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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 - PowerPoint PPT Presentation
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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 MCI-WorldCom bankruptcy
S&P 5005 min Price Data
High: 1443.7• 12/15/2006
Low: 768• 10/10/2002
S&P 500Z-tp Max Statistic
Max: 11.533• 11/23/2006
Explanation?• Rumors of
merger with BellSouth
• Acquires assets from MCI-WorldCom bankruptcy
Summary Statistics
Tri-power Quarticity and Max Statistic
Significance Level .999 z = 3.09
Mean Std. Dev.
Max Min Num of jumps
Jump Day %tage
Verizon (VZ) .5623 1.3690 7.3393 -3.3541 55 N = 1491
(3.68%)
Disney (DIS) .5832 1.3185 5.4364 -2.9944 61 N = 1492
(4.09%)
AT&T (T) 0.6523 1.4104 7.6598 -2.8460 70 N= 1486
(4.71%)
S&P 500 0.7099 1.4007 11.533 -3.051 57 N = 1514
(3.76%)
Correlation of JumpsA 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 StatisticsM&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 StatisticsInter-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