# VARMAX Example 2: Exogenous Model - Teradata Vantage

## Teradata® Vantage Machine Learning Engine Analytic Function Reference

Product
Release Number
1.0
8.00
Published
May 2019
Language
English (United States)
Last Update
2019-11-22
dita:mapPath
blj1506016597986.ditamap
dita:ditavalPath
blj1506016597986.ditaval
dita:id
lmf1502735330121
Product Category

This example models the expenditure time series as a function of exogenous variables (income and investment) and the AR and MA parameters. The function chooses the order and lag of the variables according to the degree of complexity, typically a trade-off between accuracy and over-fitting.

## SQL Call

```SELECT * FROM VARMAX (
ON finance_data3 AS "data" PARTITION BY id ORDER BY period
USING
ResponseColumns ('expenditure')
ExogenousColumns ('income', 'investment')
PartitionColumns ('id')
PDQ ('1, 1, 1')
Lag (3)
ExogenousOrder (3)
IncludeMean ('false')
) AS dt ORDER BY id;```

## Output

The model converges for all three decades.

1 coef 1, 1, 1, 0, 0, 0, 3
1 ar_params [[-0.11048447321369022]]
1 ma_params [[-0.1925561123625604]]
1 exogenous_params [[0.15184265006071107, -0.6548579365873168]], [[3.4356161960447644, -3.8815455917944566]], [[1.352629223976695, 1.6692441091760393]]
1 seasonal_ar_params
1 seasonal_ma_params
1 period 0
1 lag 3
1 sigma [[21815.169519750183]]
1 aic 10.400617266572384
1 bic 10.74186068116308
1 iterations 18
1 converged true
1     1 4601.67249271766
1     2 6375.70446779608
1     3 6353.20194246941
2 coef 1, 1, 1, 0, 0, 0, 3
2 ar_params [[0.7135109382825823]]
2 ma_params [[0.8116168306474483]]
2 exogenous_params [[-1.3199094913183353, 3.7663680262105013]], [[0.8573542123886598, -2.361564228588058]], [[0.7742458737629424, -2.39596174873262]]
2 seasonal_ar_params
2 seasonal_ma_params
2 period 0
2 lag 3
2 sigma [[41347.85268103083]]
2 aic 11.040032179034085
2 bic 11.381275593624782
2 iterations 18
2 converged true
2     1 1738.29815872784
2     2 1683.52303336657
2     3 1737.17454282084
3 coef 1, 1, 1, 0, 0, 0, 3
3 ar_params [[0.7034293980424465]]
3 ma_params [[-0.5320720491694714]]
3 exogenous_params [[0.21057556006931047, -0.5831916151232963]], [[-0.09419582311809366, 0.2501649697569839]], [[0.4552695851877213, -1.121807842101149]]
3 seasonal_ar_params
3 seasonal_ma_params
3 period 0
3 lag 3
3 sigma [[1.2480831335136702E-25]]
3 aic -55.88847298918466
3 bic -55.59909460896767
3 iterations 25
3 converged true
3     1 2321.97511577896
3     2 2404.77038121072
3     3 2433.88438933071