Stohastiskais scenāriju simulātors ar ARCH efekta modelēšanu

6533b833fe1ef96bd129c652

RESEARCH PRODUCT

Stohastiskais scenāriju simulātors ar ARCH efekta modelēšanu

Artūrs Krištapjonoks

subject

GARCH Kopula Eliptiskās kopulas Matemātika Sklāra teorēma ARCH

description

Kopulu funkcijas ir noderīgs rīks, kā izprast datu atkarības struktūru daudz dziļākajā līmenī. Tās ļauj modelēt daudzdimensionālus sadalījumus, apvienojot vairākus gadījuma vektoru komponenšu marginālos sadalījumus vienā kopējā sadalījuma funkcijā. Bakalaura darbā pirmajā daļā tiek apskatīta kopulas definīcija un tās galvenās īpašības. Tiek aplūkotas Arhimeda kopulas (Klaitona, Gumbela un Franka) un divas eliptiskās kopulas – Gausa un t-kopula. Apskatītas kopulu parametru novērtēšanas metodes un modeļa izvēle, pamatojoties uz piemērotības kritērijiem. Otrajā daļā tiek apskatīti nosacītās heteroskedascitātes modeļi: EWMA, autoregresīvais nosacītās heteroskedascitātes modelis, kā arī tās vispārinājums - GARCH modelis. Doti formulējumi, apskatīti parametru novērtējumi, piemērotā modeļa izvēle un prognozēšana. Praktiskajā daļā vairāku dimensiju datiem tiek atklāts nosacītās heteroskedascitātes efekts un konstruēti GARCH un ARIMA modeļi. Gausa un t-kopula tiek pielietotas, lai aprēķinātu tirgus riska faktoru šokus atbilstoši piedāvātai tirgus riska stresa testu scenāriju kalibrācijas metodoloģijai.

year	journal	country	edition	language
2021-01-01

https://dspace.lu.lv/dspace/handle/7/55993

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