1. Second Attempt at Jump-Detection and Analysis
Mike Schwert
ECON201FS
2/13/08

2. My Approach This Week
Last time, found too many jump days. Likely explanations include microstructure noise from using minute-by-minute prices and accidental inclusion of overnight returns in intraday calculations.
This time, rewrote code to sample prices at 5 minute frequency and exclude overnight returns. Recalculated summary statistics and number of jump days.
Examined effect of sampling frequency on jump detection by calculating z-statistics and counting jump days for 5, 10, 15, and 20 minute sampling frequencies.
Examined effect of sampling frequency on volatility calculations by creating volatility signature plots for realized variance and bipower variation.

3. GE Stock Prices (5 minute frequency)
Note: Closed at on 9/10/01, opened at on 9/17/01, bottomed out at on 9/21/01

4. Statistics Calculated
Realized Variance:
Bipower Variation:
Relative Jump:

5. Statistics Calculated
Tri-Power Quarticity:
Quad-Power Quarticity:
Z-Statistic:

6. Summary Statistics variable mean std. dev min max Realized Variance
0.0111
Bipower
Variation
x 10-4
x 10-4
x 10-6
0.0092
Relative Jump
0.0601
0.1152
0.6221
Tri-power
Quarticity
x 10-7
x 10-6
x 10-11
x 10-4
Quad-power
x 10-7
x 10-6
x 10-4
ZQP-max
Statistic
0.6545
1.2069
6.9951

7. ZQP-max Statistics – 5 minute sampling frequency
Number of jumps at 1% level of significance: 234 out of 2670 days (8.76%)
Number of jumps at 0.1% level of significance: 84 out of 2670 days (3.15%)
Number of jumps at 0.01% level of significance: 29 out of 2670 days (1.09%)
Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

8. ZQP-max Statistics – 10 minute sampling frequency
Number of jumps at 1% level of significance: 186 out of 2670 days (6.97%)
Number of jumps at 0.1% level of significance: 60 out of 2670 days (2.25%)
Number of jumps at 0.01% level of significance: 17 out of 2670 days (0.64%)
Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

9. ZQP-max Statistics – 15 minute sampling frequency
Number of jumps at 1% level of significance: 148 out of 2670 days (5.54%)
Number of jumps at 0.1% level of significance: 42 out of 2670 days (1.57%)
Number of jumps at 0.01% level of significance: 13 out of 2670 days (0.49%)
Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

10. ZQP-max Statistics – 20 minute sampling frequency
Number of jumps at 1% level of significance: 141 out of 2670 days (5.28%)
Number of jumps at 0.1% level of significance: 40 out of 2670 days (1.50%)
Number of jumps at 0.01% level of significance: 11 out of 2670 days (0.41%)
Note: 1% significance when Z > 2.33, 0.1% significance when Z > 3.09, 0.01% significance when Z > 3.71.

11. Volatility Signature Plots
Used idea introduced by Andersen, Bollerslev, Diebold, and Labys (1999).
Calculated mean daily realized variance and bipower variation over the sample period under sampling frequencies of 1 minute, 2 minutes, …, 30 minutes.
Plotted mean realized variance and bipower variation on the y-axis with sampling frequency on the x-axis.
RV and BV are higher for high-frequency samples because returns are distorted by microstructure noise such as bid-ask bounce.
RV and BV decrease as interval between samples increases because microstructure noise is cancelled out.
Must be wary of using too low of a sampling frequency, as sampling variation will affect volatility calculations.
Balance between sampling variation and microstructure noise appears to be reached around 15 minute sampling frequency.

12. Volatility Signature Plot – Realized Variance

13. Volatility Signature Plot – Bipower Variation

14. Possible Extensions
Perform same calculations on S&P 100 index and stocks highly correlated with GE, or those with similar beta, or from a similar industry, etc.
Check whether GE jumps on the same days as these other assets.
Determine how much jumps are systematic vs. idiosyncratic.
Use volatility signature plots from several stocks to determine ideal sampling frequency for jump detection, if possible.
Incorporate ARCH, GARCH, or stochastic volatility models somehow?