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Expert Dialog with DR. SIMON MÜLLER

t-test fpr CAAR

Dear Dr. Müller,

for the t-test (mentioned on eventstudytools - parametric test statistics number 1) it is possible to test H0:ARi,t=0 and H0:CARi=0.

For my study I am using the paper of MacKinlay (1997). On page 24, formula (20), he used a test of which I thougt that it is a t-test for CAAR. Dymke (2010) used this formula of MacKinlay on page 77 too. But on page 79 he talks about the parametric test of Brown/Warner (1985).

I am confused and need some help.

Thanks in advance.

Answer by Dr. Simon Müller:
Hi. You are correct formula (20) on page 24 is a CAAR t-test. This is the same test as in point 2 on our test statistic page. Brown and Warner uses this test in their publication (1985), so you may name this test "parametric test of Brown/Warner", but this is not common. More common is Cross-sectional test. Best, Simon
Test statistic formula for CARs


I am happy to use information you provide on your great website to do my event study.

I was wondering about the formula of the standard deviation of CARs for each firm. S2CAR = L2*S2*ARi.

What is meant by L2?
Is it the number of days of the event period?
Or is it the number of day of the subperiod of my event in case i want to check the significance of t-3 - t+3 for each firm (=7)??

Is L2 multipled by S2*ARi or does it mean that I should use S2*ARi of the event window?

I would be very happy to receive an answer?

Best Wolfgang

Answer by Dr. Simon Müller:
Hi, L2 is the number of non-missing days in the event window. This is a little bit confusing as we want to consider missing values. Next question ("Is L2 multipled by S2*ARi or does it mean that I should use S2*ARi of the event window?") is unclear to me. Which formula? Please be more precise. But L2AR_i means L2 * AR_i. Best, Simon 
Z -statistic in Corrado Test

Dear Mr. Mϋller
I’m conducting event study in Indonesian market for my bachelor thesis. Following Sudeck & Iatridis (2014), I will use Patell test and Corrado test to test my hypothesis. I want to ask you several questions:

1. Is it okay not to conduct normality test of my data? I mean, I understand that Patell test is used in case the data are normal, while Corrado test is used when my data are not normally distributed. But I confused, should I just do both test without doing normality test?

2. When I look at Campbell & Minguez-Vera (2010), we will find Z-statistic at the end of Corrado test calculation. Do test its significance, can I use Z-table for comparison? Or should I compare Z-statistic of Corrado test with another statistic table?

Please help me. Thank you very much.

Answer by Dr. Simon Müller:
Hello, 1. You do not need to do a normality test for the Corrado rank test, as there is no such assumption. N should be large enough for valid results. I would advice you to perform both test and have a closer look at the data when the results differs. 2. You can use this a z-table for p-values. Best, Simon
Event Study

Sehr geehrter Herr Müller,

mein Name ist Sandip Deol und ich stúdiere Internatrional Finance. Zurzeit habe ich ein Projekt am laufen. In diesem Projekt geht es um Auswertungen von Artikeln die sich auf die Weltwirtschaftskrisen beziehen. Wir bewerten die Artikeln nach einer Skalar. Das Problem vor dem ich stehe ist, dass ich nicht weiß, wie ich meine ausgewerteten Artikeln mit in meine Event Study mit hineinbeziehen kann. Da ich die Dax Kurse mit betrachte, arbeite ich eher mit den Kursen als wie mit meiner Auswertung. Meine Hypothese lautet, ob Artikel Veröffentlichungen eine Weltwirtschaftskrise hervorsehen kann. Könnten Sie mit diesbezüglich helfen ? Könnte ich Sie telefonisch erreichen?

ich wäre Ihnen sehr dankbar dafür.

Mit freundlichen Grüßen

Sandip Deol

Answer by Dr. Simon Müller:
You can find my contact details on my web page:
T Value for abnormal return

My event day is different but firms are from different industry so can i divide abnormal return by Standard error for finding the t value or Is there any other method.

Answer by Dr. Simon Müller:
Please read our test statistics page: There you find an answer to your question.
Standardized abnormal return

Dear Mr Muller,

I'm conducting an event study analysis and I would like to use the BPM test. My question is how can I calculate the sARi,t (standard deviation)? Is there one for every company at every t?
I hope you can help me and solve my doubt.
Thank you very much.

Best regards,

Answer by Dr. Simon Müller:
Hi Francesco, if you look at the definition in our documentation, you will see that there is an exact definition of all variables used. Many definitions of the BMP test formulas are in the description of the Patell test. Simon 
Testing for AAR and CAAR

Dear Dr. Müller

Brown and Warner (1985) suggest calculating the t-value as the ratio of the AAR to its estimated standard deviation from the estimation period. Is this appropriate? And don't I have to multiply it by the square root of N as your your significance test formula shows?

Furthermore, they also suggest calculating the test statistic over a interval as the ratio of CAAR to its estimated standard deviation. How can I calculate the standard deviation of the CAAR?

Thank you for your help.

Answer by Dr. Simon Müller:
There are different ways to write the formula. You can use AAR in the numerator or the sum over the AR. Depending on that definition you get different loooking formulas. 
Patell z test with Mean-Adjusted Model

Dear Mr Müller,

from my point of view using the Patell z test in combination with the mean-adjusted model seems counter-intuitive, since the S(ARi,t,) includes data from a market index (R(m,t)), which are not relevant for the calculation of mean-adjusted AR's. Still your event study engine is calculating it. Would you please elaborate whether you agree with me here, or respectively, why you don't?

Basically, I am using both the mean-adjusted and the market model and I would like to compare the two models' results, which is obviously not possible when using different significance tests. (Due to several adjustments I have made, I am using your engine solely for robustness checks.)

I am looking forward to your reply.

Best regards,

Answer by Dr. Simon Müller:
Dear Mark, for the mean-adjusted model, we use a different formula: s^2_ar = s^2_ar * (1+ 1 / M_i). Best, Simon
What is exactly M?

Dear Mr. Müller,

Regarding the parametric T-test for one sample Event: Could you explain me the size M (matched returns), please?

My event window is +/- seven days surrounding the announcement day of an acquisition. So L2 is 15 in my analysis, right? Is M also 15?

Thank you in advance!

You can also answer me in german.

Best wishes,

Tim Rothermel

Answer by Dr. Simon Müller:
Hi Mr. Rothermel,you are correct.Best,Simon Müller
Grouping Variable

I am trying to run an even study test by event study tool. I found a column called grouping variable in the "request file", and in the sample file it is given as "addition". I am not quite sure what grouping variable is and what "addition" indicates. Could you kindly instruct me?

Answer by Dr. Markus Schimmer:
The purpose of the grouping variable is described as folows: "For generating the 'average' values in your analysis (i.e., AAR and CAAR values as produced by aARC), you need to specify the 'grouping variable'. If you use only one value in the grouping variable, which is the default case, AXC will calculate the average values across all events in your request file; if you choose more than one value (e.g., 'acquisition' and 'divestiture' in a boundary choise study), AXC will produce average values across the events grouped by these values." ('Addition' was a value we used in the context of a study that investigated index changes in the S&P500 index. As index changes, we considered 'additions' and 'deletions' from the index.