Checking for Co-integration in Section 3 - video 1 in Statistical Arbitrage Trading

Installations & Python Packages
1

Hello,



I am going throught the excel sheet for checking whether Aluminium and Lead are co-integrated. I have understood all the steps for the overall duration but not for the 60-90-120 days period:

I do not get the logic behind estimating the first regression parameters (y = c+mx+epsilon) only on a shorter time window, basically the last 60-90 or 120 days of the overall duration. Then use those estimations, basically error(t-1)=y-c_hat-m_hat*x and diff(error), to perform the ADF test (which basically a regression) on the entire time window.

So my question: why do we estimate the parameters only on shorter time window which is at the end of the overall time window and then we carry on the ADF test on the entire time window?



Thank you in advance for your help.

Bests,

Ines

2

Hi Ines,



The ADF test is performed for the same 60, 90 or 120 days window and not on the entire time window.



For example, the formula for slope and variability of slope for last 90 days which is used to calculate the t-stat value of ADF test is as follows:

Slope = INDEX(LINEST($J$482:$J$571,$K$482:$K$571,,TRUE),1,1)
Variability of slope = INDEX(LINEST($J$482:$J$571,$K$482:$K$571,,TRUE),2,1)

Here, the range used is from 482 to 571 and similarly, only last 60 and 120 days period is used to compute the t-stat value for 60 and 120 days.

You may download the ADF test excel sheet from the downloads section of the course
Link: https://quantra.quantinsti.com/startCourseDetails?cid=34&section_no=6&unit_no=2

I hope this solves your query.

Thanks,
Ishan

3

Hello Ishan, Then it makes perfect sens! Thank you for your response. My best regards, Ines