Financial Risk Manager Part 1

Explanation

For a time series to be covariance stationary (weakly stationary), it must satisfy three conditions:

1. Constant Mean: The expected value of the series is constant over time: E[y_t] = μ for all t.

2. Constant Variance: The variance of the series is finite and constant over time: Var[y_t] = σ² < ∞ for all t.

3. Autocovariance depends only on lag, not on time: The autocovariance between y_t and y_{t+τ} depends only on the lag τ, not on the specific time t: Cov(y_t, y_{t+τ}) = γ(τ) for all t.

Why option C is incorrect (the EXCEPT answer): Option C states that "The autocovariance depends on time (t), but does not depend on the displacement (τ)". This is exactly the opposite of what covariance stationarity requires. For covariance stationarity, the autocovariance should NOT depend on time (t), but should depend ONLY on the displacement/lag (τ).

Verification of other options:

• Option A: Correct - Constant mean is a requirement.
• Option B: Correct - Finite autocovariance at zero displacement (which is the variance) is required.
• Option D: Correct - Stable covariance structure over time is required.

Therefore, option C is the exception as it incorrectly describes the autocovariance property for covariance stationary series.