Cointegration Models

Python ile Zaman Serisi Analizi

Rob Reider

Adjunct Professor, NYU-Courant Consultant, Quantopian

What is Cointegration?

Two series, $\large P_t$ and $\large Q_t$ can be random walks
But the linear combination $\large P_t - c \ Q_t$ may not be a random walk!
If that's true
- $\large P_t - c \ Q_t$ is forecastable
- $\large P_t$ and $\large Q_t$ are said to be cointegrated

Analogy: Dog on a Leash

$\large P_t = $ Owner
$\large Q_t = $ Dog
Both series look like a random walk
Difference, or distance between them, looks mean reverting
- If dog falls too far behind, it gets pulled forward
- If dog gets too far ahead, it gets pulled back

Example: Heating Oil and Natural Gas

Heating Oil and Natural Gas both look like random walks...

Example: Heating Oil and Natural Gas

But the spread (difference) is mean reverting

What Types of Series are Cointegrated?

Economic substitutes
- Heating Oil and Natural Gas
- Platinum and Palladium
- Corn and Wheat
- Corn and Sugar
- ...
- Bitcoin and Ethereum?
How about competitors?
- Coke and Pepsi?
- Apple and Blackberry? No! Leash broke and dog ran away

Two Steps to Test for Cointegration

Regress $\large P_t$ on $\large Q_t$ and get slope $\large c$
Run Augmented Dickey-Fuller test on $\large P_t - c \ Q_t$ to test for random walk
Alternatively, can use coint function in statsmodels that combines both steps

from statsmodels.tsa.stattools import coint
coint(P,Q)

Let's practice!

Python ile Zaman Serisi Analizi

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