3. (4 points) AR(p): (1+Ø1L + Ø2L? +...+ØpLP) X4={t MA(q): X+=(1+0,1 + 0212+...+0,29)ɛt where {ęt} is a white noise process and {xt} is a time series, a sequence of realizations of the white noise process {{t}. Et
(1 – z)-1=1+z+z2+z3 +... for [z]<1
3. (4 points) AR(p): (1+Ø1L + Ø222+...+ØpLP) X4=ęt MA(q): X+=(1+0,1 + 0212+...+0,29)ɛt where {&t} is a white noise process and {Xt} is a time series, a sequence of realizations of the white noise process {{t}. Prove that AR(2) model can be inverted to MA(00). (Use the lag operator L, and assume the conditions necessary for inversion are all fulfilled) Hint: Use the Taylor expansion for equation (1 – z)-1=1+z+z2+z3 +... for 1z|<1
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