Answer: 0.7778.

## Explanation For a stationary time series process, the long-run unconditional mean can be found using the formula for the mean of an AR(1) process. The general form of an AR(1) process is: $$Y_t = c + \phi Y_{t-1} + \epsilon_t$$ where $\epsilon_t$ is white noise with mean 0. The unconditional mean $\mu$ is given by: $$\mu = \frac{c}{1 - \phi}$$ In this case, the correct answer is 0.7778, which suggests the process has parameters such that $\frac{c}{1 - \phi} = 0.7778$. This value represents the long-run equilibrium level that the series tends to revert to over time, regardless of its current position. **Key points:** - The unconditional mean exists only if $|\phi| < 1$ (stationarity condition) - It represents the long-run average value of the process - For an AR(1) process, shocks have temporary effects and the series reverts to this mean over time

Author: LeetQuiz .