Modeli multivarijatne volatilnosti

master's thesis

• Author: Dorotea Burić
• Mentor: Azra Tafro (mentor)
• Committee member: Azra Tafro (predsjednik povjerenstva)
• Committee member: Vanja Wagner (član povjerenstva)
• Committee member: Rudi Mrazović (član povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2020-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom su radu predstavljeni neki od modela koji procjenjuju vremenski promjenjive volatilnosti i korelacije multivarijatnih vremenskih serija. Za demonstraciju koristimo mjesečne log-povrate IBM dionice, S&P 500 indeksa Coca Cola dionice u razdoblju od siječnja 1963. godine do prosinca 2019. godine.Cilj analize multivarijatnih vremenskih serija je korištenjem stvarnih podataka više vremenskih serija procijeniti valjani model i proučiti međusobnu povezanost tih serija. Uvodimo osnovna svojstva ARCH i GARCH modela. GARCH modeli se primjenjuju u (financijskim) vremenskim serijama zato što pretpostavljaju da one imaju vremenski promjenjivu varijancu. Dodatni je razlog procjene korištenjem GARCH modela taj što financijske vremenske serije kao što su povrati pokazuju svojstvo grupiranja volatilnosti, što znači da vremenske serije imaju periode visoke i niske volatilnosti. Na procjenu EWMA modela i Modela dinamičke uvjetne korelacije (DCC) utječu jedan ili dva parametra te se zato često odbacuju dijagnostičkim provjerama. Jednostavni BEKK (Baba-Engle-Kraft-Kroner) model pruža općenit postupak za modeliranje multivarijatne volatilnosti, ali se susreće s poteškoćama u procjeni već za mali broj vremenskih serija. Također uvodimo postupak za modeliranje koji koristi Choleskyjevu dekompoziciju. Naposljetku, promatramo Go-GARCH model koji je prikladan i za velik broj vremenskih serija.

Abstract (english)

In this paper, we present some models that explain how one estimates time-varying volatilities and correlations of multivariate time series. For demonstration, we consider monthly log-returns of IBM stock, S&P 500 index, and Coca Cola stock from January 1963 to December 2019. The objective of multivariate time series analysis is to study the past observations of a multiple time series to an adequate model that describes how the time series are interrelated. We give a brief description of the univariate ARCH and GARCH models. GARCH models are used in financial time series because they have time-varying variance. An additional reason for using GARCH models is a feature of time series called volatility clustering. Financial time series such as stock returns often exhibit volatility clustering, where time series show periods of high volatility and periods of low volatility. Models such as the Exponentially Weighted Moving Average (EWMA) model and Dynamic conditional correlation (DCC) model are extremely parsimonious because they estimate only one or two parameters. For that reason, they tend to be rejected by diagnostic checks. The simple Baba-Engle-Kraft-Krone (BEKK) model provides a general framework for estimating time-varying volatilities but encounters some difficulties in practice when the number of time series is large. We also give a procedure for multivariate volatility modeling using Cholesky decomposition. Finally, we employ the Go-GARCH model which is suitable for a large number of time series.

• Keywords: vremenski promjenjiva volatilnost; i korelacije multivarijatnih vremenskih serija; svojstva ARCH i GARCH modela; EWMA model; Model dinamičke uvjetne korelacije (DCC); Choleskyjeva dekompozicija; Go-GARCH model
• Keywords (english): time-varying volatilities; correlations of multivariate time series; ARCH models; GARCH models; Exponentially Weighted Moving Average (EWMA) model; Dynamic conditional correlation (DCC); Cholesky decomposition; Go-GARCH model
• Language: croatian
• URN:NBN: urn:nbn:hr:217:021530
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2020-12-07 12:14:34