non-invertible moving average process

Problem 4, 20pts: non-invertible moving average process Let {Xt} be the (non-invertible) MA(1) process Xt = Z+ + 0Zt-1, {Zt} ~ WN(0, 62) where |0| > 1. Define Wt = 2j=o (-0)7- Xt-j and show that {Wt} is white noise with variance ow; find the expression for ow in terms of 0 and o2. Finally, show that Xt has invertible representation 1 Xt = Wt+ -Wt-1