1. Econ 201 FS April 8, 2009 Pongpitch Amatyakul
Volume and Jump tests
Econ 201 FS
April 8, 2009
Pongpitch Amatyakul

2. Last time
Tried to find the relationship between volume and jump detection.
Regressed BNS test statistic with daily volume acquired from google finance
There seemed to be no significant relationship
Explored CSCO’s volume trend during each day of the week and check to see how the BNS test statistic changes throughout the week

3. This time
Use the tobit model instead of OLS regression and use multiple regression instead of just fitting them individually
Extends to other jump tests: Jiang and Oomen test (2005) and Ait-Sahalia and Jacod(2008) and regress those statistics on volume

4. Data 10 largest cap stocks in S&P 100 that has the full length of data
CSCO, GE, IBM, MSFT, PFE, JNJ, JPM, KO, T, PG
Time period is between April 1997 to January 2009
10 minute sampling frequency

5. Tobit Model Developed by James Tobin (1958)
It is a model that describes a relationship between a non-negative dependent variable with an independent variable
Since the z statistic in BNS test should not be below zero, this test is appropriate
If regressed normally like last time, the slope should have a downward bias

6. Result of tobit Volume Mon Tues Wed Thurs Constant CSCO value
Volume
Mon
Tues
Wed
Thurs
Constant
CSCO
value
-4.67E-09
0.025
0.087
0.043
-0.008
0.621 p
0.001
0.768
0.301
0.601
0.923 GE
-3.44E-09
-0.051
-0.044
-0.067
0.498
0.003
0.446
0.491
0.299
0.496
IBM
5.38E-09
-0.059
0.075
-0.048
0.029
0.402
0.432
0.48
0.366
0.56
0.718
MSFT
-1.06E-09
0.121
0.079
0.066
-0.013
0.381
0.367
0.303
0.387
0.863
PFE
1.13E-10
0.222
0.127
0.091
0.106
0.241
0.935
0.045
0.155
0.098

7. More results Vol Mon Tues Wed Thurs Constant JNJ value -7.37E-09
Vol
Mon
Tues
Wed
Thurs
Constant
JNJ
value
-7.37E-09
-0.061
-0.032
-0.035
0.082
0.514 p
0.128
0.399
0.641
0.604
0.241
JPM
-1.39E-09
-0.085
0.039
-0.017
-0.104
0.406
0.405
0.228
0.564
0.801
0.131 PG
-1.51E-10
0.127
0.105
-0.028
0.124
0.371
0.976
0.116
0.186
0.716
0.119 T
-1.11E-08
0.004
-0.02
0.05
0.994
0.954
0.784
0.456 KO
-4.95E-09
-0.067
0.056
0.038
0.021
0.419
0.451
0.364
0.434
0.594
0.762

8. Jiang Oomen Ratio Jump Test
Detecting jumps using swap variance test
Arithmatic return
Geometric return
Swap variance is defined by

9. Ratio jump test cont.
They argued that the difference between the geometric and arithmatic return should be zero if there is no jump
The test statistic is
Where BV is bipower variance
And

10. Result of regression Vol Mon Tues Wed Thurs Constant CSCO value
Vol
Mon
Tues
Wed
Thurs
Constant
CSCO
value
1.08E-08
-0.223
-0.085
0.069
0.139
2.52 p
0.091
0.539
0.62
0.307 GE
2.16E-08
-0.181
0.101
0.087
0.147
1.81
0.003
0.093
0.371
0.417
0.183
IBM
1.04E-07
-0.052
0.016
0.031
-0.034
1.72
0.604
0.863
0.762
0.734
MSFT
3.04E-09
-0.103
0.039
0.136
-0.024
2.44
0.114
0.391
0.233
0.839
PFE
1.39E-08
-0.098
-0.042
-0.118
2.04
0.701
0.403
0.719
0.323

11. Ait-Sahalia Jacod Jump Test
Uses higher return moments to detect jumps
The test statistic is
This is compared with
If ASJ<  , then a jump is detected

12. Jacod Jump Test cont
A(hat) can be calculated using multipower variation
So what I did was calculate ASJ- and regress this term with volume

13. Sample of Jacod stat

14. Jump detection Stock Percentage of Jumps detected at 95 % confidence
CSCO
7.50 GE
10.02
IBM
4.31
MSFT
7.05
PFE
13.89

15. Result of regression Vol Mon Tues Wed Thurs Constant CSCO value
Vol
Mon
Tues
Wed
Thurs
Constant
CSCO
value
-1.66E-08
-0.187
-0.236
-0.246
0.156
3.49 p
0.512
0.75
0.693
0.665
0.866
0.004 GE
3.03E-07
0.164
-0.092
-1.13
-0.445
1.83
0.914
0.954
0.412
0.786
0.252
IBM
3.29E-07
0.471
0.097
-0.249
-0.044
1.75
0.523
0.891
0.947
0.01
MSFT
3.65E-09
-0.028
-0.064
-0.157
0.2643
4.63
0.405
0.91
0.784
0.493
0.584
PFE
1.88E-07
0.255
0.032
-0.456
-0.305
3.03
0.677
0.965
0.404
0.611

16. Conclusion
All the days were insignificant, apart from a few that were at 10% level
For BNS 3/10 suggest that volume is significant and has a downward effect on jumps
For JO, 3/5 were significant and also suggest a downward effect on jumps
For Ait-Sahalia and Jacod, however, 4/5 are significant and suggest an upward effect on jumps

17. Further Research
Get more stocks into Jiang Oomen test and Ait-Sahalia test and see whether the same trends continued
Continue trying to get Tauchen and Pitts (1983) model of volume to work