Answer: is a special case of an AR(1) model with an intercept equal to 0 and a slope equal to 1.

## Explanation **A random walk process is a special case of an AR(1) model with an intercept equal to 0 and a slope equal to 1.** **Mathematical Definition:** - Random walk: $Y_t = Y_{t-1} + \epsilon_t$ - AR(1) model: $Y_t = b_0 + b_1Y_{t-1} + \epsilon_t$ - When $b_0 = 0$ and $b_1 = 1$, the AR(1) model becomes a random walk **Why other options are incorrect:** **A. Is a covariance-stationary time series** - **FALSE** - Random walks are **non-stationary** - Variance increases over time: $Var(Y_t) = t\sigma^2$ - Mean may not be constant **B. Has a well-defined mean-reverting level** - **FALSE** - Mean-reverting level for AR(1) is $\frac{b_0}{1-b_1}$ - For random walk ($b_1 = 1$), this becomes undefined (division by zero) - Random walks do not revert to any mean level **Key Properties of Random Walks:** - Unit root process ($b_1 = 1$) - Non-stationary - No tendency to revert to mean - Variance grows with time - Commonly used to model stock prices and other financial variables Therefore, option C correctly describes the relationship between random walks and AR(1) models.

Author: LeetQuiz Editorial Team