a. If forecasts are based on simple exponential smoothing, with x n t denoting the smoothed value of the series at time t, show that the error made in forecasting xt , standing at time 1 t - 12, can...

a. If forecasts are based on simple exponential smoothing, with
xnt
denoting the smoothed value of the series at time
t,
show that the error made in forecasting
xt, standing at time 1t
- 12, can be written as follows:

et
=
xt
-
xnt-1

b. Hence, show that we can write
xn

t
=
xt
- 11 - a2et,

from which we see that the most recent observation and the most recent forecast error are used to compute the next forecast.