Postscript version of these notes


STAT 804

Assignment 4

1.
Derive formulas for the L-step ahead forecast standard error for the AR(1) model $Y_t=\phi Y_{t-1}+\epsilon_t$ and for the ARIMA(1,1,0) model $(I-\phi B)(I-B) Y =\epsilon$. Compute the limits of the forecast standard errors for these two models as La tends to infinity.

2.
Delete the last 4 values for the earnings data set and use the model you selected in the previous assignment to re-estimate the parameters and forecast the deleted values. Compare the actual errors with the forecasts and the forecast standard errors.

3.
For the dataset faketrend in the usual directory (ASCII here ) remove a trend by ordinary least squares. Then fit the model you used with fake in the previous assignment to the residuals. Use the autocovariance of the fitted to re-estimate the trend by generalized squares. Does the fit change much?



Richard Lockhart
1999-10-12