Second Attempt at Jump-Detection and Analysis
Mike Schwert
ECON201FS
2/13/08
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 zstatistics 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.
GE Stock Prices (5 minute frequency)
Note: Closed at 39.28 on 9/10/01, opened at 35.50 on 9/17/01, bottomed out at
28.70 on 9/21/01
Statistics Calculated
Realized Variance:
Bipower Variation:
Relative Jump:
Statistics Calculated
Tri-Power Quarticity:
Quad-Power Quarticity:
Z-Statistic:
Summary Statistics
variable
mean
std. dev
min
max
Realized
Variance
2.6053 x 10-4
3.8553 x 10-4
1.1104 x 10-5
0.0111
Bipower
Variation
2.4719 x 10-4
3.7134 x 10-4
8.3864 x 10-6
0.0092
Relative
Jump
0.0601
0.1152
-0.2542
0.6221
Tri-power
Quarticity
3.9150 x 10-7
7.7188 x 10-6
7.8711 x 10-11
3.8164 x 10-4
Quad-power
Quarticity
3.2979 x 10-7
5.8122 x 10-6
0
2.8166 x 10-4
ZQP-max
Statistic
0.6545
1.2069
-2.7547
6.9951
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.
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.
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.
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.
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.
Volatility Signature Plot – Realized Variance
Volatility Signature Plot – Bipower Variation
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?