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Consider an ARMA(1,1) process given by Yt = c + Yt1 + t + t1. where || < 1, || < 1, t W N(0,
Consider an ARMA(1,1) process given by Yt = c + Yt1 + t + t1. where || < 1, || < 1, t W N(0, 2 ).
(a) Compute the MA() and AR() representation of the ARMA(1,1) process and state the related assumptions.
(b) Compute E(Yt|Yt1, t1) and V (Yt|Yt1, t1)
(c) Compute E(Yt) an V (Yt).
(d) Compute the autocovariance and autocorrelation function of Yt.
(e) Derive the conditional log likelihood function of the ARMA(1,1)-process above assuming that t is normally distributed and we have appropriate starting values.
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