Statistical and Applied Mathematical Sciences Institute

1
Statistical and Applied Mathematical Sciences
Institute

• Dependent SiZer Goodness of Fit Tests for Time
  Series Models
• Cheolwoo Park, Steve Marron,
• and Vitaliana Rondonotti
• SAMSI
• June 25, 2004

2
Dependent SiZerData Description

• Packet counts at 10ms intervals
• UNC main link in 2002
• 2 hour time blocks
• Different days and times
• http//www-dirt.cs.unc.edu/ts/

3
Dependent SiZerWavelet Spectrum Typical case
Apr 13 Sat 1930
Piecewise linear
4
Dependent SiZerWavelet Spectrum Strange case
Apr 13 Sat 1300
Q What causes the bump? (2-3 sec. periodic
behavior)
5
Dependent SiZerSiZer

• SIgnificance of ZERo crossings of the derivative
  of the smooths in scale space Chaudhuri and
  Marron (1999)
• Exploratory smoothing method
• Are bumps really there?
• Consider all smoothing levels
• Study (simultaneous) C. I.s for slope
  (derivative) of smooth
• Combine statistical inference with visualization
• Blue slope significantly upwards
• Red slope significantly downwards
• Purple insignificant slope

6
Dependent SiZerDependent SiZer

• Park, Marron, and Rondonotti (2004)
• SiZer compares data with white noise
• Inappropriate in time series
• Dependent SiZer compares data with an assumed
  model
• Goodness of fit test

7
Dependent SiZerDependent SiZer 2002 Apr 13 Sat
13 pm
8
Dependent SiZerDependent SiZer 2002 Apr 13 Sat
13 pm (zoom)
9
Dependent SiZerDependent SiZer Sat 1 pm (delete
periodic part)
10
Dependent SiZerSummary 2002 Apr 13 Sat 1 pm 3
pm

• H1.56, Bump in the wavelet spectrum at j8
• Big spike in the middle for 6 minutes in dep.
  SiZer
• Different behavior from FGN with H0.9
• Zooming dependent SiZer 3 seconds periodic
  behavior
• Possible explanation IP port scan

11
Dependent SiZerConclusion More Results

• Goodness of fit test for time series
• Useful for finding strange behavior beyond an
  assumed time series model
• More results
• http//www-dirt.cs.unc.edu/net_lrd/DepSiZer/SiZER_
  View.html
• Many different data sets