Question

Consider the ARIMA(0,1,1) model (1−B)zt = (1−0.8B)at. (a) Is the stochastic process for zt stationary ? Explain. (b) Show that this model can be written as zt = ¯ zt−1 + at where ¯ zt−1 =P ∞ j=1 πjzt−j. Derive the coefficients πj and show thatP∞ j=1 πj = 1. (c) Write the one- and two-step-ahead forecasts in the form zt(1) = ∞ X j=1 πjzt−j+1 and zt(2) = ∞ X j=1 π(2) j zt−j+1 Express π(2) j in terms of the πj weights.s

Answer 1

Solution -

The given ARIMA(0,1,1) model is,

Hence actually it is a ARMA(1,1) process which is always stationary.

Now any ARMA(1,1) stochastic process would be stationary if , but here its 1. Hence it's not stationary.

For your information, if it would stationary then,

Note - Kindly upload the question perfectly, 2nd part is not clearly understandable.