Financial Risk Manager Part 1
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Which of the following statements is (are) correct?
I. A time series process with a zero mean, unchanging variance, and no serial correlation is referred to as a white noise process
II. A serially independent and serially uncorrelated time series process is referred to as independent white noise
III. A serially independent, serially uncorrelated, and normally distributed time series process is referred to as normal white noise
Other
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NNikitesh
A
Only III
B
I and II
C
I, II and III
D
II and III
Explanation:
Explanation
All three statements are correct:
Statement I: A white noise process is defined as a time series process with:
- Zero mean: E(e_t) = 0
- Constant (unchanging) variance: Var(e_t) < ∞
- No serial correlation: Cor(e_t, e_s) = 0 for t ≠ s
Statement II: Independent white noise is a stronger condition than regular white noise. While regular white noise only requires no serial correlation, independent white noise requires both:
- No serial correlation
- Serial independence (a stronger condition than just no correlation)
Statement III: Normal white noise (also called Gaussian white noise) adds the additional condition of normal distribution to independent white noise:
- Serial independence
- No serial correlation
- Normally distributed
Key relationships:
- Normal white noise ⊂ Independent white noise ⊂ White noise
- All normal white noise processes are independent white noise
- All independent white noise processes are white noise
- But not all white noise processes are independent white noise
- And not all independent white noise processes are normal white noise
The correct answer is C because all three statements accurately describe these different types of white noise processes.
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