Change in the coefficients or in the mean of the innovation of an INAR(p) process is a sign of disturbance that is important to detect. The proposed methods can test for change in any one of these quantities separately, or in any collection of them. They make both one-sided and two-sided tests possible, furthermore, they can be used to test against the 'epidemic' alternative. The tests are based on a CUSUM process using CLS estimators of the parameters. Under the one-sided and two-sided alternatives consistency of the tests is proved and the properties of the change-point estimator are also explored.
In the paper a change detection procedure is introduced for integervalued autoregressive processes which are inspired by the ordinary autoregressive model. The power of the test is investigated in a simulation study to determine how effectively it can detect changes in the key parameters of the process.Zusammenfassung: In diesem Artikel schlagen wir eine Methode vor, die für das Erkennen von Veränderungen in einem ganzzahligen autoregressiven Prozess gebraucht werden kann. Dann wird eine Simulationsstudie ausgeführt, um zu bestimmen, wie oft der Test eine Veränderung in den verschiedenen Parametern ermitteln kann.
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified parameters.
AcknowledgmentsThis thesis could never have been written without the help of a great many people.First and foremost, I am eternally grateful to my advisor, Professor Gyula Pap, who has been an extraordinary mentor to me throughout the years, and even dealt with my occasional displays of stereotypical graduate-student behavior gracefully. He has constantly opened up new avenues of research (many of which are still unexplored), and accompanied me every step of the way. A glance at the references at the end of this thesis will convince the reader about the results of the school he has built over the years, which I am proud to be a student of.Mátyás Barczy has been a very supportive co-author, and the incredible keenness of his eye has uncovered numerous mistakes, both large and small, in my manuscripts. The Bolyai Institute has been an outstanding place for study, and for starting my scientific career; I have received nothing but kind assistance from every teacher and colleague I had there.In particular, Gábor Szűcs has taught me most of what I know about the foundations of probability theory, and through his example in the teaching and practice of mathematics he has influenced me more in these matters than almost anyone else. I also owe thanks to my I cannot imagine ever coming this far without my extended family. They have stood with me through the good times and the bad, and have always provided me with a stable foundation, which is essential in completing any enterprise. I am, and will always be, deeply indebted to my parents, who first kindled my intellectual curiosity, to my sister, and especially to my lovely wife, who has witnessed firsthand the emotional hardships that were unavoidable in the process of putting this thesis together, had to relieve me of my parental duties when deadlines were around the corner, and yet never wavered in her support. My dear sons have successfully prevented me from sleeping through late-night flashes of intuition, and cheered me up when the writing became too difficult.I am blessed to have so many good people standing by me. One way or another, big or small, they all had a hand in this thesis, except for the errors -those are mine alone.
We propose a change detection method for the famous Cox-Ingersoll-Ross model. This model is widely used in financial mathematics and therefore detecting a change in its parameters is of crucial importance. We develop one-and two-sided testing procedures for both drift parameters of the process. The test process is based on estimators that are motivated by the discrete time least-squares estimators, and its asymptotic distribution under the no-change hypothesis is that of a Brownian bridge. We prove the asymptotic weak consistence of the test, and derive the asymptotic properties of the change-point estimator under the alternative hypothesis of change at one point in time.
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