An autoregressive stationary time series W, is defined by the relationship: W, = 0.5W-1+0.4W-2-0.1W-3 + Z for integer times 1, where {Z} represents a set of uncorrelated random variables with mean 0 and variance . (1) Explain why cov (W,.Z,)= 0 and cov (W.W)=cov (W-.W-2). (ii) By considering cov(W, W-) when k=0,1,2,3 write down a set of four equations relating the values of the autocovariance function 7 at lags k=0,1,2,3.