excans:8c39fe6a58: Difference between revisions

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(Created page with "'''Key: D''' The smoothed forecast at 100 is 0.2(100.2) + 0.8(95.1) = 96.1. This is also the forecast at 102. The smoothed values are at 99: 0.2(95.1) + 0.8(89.9) = 9...")
 
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'''Key: D'''
'''Key: B'''


The smoothed forecast at 100 is
The three one-step predicted values are 12+2.25 = 14.25; 15+2.25 = 17.25; and 21+2.25 = 23.25.


0.2(100.2) + 0.8(95.1) = 96.1.  
The errors are 15 – 14.25 = 0.75; 21 – 17.25 = 3.75; and 22 – 23.25 = –1.25.  


This is also the forecast at 102. The smoothed values are at 99:
F = (0.75 + 3.75 – 1.25)/3 = 1.083


0.2(95.1) + 0.8(89.9) = 90.9. At 100: 0.2(96.1) + 0.8(90.9) = 91.9.  
G = (0.75<sup>2</sup> + 3.75<sup>2</sup> + 1.25<sup>2</sup>)/3 = 5.396


The trend is
The absolute difference is 4.313.
 
0.2(96.1 – 91.9)/.8 = 1.05.
 
The intercept (value at 100) is  
 
2(96.1) – 91.9 = 100.3.
 
The forecast at time 102 is
 
100.3 + 2(1.05) = 102.4.
The difference is 6.3.


{{soacopyright | 2023}}
{{soacopyright | 2023}}

Latest revision as of 17:27, 26 May 2023

Key: B

The three one-step predicted values are 12+2.25 = 14.25; 15+2.25 = 17.25; and 21+2.25 = 23.25.

The errors are 15 – 14.25 = 0.75; 21 – 17.25 = 3.75; and 22 – 23.25 = –1.25.

F = (0.75 + 3.75 – 1.25)/3 = 1.083

G = (0.752 + 3.752 + 1.252)/3 = 5.396

The absolute difference is 4.313.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.