The observations: 166, 163, 162, 164, 167, 171, 172, 174, 172, 169 represent the values Y91, Y92, ..., Y100 from a time

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The Observations 166 163 162 164 167 171 172 174 172 169 Represent The Values Y91 Y92 Y100 From A Time 1 (83.06 KiB) Viewed 98 times

The observations: 166, 163, 162, 164, 167, 171, 172, 174, 172, 169 represent the values Y91, Y92, ..., Y100 from a time series fitted by the model (1 – 0.8B)(1 – B)Y4 = Et + 0.6Et-1 - 0.5€t-2. Answer the following questions. (a) (3 points) Compute the optimal forecasts Ķ100(1) for 1 = 1, 2, 3, 4 and draw a graph of the series values and the forecasts (use E91 = €92 = 0). (b) (3 points) Determine the coefficients ur in the infinite MA form of the above model for l = 1,2,3. (e) (2 points) With ô = 1.1, calculate the estimated standard deviations o(l) = St. Ôev.(100()) of the forecast error e100(l) for 1 = 1,2,3,4 and use them to determine 90% prediction intervals for the future values Y100(1). Insert these prediction limits on your graph from (a). (d) (2 points) Show the following updating formula for the AMIMA(p,d,q) model Ý (0) = Ý(1+1) + 1/(X+1- Ý(1). (e) (3 points) Given the new observation Y101 = 170, calculate the new forecast Ý101(l) for 1 = 1,2,3 using the updating formula in (d). (f) (2 points) Determine the general form of the “eventual” forecast function Ỹt(l) for this process. =