Original title: Bilineární model pro časové řady
Translated title: A bilinear model for time series
Authors: Čorejová, Katarína ; Zichová, Jitka (advisor) ; Vejmělka, Petr (referee)
Document type: Bachelor's theses
Year: 2024
Language: slo
Abstract: [eng] [cze]
Title: A bilinear model for time series Author: Katarína Čorejová Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Jitka Zichová, Dr., Department of Probability and Mathema- tical Statistics Abstract: The bilinear model is used to describe the structure of non-linear time series. In this thesis, we discuss the bilinear model BL(P,0,P,1). The main goal is to derive conditions for the first-order and the second-order stationarity, to present its moment and covariance structure, to derive the condition for invertibility and to discuss the method of estimating parameters. The theoretical part of this thesis also presents a test of linearity, which enables to test the presence of the bilinear effect in a given time series. In the following simulation study, we apply the theory to several generated time series from the BL(1,0,1,1) model. Depending on the chosen parameters and length of the generated time series, we examine the accuracy of parameter estimation, the empirical level and the empirical power of the test of linearity. Keywords: time series, bilinear model, stationarity, invertibility, parameter esti- mation, linearity testing. 1 Názov práce: Bilineárny model pre časové rady Autor: Katarína Čorejová Katedra: Katedra pravděpodobnosti a matematické statistiky Vedúci bakalárskej práce: RNDr. Jitka Zichová, Dr., Katedra pravděpodobnosti a matematické statistiky Abstrakt: Bilineárny model je schopný popísat' správanie nelineárnych časových radov. V tejto práci sa primárne venujeme bilineárnemu modelu BL(P,0,P,1). Ciel'om je odvodit' podmienky stacionarity prvého a druhého rádu, ukázat' jeho momentovú a kovariančnú štruktúru, odvodit' podmienku invertibility a uviest' metódu odhadovania parametrov. Súčast'ou teoretickej časti je aj zavedenie testu linearity, ktorý je schopný overit' prítomnost' bilineárneho efektu v danom časovom rade. V praktickej časti práce aplikujeme teóriu na generované časové rady z modelu BL(1,0,1,1). Na jej základe následne skúmame presnost' odhadov para- metrov, empirickú hladinu a empirickú silu testu linearity, v závislosti od vol'by parametrov modelu a d'lžky generovaných radov. Kl'účové slová: časový rad, bilineárny model, stacionarita, invertibilita, odhad parametrov, test linearity. 1
Keywords: time series|bilinear model|stationarity|invertibility|parameter estimation|linearity testing; časový rad|bilineárny model|stacionarita|invertibilita|odhad parametrov|test linearity

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/192010

Permalink: http://www.nusl.cz/ntk/nusl-621486


The record appears in these collections:
Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses