Sampling Frequency and Jump Detection
Mike Schwert
ECON201FS
2/27/08
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
Realized Semivariance
• Introduced by Barndorff-Nielsen, Kinnebrock, and Shephard
• Separates positive and negative components of realized variance
M
M
RS t   rj 1rj  0

RS t   rj 1rj  0

2
j 1
2
j 1
Summary Statistics – GE Price Data, 5-minute sampling frequency
Mean
Std. Dev
Min
Max
RVolannualized
0.2562
0.3117
0.0529
1.6693
RV
2.6053 x 10-4
3.8553 x 10-4
1.1104 x 10-5
0.0111
RS-
1.2866 x 10-4
1.8166 x 10-4
4.8495 x 10-6
0.0041
RS+
1.3187 x 10-4
2.1816 x 10-4
4.3544 x 10-6
0.0069
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
Volatility Signature Plot – Relative Jump
Volatility Signature Plot – Negative Semivariance
Volatility Signature Plot – Positive Semivariance
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)
Contingency Tables
GE
freq
S&P 500
5-min
10-min
15-min
20-min
5-min
84
5
1
1
10-min
5
60
4
15-min
1
4
20-min
1
5
freq
5-min
10-min
15-min
20-min
5-min
151
10
5
8
5
10-min
10
95
10
5
42
5
15-min
5
10
92
6
5
40
20-min
8
5
6
76
Exxon Mobil
freq
AT&T
5-min
10-min
15-min
20-min
5-min
48
6
1
1
10-min
6
34
5
15-min
1
5
20-min
1
4
freq
5-min
10-min
15-min
20-min
5-min
185
22
8
7
4
10-min
22
113
8
11
31
4
15-min
8
8
94
16
4
28
20-min
7
11
16
76
Correlation Matrices - Z-Statistics
S&P 500 – N/A
GE
freq
5-min
10-min
15-min
20-min
freq
5-min
10-min
15-min
20-min
5-min
1.000
.1030
.0150
.0431
5-min
1.000
NaN
NaN
NaN
10-min
.1030
1.000
.2241
.0969
10-min
NaN
NaN
NaN
NaN
15-min
.0150
.2241
1.000
.2809
15-min
NaN
NaN
NaN
NaN
20-min
.0431
.0969
.2809
1.000
20-min
NaN
NaN
NaN
NaN
Exxon Mobil
AT&T
freq
5-min
10-min
15-min
20-min
freq
5-min
10-min
15-min
20-min
5-min
1.000
.0849
.0728
.0631
5-min
1.000
.1644
.0844
.0607
10-min
.0849
1.000
.2274
.1273
10-min
.1644
1.000
.2694
.1753
15-min
.0728
.2274
1.000
.2996
15-min
.0844
.2694
1.000
.3270
20-min
.0631
.1273
.2996
1.000
20-min
.0607
.1753
.3270
1.000
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?