡ ♣♦♥t♦✱ ♣♦❞❡♠♦s ❝✐t❛r✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡✱ ❛s ❝r✐s❡s ❞♦ ❙✉❜♣r✐♠❡ ❞❡ ✷✵✵✽ ❡ ❞❛ ❞í✈✐❞❛ ♥❛ ❊✉r♦♣❛ ❛❣r❛✈❛❞❛ ❡♠ ✷✵✶✶✳ P♦ré♠✱ ❝♦♥❢♦r♠❡ ❢♦✐ ❛♥t❡r✐♦r♠❡♥t❡ ♠❡♥❝✐♦♥❛❞♦✱ ♥ã♦ s❡rá ♥❡❝❡ssár✐♦ ❞❡✜♥✐r ❞❡ ❢♦r♠❛ ❛❞ ❤♦❝ q✉❛✐s ♦s ♠♦♠❡♥t♦s ❞❡ ♠❛✐♦r ✈♦❧❛t✐❧✐❞❛❞❡ ❣❡r❛❞♦s ♣♦r ❝r✐s❡s ✜♥❛♥❝❡✐r❛s✳ ❖ ▼♦❞❡❧♦ ❞❡ ▼✉❞❛♥ç❛ ❞❡ ❘❡❣✐♠❡ ▼❛r❦♦✈✐❛♥♦ é ❝❛♣❛③ ❞❡ ❞❡t❡r♠✐♥❛r ❡♥❞♦❣❡♥❛♠❡♥t❡ t❛✐s ❢❛s❡s✳

600 800 1,000 1,200 1,400 1,600

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

SP500 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

IBOV 3,200 3,600 4,000 4,400 4,800 5,200 5,600 6,000 6,400 6,800

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

FTSE100 400 800 1,200 1,600 2,000 2,400

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

KOSPI

❋✐❣✉r❛ ✶✿ ❙ér✐❡s ❞♦s ❮♥❞✐❝❡s

❉❛❞♦s ♦❜t✐❞♦s ♣❡❧♦ s✐st❡♠❛ ❊❝♦✇✐♥ ❞❛ ❘❡✉t❡rs ❛ ♣❛rt✐r ❞♦s s❡❣✉✐♥t❡s ❝ó❞✐❣♦s✿ ✉s❛✶✺✺✶✵ ✭s♣✺✵✵✮ ✴

(23)

✶✻

❖s ❣rá✜❝♦s ❞♦s ❮♥❞✐❝❡s ✐❧✉str❛♠ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞❛s sér✐❡s ❡ r❡✈❡❧❛♠ ❛ ♠❛✐♦r ❛♠♣❧✐✲ t✉❞❡ ❞♦s ✈❛❧♦r❡s ♣❛r❛ ❛ ♠❡t❛❞❡ ✜♥❛❧ ❞❛ ❛♠♦str❛✳ ❆❧é♠ ❞✐ss♦✱ ✉♠❛ ❛♥á❧✐s❡ ✈✐s✉❛❧ ♣r❡❧✐♠✐♥❛r r❡✈❡❧❛ ✉♠❛ q✉❡❞❛ ❝♦♥❥✉♥t❛ ❞❛s ✈❛r✐á✈❡✐s ♥❛s ❝r✐s❡s ♠❡♥❝✐♦♥❛❞❛s ❛♥t❡r✐♦r♠❡♥t❡✳

