Jump Correlation within an Industry

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Jump Correlation within an Industry A Beginning
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• By Zed Lamba

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Background Mathematics
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• All data is for a 10 year period
• 5-minute returns examined to minimize
  microstructure noise
• Use log returns and daily realized variation
• Tri-power and quad-power quarticity
• Test Statistics (jump if exceeds critical value
  of 3.09, a .001 significance level)

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MSFT Prices Line Graph
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MSFT Prices Scatter Plot
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MSFT Max Test Statistics I
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MSFT Max Test Statistics II
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IBM Prices Line Graph
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IBM Prices Scatter Plot
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IBM Max Test Statistics I
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IBM Max Test Statistics II
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HPQ Prices Line Graph
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HPQ Prices Scatter Plot
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HPQ Max Test Statistics I
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HPQ Max Test Statistics II
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Summary Statistics
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Mean StDev Min Max Jumps MSFT ztpmax 0.6232
1.1551 -2.5599 6.1618 76 zqpmax 0.6492 1.1902 -2.
5201 6.1616 91 IBM ztpmax 0.5485 1.158 -2.42
56 5.3807 76 zqpmax 0.5733 1.1964 -2.3353 5.4534
87 HPQ ztpmax 0.794 1.2239 -2.6778 5.201
124 zqpmax 0.8394 1.2834 -2.4821 5.7732 146
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Correlation Calculation
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• If both companies are being compared over 10
  days, and
• the 1st has jumps on days 1, 4, and 6
• the 2nd has jumps on days 2, 5, and 9
• Then simply create two arrays of size 3, one with
  1, 4, and 6 and the other with 2, 5, and 9
• Then calculate the correlation between the two
  arrays

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High Positive Correlation
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• Using technique previously described, and the
  good fortune that according to Tri-Power
  Quarticity Max Statistics, MSFT and IBM had the
  same number of jumps (76) from 1997 2008, the
  correlation coefficient is an astounding 0.9762!

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Size inequalities will occur
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• However, for the most part, the number of jumps
  will differ over the same range
• Correlation calculation requires arrays of the
  same size
• Possible solutions
• Fill up smaller array with average of other data
  points (days on which jump occurred)
• Prune down bigger array by only looking at
  biggest jumps (problem what if a small jump
  correlates with a big jump in another company?)
• Other ideas?

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Questions for discussion with audience
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• For comparing with limited data (ex GOOG),
  should jumps over the same range be examined for
  comparison and correlation calculation (ex 2004
  2008 for both MSFT and GOOG)?
• Possible regression to explain jumps
• JumpsMSFT B1(JumpsIBM) B2(JumpsHPQ) all
  other technology firms
• Will all arrays have to be over same range as
  that of the smallest array (so if GOOG were
  included in calculation, would we have to
  restrict all the firms data being considered to
  the range 2004 2008?