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A random walk series $y_t = y_{t-1} + u_t$, where $u_t \sim (0,\sigma_u^2)$ is a white noise term, is

stationary because the expected value and variance of $y_t$ are both constant over time.

non-stationary because the expected value of $y_t$ is not constant over time, even though the variance is constant.

non-stationary because while the expected value of $y_t$ is constant over time, the variance is not constant.

non-stationary because both the expected value and the variance of $y_t$ are non-constant over time.

stationary because regardless of whether the variance of $y_t$ is constant over time or not, the expected value of $y_t$ is constant.