1. Sampling Frequency and Jump Detection
Mike Schwert
ECON201FS
2/27/08

2. This Week’s Approach Last time:
Counted jump days at various sampling frequencies
Volatility signature plots for RV and BV
This week:
Semivariance calculations for GE price data
Volatility signature plots for RJ, RS- and RS+
Counted common jump days between different sampling frequencies
Correlation matrices for ZQP-max statistics at different sampling frequencies

3. Realized Semivariance
Introduced by Barndorff-Nielsen, Kinnebrock, and Shephard
Separates positive and negative components of realized variance
Summary Statistics – GE Price Data, 5-minute sampling frequency
Mean
Std. Dev
Min
Max
RVolannualized
0.2562
0.3117
0.0529
1.6693 RV
x 10-4
x 10-4
x 10-5
0.0111
RS-
x 10-4
x 10-4
x 10-6
0.0041
RS+
x 10-4
x 10-4
x 10-6
0.0069

4. Volatility Signature Plots
Introduced by Andersen, Bollerslev, Diebold, and Labys (1999).
Calculate RJ, RS-, RS+ at 1, 2, …, 30 minute sampling frequencies
Plot relationship between sampling frequency and mean RJ, mean RS
RJ and RS are higher for high-frequency samples because returns are distorted by microstructure noise such as bid-ask bounce
Must be wary of using too low of a sampling frequency, as sampling variation will affect volatility calculations

5. Volatility Signature Plot – Relative Jump

6. Volatility Signature Plot – Negative Semivariance

7. Volatility Signature Plot – Positive Semivariance

8. Contingency and Correlation Matrices
Calculated ZQP-max statistics and counted jump days for GE, ExxonMobil, AT&T, and S&P 500 at 5, 10, 15 and 20 minute sampling frequencies
Counted common jump days between each sampling frequency and organized in contingency matrices
Surprisingly few common jump days exist between sampling frequencies
Calculation of jump days seems to depend a great deal on sampling choices
ZQP-max statistics are relatively uncorrelated between sampling frequencies
GE data minute-by-minute for 1997 – 2007 (2670 days)
ExxonMobil data minute-by-minute for 1999 – 2008 (2026 days)
AT&T data minute-by-minute for 1997 – 2008 (2680 days)
S&P data every 5 minutes, 1985 – 2007 (5545 days, excluding short days)

9. Contingency Tables GE S&P 500 Exxon Mobil AT&T freq 5-min 10-min84 5 1 60 4 42 40
freq
5-min
10-min
15-min
20-min
151 10 5 8 95 92 6 76
Exxon Mobil
AT&T
freq
5-min
10-min
15-min
20-min 48 6 1 34 5 4 31 28
freq
5-min
10-min
15-min
20-min
185 22 8 7
113 11 94 16 76

10. Correlation Matrices - Z-StatisticsGE
S&P 500 – N/A
freq
5-min
10-min
15-min
20-min
1.000
.1030
.0150
.0431
.2241
.0969
.2809
freq
5-min
10-min
15-min
20-min
1.000
NaN
Exxon Mobil
AT&T
freq
5-min
10-min
15-min
20-min
1.000
.0849
.0728
.0631
.2274
.1273
.2996
freq
5-min
10-min
15-min
20-min
1.000
.1644
.0844
.0607
.2694
.1753
.3270

11. Possible Extensions
Try other jump test statistics to see if one outperforms the others in detecting jumps consistently between sampling frequencies
Regress z-statistics on changes in daily volume to see if days with high volume correspond to jump days, common jump days between samples
Other ways to formally analyze effects of sampling frequency on jump detection?
Any way to separate negative jumps from positive jumps?
Effect of sampling frequency on volatility forecasts?