Test Statistics for Parameter Changes in INAR(p) Models and a Simulation Study

Szabó, Tamás T.

doi:10.17713/ajs.v40i4.216

Cited by 8 publications

(6 citation statements)

References 9 publications

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“…Finally, we compare the results for our tests with the procedure suggested in Szabó (), where an offline test for a parameter change in INAR( p ) models is proposed. The test is based on a CUSUM process, and it can be adapted to the online monitoring in a standard way.…”

Section: Simulations and Real Datamentioning

confidence: 99%

“…Their offline procedure detected a change at 35th observation. Pap & Szabó () modelled the data using INAR(1) and tested for a change point using a procedure from Szabó (), but their test statistic did not reveal any change.…”

Section: Simulations and Real Datamentioning

confidence: 99%

“…This aspect is relatively new in the literature of time series of counts. The interested reader is referred to Fokianos & Fried (), Szabó (), Franke et al (), Weiss & Testik (), Weiss (), Hudecová () and Kang & Lee (). Most recently, Kirch & Tadjuidje Kamgaing () developed retrospective change‐point statistics on the basis of general principles, which allow the corresponding detectors to be applied in a variety of situations.…”

Section: Introductionmentioning

confidence: 99%

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Tests for Structural Changes in Time Series of Counts

Hudecová¹,

Hušková²,

Meintanis

2017

Scandinavian J Statistics

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We propose methods for detecting structural changes in time series with discretevalued observations. The detector statistics come in familiar L2-type formulations incorporating the empirical probability generating function. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. For both models, we study mainly structural changes due to a change in distribution, but we also comment for the classical problem of parameter change. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is also included along with a real data example.

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Section: Simulations and Real Datamentioning

confidence: 99%

Section: Simulations and Real Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tests for Structural Changes in Time Series of Counts

Hudecová¹,

Hušková²,

Meintanis

2017

Scandinavian J Statistics

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“…In the field of integer-valued time series, Fokianos and Fried [ 6 , 7 ] investigated a testing procedure for the detection of intervention effects in linear and log-linear Poisson autoregressive (AR) models. Szabó [ 8 ] proposed the test for a change in several crucial parameters of integer-valued autoregressive (INAR) (p) models. Kang and Lee [ 5 , 9 ] constructed the estimate-based cumulative sum (CUSUM) tests for parameter change in random coefficient integer-valued autoregressive (RCINAR) models and Poisson AR models, respectively.…”

Section: Introductionmentioning

confidence: 99%

Detection of Parameter Change in Random Coefficient Integer-Valued Autoregressive Models

Kang

2018

Entropy

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This paper considers the problem of testing for parameter change in random coefficient integer-valued autoregressive models. To overcome some size distortions of the existing estimate-based cumulative sum (CUSUM) test, we suggest estimating function-based test and residual-based CUSUM test. More specifically, we employ the estimating function of the conditional least squares estimator. Under the regularity conditions and the null hypothesis, we derive their limiting distributions, respectively. Simulation results demonstrate the validity of the proposed tests. A real data analysis is performed on the polio incidence data.

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“…We briefly recall the motivation of the test process as given in T. Szabó (2011b). Due to the martingale central limit theorem,…”

Section: Construction Of the Testmentioning

confidence: 99%

Change detection problems in branching processes

Szabó

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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.

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Test Statistics for Parameter Changes in INAR(p) Models and a Simulation Study

Cited by 8 publications

References 9 publications

Tests for Structural Changes in Time Series of Counts

Tests for Structural Changes in Time Series of Counts

Detection of Parameter Change in Random Coefficient Integer-Valued Autoregressive Models

Change detection problems in branching processes

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