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Consider a series represented by the function:
$$y_t = \delta + \beta t + u_t$$
This function represents data that are a random walk with a drift.
This series can be described as being:
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.