Using the results of Exercise 4.44. determine the number of periods following the step change for the expected value of the exponential smoothing statistic to be within 0.10 ?? of the new time series...

Using the results of Exercise 4.44. determine the number of periods following the step change for the expected value of the exponential smoothing statistic to be within 0.10
??of the new time series level
??+
??
.
Plot the number of periods as a function of the smoothing constant. What conclusions can you draw?

Exercise 4.44
Suppose that simple exponential smoothing is being used to forecast a process. At the start of period
t*,
the mean of the process shifts to a new level
??+
??
.
The mean remains at this new level for subsequent time periods. Show that the expected value of the exponentially smoothed statistic is