Given

• Order: ,

• Coefficient matrix:

• Intercept:
• Initial innovation:
• Two series stacked into :

	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

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

Step 1 — formula

Substitute into the VMA recursion:

Forecast (set ):

Componentwise:

Innovation:

Step 2 — apply at

Plug in , , :

Step 3 — iterate

Each row uses the previous innovation . Values rounded to 4 decimal places at every step (computation continues from the rounded value).

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