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Quadratic sample entropy as a measure of burstiness: A study in how well Rényi entropy rate and quadratic sampleentropy can capture the presence of spikes in time-series data
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2017 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Requests to internet servers do not in general behave in a manner which can be easily modelled and forecast with typical time-series methods, but often have a significant presence of spikes in the data, a property we call “burstiness”. In this thesis we study various entropy measures and their properties for different distributions, both theoretically and via simulation, in order to better find out how these measures could be used to characterise the predictability and burstiness of time series. We find that a low entropy can indicate a heavy-tailed distribution, which for time series corresponds to a high burstiness. Using a previous result that connects the quadratic sample entropy for a time series with the Rényi entropy rate of order 2, we suggest a way of detecting burstiness by comparing the quadratic sample entropy of the time series with the Rényi entropy rate of order 2 for a symmetric and a heavy-tailed distribution.

Abstract [sv]

Anrop till internetservrar beter sig i allmänhet inte på sätt som lätt kan modelleras och prediceras med typiska tidsseriemetoder, utan har ofta en signifikant andel spikar i datan, en egenskap som kallas “burstiness” (adekvat svensk översättning saknas). I den här uppsatsen studerar vi diverse entropimått och deras egenskaper för olika fördelningar, både teoretiskt och via simulering, för att kunna ta reda på hur dessa mått kan användas för att karaktärisera förutsägbarhet och burstiness hos tidsserier. Vi finner att en låg entropi kan indikera en tungsvansad fördelning, vilket för tidsserier motsvarar hög burstiness. Genom att använda ett tidigare resultat som sammankopplar kvadratisk stickprovsentropi med Rényis entropitakt av ordning 2 föreslår vi ett sätt att upptäcka burstiness genom att jämföra den kvadratiska stickprovsentropin för en tidsserie med Rényis entropitakt av ordning 2 för en symmetrisk och en tungsvansad fördelning.

Place, publisher, year, edition, pages
2017. , 37 p.
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:umu:diva-130593OAI: oai:DiVA.org:umu-130593DiVA: diva2:1068270
Supervisors
Examiners
Available from: 2017-01-30 Created: 2017-01-30Bibliographically approved

Open Access in DiVA

fulltext(828 kB)58 downloads
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Department of Mathematics and Mathematical Statistics
Probability Theory and Statistics

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • text
  • asciidoc
  • rtf