This example models the expenditure time series as a function of exogenous variables (income and investment) and the AR and MA parameters.
Input
- finance_data3, as in VARMAX Example: No Exogenous Model
SQL Call
SELECT * FROM VARMAX ( ON finance_data3 AS InputTable PARTITION BY id ORDER BY period USING TargetColumns ('expenditure') ExogenousColumns ('income', 'investment') PartitionColumns ('id') PDQ ('1, 1, 1') Lag (3) ExogenousOrder (3) IncludeMean ('false') StepAhead (3) ) AS dt ORDER BY id;
Output
The model converges for all three decades.
id coef coef_value stepahead predict_expenditure -- ------------------ ------------------------------------------------------------------------------------------------------------------------------------- --------- ------------------- 1 lag 3 NULL NULL 1 exogenous_params [[0.1519680005451124, -0.6551050387116059]],[[3.435192616763898, -3.882673202143499]],[[1.3541313678881937, 1.6646325777482736]] NULL NULL 1 bic 10.741829043275684 NULL NULL 1 seasonal_ar_params NULL NULL NULL 1 ar_params [[-0.11089814304828957]] NULL NULL 1 iterations 52 NULL NULL 1 seasonal_ma_params NULL NULL NULL 1 NULL NULL 1 4600.7706184855 1 period 0 NULL NULL 1 ma_params [[0.19307253407851677]] NULL NULL 1 aic 10.400585628684988 NULL NULL 1 coef 1, 1, 1, 0, 0, 0, 3 NULL NULL 1 sigma [[21814.479344791267]] NULL NULL 1 converged true NULL NULL 1 NULL NULL 2 6373.998107354011 1 NULL NULL 3 6350.744363017893 2 NULL NULL 2 1687.7469213444433 2 NULL NULL 1 1738.714144436625 2 period 0 NULL NULL 2 converged true NULL NULL 2 iterations 41 NULL NULL 2 seasonal_ma_params NULL NULL NULL 2 ma_params [[-0.8359845907086888]] NULL NULL 2 bic 11.376308711954195 NULL NULL 2 aic 11.035065297363499 NULL NULL 2 seasonal_ar_params NULL NULL NULL 2 sigma [[41142.99197004428]] NULL NULL 2 NULL NULL 3 1741.1916880853182 2 lag 3 NULL NULL 2 exogenous_params [[-1.2720319560315987, 3.655852449852053]],[[0.8360385941734287, -2.302383393590858]],[[0.7593553302868498, -2.374110320858793]] NULL NULL 2 ar_params [[0.7108652352664463]] NULL NULL 2 coef 1, 1, 1, 0, 0, 0, 3 NULL NULL 3 ma_params [[-0.0614288647351308]] NULL NULL 3 seasonal_ar_params NULL NULL NULL 3 seasonal_ma_params NULL NULL NULL 3 period 0 NULL NULL 3 sigma [[6.363011312881083E-13]] NULL NULL 3 aic -26.62855901221182 NULL NULL 3 bic -26.33918063199482 NULL NULL 3 iterations 100 NULL NULL 3 converged false NULL NULL 3 NULL NULL 1 2322.3532307390687 3 NULL NULL 2 2383.7876893596203 3 NULL NULL 3 2361.660078073284 3 lag 3 NULL NULL 3 exogenous_params [[0.25875628651307314, -0.6072084966292083]],[[-0.05294450371858871, 0.1933161164790199]],[[0.5381262647961994, -1.2967359488966945]] NULL NULL 3 ar_params [[0.18907298111234366]] NULL NULL 3 coef 1, 1, 1, 0, 0, 0, 3 NULL NULL
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