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