18.6 Suppose that a particular nonstationary time series y, can be modeled as a stochastic process that is ARIMA(1, 1, 1). (4) After you have estimated the model's parameters, how would you forecast y, one period ahead? Express this one-period forecast, y,(1), as a function of observable data. In what sense is this forecast adaptive?

(b) How would you calculate the standard error of the one-period forecast (1) assuming that the parameters of the model are known perfectly? Note that this is analogous to calculating the standard error of a regression forecast under the assumption that the coefficients are known perfectly.

(c) What will be the difference between the I-period forecast 9,(I) and the (+1) period forecast ,(+ 1) when I is very large?