✹✳✷ ❚r❛t❛♠❡♥t♦s ❡ ❆♥á❧✐s❡s ■♥✐❝✐❛✐s

❆♥t❡s ❞❛ ❡t❛♣❛ ❞❛s ❡st✐♠❛çõ❡s✱ ❛ ❜❛s❡ ❞❡ ❞❛❞♦s ❜r✉t❛ s♦❢r❡✉ ❛❧❣✉♥s tr❛t❛♠❡♥t♦s✳ ❖ ♣r✐♠❡✐r♦ ❞❡❧❡s ❝♦♥s✐st✐✉ ❡♠ ❡st✐♠❛r ✉♠ ▼♦❞❡❧♦ ❞❡ ◆í✈❡❧ ▲♦❝❛❧ ♣❛r❛ ❝❛❞❛ sér✐❡ ❝♦♠ ❛ ✜♥❛❧✐❞❛❞❡ ❞❡ ✐♠♣✉t❛r ✉♠❛ ❡st✐♠❛t✐✈❛ ♣❛r❛ ♦s ✈❛❧♦r❡s ❢❛❧t❛♥t❡s ✭♠✐ss✐♥❣s✮ r❡❢❡r❡♥t❡s ❛♦s ❞✐❛s ❡♠ q✉❡ ♥ã♦ ❤♦✉✈❡ ♥❡❣♦❝✐❛çã♦✹✳ ❖s ✈❛❧♦r❡s ❢❛❧t❛♥t❡s ❢♦r❛♠ s✉❜st✐t✉í❞♦s ♣❡❧❛s

❡st✐♠❛t✐✈❛s s✉❛✈✐③❛❞❛s ❞♦ ❝♦♠♣♦♥❡♥t❡ ❞❡ ♥í✈❡❧✳ ❚❛❧ ♣r♦❝❡❞✐♠❡♥t♦ ❢♦✐ r❡❛❧✐③❛❞♦ ♥♦ s♦❢t✇❛r❡ ❖①▼❡tr✐❝s ❝♦♠ ♦ ♣❛❝♦t❡ ❙❚❆▼P ✽✳✷ ❝♦♥❢♦r♠❡ s✉❣❡r✐❞♦ ♣♦r ❑♦♦♣♠❛♥ ❡t ❛❧ ✭✷✵✵✾✮✳ ❖s ❣rá✜❝♦s ❞♦s ✈❛❧♦r❡s ❣❡r❛❞♦s ♣❛r❛ ♦s ❝♦♠♣♦♥❡♥t❡s ❡stã♦ ♣r❡s❡♥t❡s ♥♦s ❆♥❡①♦s✳

❖ s❡❣✉♥❞♦ tr❛t❛♠❡♥t♦ ❡♥✈♦❧✈❡✉ ❛ s✐♥❝r♦♥✐③❛çã♦ ❞♦s ❞✐❛s ❞❡ ♥❡❣♦❝✐❛çã♦ ♣♦r ❝♦♥t❛ ❞❛s ❞✐❢❡r❡♥ç❛s ❞❡ ❢✉s♦ ❤♦rár✐♦✳ ❈♦♠ r❡❧❛çã♦ ❛♦ ❤♦rár✐♦ ❞❡ ●r❡❡♥✇✐❝❤ ✭●▼❚✮✱ ❙❡✉❧ ❡stá ●▼❚✰✾ ❡✱ ❞❡ss❛ ❢♦r♠❛✱ ♦♣❡r❛❝✐♦♥❛❧♠❡♥t❡ ✉♠ ❞✐❛ à ❢r❡♥t❡ ❞❛s ♥❡❣♦❝✐❛çõ❡s ♥❛s ♦✉tr❛s r❡❣✐õ❡s ❞❛s sér✐❡s ❡s❝♦❧❤✐❞❛s✳ ❈♦♥❢♦r♠❡ ❡♠ ❙❛♥t♦s ❡ ❱❛❧❧s P❡r❡✐r❛ ✭✷✵✶✶✮✱ ❛ s✐♥❝r♦♥✐③❛çã♦ ❞♦s ❞❛❞♦s r❡s♣❡✐t♦✉ ♦ s❡❣✉✐♥t❡ ❝♦r♣♦r❛❧✿ [SP500t, IBOVt, F T SEt, KOSP It+1]✳

