Final Presentation: Jump statistics and volume

Econ 201 FS

April 22, 2009

Pat Amatyakul

Last time

Regressed jump statistics on daily volume for the BNS test, Jiang-Oomen test, and Ait-Sahalia Jacod test.

Note that for the stocks where the value is statistically significant, BNS and Ait-Sahalia test yields a positive relationship while Jiang Oomen yiled a negative relationship

This time

Plotted out the Jiang-Oomen test statistic to see why the relationship is different

Revise coding Regress volume on the jump statistics, as

well as the lag of volume

Volume vs. Day of the week revisited

JNJ KO

PGT

Jiang Oomen swap variance ratio jump test The assumption here is that the swap variance

should equal the realized variance if no jumps are detected

Swap variance is defined as:

The test statistic is

)1(SwV

RVnBV

)(2 ii rRSwV

One sample plot of the test statistic

Jump detection

This is a two-sided jump test. These are the percentage of jumps detected at the 95% confidence level

Jump days      

JNJ 28.4% CSCO 26.4%

JPM 26.9% GE 23.8%

PG 25.2% IBM 28.7%

KO 24.8% MSFT 26.0%

T 29.1% PFE 27.4%

Redoing the simple jiang regression Regressing the absolute value of the jiang statistics

on volume

  coefficient p-value   coefficient p-value

JNJ -3.06E-05 0.007 CSCO -2.65E-07 0.315

JPM -9.43E-07 0.319 GE -1.86E-06 0.175

PG -3.10E-06 0.335 IBM 4.28E-08 0.000

KO -3.78E-05 0.011 MSFT -1.21E-13 0.999

T -2.67E-05 0.000 PFE -5.66E-06 0.049

Rethinking the regression

Volume clustering tend to occur, that is, volume today tend to affect volume tomorrow so I included a few lag volume terms into the regressors

Volume on Monday seemed to be lower than every other day of the week, so I included that into my regressors

Made some minor adjustment from last time to make sure that the signs of the coefficient means the same thing in all of the three jump statistics

The regression

The regression is as follows

Where the stat is either the BNS z-stat, the absolute value of the Jiang-Oomen z-stat, and -ASJ variable for the Ait-Sahalia Jacod test

Monday is a 0 or 1 dummy variable

5453121 mondayvolumevolumestatvolume tttt

    statVolume(t-1)

Volume(t-5) Monday cons

JNJ BNS coef -24529 0.617 0.183 -804823 1774046

  p-value 0.625 0.000 0.000 0.000 0.000

  JO coef -19.4 0.617 0.183 -808374 1769514

  p-value 0.007 0.000 0.000 0.000 0.000

  ASJ coef -210570 0.606 0.178 -759708 1195326

  p-value 0.000 0.000 0.000 0.000 0.000

JPM BNS coef -86680 0.677 0.255 -1130987 1139686

  p-value 0.461 0.000 0.000 0.000 0.001

  JO coef -58.89 0.677 0.255 -1119301 1101014

  p-value 0.000 0.000 0.000 0.000 0.001

  ASJ coef -311678 0.668 0.248 -1094316 9439

  p-value 0.000 0.000 0.000 0.000 0.984

    statVolume(t-1)

Volume(t-5) Monday cons

PG BNS coef 29647 0.628 0.194 -911074 1546234

  p-value 0.664 0.000 0.000 0.000 0.000

  JO coef -18.1 0.628 0.195 -907486 1563439

  p-value 0.001 0.000 0.000 0.000 0.000

  ASJ coef -146012 0.62 0.197 -896802 1104471

  p-value 0.000 0.000 0.000 0.000 0.000

KO BNS coef 51395 0.623 0.219 -684217 1050682

  p-value 0.315 0.000 0.000 0.000 0.000

  JO coef -7.19 0.622 0.219 -686682 1081704

  p-value 0.167 0.000 0.000 0.000 0.000

  ASJ coef -118132 0.612 0.217 -661303 776304

  p-value 0.000 0.000 0.000 0.000 0.000

    statVolume(t-1)

Volume(t-5) Monday cons

T BNS coef 20497 0.709 0.223 -767669 895376

  p-value 0.773 0.000 0.000 0.000 0.000

  JO coef -11.6 0.708 0.223 -769438 915219

  p-value 0.004 0.000 0.000 0.000 0.000

  ASJ coef -137870 0.702 0.222 -769628 520518

  p-value 0.000 0.000 0.000 0.000 0.001

CSCO BNS coef -825689 0.215 0.07 -2128233 3.82E+07

  p-value 0.003 0.000 0.001 0.010 0.000

  JO coef 13.6 0.217 0.071 -2131859 3.77E+07

  p-value 0.164 0.000 0.001 0.010 0.000

  ASJ coef -429192 0.212 0.068 -2051934 3.61E+07

  p-value 0.010 0.000 0.001 0.012 0.000

    statVolume(t-1)

Volume(t-5) Monday cons

GE BNS coef -205962 0.645 0.241 -2639564 3449616

  p-value 0.264 0.000 0.000 0.000 0.000

  JO coef -49.1 0.645 0.241 -2642372 3355109

  p-value 0.344 0.000 0.000 0.000 0.000

  ASJ coef -646179 0.635 0.237 -2405096 1313639

  p-value 0.000 0.000 0.000 0.000 0.171

IBM BNS coef 68688 0.543 0.106 -859660 2.84E+06

  p-value 0.206 0.000 0.000 0.000 0.000

  JO coef 110626 0.541 0.106 -874290 2.70E+06

  p-value 0.000 0.000 0.000 0.000 0.000

  ASJ coef -196062 0.524 0.097 -843212 2.34E+06

  p-value 0.000 0.000 0.000 0.000 0.000

    statVolume(t-1)

Volume(t-5) Monday cons

MSFT BNS coef -301332 0.201 0.084 -3329492 4.12E+07

  p-value 0.369 0.000 0.000 0.000 0.000

  JO coef 33826 0.201 0.084 -3353880 4.10E+07

  p-value 0.836 0.000 0.000 0.000 0.000

  ASJ coef -73671 0.2 0.084 -3348919 4.08E+07

  p-value 0.673 0.000 0.000 0.000 0.000

PFE BNS coef 366111 0.591 0.297 -1743534 2.58E+06

  p-value 0.034 0.000 0.000 0.000 0.000

  JO coef 5.54 0.591 0.297 -1703645 2.74E+06

  p-value 0.845 0.000 0.000 0.000 0.000

  ASJ coef -435942 0.587 0.297 -1709422 1.33E+06

  p-value 0.000 0.000 0.000 0.000 0.003

Summary of results

The correlation between volume and its lag term seems quite high and significant

BNS test does not yield any conclusive results, only 2/10 are significant and it is a split between a positive correlation and negative correlation

For the JO test, 5/10 are significant and 4 showed a negative relationship and 1 showed a positive relationship.

For the Ait-Sahalia Jacod test, 9/10 are significant and all showed a negative relationship between volume and jump statistics

Interpretation

According to Tauchen and Pitts (1983), changes in prices and volume are related

Need to investigate how this is related to each test statistics, since the change in prices provide the basis for calculating all the test statistics

Applications

In general, at least for JO and ASJ tests, lower volume corresponds with higher chance of jump days

Since volume is an easy indicator to observe in the market, one could flag an especially low volume day to possibly correspond with a jump. This would work only for the ASJ test, because it seems like the coefficient in the JO test regression are rather small.

Might be able to somehow incorporate this into asset pricing