Partial Cointegration

Concept

Classical cointegration assumes that spreads between assets are fully mean-reverting. In practice many spreads exhibit hybrid dynamics, combining temporary mean reversion with persistent stochastic drift.

Partial cointegration extends the classical framework by decomposing the spread into stationary and non-stationary components.

Model Representation

W_t = M_t + R_t

M_t = ρ M_t−1 + ε_t

R_t = R_t−1 + η_t

M_t mean-reverting component
R_t stochastic trend
W_t observed spread

State-Space Representation

The model can be written in state-space form and estimated using Kalman filtering. This allows the latent components of the spread to be inferred from observed prices.

Interpretation

In trading applications the mean-reverting component represents temporary mispricing, while the stochastic trend captures persistent structural deviations.

Related Project

Application of this model in statistical arbitrage:

Partial Cointegration Strategy