A Statistician Claims To Have Fitted Both An Ma 1 Model And An Ar 1 Model To Some An 1864379

A statistician claims to have fitted both an MA(1) model and an AR(1) model to some annual factory accident data with a mean removed, denoted xt. The two models he provides are

where εt is supposed to represent white noise. Why might you be surprised that he is unable to distinguish between these two models?

Given the following observations from the xt series

form one-and two-step forecasts during each of the years t = 1 to t = 6 using both of the models, and compare the relative forecasting abilities of the models. (Assume ε0 = 0.)