1. Deeper exploration of volume and Jump statistics
Pat Amatyakul
Econ 201FS
18 March 2009

2. Last time
Comparing the number of jump days when the volume is high and the number of jump days when the volume is low
Left out a lot of data because only checked whether the day is a jump day and not the z-statistics related to that

3. This time
Extends to more stocks using 8 minute sampling rates instead of 5 that was used originally
-CSCO (April 16,1997-Jan 7, 2009)
-GE (April 9,1997-Jan 7, 2009)
-IBM (April 9,1997-Jan 7, 2009)
-MSFT (April 16,1997-Jan 7, 2009)
-PFE (April 9,1997-Jan 7, 2009)
Regress the resulting z-statistics from the BNS jump test with Quadpower Quarticity with daily volume data from google finance
Explore a related topic: how does volume change during each day of the week and see whether there’s any trend to the jump tests

4. Some observations from literature
If volume is trended over the sampled period, then the result of the price-variability volume can be very misleading (Tauchen and Pitts, 1983)
Average daily trading volume is lowest on Monday, increases monotonically from Monday to Wednesday, and decreases from Wednesday to Friday. (Jain and Joh, 1988)

5. Volume plots

6. Volume

7. Volume (Cont)

8. Volume trends
Regress daily volume with the index (1st day is 1, 2nd is 2, and so on) to see the trends
VolCSCO(000s)=5.39*10^4-1.16*n
se=(7.16*10^2) (.424)
VolGE(000s)=1.21*10^4+5.99*n
se=(2.73*10^2) (.162)
VolIBM(000s)=7.96*10^3-.585*n
se=(9.85) (.0583)
VolMSFT(000s)=5.58*10^4+.984*n
se=(7.72*10^4) (.457)
VolPFE(000s)=4.63*10^3+1.02*n
se=(2.56*10^2) (.151)

9. Results of Robust Regression: regressing Zstat values with volume
ZstatCSCO= *10^-4* volume(in millions)
se= (.0545) (.0149)
p=(~0) (.96)
ZstatGE= *10^-3*volume(in millions)
se=(.0358) (.0148)
p=(~0) (.7038)
ZstatIBM= *10^-3*volume(in millions)
se=(.0550) (.0149)
p=(~0) (.7953)

10. Results of regresssion(cont)
ZstatMSFT= *10^-4*volume(millions)
se=(.0613) (.0149)
p=(~0) (.9931)
ZstatPFE= *10^-3*volume(millions)
se=(.0356) (.0149)
p=(~0) (.7141)

11. Analysis
There seemed to be no conclusive evidence that high volume days are more likely to have jumps, this is contradictory to last time.
Last time I divided days into 3 groups and saw that high volume days have more jumps. A hypothesis is that maybe the jumps occur more frequently at the higher end of the volume spectrum, but not as a whole.
There is a positive relationship for 2 of them, and negative for 3 of them, and none of them are even relatively significant.

12. Effects of day of the week on volume (this is for CSCO)

13. Effects of day of the week on Zstat

14. Number of jumps detected on each day
This is done at the 99% level using BNS test with Quadpower Quarticity
Monday- 22 out of 550 (4.00%)
Tuesday -25 out of 601 (4.16%)
Wednesday -31 out of 604 (5.13%)
Thursday – 21 out of 590 (3.56%)
Friday -25 out of 576 (4.34%)
Overall – 124 out of 2921 (4.25%)

15. Conclusions
It seems a bit counterintuitive but it seems like a high average z-stat from the BNS jump tests doesn’t translate directly to the number of jumps detected.

16. Further extensions
Do more research and find more literature that is related
Use other models to detect jumps and compare those to the volume data