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I am trying to understand how to apply cointegration. I got the intution behind cointegration but can't understand what coint output value means or how to use it? I know statsmodels.tsa.stattools.coint output returns coint,p value and Critical values. I know about pvalue but I want to understand the application of coint values.

This is my code

import numpy as np
for i in range(20):
    from statsmodels.tsa.stattools import coint
    a=np.random.random(100)
    b=np.random.random(100)
    coint,p,_=coint(c,b)
    print(i,coint)

# OUTPUT 
0 -10.012509186879504
1 -10.148980701656976
2 -10.05063830689571
3 -9.902422179521555
4 -9.924994070972073
5 -10.113824848584692
6 -9.991961287348031
7 -9.814875744787326
8 -9.888604151754262
9 -10.025288638986451
10 -10.097071339486405
11 -10.024256435982936
12 -10.144416761500892
13 -9.993703253667176
14 -10.117822090604891
15 -9.946427700397303
16 -9.647406692920766
17 -10.040240054854626
18 -9.750656922327343
19 -10.120270889798519

The coint values hover between -9 and -10; what does these numbers even mean? if coint values is positive what happens to the two series? What is the minimum and maximum value a coint value can attain?

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1 Answer 1

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https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.coint.html

If you read the documentation, you would find that your "coint" variable is the first output returned by the function, thus it is the t-statistic of the unit-root test on the residuals; I believe the unit root test used is the ADF.

The t-statistic should be negative and if it is not negative, then the Dickey-Fuller test is not an appropriate test to use since $|\phi|>1$ in $y_i=\phi y_{i-1}+\epsilon_i$, which means that the process is explosive. You should probably read up on ADF root testing.

Is there a limit to the magnitude of a t-statistic? No and that should answer your last question.

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