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master's thesis
Modeliranje koncentracije peludi ambrozije vektorskim autoregresivnim modelom
2018. urn:nbn:hr:126:981679
Knežević, Marinela
Josip Juraj Strossmayer University of Osijek
Department of Mathematics
Chair of Pure Mathematics and Mathematics Teaching
Probability, Mathematical Statistics and Data Science Research Group

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Knežević, M. (2018). Modeliranje koncentracije peludi ambrozije vektorskim autoregresivnim modelom (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:981679

Knežević, Marinela. "Modeliranje koncentracije peludi ambrozije vektorskim autoregresivnim modelom." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:981679

Knežević, Marinela. "Modeliranje koncentracije peludi ambrozije vektorskim autoregresivnim modelom." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2018. https://urn.nsk.hr/urn:nbn:hr:126:981679

Knežević, M. (2018). 'Modeliranje koncentracije peludi ambrozije vektorskim autoregresivnim modelom', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 07 April 2025, https://urn.nsk.hr/urn:nbn:hr:126:981679

Knežević M. Modeliranje koncentracije peludi ambrozije vektorskim autoregresivnim modelom [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2018 [cited 2025 April 07] Available at: https://urn.nsk.hr/urn:nbn:hr:126:981679

M. Knežević, "Modeliranje koncentracije peludi ambrozije vektorskim autoregresivnim modelom", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:126:981679

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Metadata
TitleModeliranje koncentracije peludi ambrozije vektorskim autoregresivnim modelom
Title (english)Modelling of Ambrosia Pollen Concentration with the Vector Autoregressive Model
AuthorMarinela Knežević
MentorNenad Šuvak (mentor)
Committee memberMirta Benšić (predsjednik povjerenstva)
Committee memberKristian Sabo (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 country2018-06-19, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Applied Mathematics and Mathematical Modeling
Abstract
U ovom radu su predstavljeni osnovni pojmovi, svojstva i rezultati analize vremenskih nizova. Navedeni su modeli za stacionarne i nestacionarne jednodimenzionalne vremenske nizove - procesi pomičnih prosjeka (MA), autoregresivni procesi (AR), autoregresivni (integrirani) procesi pomičnih prosjeka (ARMA i ARIMA) te sezonalni autoregresivni (integrirani) procesi pomičnih prosjeka (SARMA i SARIMA). Pokazani su i neki primjeri takvih procesa. Od modela za višedimenzionalne vremenske nizove je ... More opisan vektorski autoregresivni proces (VAR). Navedene su metode procjene parametara i odredivanja reda modela i analizirana je uzročnost u smislu Grangera. Opisana je i dijagnostika modela koja se zasniva na analizi reziduala te je opisana predikcija pomoću odabranog modela. Na temelju podataka o koncentraciji peludi u Somboru i meteoroloških podataka s mjerne postaje Rimski Šančevi je napravljen vektorski autoregresivni model s ciljem predviđanja maksimalne dnevne koncentracije peludi. Za potrebe modela su odabrane i varijable vlažnost zraka i prosječna dnevna temperatura, a red modela je 16, što znači da za predikciju maksimalne koncentracije peludi pojedinog dana koristimo vrijednost koncentracije peludi, vlažnosti zraka i prosječne temperature prethodnih 16 dana. Dobivene vrijednosti su podijeljene u sljedeće kategorije - niska, umjerena, visoka i vrlo visoka koncentracija. S obzirom na nezadovoljene pretpostavke o svojstvima reziduala, model se ne može koristiti u svrhu interpretacije, no za predikciju se pokazao točnim u 92.49 % promatranih dana. Navedena je i mogućnost poboljšanja korištenog modela. Less
Abstract (english)
This graduate thesis presents basic terms, properties and results of time series analysis. Models of stationarity and non-stationarity univariate time series are described – moving average processes (MA), autoregressive processes (AR), autoregressive (integrated) moving average processes (ARMA and ARIMA) and seasonal autoregressive (integrated) moving average processes (SARMA and SARIMA). Some examples of these processes are also shown. Out of many multivariate time series models, the... More vector autoregressive process (VAR) is described. Methods of parameter estimation and order determination are shown and Granger causality is analysed. The diagnostic of models based on the residual analysis and the prediction by the chosen model are also described. Based on the data of pollen concentration in Sombor and the meteorological data from the measuring station Rimski Sanˇcevi, a vector autoregressive model is made with the ˇ aim of predicting the maximum daily pollen concentration. For the needs of the model, the choosen variables are also air humidity and average daily temperature and the order of the model is 16, meaning that for the prediction of the maximum pollen concentration of a single day, we use the values od pollen concentration, air humidity and average temperature od the previous 16 days. The obtained values are divided into the following categories - low, moderate, high and very high concentrations. Since the assumptions on model residuals are not satisfied, the model can not be used for the purpose of interpretation, but for prediction purposes it would be accurate for 92.49 % of observed days. Possible correction of the used model is also mentioned. Less
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:981679
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 on2018-06-26 05:59:37
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