❖ t❡r❝❡✐r♦ tr❛t❛♠❡♥t♦ ♥❛ ❜❛s❡ ❡♥✈♦❧✈❡✉ ❛ ❝♦♥str✉çã♦ ❞♦s r❡t♦r♥♦s ❞♦s í♥❞✐❝❡s ♣♦r ♠❡✐♦ ❞♦ ❝á❧❝✉❧♦ ❞❛ ❞✐❢❡r❡♥ç❛ ❞♦ ❧♦❣❛r✐t♠♦ ♥❡♣❡r✐❛♥♦ ♠✉❧t✐♣❧✐❝❛❞♦ ♣♦r ✶✵✵✳ ❆s ❡st❛tíst✐❝❛s ❞❡s✲ ❝r✐t✐✈❛s✱ ❣rá✜❝♦s ❡ ❤✐st♦❣r❛♠❛s ✭❆♥❡①♦s✮ ❞♦s r❡t♦r♥♦s ❝♦♥✜r♠❛♠ ♦s ❢❛t♦s ❡st✐❧✐③❛❞♦s ❞❡ sér✐❡s ✜♥❛♥❝❡✐r❛s✳ ❆ ❞✐str✐❜✉✐çã♦ ❛♠♦str❛❧ ❞♦s r❡t♦r♥♦s ❞♦s q✉❛tr♦ í♥❞✐❝❡s sã♦ ❝❛r❛❝t❡r✐✲ ③❛❞❛s ♣♦r ❝❛✉❞❛s ♠❛✐s ♣❡s❛❞❛s ✭❧❡♣t♦❝úrt✐❝❛s✮ ❞♦ q✉❡ ❞❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧✱ ♣♦r ♠é❞✐❛ ❛♦ r❡❞♦r ❞❡ ③❡r♦ ❡ ♣♦r ❛❣r✉♣❛♠❡♥t♦ ❞❡ ✈♦❧❛t✐❧✐❞❛❞❡s✳ ❆❧é♠ ❞✐ss♦✱ t♦❞♦s ♦s r❡t♦r♥♦s r❡❣✐str❛r❛♠ ❛ss✐♠❡tr✐❛ ♥❡❣❛t✐✈❛✳

(24)

✶✼

❙P✺✵✵ ■❇❖❱❉ ❋❚❙❊✶✵✵ ❑❖❙P■

▼é❞✐❛ 0.019 0.066 0.015 0.045

❊rr♦ ♣❛❞rã♦ 0.026 0.036 0.024 0.029

▼❡❞✐❛♥❛ 0.071 0.140 0.057 0.105

❉❡s✈✐♦ ♣❛❞rã♦ 1.290 1.796 1.232 1.455

❱❛r✐â♥❝✐❛ ❞❛ ❛♠♦str❛ 1.665 3.224 1.517 2.118

❈✉rt♦s❡ 10.745 5.692 8.289 5.878

❆ss✐♠❡tr✐❛ −0.280 −0.117 −0.130 −0.470

❏❛rq✉❡✲❇❡r❛ 12175.6 3411.8 7231.3 3724.6

■♥t❡r✈❛❧♦ 20.43 25.77 18.65 22.46

▼í♥✐♠♦ −9.47 −12.10 −9.27 −11.17

▼á①✐♠♦ 10.96 13.68 9.38 11.28

❙♦♠❛ 47.40 167.08 37.86 114.22

❈♦♥t❛❣❡♠ 2531 2531 2531 2531

❚❛❜❡❧❛ ✶✿ ❊st❛tíst✐❝❛s ❉❡s❝r✐t✐✈❛s ❞♦s ❘❡t♦r♥♦s ❞♦s ❮♥❞✐❝❡s

-10 -5 0 5 10 15

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 SP500 -15 -10 -5 0 5 10 15

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 IBOV -10 -5 0 5 10

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 FTSE100 -12 -8 -4 0 4 8 12

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 KOSPI

(25)

