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# P1.T2.507. White noise

#### Nicole Seaman

##### Director of FRM Operations
Staff member
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Learning outcomes: Define, white noise describe independent white noise and normal (Gaussian) white noise. Explain the characteristics of the dynamic structure of white noise. Explain how a lag operator works.

Questions:

507.1. In regard to white noise, each of the following statements is true EXCEPT which is false?

a. If a process is zero-mean white noise, then is must be Gaussian white noise
b. If a process is Gaussian (aka, normal) white noise, then it must be (zero-mean) white noise
c. If a process is Gaussian (aka, normal) white noise, then it must be independent white noise
d. If a process is stationary, has zero mean, has constant variance and it serially uncorrelated, then the process is white noise

507.2. Your colleague Jeff makes the following four claims about white noise:

I. 1-step-ahead forecast errors from good models should never be white noise
II. Forecasting white noise is easy due to obvious patterns implied by its stringent conditions
III. Processes with rich dynamics can be built up by taking simple transformations of white noise
IV. What happens to a white noise series at any time in the future is uncorrelated with anything in the present or past

a. None are true
b. Only I. and II. are true
c. Only III. and IV. are true
d. All are true.

507.3. Let B(L) be a lag operator polynomial of degree (m) that operates on y(t). Which best characterizes y(t)?

a. B(L)y(t) --> y(t) = b(0)^m*y(t)
b. B(L)y(t) --> y(t) = b(0)*y(t-m)
c. B(L)y(t) --> y(t) = b(0)*y(t) + b(1)*y(t-1) + b(2)*y(t-2) + .... + b(m)*y(t-m)
d. B(L)y(t) --> y(t) = b(0)*y(t) + b(1)*y(t-1)^2 + b(2)*y(t-2)^3 + .... + b(m)*y(t-m)^(m+1)

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