Modeliranje s kopulami

magistrsko delo

Tina Bertok (Author), Tomaž Košir (Mentor), Ganna Kudryavtseva (Co-mentor)

Abstract

Modeliranje s kopulami je v zadnjih letih postalo vedno bolj priljubljeno področje, saj se kopulni modeli uporabljajo v financah, medicini, geodeziji ter nenazadnje tudi v hidrologiji. V delu zato najprej predstavimo osnove teorije kopul, potrebne za razumevanje samega modela. Nato se osredotočimo na uporabo kopulnih modelov v hidrologiji, ter vpeljemo različne mere skladnosti, grafična orodja ter metode ocenjevanja, ki so nam v pomoč pri iskanju najbolj primernega kopulnega modela. Analizo iz vzorčne množice podatkov uporabimo za prikaz odvisnosti med maksimalnim letnim pretokom in pripadajočim volumnom reke Harricana. Iz predstavljenih podatkov in analiz skozi delo smo videli, da več družin kopul zagotavlja zadovoljive modele za podatke reke Harricana. Ni presenetljivo dejstvo, da je večina teh kopulnih modelov ekstremnih vrednosti. S pomočjo dodatnih analiz pridemo do ugotovitve, da najbolj optimalen model predstavlja Tawnova kopula tipa 1, ki je sicer asimetrična kopula. Čeprav smo se v naših analizah omejili na bivariatni primer, bi lahko večino predstavljenih orodij posplošili na večdimenzionalni primer. S povečanjem števila spremenljivk, se povečuje tudi zapletenost modelov, zato konstrukcija ustreznih kopulnih modelov ostaja odprto vprašanje.

Keywords

finančna matematika;kopule;Sklarov izrek;kopulni modeli;hidrologija;mere skladnosti;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[T. Erzin]
UDC:	519.2
COBISS:	113675011
Views:	700
Downloads:	69
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Modelling with Copulas
Secondary abstract:	Modelling with copulas has become an increasingly popular field in recent years, as copula models are used in finance, medicine, geodesy and, last but not least, hydrology. In this diploma thesis we first present the basics of the theory needed to understand the model itself. We then focus on the use of copula models in hydrology, and introduce various measures of dependence, graphical tools, and estimation methods that help us find the most appropriate copula model. The analysis from the sample data set is then used to show the relationship between the maximum annual flow and the corresponding volume of the Harricana River. From the data presented and analyzed through work, we have seen that several copula families provide satisfactory models for Harricana River data. Not surprisingly, most of these models are extreme value copulas. With the help of additional analyzes, we come to the conclusion that the most optimal model is Tawn's type 1 copula, which is an asymmetric copula. Although we limited ourselves to the bivariate case in our analyzes, most of the tools presented could be generalized to the multidimensional case. As the number of variables increases, the complexity of the models also increases, so the construction of appropriate copula models remains an open question.
Secondary keywords:	copulas;Sklar theorem;copula models;hydrology;measures of dependence;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 2. stopnja
Pages:	IX, 58 str.
ID:	15795551