Question 4: [15 marks] This is a theory-only question. Do not attempt
to use data in this question.
Consider the ARMA(2,1) process with drift
44 ~ N(0,02) white noise
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a) Compute the autocovariance function of y. You may assume the pro-
cess is covariance stationary. [You may take a maximum of 10 points
on this question by setting 4 = 0 if you wish in this part only. Please
be clear and indicate if you do this.]
b) Explain how to produce a two-step-ahead forecast using this model.
c) Consider the poorly-formed model
4 ~ N(0, 0?) white noise
Suppose 0*
= (H*, Pi, 92, 40, 45, (02)*) is a MLE for this model (given
some hypothetical data). Find another MLE for this model. That is,
show that the MLE for this model is not unique. (Hint: Your new
MLE values will be in terms of the parameters in 0*.)
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