You are estimating the expected value of the annual return of a stock-market index using an EWMA

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You are estimating the expected value of the annual return of a stock-market index using an EWMA estimator with a decay factor of 0.98. The current estimate of the mean is 10%. Over the next three years, the index returns 15%, –4%, and finally 8%.

Recalculate the estimate of the mean in each of these three years. Assume that the window length is infinite.

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