Financial Risk Manager Part 1
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Distinguish between independent white noise and normal (Gaussian white noise).
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NNikitesh
A
An independent white noise is a time series that exhibits both serial independence and a lack of serial correlation while a normal white process is a time series that's serially independent, serially uncorrelated, and is normally distributed
B
A normal white noise is a time series that exhibits both derail independence and a lack of serial correlation while an independent white noise is a time series that's serially independent, serially uncorrelated, and is normally distributed
C
An independent white noise is a time series with equal mean and variance while a normal white noise is a time series where the mean is not equal to the variance
D
An independent white noise is discrete while a normal white noise is continuous
Explanation:
Explanation
Independent white noise and normal (Gaussian) white noise are both types of white noise processes, but they have different properties:
Independent White Noise:
- Exhibits serial independence (each observation is independent of all others)
- Exhibits lack of serial correlation (autocorrelation is zero for all lags)
- Does not necessarily follow a normal distribution
Normal (Gaussian) White Noise:
- Has all the properties of independent white noise (serial independence and lack of serial correlation)
- Additionally follows a normal (Gaussian) distribution
Key Distinction:
- All normal white noise is independent white noise, but not all independent white noise is normal white noise
- The normal distribution requirement is the additional condition that distinguishes Gaussian white noise from independent white noise
Why Other Options Are Incorrect:
- Option B: Reverses the definitions incorrectly
- Option C: Incorrectly relates to mean-variance equality (white noise typically has constant mean and variance, but this doesn't distinguish the two types)
- Option D: Incorrectly relates to discrete vs. continuous (both can be either discrete or continuous)
Correct Answer: A - It correctly identifies that normal white noise has the additional requirement of normal distribution beyond the properties of independent white noise.
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