Financial Risk Manager Part 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.