Given

• Orders: , , , , (one exog)

• Coefficient matrices:

• Intercept:
• Initial conditions: ,
• Endogenous :

	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

• Exogenous :

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

Step 1 — formula

Substitute orders into the VARIMAX recursion (with , no differencing):

Forecast (set ):

Three contributions: AR product, exogenous regression , MA product.

Componentwise:

Innovation:

Step 2 — apply at

Compute the three contributions separately, then sum.

AR part:

Exog part:

MA part: . With , the step gives and .

Sum:

Step 3 — iterate

Three contributions per row: AR , exog , MA . Values rounded to 4 decimal places.

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