Comparing%20Realized%20and%20Bi-Power%20Variation%20in%20Lee-Mykland%20Statistic

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Comparing Realized and Bi-Power Variation in
Lee-Mykland Statistic

• Warren Davis
• April 11 Presentation

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Outline

• Discussion of Lee-Mykland
• Change of Statistic
• Simulation Set-Up
• Simulation Results
• Future Directions

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Lee and Mykland (2006)
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The Bi-Power multiplied term in the denominator
of the statistic was replaced by a simple
realized variance, with a sum of returns squared,
as was used in the BNS statistics earlier in the
course
This statistic was run on Bristol-Myers stock
data, yielding 713 hits, as opposed to 1912 with
the Bi-Power statistic.
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Simulation Set-Up

• The following random variables were used
• A set of normally distributed returns with
  mean0, St. Dev. .015 (95 of returns less than
  3)
• A random Poisson variable with mean .01
• A normally distributed variable with mean 0, St.
  Dev..1 or .05

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Simulation Set-Up

• The Poisson integers were multiplied by the
  second random normal distribution to create a
  series of jumps
• These jumps were added to the original normally
  distributed returns
• The Bi-Power and Realized Variance versions of
  Lee-Mykland were then ran on the data, seeing how
  accurately they performed in flagging jumps

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Simulation Results- No Jumps Added

• Bi-Power Results

Realized Variance Results
Bi-Power Results
Realized Variance Results
of Hits 28.03
7.54 (4.57) (2.68)
of Hits 28.03
7.54 (4.57) (2.68)
Returns Flagged .2803 .0754

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Results- Poisson Integer Jumps
Bi-Power Results
Realized Variance Results
Hits False
10.60 3.07
Correct Hits .98.17
99.05
Jumps Missed
.9569 1.609
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Poisson x N(0,.0025)
Bi-Power Results
Realized Variance Results
Hits False
21.62 5.65
Correct Hits 35.05
23.81
Jumps Missed 62.67
76.19
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Poisson x N(0,.01)
Bi-Power Results
Realized Variance Results
Hits False
19.31 4.47
Correct Hits 53.33
32.76
Jumps Missed 37.27
67.77
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Future Directions

• GET RV TO WORK
• Explore iteration process of removing jumps, then
  retesting results
• Explore other estimators of local variance and
  test these, particularly exponential variations
  of bi-power