What results from first-order differencing a random walk series?

First-order differencing a random walk series transforms the original series into a white noise series. In the context of a random walk, which is characterized by a stochastic trend and a unit root, first-order differencing essentially computes the differences between consecutive observations. This process removes the trend component present in the random walk, leading to a series where the values are not correlated over time.

A white noise series consists of uncorrelated random variables that have a mean of zero and a constant finite variance. When a random walk undergoes first-order differencing, what is left is a series of random shocks, or innovations, from each step of the original random walk. These shocks are independent and identically distributed (i.i.d.), characteristic of white noise.

The other options do not accurately describe the result of first-order differencing the random walk. A stationary series would imply constant mean and variance over time, which does not hold after first differencing a random walk. While the original random walk series remains non-stationary, the differenced version achieves stationarity in that it removes the stochastic trend component. Lastly, a non-stationary series would still have moment characteristics that change over time, which does not apply once the differencing has taken place. Thus