Consider the Autoregressive (AR(3)) process of order 3 satisfying the equation: x₁ = ₁x₁-1 + 0.25x1-2 - 0.10x1-3+ 8 + u, where var(u) = o². Suppose that the autocorrelation function, p(h), at lag h = 1 takes on the values p(1) = 0.50. In addition var(x,) = 10 and E[x₂] = µ = 25 a) Determine the values of ß₁, § and ♂² . b) Compute and plot a graph of o(h), the auotocovariance function of the process at lag h, for h = 0, 1, 2, 3, 4. c) Find the values of $11, Ø22, Ø33 and Þ44 - the values of the partial autocorrelation function (PAFC) at lags 1, 2, 3 and 4 respectively.

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