Explanation

Random walks have a unit root.

Key definitions:

• Unit root: When the autoregressive coefficient in an AR(1) model equals 1
• Random walk: $x_t = x_{t-1} + \varepsilon_t$ where the coefficient on $x_{t-1}$ is exactly 1
• AR(0) models: White noise processes with no autoregressive component
• Covariance-stationary AR(1) models: Require $|\phi| < 1$ for stationarity

Analysis:

• Option A (AR(0)): No autoregressive component, so no unit root
• Option B (Random walks): By definition, have unit root (coefficient = 1)
• Option C (Covariance-stationary AR(1)): By definition, $|\phi| < 1$, so no unit root

Therefore, only random walks have a unit root.