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220201018188
Aalto University publication series
DOCTORAL DISSERTATIONS 214/2018
Change-point analysis in predictive
relationships
Olga Gorskikh
Aalto University
School of Business
Department of Information and Service Management
Supervising professor
Assistant Professor Doctor Pekka Malo, Aalto University, Finland
Thesis advisor
Assistant Professor Doctor Pauliina Ilmonen, Aalto University, Finland
Preliminary examiners
Assistant Professor Doctor Klaus Nordhausen, Vienna University of Technology, Austria
Assistant Professor Doctor Germain Van Bever, Université de Namur, Balgium
Opponent
Assistant Professor Doctor Germain Van Bever, Université de Namur, Balgium
Aalto University publication series
DOCTORAL DISSERTATIONS 214/2018
© 2018 Olga Gorskikh
ISBN 978-952-60-8271-4 (printed)
ISBN 978-952-60-8272-1 (pdf)
ISSN 1799-4934 (printed)
ISSN 1799-4942 (pdf)
http://urn.fi/URN:ISBN:978-952-60-8272-1
Unigrafia Oy
Helsinki 2018
Finland
Abstract
Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi
Author
Olga Gorskikh
Name of the doctoral dissertation
Change-point analysis in predictive relationships
Publisher School of Business
Unit Department of Information and Service Management
Series Aalto University publication series DOCTORAL DISSERTATIONS 214/2018
Field of research Quantitative methods
Date of the defence 23 November 2018
Language English
Monograph Article dissertation Essay dissertation
Abstract
Data is the foundation of the Information Age. Knowing how to perform proper data analysis is
essential and unavoidable for most companies today because it gives meaning to meaningless
numbers and shows the hidden insights of information behaviour. From this perspective, change-
point analysis is one of the most interesting and crucial fields, as it studies change detection in data
structures and the way these changes affect underlying relationships.
Change-point analysis has a considerably long history. However, the biggest part of the proposed
techniques in this field are designed with a number of model restrictions, which significantly
reduces the number of possible applications. In this Dissertation, we aim to study and develop
robust approaches to solve the change detection problem in high-dimensional predictive
structures. In Essay I, we develop a technique that allows to estimate the unknown number of
changes in large datasets under normality assumptions. The proposed approach, called PSA
(Parametric Splitting Algorithm), appears to be considerably accurate and efficient.
In Essay II, we study away to extend the PSA method to nonparametric settings and test it with
different artificial datasets. We describe this extension as the new algorithm NSA (Nonparametric
Splitting Algorithm), which solves the change detection problem in a robust manner.
In Essay III, we continue considering the same problem and present the new method NDP
(Nonparametric Dynamic Programming) along with the proofs of its consistency. We test NDP
against NSA and other baselines and conclude that, although NDP has a higher accuracy, NSA is
still more preferred due to its computational efficiency. Finally, we apply NSA to news analytics to
study the financial crisis of 2006–2009.
Taken all together, the Essays in this Dissertation present the continuous development of the ideas
towards finding a robust solution for structural changepoint detection problems in predictive
relationships.
Keywords data analysis, structural change, time-series, predictive relationships
ISBN (printed) 978-952-60-8271-4 ISBN (pdf) 978-952-60-8272-1
ISSN (printed) 1799-4934 ISSN (pdf) 1799-4942
Location of publisher Helsinki Location of printing Helsinki Year 2018
Pages 132 urn http://urn.fi/URN:ISBN:978-952-60-8272-1

Preface
"IwillnevercomebacktoFinland".
"Iwillalwayshatestatistics".
"Economicsisnotarealscience".
Theseweremyactualwordsintheyear2013. Fiveyearslater,I’mdefending
aPhDinEconomicsdealingwithstatisticsatAaltoUniversity,Finland. Little
didIknowthatmyviewswouldchangethatdrastically. Indeed,change-point
analysisiscrucialnotonlywithrespecttonumericaldata,butwithrespectto
ourlivesaswell.
Alltheselife-shiftingchangeswouldhaveneverhappenedwithoutthepeo-
ple by whom I’ve been surrounded for the last four years. People like Pekka
Malo. Pekka,beingthemostsupportivesupervisoronecouldeverwishfor,has
taughtmetonevergiveuponmydreamsandgoals. TogetherwithPauliina
Ilmonen,anotheroutstandingsupervisorIwashappytohaveguidingme,they
notonlyhelpedmetobecomeabetterscientistbutalsomademefeelwelcomed
inFinnishsociety.
