(a) Suppose that from a time series of 100 observations, r = -0.49, r2 = 0.31,...

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(a) Suppose that from a time series of 100 observations, r₁ = -0.49, r2 = 0.31, r3 = -0.21, r4 = 0.11, and Irkl< 0.09 for k> 4. On this basis alone, which ARIMA model would be tentatively chosen for the series? (3 marks) (b) Suppose that from a stationary time series of length 121, the sample partial autocorrelations are 11=0.8, 22 = -0.6, 33 = 0.08, and 44 = 0.0. Based on this information alone, which ARIMA model would be tentatively chosen for the series? (3 marks) (c) For a time series of 169 observations, we find that r₁=0.41, r2 = 0.32, r3 = 0.26, 14 = 0.21, and r5 = 0.16. Which ARIMA model fits this pattern of autocorrelations? (4 marks) (d) If {Y,} satisfies an AR(1) model with of about 0.7, how long should the series be if we need to estimate = P₁ with 95% confidence that our estimation error is no more than ±0.1? (4 marks) (a) Suppose that from a time series of 100 observations, r₁ = -0.49, r2 = 0.31, r3 = -0.21, r4 = 0.11, and Irkl< 0.09 for k> 4. On this basis alone, which ARIMA model would be tentatively chosen for the series? (3 marks) (b) Suppose that from a stationary time series of length 121, the sample partial autocorrelations are 11=0.8, 22 = -0.6, 33 = 0.08, and 44 = 0.0. Based on this information alone, which ARIMA model would be tentatively chosen for the series? (3 marks) (c) For a time series of 169 observations, we find that r₁=0.41, r2 = 0.32, r3 = 0.26, 14 = 0.21, and r5 = 0.16. Which ARIMA model fits this pattern of autocorrelations? (4 marks) (d) If {Y,} satisfies an AR(1) model with of about 0.7, how long should the series be if we need to estimate = P₁ with 95% confidence that our estimation error is no more than ±0.1? (4 marks)

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a Based on the given information the tentative ARIMA model chosen for the series would be ARIMA202 The autocorrelation coefficients indicate that a si... View the full answer