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Modified segmentation methods of quasi-stationary time series Irina - - PowerPoint PPT Presentation

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Modified segmentation methods of quasi-stationary time series Irina Roslyakova Department of Scale Bridging Thermodynamic and Kinetic Simulation ICAMS (Interdisciplinary Centre for Advanced Materials Simulation) Ruhr-Universitt Bochum, UHW

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SLIDE 1

Modified segmentation methods

  • f quasi-stationary time series

Irina Roslyakova

Department of Scale Bridging Thermodynamic and Kinetic Simulation ICAMS (Interdisciplinary Centre for Advanced Materials Simulation) Ruhr-Universität Bochum, UHW 10/1022 Stiepeler Str. 129, 44801 Bochum Tel.: +49 234 32 22449, Mobil: +49 (163) 196 3327 E-mail: irina.roslyakova@rub.de

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SLIDE 2
  • Problem importance
  • Method of Pedro Bernaola-Galván et al.
  • Modified segmentation algorithm
  • Comparison: Modified segmentation algorithm vs. R-Package

“strucchange”

  • Conclusion

This work is part of my master thesis performed in BASF SE, Germany

Contents

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SLIDE 3

Problem importance

  • Many time series are a sequence of stationary intervals
  • The statistical analysis of such quasi-stationary processes

requires a division of the measurements into different stationary time segments.

  • The segmentation of quasi-stationary time series is a tedious

computational problem

  • For large samples statistical methods will be too time
  • consuming. Heuristics have to be applied.
  • Possible application

Medicine Chemical production processes Internet traffic fluctuations

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SLIDE 4

Method of Pedro Bernaola-Galván et al.

interval

  • f

start from intervall

  • f

end the till

D D right x left x i

S S m m p t , ) ( − =

( )

{ }

2 max

max [ /( )]

( ) 1- ,

t

P t I

η ν ν

δν δ

+

≈

DOI: 10.1103/PhysRevLett.87.168105

is the pooled variance where

2 v N = −

is the number of degrees of freedom,

x

I ( a,b ) is the incomplete beta function

( )

95 .

max

= ≥ P t P l l l l

right left

≥ ≥

and we cut the series at point

( )

max

t p pc =

Statistic t for comparison mean value of two samples is calculated for every position of sliding point p Point p with maximal difference in mean value is checked by using modified T-Test Significance of cutting point p is checked under condition that minimal length of subintervals have to be not less that some used defined value

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SLIDE 5

Analysis of the vapor consumption in a chemical production

Method is sensitive but not robust against significant outliers near boundaries

Vapor consumption Vapor consumption Time

  • utliers

no segmentation 30 days 85 days 30 days 85 days Observation window:

Method of Pedro Bernaola-Galván et al.

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SLIDE 6
  • Bernaola-Galván’s method is sensitive but not robust against significant
  • utliers near boundaries
  • Modification to make algorithm robust against outliers near boundaries

Time Vapor consumption

Observation window: 85 days

Modified segmentation algorithm

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Modified method Pedro Bernaola-Galván

The length of right subinterval is less than minimal allowed value l0

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SLIDE 7

Vapor consumption Time index Vapor consumption Time

Segmentation result are independent of observation window and outliers.

  • utliers

30 days 85 days

Analysis of the vapor consumption in a chemical production

30 days 85 days Observation window:

Modified segmentation algorithm

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SLIDE 8

Pedro Bernaola-Galván Modified method

1 2 3 4 5 6 1 2 3 4 5 6

Segmentation Steps in Comparison

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SLIDE 9

Modified Segmentation: Steps

Vapor consumption

30 days Observation window:

Vapor consumption Vapor consumption Vapor consumption Time Time Time Time

9

30 days 30 days

1

t

2

t

3

t

4

t

1

t

1

t

2

t

1

t

2

t

3

t

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SLIDE 10

Modified segmentation vs. "strucchange"

(+) much faster (0.68 sec) (-) only for breaks in stationary data

Time index

100 200 300 400 500 600 700 0.165 0.175 Vapor concsumption, t/h

Modified segmentation

Time index

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(+) breaks in time series with trends can also be recognized (-) slower (49.08 sec)

Vapor consumption, t/h

R-Package strucchange

Time index

100 200 300 400 500 600 700 0.165 0.175

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SLIDE 11
  • Heuristic method proposed by Pedro Bernaola-Galván et al.

was implemented in R and analyzed

  • Analysis of original segmentation algorithms showed that this

method in not robust to outliers near to bounds

  • Original algorithms was modified and show good resistant to

influence of outliers near bounds

  • Algorithm is limited to stationary segments.
  • The modified segmentation method was compared with

functions breakpoints from R-package strucchange and its computational efficiency was shown

Conclusion

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SLIDE 12

Literature

  • Bernaola-Galván, Pedro; Ivanov, Plamen Ch.; Amaral, Luís A. Nunes; Stanley,
  • H. Eugene: Scale Invariance in the Nonstationarity of Human Heart Rate. In:

Physical review letters (2001), Volume 87, number 16 (abgerufen am 13. August 2009). http://polymer.bu.edu/hes/articles/bias01.pdf

  • Fukuda, Kensuke; Stanley, H. Eugene; Amaral, Luı´s A. Nunes: Heuristic

segmentation of a nonstationary time series. In: Physical review letters 69 (2004).

  • Zeileis, Achim; Leisch, Friedrich; Hansen, Bruce; Hornik, Kurt; Kleiber,

Christian: Package „strucchange“, 2009 (Version 1.3-7 )

  • Zeileis, Achim; Leisch, Friedrich; Hornik, Kurt; Kleiber: strucchange: An R

Package for Testing for Structural Change in Linear Regression Models (Version 1.3-7 ) http://cran.r- project.org/web/packages/strucchange/vignettes/strucchange-intro.pdf

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