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

Comparing Realized and Bi-Power Variation in Lee-Mykland Statistic. Warren Davis April 11 Presentation. Outline. Discussion of Lee-Mykland Change of Statistic Simulation Set-Up Simulation Results Future Directions. Lee and Mykland (2006).

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

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  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, 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

  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. Simulation Results- No Jumps Added Bi-Power Results Bi-Power Results Realized Variance 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

  8. 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

  9. 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

  10. 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

  11. 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

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