Answer: It is a random walk time series with a drift described using AR(1) model whose lag coefficient is 1

## Explanation A time series with a unit root is characterized by having a lag coefficient of 1 in its autoregressive representation. Specifically: 1. **Option A is correct**: A unit root time series can be described as a random walk (with or without drift) using an AR(1) model where the lag coefficient equals 1. This means the series has a stochastic trend and is non-stationary. 2. **Option B is incorrect**: If the lag coefficient were 0, it would not be a unit root process. A lag coefficient of 0 would imply no persistence from previous values, which is not characteristic of a unit root. 3. **Option C is incorrect**: Time series with unit roots are **not** covariance stationary. In fact, unit roots are a primary cause of non-stationarity in time series. Covariance stationarity requires that the mean, variance, and autocovariance structure remain constant over time, which is violated when a unit root is present. 4. **Option D is incorrect**: Since options B and C are incorrect, "All of the above" cannot be correct. **Key Concept**: A unit root occurs when the characteristic equation of an autoregressive process has a root equal to 1. In an AR(1) model: \(y_t = \phi y_{t-1} + \epsilon_t\), if \(\phi = 1\), the series has a unit root and follows a random walk process. Such series exhibit non-stationary behavior with variance that grows over time.

Author: Nikitesh Somanthe