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master's thesis
Procjena autokorelacijske funkcije
2020. urn:nbn:hr:126:769181
Paprić, Doris
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Algebra, Analysis and Number Theory Research Group

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Paprić, D. (2020). Procjena autokorelacijske funkcije (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:769181

Paprić, Doris. "Procjena autokorelacijske funkcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:769181

Paprić, Doris. "Procjena autokorelacijske funkcije." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2020. https://urn.nsk.hr/urn:nbn:hr:126:769181

Paprić, D. (2020). 'Procjena autokorelacijske funkcije', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 05 February 2025, https://urn.nsk.hr/urn:nbn:hr:126:769181

Paprić D. Procjena autokorelacijske funkcije [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2020 [cited 2025 February 05] Available at: https://urn.nsk.hr/urn:nbn:hr:126:769181

D. Paprić, "Procjena autokorelacijske funkcije", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:126:769181

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Metadata
TitleProcjena autokorelacijske funkcije
Title (english)Estimation az Autocorrelation Function
AuthorDoris Paprić
MentorMirta Benšić (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberMirta Benšić (član povjerenstva)
Committee memberDanijel Grahovac (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
(Chair of Pure Mathematics and Mathematics Teaching)
(Algebra, Analysis and Number Theory Research Group)
Osijek
Defense date and country2020-10-02, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Probability Theory and Statistics
Abstract
U ovom diplomskom radu obradena je procjena autokorelacijske funkcije. Na samom početku rada napravljena je teorijska osnova vremenskih nizova, uveden je pojam stacionarnosti i opisani su osnovni modeli stacionarnih vremenskih nizova. Zatim, objašnjena je procjena očekivanja koja je bitna karakteristika stacionarnih procesa. U nastavku rada navedeno je nekoliko vrsta procjenitelja autokorelacijske funkcije. Kao klasični procjenitelj promatrana je uzoračka funkcija autokorelacija. Kako postojanje stršećih vrijednosti medu podacima značajno utječe na kvalitetu procjene uvedeni su robusni procjenitelji. Navedena su svojstva i prednosti procjenitelja dobivenih na temelju tri regresijske metode: L1 metoda, metoda najmanjih odrezanih kvadrata i MM metoda. Na kraju rada napravljena je usporedba procjenitelja na simulacijama stacionarnih procesa koja ukazuje na prednosti korištenja robusnih procjenitelja.
Abstract (english)
This diploma thesis presents an estimation of autocorrelation function. In the first part, theoretical basis of time series, concept of stationarity and the most important models of stationary time series are described. Furthermore, an estimate of the mean is explained, which is an important characteristic of stationary processes. Several types of estimators of autocorrelation function are presented. Sample autocorrelation function was observed as a classical estimator. Since the presence of outliers among data can significantly affect the quality of estimation, robust estimators have been introduced. The properties of estimators based on three regression methods are given: L1 method, least trimmed squares and MM method. At the end of the paper, a comparison of estimators on stationary process simulations is made, which indicates the advantages of using robust estimators.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:769181
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 on2020-10-13 07:45:31