Financial Risk Manager Part 1

Explanation

White Noise Process Characteristics:

1. Constant Unconditional Mean and Variance (Option A): This is correct. For any covariance stationary process, including white noise, the unconditional mean and variance must be constant over time.

2. Zero Autocovariance and Autocorrelation (Option B): This statement is incorrect and therefore the answer. The correct characteristic is that all autocovariances and autocorrelations are zero beyond displacement zero (not "not zero"). In a white noise process, there is no correlation between observations at different time lags.

3. No Correlation Between Past and Present (Option C): This is correct. White noise processes have no serial correlation, meaning past values don't predict future values.

4. Same Conditional and Unconditional Moments (Option D): This is correct for an independent white noise process. Since there's no dependence structure, conditional moments equal unconditional moments.

Key Points:

• White noise: ε_t ~ i.i.d.(0, σ²) or at least uncorrelated with zero mean and constant variance
• Autocorrelation function: ρ_k = 0 for all k ≠ 0
• Covariance stationary: mean, variance, and autocovariance structure don't change over time
• The error in Option B is the double negative "not zero" when it should be "zero" for autocovariances beyond displacement zero.