Financial Risk Manager Part 1
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Which of the following characteristics apply to a white noise process?
I. Zero mean
II. Autocovariances that are constant
III. Autocovariances that are zero except at lag zero
IV. Constant variance
Other
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NNikitesh
A
I and III
B
II and III
C
I and IV
D
I, III and IV
Explanation:
A white noise process has the following characteristics:
- Zero mean (I) - The expected value of the process is zero
- Constant variance (IV) - The variance does not change over time
- No autocorrelation except at lag zero (III) - Autocovariances are zero for all lags except lag zero, where it equals the variance
Statement II is incorrect because autocovariances are not constant - they are zero for all non-zero lags. The correct combination is I, III, and IV.
Mathematically, a white noise process εₜ satisfies:
- E[εₜ] = 0 (zero mean)
- Var[εₜ] = σ² (constant variance)
- Cov[εₜ, εₜ₋ₖ] = 0 for all k ≠ 0 (no autocorrelation)
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