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QUESTION 2 (a) For each of the ARIMA models below, give the values for E(VY) and Var(VY) 0.Tet-1 (ii) Yt = 10 + 1.25%-1-0.25Yt-2 et-0.14-i (b) Show that the function Z, a t-1 not stationary, but the first difference of Z, is stationary

QUESTION 5 (a) From a series Y, of length 100, the sample autocorrelations at lags 1-3 are 0.8, 0.5 and 0.4, respectively. Furthermore, the respective sample mean and sample variance of the series are 2 and s-5. Suppose that the appropriate model for the series is the AR (2) model where φί, φ2 and θί are model parameters, and €1,e2, distributed random variables with mean 0 and variance ơ2 Find the method of moments estimates of o-a, фг and ơ are independent and identically (b) For the ARMA (1,2) model Y0.8Y-1et 0.7e,-1 +0.6et-2, show that: (i) (ii) ρ,-0.8A-1 for k > 2. ρ,-0.8P1 +0.6/70

math   Statistics-And-Probability   
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