Final presentation jump statistics and volume
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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.

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Final Presentation: Jump statistics and volume

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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





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

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

Redoing the simple jiang regression

  • Regressing the absolute value of the jiang statistics on volume

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

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


  • 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


  • 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

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