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Jump Correlation within an Industry – A Beginning

ECON 201FS. Jump Correlation within an Industry – A Beginning. By: Zed Lamba. ECON 201FS. Background + Mathematics. 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

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Jump Correlation within an Industry – A Beginning

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  1. ECON 201FS Jump Correlation within an Industry – A Beginning By: Zed Lamba

  2. ECON 201FS Background + Mathematics • 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):

  3. ECON 201FS MSFT Prices – Line Graph

  4. ECON 201FS MSFT Prices – Scatter Plot

  5. ECON 201FS MSFT – Max Test Statistics I

  6. ECON 201FS MSFT – Max Test Statistics II

  7. IBM Prices – Line Graph ECON 201FS

  8. IBM Prices – Scatter Plot ECON 201FS

  9. IBM – Max Test Statistics I ECON 201FS

  10. IBM – Max Test Statistics II ECON 201FS

  11. HPQ Prices – Line Graph ECON 201FS

  12. HPQ Prices – Scatter Plot ECON 201FS

  13. HPQ – Max Test Statistics I ECON 201FS

  14. HPQ – Max Test Statistics II ECON 201FS

  15. ECON 201FS Summary Statistics 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 -2.4256 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

  16. ECON 201FS Correlation Calculation • 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

  17. ECON 201FS High Positive Correlation • 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!

  18. ECON 201FS Size inequalities will occur • 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?

  19. ECON 201FS Questions for discussion with audience • 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?

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