ThisDissertationwouldhaveneverseenthelightofdaywithouthelpfromthe
personwhohasbeenaconstantinspirationthroughmywholelife–mymother.
Mom,youhavebeenthereformeduringmyfirststepsasachildandmyfirst
stepsasascientist. Thankyou.
Iwouldalsoliketothankpeoplewhotaughtmetoseethebeautyofscience
whileIwasstudyingattheNationalResearchNuclearUniversityMEPhI.These
peopleareValeriiGalkinandSergeyErmakov(headsoftheAppliedMathemat-
ics Department at the time of my studies). Additionally, with the help of my
formersupervisor,AndreiAndrianov,Irealizedthatscientificresearchcanbea
fruitfulprocessthatletsyouenjoyyourwork.
Abunchwhodeservesaspecialplaceinthisprefacearemyfriends. Notonly
becauseIlovethem,butbecausetheywon’ttalktomeifIamnottomention
1
Preface
themhere. AntonFrantsev,thanksformakingmydaysinAcademiafulloffun
and joy. Victoria Budarina, as you have always believed in me, I will always
believe in you and our friendship, which began when we were only six years
old. Andofcoursemydearestfriendsandsisters,NinaGorskikhandGalina
Gorskikh: yourhard-workingnaturehasalwaysbeenaninspirationforme.
Iamatrulyluckypersonasatthebeginningofmypathtowardsthisachieve-
mentIhavemetthebestpersonofmylife–mybelovedhusbandPavelSelezniov.
Thankyouforyoursupport,yourlove,andyourpatience. Iwillalwayscherish
it. ThisDissertationisyoursaswell.
Helsinki,October31,2018,
OlgaGorskikh
2
Contents
Preface 1
Contents 3
ListofPublications 5
Author’sContribution 7
1. Introduction 9
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Objectivesandresearchproblem . . . . . . . . . . . . . . . . . . 11
2. Change-pointanalysis 13
2.1 Problemsetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Useofenergydistanceinstructuralchangedetection . . . . . . 14
2.3 Overviewoftheliterature . . . . . . . . . . . . . . . . . . . . . . 16
2.3.1 Parametrictechniques. . . . . . . . . . . . . . . . . . . 17
2.3.2 Nonparametrictechniques . . . . . . . . . . . . . . . . 19
2.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.1 Inflationmodelling . . . . . . . . . . . . . . . . . . . . . 20
2.4.2 Stockreturnmodelling . . . . . . . . . . . . . . . . . . 21
2.4.3 Wagegrowthmodelling . . . . . . . . . . . . . . . . . . 21
2.4.4 Bioinformaticalmodelling . . . . . . . . . . . . . . . . 22
2.4.5 Climatologicalmodelling . . . . . . . . . . . . . . . . . 22
2.4.6 Financialnewsanalytics . . . . . . . . . . . . . . . . . 22
2.4.7 Possiblefutureapplications . . . . . . . . . . . . . . . 23
3. Summaryoforiginalarticles 25
3.1 EssayI:SplittingAlgorithmforDetectingStructuralChanges
inPredictiveRelationships . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Essay II: Nonparametric Splitting Algorithm for Detecting
StructuralChangesinPredictiveRelationships . . . . . . . . . 26
3
Contents
3.3 Essay III: Non-parametric Structural Change Detection in
MultivariateSystems . . . . . . . . . . . . . . . . . . . . . . . . . 27
References 29
Publications 33
4
List of Publications
Thisthesisconsistsofanoverviewandofthefollowingpublicationswhichare
referredtointhetextbytheirRomannumerals.
I OlgaGorskikh. SplittingAlgorithmforDetectingStructuralChangesinPre-
dictiveRelationships. InICDM2016,NewYork,405-419,andotherdetailed
information,June2016.
II Olga Gorskikh, Pekka Malo, Pauliina Ilmonen. Nonparametric Splitting
AlgorithmforDetectingStructuralChangesinPredictiveRelationships. In
ICCDA2017,Lakeland,FL,USA,143-149,May2017.
III Pekka Malo, Lauri Vitasaari, Olga Gorskikh, Pauliina Ilmonen. Non-
parametricStructuralChangeDetectioninMultivariateSystems. Submitted
toJournaloftheAmericanStatisticalAssociation,May2018.
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