On the detection of changes in autoregressive time series I. Asymptotics

Hušková, Marie; Prášková, Zuzana; Steinebach, Josef

doi:10.1016/j.jspi.2006.02.010

Cited by 63 publications

(43 citation statements)

References 10 publications

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“…Conversely, the segmentation produced by BS does not (Figure 4 Changes in AR models have been considered by many authors including Davis et al (2006), Huskova et al (2007) and Gombay (2008). This section describes a simulation study that compares the properties of PELT and the genetic algorithm used in Davis et al (2006) to implement the minimum description length (MDL) test statistic.…”

Section: Application To Canadian Wave Heightsmentioning

confidence: 99%

Optimal Detection of Changepoints With a Linear Computational Cost

Killick

Fearnhead

Eckley

2012

Journal of the American Statistical Association

1,627

1,426

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We consider the problem of detecting multiple changepoints in large data sets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example in genetics as we analyse larger regions of the genome, or in finance as we observe time-series over longer periods. We consider the common approach of detecting changepoints through minimising a cost function over possible numbers and locations of changepoints. method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost which, under mild conditions, is linear in the number of observations. This compares favourably with existing methods for the same problem whose computational cost can be quadratic or even cubic. In simulation studies we show that our new method can be orders of magnitude faster than these alternative exact methods. We also compare with the Binary Segmentation algorithm for identifying changepoints, showing that the exactness of our approach can lead to substantial improvements in the accuracy of the inferred segmentation of the data.

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Section: Application To Canadian Wave Heightsmentioning

confidence: 99%

Optimal Detection of Changepoints With a Linear Computational Cost

Killick

Fearnhead

Eckley

2012

Journal of the American Statistical Association

1,627

1,426

View full text Add to dashboard Cite

show abstract

“…This result is slightly stronger than the similar Proposition 3.1 in Hušková et al (2007). Similar results are valid for change in a location parameter (see Csörgő and Horváth, 1997), and in these cases the limit distribution is nondegenerate.…”

Section: 82supporting

confidence: 70%

“…The following theorem, the analogue of Theorem 3.1 in Hušková et al (2007), describes the behavior of the maximum of the test process if a change occurs in the mean of the innovation. An immediate consequence of the theorem is that the test statistic tends to infinity stochastically as n → ∞, which suffices for the weak consistency of the proposed test.…”

Section: Consistency Of the Testmentioning

confidence: 99%

“…We will follow the proof of Lemma 4.2 in Hušková et al (2007) and apply Lemma 2.9.1 with c k = k γ−1 and Y i,q = X i−1−q − E(X i−1−q ) for 0 q p − 1 to show that the result holds for each component of the vectors. This implies convergence of the 1-norm, and because of the equivalence of vector norms, it is sufficient for the proof of the statement.…”

Section: 82mentioning

confidence: 99%

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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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“…The approach we take is in the spirit of Chu, Stinchcombe, and White (1996), a paper which has been the foundation for many subsequent developments in the sequential monitoring of stochastic processes. Contributions to the area include, but are not limited to, Leisch, Hornik, and Kuan (2000), Zeileis et al (2005), Aue et al (2006), and Hušková, Prašková, and Steinebach (2007). A recent survey of research in the area is given in Aue and Horváth (2013).…”

Section: Functional Monitoringmentioning

confidence: 99%