Consider the time series model defined by X =x-ax-2 +3X-3 +&+ where {E} is white noise....

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Consider the time series model defined by X =x-ax-2 +3X-3 +&+ where {E} is white noise. (i) Show that the autocorrelation coefficient with lag 1 for this process is: Pi - (ii) Consider the case where a-02-03 -0.2. (a) Comment on the stationarity of this model. Hint: 5-x-x-x=(1.278-x)(3.912+2.278x+x) (b) Calculate p and p. [3] (c) Calculate the partial autocorrelation coefficients and . T (d) Sketch comelograms of the autocorrelation function and the partial autocorrelation function. (You are not required to calculate the coefficients for higher lags.) [9] [Total 12] Consider the time series model defined by X =x-ax-2 +3X-3 +&+ where {E} is white noise. (i) Show that the autocorrelation coefficient with lag 1 for this process is: Pi - (ii) Consider the case where a-02-03 -0.2. (a) Comment on the stationarity of this model. Hint: 5-x-x-x=(1.278-x)(3.912+2.278x+x) (b) Calculate p and p. [3] (c) Calculate the partial autocorrelation coefficients and . T (d) Sketch comelograms of the autocorrelation function and the partial autocorrelation function. (You are not required to calculate the coefficients for higher lags.) [9] [Total 12]