Which of the following indicates that a nonstationary time series can be represented as a random walk?

A nonstationary time series can be represented as a random walk if the differenced series follows a white noise model. A random walk is characterized by the presence of random shocks that influence the series in an unpredictable manner. When you difference a nonstationary time series, you are effectively removing trends or systematic patterns to examine the actual random fluctuations. If the differenced series exhibits characteristics of white noise, it suggests that the remaining fluctuations are unpredictable and random, which aligns perfectly with the definition of a random walk.

In contrast, if a time series shows cyclical patterns or seasonal trends, it implies that there are predictable elements in the data that are not indicative of a random walk. Cycles and seasonality introduce structure into the time series that would not be present if the series were purely a random walk. Additionally, considering the standard deviation of the original series in comparison to the differenced series does not directly address the presence of a random walk. Instead, it primarily informs us about the variance present before and after differencing, which may not clearly indicate whether the series behaves as a random walk.