## Expert Dialog

Question #2: Possible error in the demo work of J-test

Dear Dr Muller,

I am Vineet, a PhD student and who is referring to your demo work in excel for various event study methodology.

I appreciate the work done here and I find it very helpful.

I am currently referring to your work done on J-Test on the following page:
http://www.eventstudytools.com/significance-tests

I tried to replicate the methodology and got different results. I wish to resolve the inconsistencies.

Calculation of average correlation is certainly one problematic area. The paper says to use Residuals in estimation period to calculate that. However, your work is using Standardized Residuals in estimation period. Probably, I am misinterpreting the paper. Please verify.

Also, would it be possible for you to extend your work to demonstrate t-test for SCARs as well. That is where I think the analysis gets very tricky. And I am struggling a lot.

Thank you very much for your help,

Vineet

Dear Vineet,I am glad that our websites helps you. As our team is actually in the final step of our php/R API development, I was not able to verify all Excel sheets on our website. Please, excuse me for that. You do not misinterprete the paper or the description on our website. The calculation of the cross-correlation is calculated on the abnormal returns on the estimation window. But, as the standard deviation for the estimation window is independent from time and the pearson product-moment correlation coefficient is independent on linear transformations (e.g. set $\hat{X}_i := \frac{X_i}{a}$ and $\hat{Y}_i := \frac{Y_i}{b}$ with $a,b \in \R$ in the Pearson product-moment formula, you will see that you get the same correlation coefficient for $(X_i, Y_i)_i$ and $(\hat{X}_i, \hat{Y}_i)_i$). The reason for the different results resides in the calculation of the correlation coefficient between time series of firm 1 and firm 3 in that Excel sheet (see row 1 and column 3 in the correlation matrix of the Excel sheet). If you look at the formula, you will see that in that cell the window is misaligned (it includes estimation and event window; that's definitly wrong). I will correct this sheet this evening. Please feel free to contact me, if this do not solve the inconsistency. Best,SimonP.S.: Kolari, J. W. and Pynnonen (2010) standardize with the standard deviation with correction for forecast error (as we describe on our website and will do in our API calculation). Actually, in the Excel sheet we do not correct for the forecast error. In that short estimation window of n=10 this leads to significantly different results. Please, consider this. All Excel sheets will be revised and extended (e.g. t-Test for SCARs) after our API is online.