✶✽

✹✳✸ ❋✐❧tr❛❣❡♠

❈♦♥s✐❞❡r❛♥❞♦ q✉❡ ♦s ♠♦❞❡❧♦s ❞❡ ✈♦❧❛t✐❧✐❞❛❞❡ ♣♦ss✉❡♠ ❝♦♠♦ ♣r❡♠✐ss❛ ❛ ❛✉sê♥❝✐❛ ❞❡ ❝♦rr❡❧❛çã♦ s❡r✐❛❧ ♥♦s ❞❛❞♦s ❝♦♥❢♦r♠❡ ♠❡♥❝✐♦♥❛❞♦ ❛♥t❡r✐♦r♠❡♥t❡✱ ❢♦✐ ♥❡❝❡ssár✐♦ ❛♥❛❧✐s❛r ❛ ✈❛❧✐❞❛❞❡ ❞❡st❛ ❤✐♣ót❡s❡✳ ❖s ❝♦rr❡❧♦❣r❛♠❛s ♣❛r❛ ♦s r❡t♦r♥♦s ❡ ♦s r❡t♦r♥♦s ❛♦ q✉❛❞r❛❞♦ sã♦ ❛♣r❡s❡♥t❛❞♦s ♥♦s ❆♥❡①♦s✳ ➱ ♣♦ssí✈❡❧ ♥♦t❛r q✉❡ ❛s ❛✉t♦❝♦rr❡❧❛çõ❡s ♣❛r❛ ❛s sér✐❡s ❞♦s r❡t♦r♥♦s✱ ❛♣❡s❛r ❞❡ ♥ã♦ ❛♣r❡s❡♥t❛r❡♠ ✈❛❧♦r❡s ❡❧❡✈❛❞♦s✱ sã♦ ❡st❛t✐st✐❝❛♠❡♥t❡ ❞✐❢❡r❡♥t❡s ❞❡ ③❡r♦✳ ❈♦♠ ♦ ♦❜❥❡t✐✈♦ ❞❡ ♠♦❞❡❧❛r ❛ ❡str✉t✉r❛ ❞❡ ❛✉t♦❝♦rr❡❧❛çã♦ ❞♦s ❞❛❞♦s✱ ❢♦✐ r❡❛❧✐③❛❞❛ ✉♠❛ ✜❧tr❛❣❡♠ ♣❛r❛ ❛ ♠é❞✐❛ ❝♦♥❞✐❝✐♦♥❛❧ ❞❛s sér✐❡s ♣♦r ♠❡✐♦ ❞❛ ❡st✐♠❛çã♦ ❞❡ ▼♦❞❡❧♦s ❞❛ ❝❧❛ss❡ ❆❘▼❆✭♣✱q✮✳

