Title
Contribution to the theory of random environment integer-valued autoregressive processes: doctoral dissertation
Creator
Pirković, Bogdan, 1988-
CONOR:
25106535
Copyright date
2022
Object Links
Language
English
Cobiss-ID
Inventory ID
3565
Theses Type
Doktorska disertacija
description
Datum odbrane: 03.12.2022.
Other responsibilities
University
Univerzitet u Kragujevcu
Faculty
Prirodno-matematički fakultet
Alternative title
Doprinos teoriji celobrojnih autoregresivnih procesa u slučajnoj okoloini
: doktorska disertacija
Publisher
[B. A. Pirković]
Format
[VI], 117, [2] lista
Abstract (en)
This dissertation has 2 basic goals. The first goal is to construct the random environment
INAR time series that can take both positive and negative values. The realization of
such 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 in
real-life data modeling using models in random environment, the goal is to adapt existing
clustering 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 a
historical overview of the INAR models development. Also, this chapter offers important
theorems and distributions known from before, necessary to adduce proofs in subsequent
chapters. Relying on results given in [15], Chapter 2 discusses possibilities of extracting
and predicting latent components of the true INAR time series with skewed Skellam
marginal distribution. In Chapter 3, a construction of the new non-stationary random
environment INAR model with values over entire Z is given. Unknown model parameters
are estimated using adapted estimation techniques. The efficiency of estimates is tested
on simulated data. A quality of the introduced model is examined on appropriate real-life
data. In Chapter 4, the K-means clustering technique adaptation is provided, in order
to make it suitable for estimating environment states of realizations corresponding to the
generalized random environment INAR time series. The adaptation efficiency is tested
on simulated and real-life data and compared to clustering results obtained using standard K-means.
Abstract (sr)
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 nizova
podataka. Dodatno, kako je ocena stanja okoline svake realizacije kljuˇcni korak u modeliranju stvarnih procesa pomo´cu novouvedenih modela u sluˇcajnoj okolini, cilj disertacije
je prilagod¯avanje postoje´cih metoda klasterovanja sa namerom da ocene stanja budu ˇsto
preciznije. Oba navedena cilja bi, u sluˇcaju realizacije, predstavljala originalan doprinos
autora analizi celobrojnih vremenskih serija.
Disertacija sadrˇzi 4 glave. Glava 1 je uvodnog karaktera i daje istorijski pregled razvoja
INAR 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. U
Glavi 3 pristupa se konstrukciji novog nestacionarnog INAR modela u sluˇcajnoj okolini
koji moˇze uzeti vrednosti na ˇcitavom skupu Z. Nepoznati parametri modela ocenjeni su
pomo´cu prilagod¯enih tehnika ocenjivanja. Efikasnost ocena je testirana na simuliranim
podacima. Kvalitet modela ispitan je na odgovaraju´cim realnim nizovima podataka. U
Glavi 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 podacima
i upored¯ena sa rezultatima klasterovanja dobijenim pomo´cu standardne K-means tehnike.
Authors Key words
INAR(1), DLINAR(1), thinning operator, random environment, discrete Laplace marginals, geometric marginals, K-means technique, state estimation, Markov chain
Authors Key words
INAR(1), DLINAR(1), tining operator, sluˇcajna okolina, diskretna
Laplasova marginalna raspodela, geometrijska marginalna raspodela, K-means tehnika,
ocena stanja, lanac Markova
Classification
519.2(043.3)
Type
Tekst
Abstract (en)
This dissertation has 2 basic goals. The first goal is to construct the random environment
INAR time series that can take both positive and negative values. The realization of
such 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 in
real-life data modeling using models in random environment, the goal is to adapt existing
clustering 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 a
historical overview of the INAR models development. Also, this chapter offers important
theorems and distributions known from before, necessary to adduce proofs in subsequent
chapters. Relying on results given in [15], Chapter 2 discusses possibilities of extracting
and predicting latent components of the true INAR time series with skewed Skellam
marginal distribution. In Chapter 3, a construction of the new non-stationary random
environment INAR model with values over entire Z is given. Unknown model parameters
are estimated using adapted estimation techniques. The efficiency of estimates is tested
on simulated data. A quality of the introduced model is examined on appropriate real-life
data. In Chapter 4, the K-means clustering technique adaptation is provided, in order
to make it suitable for estimating environment states of realizations corresponding to the
generalized random environment INAR time series. The adaptation efficiency is tested
on simulated and real-life data and compared to clustering results obtained using standard K-means.
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