Exercises

May 25'23

A time series was observed at times 0, 1, …, 100. The last four observations along with estimates based on exponential and double exponential smoothing with [math]w = 0.8[/math] are:

Time (t)	97	98	99	100
Observation ( [math]y_t[/math] )	96.9	98.1	99.0	100.2
Estimates ( [math]\hat{s_1}(t) [/math]	93.1	94.1	95.1
Estimates ( [math]\hat{s_2}(t)[/math]	88.9	89.9

All forecasts should be rounded to one decimal place and the trend should be rounded to three decimal places.

Let [math]F[/math] be the predicted value of [math]y_{102}[/math] using exponential smoothing with [math]w = 0.8.[/math]

Let [math]G[/math] be the predicted value of [math]y_{102}[/math] using double exponential smoothing with [math]w = 0.8.[/math]

Calculate the absolute difference between [math]F[/math] and [math]G[/math], [math]| F − G |[/math] .

0.0
2.1
4.2
6.3
8.4