Hi, I followed the course and I would like to ask you something about the excel template file: Pairs Trading in Excel. In Sheet ADF test, there is no final check about the cointegration. Its only mentioned that T-stat should be lower than Critical value but there is no calculation of the Critical value for each of the periods: 60 days, 90 days, 120 days, Overall duration. Can you please give me more details about the Critical value calculation ? Thank you
Hello Marian,
The critical values are not computed there. In the other excel book called "ADF Test", we provide the t-stat computation to check cointegration on a daily basis. However, the critical value is entered in cell H10.
Nonetheless, critical values for the ADF test are obtained with the Augmented Dickey-Fuller distribution. The computation of these critical values has already been provided by MacKinnon, J. G. (1994). You can check this link to find the approximate critical values necessary for your ADF tests.
We can help you also to choose which critical value might be suitable for each 60, 90 and 120 spans as per the link.
First, we should say that the ADF test has been applied with a constant. You can check that in the VBA macros named "adf" (Press ALT+F11 when you are located in the "ADF Test" excel sheet to get inside the VBA code).
Having said that, we can choose the critical value for our 60, 90 and 120 spans.
Checking the link, we choose to go the first table. We look at the Model 1 table, because we have a constant and no trend in the estimation of the ADF regression.
Then, we can use the formula shown there in the link, which is: crit = t + u/N + v/N^2 + w/N^3.
Where N can be 60, 90 or 120 days.
Let's imagine we want a 5% significant level. Consequently, we go to the below table (Model 1 - constant, no trend) and choose the column 0.05 and apply the numbers of that column to get our desired critical value.
I hope this helps,
Thanks and regards,
Reference
MacKinnon, J. G. (1994), “Approximate asymptotic distribution functions for unit root and cointegration tests,” Journal of Business and Economic Statistics, 12, 167–176.
José Carlos