Discussion
A random walk time series is :
Answer: C
A random walk is non-stationary.
A random walk is \(Y_{t} = Y_{t-1} + e_{t}\). Each shock is permanently added in, so \(Y_{t} = Y_{0} + e_{1} + \cdots + e_{t}\) and its variance \(t\sigma^{2}\) grows with time. A series whose variance changes over time is not stationary; this one has a unit root.
It is not impossible to analyse: taking first differences gives \(\Delta Y_{t} = e_{t}\), which is stationary, and unit-root tests such as Dickey-Fuller are built for it. It is also very useful in practice, as the standard model of stock prices and exchange rates.
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