http://creativecommons.org/licenses/by-nd/3.0/at/legalcode [VI], 117, [2] lista 5014018 bytes srp This dissertation has 2 basic goals. The first goal is to construct the random environmentINAR time series that can take both positive and negative values. The realization ofsuch goal would create new possibilities in integer-valued data modeling. In addition,since the environment state estimation of each individual realization is a crucial step inreal-life data modeling using models in random environment, the goal is to adapt existingclustering techniques in order to make the environment state estimates more accurate.Both goals, if realized, would represent an original authorial contribution to the integervalued time series analysis.The dissertation contains 4 chapters. Chapter 1 is the introductory one and provides ahistorical overview of the INAR models development. Also, this chapter offers importanttheorems and distributions known from before, necessary to adduce proofs in subsequentchapters. Relying on results given in [15], Chapter 2 discusses possibilities of extractingand predicting latent components of the true INAR time series with skewed Skellammarginal distribution. In Chapter 3, a construction of the new non-stationary randomenvironment INAR model with values over entire Z is given. Unknown model parametersare estimated using adapted estimation techniques. The efficiency of estimates is testedon simulated data. A quality of the introduced model is examined on appropriate real-lifedata. In Chapter 4, the K-means clustering technique adaptation is provided, in orderto make it suitable for estimating environment states of realizations corresponding to thegeneralized random environment INAR time series. The adaptation efficiency is testedon simulated and real-life data and compared to clustering results obtained using standard K-means. Ova disertacija ima 2 cilja. Najpre, cilj disertacije je konstrukcija novih INAR vremenskih serija u sluˇcajnoj okolini koji mogu uzeti kako pozitivne, tako i negativne vrednosti.Uspeˇsna realizacija ovog cilja donela bi nove mogu´cnosti u modeliranju celobrojnih nizovapodataka. Dodatno, kako je ocena stanja okoline svake realizacije kljuˇcni korak u modeliranju stvarnih procesa pomo´cu novouvedenih modela u sluˇcajnoj okolini, cilj disertacijeje prilagod¯avanje postoje´cih metoda klasterovanja sa namerom da ocene stanja budu ˇstopreciznije. Oba navedena cilja bi, u sluˇcaju realizacije, predstavljala originalan doprinosautora analizi celobrojnih vremenskih serija.Disertacija sadrˇzi 4 glave. Glava 1 je uvodnog karaktera i daje istorijski pregled razvojaINAR modela. Takod¯e, ova glava nudi neke bitne teoreme i raspodele poznate od ranije,neophodne za izvod¯enje dokaza u narednim glavama. Oslanjaju´ci se na rezultate date u[15], u Glavi 2 su razmotrene mogu´cnosti identifikovanja i predvid¯anja latentnih komponenti INAR vremenske serije sa asimetriˇcnom Skelamovom marginalnom raspodelom. UGlavi 3 pristupa se konstrukciji novog nestacionarnog INAR modela u sluˇcajnoj okolinikoji moˇze uzeti vrednosti na ˇcitavom skupu Z. Nepoznati parametri modela ocenjeni supomo´cu prilagod¯enih tehnika ocenjivanja. Efikasnost ocena je testirana na simuliranimpodacima. Kvalitet modela ispitan je na odgovaraju´cim realnim nizovima podataka. UGlavi 4 pristupa se adaptaciji K-means tehnike klasterovanja, sa ciljem da se ona prilagodi ocenjivanju stanja okoline realizacija koje odgovaraju uopˇstenoj INAR vremenskoj seriji u sluˇcajnoj okolini. Efikasnost adaptacije testirana je na simuliranim podacimai upored¯ena sa rezultatima klasterovanja dobijenim pomo´cu standardne K-means tehnike. - Nastić, Aleksandar, 1978- Popović, Božidar V., 1979- Milošević, Marija G., 1982- Popović, Predrag, 1982- Đorđević, Miodrag, 1974- Dimitrijević, Slađana, 1975- Contribution to the theory of random environment integer-valued autoregressive processes: doctoral dissertation info:eu-repo/semantics/baccalaureateDissertation 2022 Pirković, Bogdan, 1988- https://phaidrakg.kg.ac.rs/o:1579 cobiss:82016009 thesis:8620