Financial Risk Manager Part 1
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Distinguish between independent white noise and normal (Gaussian white noise).
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TTanishq
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 serial 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 time series data with distinct characteristics:
Independent White Noise:
- Exhibits serial independence (values are not influenced by previous values)
- Has lack of serial correlation (no predictable patterns or trends)
- Does not necessarily follow a normal distribution
Normal (Gaussian) White Noise:
- Has all properties of independent white noise:
- Serial independence
- Lack of serial correlation
- Additionally follows a normal distribution
- Characterized by a bell-shaped curve defined by mean and standard deviation
Why Choice A is Correct: It accurately distinguishes that independent white noise has serial independence and lack of serial correlation, while normal white noise has these same properties PLUS normal distribution.
Why Other Choices are Incorrect:
- Choice B: Incorrectly swaps the definitions
- Choice C: Incorrectly focuses on mean-variance equality, which doesn't define these concepts
- Choice D: Incorrectly associates discrete/continuous distinction with these noise types
Both types of white noise can be used in time series analysis, with normal white noise being a more specific case that includes distributional assumptions.
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