We can combine the autoregressive model with the moving average model to form an ARMA model. Here is an example. Suppose ut is stationary with mean zero, e is mean zero, variance o, and each draw is iid. Suppose we have serial correlation so that: Ut = pUt–1 + et + Oer-1

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We can combine the autoregressive model with the moving average model to form an
ARMA model. Here is an example. Suppose uz is stationary with mean zero, e is
mean zero, variance o, and each draw is iid. Suppose we have serial correlation so
that:
Ut = pUt_1 + et + Oe,-1
a. Find the cov (ut, et) as function of the parameters and o.
b. Find the cov (ut, ut-1) as a function of the parameters, o and o.
c. Find the var(ut) as a function of the parameters and o̟.
d. Now find cov(ut, ut-1) again, but this time write it as only a function of the
parameters and o?.
Transcribed Image Text:We can combine the autoregressive model with the moving average model to form an ARMA model. Here is an example. Suppose uz is stationary with mean zero, e is mean zero, variance o, and each draw is iid. Suppose we have serial correlation so that: Ut = pUt_1 + et + Oe,-1 a. Find the cov (ut, et) as function of the parameters and o. b. Find the cov (ut, ut-1) as a function of the parameters, o and o. c. Find the var(ut) as a function of the parameters and o̟. d. Now find cov(ut, ut-1) again, but this time write it as only a function of the parameters and o?.
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