Given

• Smoothing parameter:
• Initial level:
• Data:

	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
	12	10	8	11	14	12	9	13	16	14	11	15	18	16	13	17

Step 1 — formula

Observation:

Innovation (rearrange):

State update:

One-step-ahead forecast:

Step 2 — apply at

Use and :

Step 3 — iterate

Values rounded to 4 decimal places; arithmetic performed at full precision.

1	12
2	10
3	8
4	11
5	14
6	12
7	9
8	13
9	16
10	14
11	11
12	15
13	18
14	16
15	13
16	17

Forecast for any future : (flat — SES has no trend).