Jump Detection and Analysis
Investigation of Media/Telecomm Industry
Prad Nadakuduty
Presentation 3
3/5/08
Outline
• Introduction
• Mathematical Background
• Price and Z-max Statistics
– Graphs
– Summary
• Correlation of Jumps
• Data taken from 1/2/2001 to 12/29/2006
– 5 min interval (78 observations per day)
– Over ~100K total observations
• Qualitative findings linking clusters of jumps to industry
events / macroeconomic shocks
Introduction
• Investigate Media/Telecomm Industry
– Verizon Telecommunications (VZ)
– AT&T Inc. (T)
– Walt Disney Inc. (DIS)
• Data taken from 1/2/2001 to 12/29/2006
– 5 min interval (78 observations per day)
– Over ~100K total observations
• Qualitative findings linking clusters of jumps to
industry events / macroeconomic shocks
Mathematical Background
• Realized Variation (IV with jump contribution)
• Bipower Variation (robust to jumps)
Mathematical Background
• Tri-Power Quarticity
• Z Tri-Power Max Statistic
– Significance Value .999  z > 3.09
Mathematical Background
• Previous equations used to estimate
integrated quarticity
• Relative Jump (measure of jump
contribution to total price variance)
Verizon Communications (VZ)
5 min Price Data
High: 57.40
• 7/19/2001
Low: 26.16
• 7/24/2002
Verizon Communications (VZ)
Z-tp Max Statistic
Max: 7.3393
• 8/24/2004
Explanation?
• Won civil case
against text
message
spammer
• Acquisition of
MCI 6 months
later
Walt Disney Inc. (DIS)
5 min Price Data
High: 34.88
• 12/19/2006
Low: 13.15
• 8/8/2002
Walt Disney Inc. (DIS)
Z-tp Max Statistic
Max: 5.4364
• 5/11/2005
Explanation?
• Launch of 50
year celebration
at theme parks
• Released
positive earning
statements from
film/DVD
earnings
AT&T (T)
5 min Price Data
High: 43.95
• 7/12/2001
Low: 13.50
• 4/16/2003
AT&T (T)
Z-tp Max Statistic
Max: 7.6598
• 9/23/2003
Explanation?
• Rumors of
merger with
BellSouth
• Acquires
assets from
MCIWorldCom
bankruptcy
S&P 500
5 min Price Data
High: 1443.7
• 12/15/2006
Low: 768
• 10/10/2002
S&P 500
Z-tp Max Statistic
Max: 11.533
• 11/23/2006
Explanation?
• Rumors of
merger with
BellSouth
• Acquires
assets from
MCIWorldCom
bankruptcy
Summary Statistics
Mean
Std.
Dev.
Verizon (VZ)
.5623
1.3690
Disney (DIS)
.5832
AT&T (T)
S&P 500
Max
Min
Num of
jumps
Jump Day
%tage
7.3393 -3.3541
55
N = 1491
(3.68%)
1.3185
5.4364 -2.9944
61
N = 1492
(4.09%)
0.6523
1.4104
7.6598 -2.8460
70
N= 1486
(4.71%)
0.7099
1.4007
11.533
57
N = 1514
(3.76%)
-3.051
Tri-power Quarticity and Max Statistic
Significance Level .999  z = 3.09
Correlation of Jumps
A Visual Exercise
Count
Frequency
No
Jumps
1267
85.26%
Only 1
Jump
200
13.46%
Only 2
Jumps
17
1.14%
Only 3
Jumps
2
0.13%
4 Jumps
0
0.00%
Triple Jump Dates
- Jan 3, 2001
-
-
-
Investors jumping on
New Year of trading
AT&T announce price
increase
Jun 4, 2004
-
AT&T announces VoIP
Verizon enters Yellow
Pages business
Regression
• Regress tri-power Z max statistic of each
firm with that of S&P 500 one week forward
• Look for predictive power of any firm
• Newey-West  heteroskedasticity robust
standard errors
– Will provide consistent estimators even if error
term is correlated with its own past
• Newey command in STATA
– newey SPztp l5.ATTztp, lag(5)
Regression Statistics
M&T Firms with S&P 500
SPztp
Coef.
Newey-West
Std. Err.
t
P>|t|
95% Conf Interval
Verizon
L5.VZztp
-.0447
.0277
-1.62
0.106
[-0.9902 .00957]
Disney
L5.DISztp
.01154
.0286
0.40
0.686
[-.04447 .06754]
AT&T
L5.ATTztp
-.0357
.025507
-1.40
0.162
[-.08574 .01432]
SPztp = β1 * L5.VZztp + β0
No coefficients statistically significant  None of these three firms have
significant predictive power of S&P 500
Regression Statistics
Inter-industry Analysis
VZztp
DISztp
ATTztp
Coef
Std. Err
t
Coef
Std.
Err
t
Coef
Std.
Err
t
Verizon
L5.VZztp
.0236
.0264
0.90
.0169
.0267
.063
.0718
.0261
2.75
Disney
L5.DISztp
-.0466
.0277
-1.68
.0048
.0252
0.19
-0.246
.0299
-0.82
AT&T
L5.ATTztp
.0166
.0250
0.66
.0031
.0249
0.13
.0325
.0261
1.25
No statisitically significant coefficients, so these firms are poor indicators of
the jump statistic, even of themselves.
Further Exploration
• Determine HAR-RV-CJ Forecasts
• Include more companies for wider view
– Consider investigating industry with more readily
available data  Technology, Financial Services
• Investigate effect of mergers & acquisitions
– Correlate “size” of acquisition with size of test
statistic