What is the outcome of first-order differencing a random walk series?

First-order differencing a random walk series involves calculating the differences between consecutive observations in the time series. A random walk is characterized by having a unit root, indicating that it is non-stationary: its mean and variance change over time, and it exhibits a random path with a tendency to wander.

When first-order differencing is applied to a random walk, the result is a series that consists of the changes between observations, rather than the absolute values of the observations themselves. This differenced series effectively removes the stochastic trend present in the random walk, resulting in a series where the mean and variance are constant over time, which is the hallmark of stationarity.

Therefore, the outcome of first-order differencing a random walk series is a stationary series, which allows for the application of various statistical models that assume stationarity, enhancing the potential for meaningful analysis and forecasting.