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Answer: I, II and III
## 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.
Author: Nikitesh Somanthe
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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
A
Only III
B
I and II
C
I, II and III
D
II and III
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