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You have access to a time series data on stock returns. You know that stock returns follow a first order autoregressive model in population with an intercept (constant). However, you are not certain about how the return variable should be used in the regression. You can either use it in levels with no transformation or demean the variable by differencing with its long run (expected) mean.
(i.) If stock returns in levels follow an AR(l) model with an intercept, what model does the demeaned stock return follow?
(ii.) Analyse the behaviour of the long run forecasts of both stock returns and demeaned stock returns conditional on sample data. You can assume that the slopeof both the models lie in the unit interval (0,1)