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Question 4 Which of the following time sequence is a weak stationary? Justify your answer! zt =at,whereat ∼i.i.d.(0,1)forallt∈R. zt...

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Statistics

Question 4

Which of the following time sequence is a weak stationary?Justify your answer!

  • zt =at,whereat ∼i.i.d.(0,1)forallt∈R.
  • zt =t+at,whereat ∼i.i.d.(0,1)forallt∈R.
  • zt = A sin(t + B), where A is a random variable with a zeromean and a unit variance and B is a random variable with a Uniformdistribution (−π, Ï€) independent of A. Hint: You may need to usethe trigonometric formula 2 sin A sin B = cos(A − B) − cos(A + B)and others. You may also need to use the mean and the variance ofUniform random variable.

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