# Suppose that { X t } is an ARIMA( p, d, q ) process satisfying the difference equations 1 answer below »

Suppose that {*X _{t}*} is an ARIMA(

*p, d, q*) process satisfying the difference equations

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Suppose that { X t } is an ARIMA( p, d, q ) process satisfying the difference equations
1 answer below »

Just from $13/Page

*φ(B)(*1 − *B) ^{d}X_{t}*=

*θ(B)Z*{

_{t},*Z*} ∼ WN(0

_{t}*,σ*

^{2})

*.*

Show that these difference equations are also satisfied by the process *W _{t}*=

*X _{t}*+

*A*

_{0}+

*A*

_{1}

*t*+ · · · +

*A*

_{d}_{−1}

*t*

^{d}^{−1}, where

*A*

_{0}

*, . . . , A*

_{d}_{−1}are arbitrary random variables.