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

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

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

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

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

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

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 0.56562 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

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

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

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 -0.0462 -0.098 -0.042 -0.118 2.04 0.701 0.403 0.719 0.323

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

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

Sample of Jacod stat

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

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

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

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