An autoregressive stationary time series W, is defined by the relationship: W, = 0.5W-1+0.4W-2-0.1W-3 + Z...

Transcribed Image Text:

An autoregressive stationary time series W, is defined by the relationship: W, = 0.5W-1+0.4W-2-0.1W₁-3 + Z₂ for integer times 1, where {Z} represents a set of uncorrelated random variables with mean 0 and variance ². (1) Explain why cov (W,.Z,₁)= 0 and cov (W₁₁.W₂)=cov (W₁-₁.W₁-2). (ii) By considering cov(W₁, W₁-) 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. An autoregressive stationary time series W, is defined by the relationship: W, = 0.5W-1+0.4W-2-0.1W₁-3 + Z₂ for integer times 1, where {Z} represents a set of uncorrelated random variables with mean 0 and variance ². (1) Explain why cov (W,.Z,₁)= 0 and cov (W₁₁.W₂)=cov (W₁-₁.W₁-2). (ii) By considering cov(W₁, W₁-) 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.

Answer rating: 100% (QA)

i Why covWtZt1 0 and covWt1Wt covWt1Wt2 Wt is defined as a line... View the full answer