Tests for time series of counts based on the probability-generating function

Hudecová, Šárka; Hušková, Marie; Meintanis, Simos G.

doi:10.1080/02331888.2014.979826

Cited by 14 publications

(18 citation statements)

References 35 publications

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“…In the special cases of INAR(1) and Poisson INARCH(1) processes, a similar result as that of Corollary 2.3 is shown in Hudecová et al (2015), Theorems 4.1 and 4.4 respectively with two differences: First, the authors use the particular structure of these models to obtain semi-parametric estimates of the marginal pgf under the null hypothesis, whereas the structure here is non-parametric, rendering the result viable in a much more general setting. Second, the authors consider the one-dimensional epgf instead of the (two-dimensional) ejpgf; see also Section 5.3.…”

Section: Theorem 22supporting

confidence: 78%

“…In Hudecová et al (2015), a goodness-of-fit test very similar to the one discussed in this article is considered. As an application, the authors analyse several time series previously considered by Freeland (1998).…”

Section: Comparison With Hudecová Et Al (2015)mentioning

confidence: 99%

“…In order to assess differences in performance, the procedure of the previous section is carried out for three selected time series for the same weights a and the same number of bootstrap samples, the results are reported in Table IV. The bold font values are those calculated from Algorithm 1, the others from Table 3 of Hudecová et al (2015).…”

Section: Comparison With Hudecová Et Al (2015)mentioning

confidence: 99%

“…In Meintanis and Karlis (2014), such a test statistic is used in the framework of several INAR(1) processes, the authors present a Monte Carlo power study of the test as well as an application to a real data set. The contribution of Hudecová et al (2015) considers a very similar approach, focusing on the one-dimensional marginal distributions of .Y t / t2Z by basing their test on the empirical probability generating function (epgf), b g T .u/ WD 1 T P T iD1 u y i . They provide asymptotic properties of the proposed test statistics via a semi-parametric approach in the special cases of INAR(1) and Poisson INARCH(1) processes.…”

Section: Introductionmentioning

confidence: 99%

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A Goodness‐of‐Fit Test for Integer‐Valued Autoregressive Processes

Schweer

2015

Journal Time Series Analysis

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For autoregressive count data time series, a goodness-of-fit test based on the empirical joint probability generating function is considered. The underlying process is contained in a general class of Markovian models satisfying a drift condition. Asymptotic theory for the test statistic is provided, including a functional central limit theorem for the non-parametric estimation of the stationary distribution and a parametric bootstrap method. Connections between the new approach and existing tests for count data time series based on moment estimators appear in limiting scenarios. Finally, the test is applied to a real data set.

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Section: Theorem 22supporting

confidence: 78%

Section: Comparison With Hudecová Et Al (2015)mentioning

confidence: 99%

Section: Comparison With Hudecová Et Al (2015)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Goodness‐of‐Fit Test for Integer‐Valued Autoregressive Processes

Schweer

2015

Journal Time Series Analysis

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“…Also, Hudecová et al (2015) used the probability generating function to detect changes in the process. They prove the consistency of their test, but do not give the asymptotics of the change-point estimator.…”

Section: The Inar(p) Processmentioning

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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