Consider an exponential smoothing forecast with smoothing parameter $$

and answer following questions:

$($i$)$ In this exponential smoothing forecast, what is the weight

applied to data $$ periods old? What will happen if $$ increases?

Show your calculations.

$($ii$)$ What is the average age of data in this exponential smoothing

forecast? Show your calculations.

$($iii$)$ Show and compare the effect of an observation from $6$ periods

back for $1=0\mathrm{.}1$ and $2=0\mathrm{.}8.$