H8 - H8 HW4 (due Feb. 7). Exercises 5.1, 5.2 from the...

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H8 HW4 (due Feb. 7). Exercises 5.1, 5.2 from the textbook and Problem 1 Suppose that in a sample of size 100, you obtain ˆ(1) 0.432 ρ = and ˆ(2) 0.145 = . Assuming that the data were generated from an MA(1) model, construct approximate 95% CIs for (1) and (2) . Based on these two confidence intervals, are the data consistent with a MA(1) model with 0.6 θ = ? Problem 2 The graphs below show the sample ASF (left) and PASF (right) of a time series. On the basis of the available information, choose an ARMA model for the data and explain your choice. -1.00 -.80 -.60 -.40 -.20 .00 .20 .40 .60 .80 1.00 0 5 10 15 20 25 30 35 40 Sample ACF 0 5 Sample PACF _______________________________________________________________________________________________________ The prediction problem : from the observed values of a time series at past points, 1 , ... , t X X , predict the value it will assume at some specific future time point, + th X . In forecasting X + , t is called the forecast origin and positive integer h is the forecast horizon . We refer to as the h -step ahead forecast of ˆ X + t X at the forecast origin . t The accuracy of is measured in terms of the smallness of the quantity ˆ + X ( ) 2 ˆ EX X ++ .
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H8 - H8 HW4 (due Feb. 7). Exercises 5.1, 5.2 from the...

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