Cointegration Models

Phân tích chuỗi thời gian với 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
Phân tích chuỗi thời gian với Python

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
Phân tích chuỗi thời gian với Python

Example: Heating Oil and Natural Gas

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

Phân tích chuỗi thời gian với Python

Example: Heating Oil and Natural Gas

  • But the spread (difference) is mean reverting

Phân tích chuỗi thời gian với Python

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
Phân tích chuỗi thời gian với Python

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)
Phân tích chuỗi thời gian với Python

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Phân tích chuỗi thời gian với Python

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