❆ ❞❡t❡r♠✐♥❛çã♦ ❞❛ ♦r❞❡♠ ♣ ❡ q ❞❡st❡s ♠♦❞❡❧♦s ❢♦✐ ❢❡✐t❛ ❝♦♠ ❜❛s❡ ♥♦s ❈r✐tér✐♦s ❞❡ ■♥❢♦r♠❛çã♦ ❆❦❛✐❦❡ ✭❆■❈✮✱ ❍❛♥♥❛♥✲◗✉✐♥♥ ✭❍◗✮ ❡ ❙❝❤✇❛r③ ✭❙❈ ♦✉ ❇■❈✮✱ ♥♦s t❡st❡s s♦❜r❡ ♦s r❡sí❞✉♦s ❡ ♥❛ s✐❣♥✐✜❝â♥❝✐❛ ❞♦s ♣❛râ♠❡tr♦s✳ ◆♦s ❆♥❡①♦s é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ t❛❜❡❧❛ ❝♦♠ ♦s ❈r✐tér✐♦s ❞❡ ■♥❢♦r♠❛çã♦ ♣❛r❛ t♦❞❛s ❛s ♣♦ssí✈❡✐s ❝♦♠❜✐♥❛çõ❡s ❛té ❛ t❡r❝❡✐r❛ ♦r❞❡♠✱ ♦✉ s❡❥❛✱ ♣❛r❛ ♣❂✵✱✶✱✷ ❡ ✸ ❡ q❂✵✱✶✱✷ ❡ ✸✳ ❈♦♠ r❡❧❛çã♦ ❛♦s r❡sí❞✉♦s✱ t❛♥t♦ ♦s r❡s✉❧t❛❞♦s ❞♦ t❡st❡ ▲▼ q✉❛♥t♦ ❉✉r❜✐♥ ❲❛ts♦♥ ❝♦rr♦❜♦r❛♠ ♣❛r❛ ❝♦♥❝❧✉sã♦ ❞❡ ♥ã♦ ❛✉t♦❝♦rr❡❧❛çã♦ s❡r✐❛❧✳ P♦r ú❧t✐♠♦✱ t❛♠❜é♠ ❢♦r❛♠ ❝❛❧❝✉❧❛❞❛s ❛s ❡st❛tíst✐❝❛s ♣❛r❛ ♦ t❡st❡ ❆❘❈❍ ❞❡ ❍❡t❡r♦❝❡❞❛s✲ t✐❝✐❞❛❞❡ ❡ ❛ ❤✐♣ót❡s❡ ♥✉❧❛ ❞❡ ❛✉sê♥❝✐❛ ❞❡ ❤❡t❡r♦❝❡❞❛st✐❝✐❞❛❞❡ é r❡❥❡✐t❛❞❛ ❥✉st✐✜❝❛♥❞♦ ❛ ❛♣❧✐❝❛çã♦ ❞♦s ♠♦❞❡❧♦s ❞❡ ✈♦❧❛t✐❧✐❞❛❞❡ ❞♦ ♣r❡s❡♥t❡ ❡st✉❞♦✳

ARM A ❆✉t♦❝♦rr❡❧❛çã♦✯ DW ❍❡t❡r♦❝❡❞❛st✐❝✐❞❛❞❡✯✯

Lag(1) Lag(3) Lag(6) Lag(9) Lag(1) Lag(3) Lag(6) Lag(9)

❙P✺✵✵ (3,3) 0.01 0.73 0.70 1.88 2.0006 99.0 201.8 165.3 120.5 ✭✵✳✾✶✮ ✭✵✳✺✸✮ ✭✵✳✻✺✮ ✭✵✳✵✺✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ■❇❖❱ (2,3) 1.20 1.37 1.05 1.20 1.9987 83.6 176.2 115.5 99.5

✭✵✳✷✼✮ ✭✵✳✷✹✮ ✭✵✳✸✾✮ ✭✵✳✷✾✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ❋❚❙❊ (3,3) 1.15 0.95 1.16 1.34 2.0046 138.4 157.7 104.0 73.7

✭✵✳✷✽✮ ✭✵✳✹✶✮ ✭✵✳✸✷✮ ✭✵✳✷✵✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ❑❖❙P■ (3,3) 0.10 0.88 1.33 1.54 2.0053 111.5 84.8 123.6 85.0

✭✵✳✼✺✮ ✭✵✳✹✹✮ ✭✵✳✷✸✮ ✭✵✳✶✷✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ✭✵✳✵✵✮ ✯❊st❛tíst✐❝❛ ❋ ❡ Pr♦❜✳ ❋ ❡♠ ♣❛rê♥t❡s❡s ❞♦ ❚❡st❡ ▲▼ ❞❡ ❆✉t♦❝♦rr❡❧❛çã♦ ❙❡r✐❛❧

✯✯❊st❛tíst✐❝❛ ❋ ❡ Pr♦❜✳ ❋ ❡♠ ♣❛rê♥t❡s❡s ❞♦ ❚❡st❡ ❆❘❈❍ ❞❡ ❍❡t❡r♦❝❡❞❛st✐❝✐❞❛❞❡ ❚❛❜❡❧❛ ✷✿ ❚❡st❡s s♦❜r❡ ❛s ❙ér✐❡s ❞♦s ❘❡sí❞✉♦s

(26)

✶✾

Referências

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