1. Comparing Realized and Bi-Power Variation in Lee-Mykland Statistic
Warren Davis
April 11 Presentation

2. Outline Discussion of Lee-Mykland Change of Statistic
Simulation Set-Up
Simulation Results
Future Directions

3. Lee and Mykland (2006)

4. 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.

5. Simulation Set-Up The following random variables were used:
A set of normally distributed returns with mean=0, Var= .015 (95% of returns less than 3%)
A random Poisson variable with mean .01
A normally distributed variable with mean 0, Var=.1

6. 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

7. Realized Variance Results
Simulation Results
Bi-Power Results
Realized Variance Results
% Hits True
(7.68)
% Jumps Missed
(6.60) (2.60)
% Hits False
(7.69) (3.59)

8. Future Directions Further Examine Window Size
Explore Dr. Eraker’s process of removing jumps, then retesting results
Explore other estimators of local variance and test these