Consider the following variables,andwhich follow different processes involving moving averages:

= + 0.98₁

= 2 + ₂

-0.5₁= 0.75₁+ 0.125₂

where,andare all uncorrelated white noise error terms.

i)Using the definition of invertibility, demonstrate which of the processes,andcan be inverted and written as a pure autoregressive (AR) model. What are the implications of this? For the process(es) which you find to be

invertible, derive an expression for the inverted series and provide a discussion of the results.

ii)Suppose you observed a sample of data for the variablefrom Equation 3 and decide to estimate an AR(1) model. Would you expect to obtain an unbiased estimator of the autoregressive coefficient? Explain your answer.