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master's thesis
Dugoročna zavisnost
Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. urn:nbn:hr:126:480768
Grgić, Lucijana
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

Institutional repository: Repository of School of Applied Mathematics and Informatics

Cite this document

Grgić, L. (2018). Dugoročna zavisnost (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:480768

Grgić, Lucijana. "Dugoročna zavisnost." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:480768

Grgić, Lucijana. "Dugoročna zavisnost." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:480768

Grgić, L. (2018). 'Dugoročna zavisnost', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 18 February 2025, https://urn.nsk.hr/urn:nbn:hr:126:480768

Grgić L. Dugoročna zavisnost [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2025 February 18] Available at: https://urn.nsk.hr/urn:nbn:hr:126:480768

L. Grgić, "Dugoročna zavisnost", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:480768

Metadata
TitleDugoročna zavisnost
Title (english)Long-range Dependence
AuthorLucijana Grgić
MentorDanijel Grahovac (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
Committee memberNenad Šuvak (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Probability, Mathematical Statistics and Data Science Research Group)
Osijek
Defense date and country2018-07-06, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovom diplomskom radu predstavljeni su procesi čija autokorelacijska funkcija nije apsolutno sumabilna. Takvi procesi se nazivaju stacionarni procesi s dugoročnim pamćenjem i svoju primjenu nalaze u različitim područjima poput klimatologije i hidrologije. Navedene su definicije i osnovni rezultati stacionarnih procesa s dugoročnim pamćenjem te dvije klase takvih procesa. Jedna od njih su frakcionalni ARIMA procesi koji su prirodno proširenje klasičnih ARIMA procesa. Prikazane su strukture autokorelacijske funkcije i spektralne gustoće takvih procesa. Zatim su uvedeni statistički procjenitelji koji služe za uočavanje dugoročne zavisnosti u nekom vremenskom nizu. To su R/S statistika, log–log korelogram, graf varijance, periodogram te Whittleov aproksimativni ML procjenitelj. Uvedeni koncept dugoročne zavisnosti primijenjen je na dva vremenska niza: godišnji minimalni vodostaj rijeke Nil i globalnu temperaturu sjeverne polutke Zemlje.
Abstract (english)
In this graduate work, the processes of which the autocorrelation function is not absolutely summable are presented. Such processes are called stationary processes with long memory and its application are found in different areas such as climate and hydrology. Definitions and basic results of stationary processes with long memory and two classes of such processes are presented. One of them are fractional ARIMA processes that are the natural expansion of the classical ARIMA processes. The structures of autocorrelation function and spectral density of such processes are presented. Then, statistical estimators are introduced to identify long–range dependence in some time series. These are R/S statistic, log–log correlogram, variance plot, periodogram and Whittle’s approximate ML estimator. The concept of long–range dependence has been introduced in two time series: yearly minimum water level of the Nile River and the global temperature of the northern hemisphere of the Earth.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:480768
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2018-07-12 06:57:08