Cointegration Models

Analisi delle serie temporali in Python

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!

Analisi delle serie temporali in Python

Preparing Video For Download...