This example models all three time series, assuming seasonality in the trends, and without any exogenous variables.
Input
- finance_data3, as in VARMAX Example 1: No Exogenous Model
SQL Call
Seasonal modeling are specified by the Period and SeasonalPDQ arguments.
SELECT * FROM VARMAX ( ON finance_data3 AS "data" PARTITION BY id ORDER BY period USING ResponseColumns ('expenditure', 'income', 'investment') PartitionColumns ('id') PDQ ('1,1,1') SeasonalPDQ ('1,0,0') Period (4) IncludeMean ('false') StepAhead (3) ) AS dt ORDER BY id;
Output
id | coef | coef_value | stepahead | id | predict_expenditure | predict_income | predict_investment |
---|---|---|---|---|---|---|---|
1 | coef | 1, 1, 1, 1, 0, 0, 0 | 1 | 1 | |||
1 | ar_params | [[1.2280127869768733, 0.10369097626637279, 0.7141124344630049], [1.6892503311514915, -0.7866365569885521, 1.2398648486516826], [2.5905232539842906, -1.9806470096597304, 0.848961995714201]] | 1 | 1 | |||
1 | ma_params | [[-1.3578087849315306, 3.1929513989417986, -0.507843441200345], [-0.27161298036695314, 2.0434556838776285, -0.6532994061098848], [-0.3314681626075737, 0.9709146220990982, 0.4986214533613408]] | 1 | 1 | |||
1 | exogenous_params | 1 | 1 | ||||
1 | seasonal_ar_params | [[-0.8516241752486389, 1.4543285878588237, -1.717424059774754], [0.27802014575224626, 1.1028023698734997, -1.981710680445198], [3.6436081834691665, -0.6515504279942187, 0.2101671051863758]] | 1 | 1 | |||
1 | seasonal_ma_params | 1 | 1 | ||||
1 | period | 4 | 1 | 1 | |||
1 | lag | 0 | 1 | 1 | |||
1 | sigma | [[8687.149620951508, 7948.571854972013, 2273.0461867165814], [7948.571854972013, 12790.637540035925, 1116.4386244141892], [2273.0461867165814, 1116.4386244141892, 3484.41990598517]] | 1 | 1 | |||
1 | aic | 26.97888751820004 | 1 | 1 | |||
1 | bic | 28.130584042443644 | 1 | 1 | |||
1 | iterations | 60 | 1 | 1 | |||
1 | converged | true | 1 | 1 | |||
1 | 1 | 2142.78715878754 | 3092.86303423376 | 1 | 3673.84547642858 | ||
1 | 1 | 4144.01202399602 | 7019.73780801767 | 1 | 2413.26665396173 | ||
1 | 1 | 6182.11119125155 | 5848.79519783584 | 1 | -1227.61804348869 | ||
2 | coef | 1, 1, 1, 1, 0, 0, 0 | 2 | 2 | |||
2 | ar_params | [[-2.8588217461202174, 2.132413356693889, 0.048031825091634464], [-1.6669033637617956, 1.0810782826131897, 0.2430782867637148], [-0.4730750055653358, 0.024891878448287257, 0.2376339870230307]] | 2 | 2 | |||
2 | ma_params | [[1.7104434579564591, -2.139631490133681, -0.4000963233539877], [2.995949635314298, -2.2697549832800177, -2.5616082579956614], [0.30188472672917305, -0.7646261744793058, -0.21255497859171532]] | 2 | 2 | |||
2 | exogenous_params | 2 | 2 | ||||
2 | seasonal_ar_params | [[-2.8260118262809155, 2.7154238951166594, -0.8509533086123783], [-2.9395646286325388, 3.1247969541738883, -1.7883773157208929], [-1.3822487137932813, 1.1513048428957071, 0.29884692571288657]] | 2 | 2 | |||
2 | seasonal_ma_params | 2 | 2 | ||||
2 | period | 4 | 2 | 2 | |||
2 | lag | 0 | 2 | 2 | |||
2 | sigma | [[8931.17883016103, 9690.562795737687, 4251.384014300442], [9690.562795737687, 17621.68165475026, 4888.406402279781], [4251.384014300442, 4888.406402279781, 3825.021513435783]] | 2 | 2 | |||
2 | aic | 26.841090807077666 | 2 | 2 | |||
2 | bic | 27.99278733132127 | 2 | 2 | |||
2 | iterations | 89 | 2 | 2 | |||
2 | converged | true | 2 | 2 | |||
2 | 2 | 1879.13079317076 | 2309.21928969857 | 2 | 667.801515797637 | ||
2 | 2 | 2029.37000308685 | 2277.98815737177 | 2 | 568.158627956374 | ||
2 | 2 | 1590.12072329947 | 2093.70018052511 | 2 | 491.215852756901 | ||
3 | coef | 1, 1, 1, 1, 0, 0, 0 | 3 | 3 | |||
3 | ar_params | [[-1.4296101261525473, 2.5315319963982015, 1.541536836147999], [0.5068978405697062, 0.34804164987971653, 0.27906793587515316], [-1.0150487527027767, -0.2032855566913086, 0.07866915491037613]] | 3 | 3 | |||
3 | ma_params | [[1.684265978492897, -1.0116180666097978, -5.533178263753073], [-1.0550984768730498, 1.5756063090213763, 4.70570346190122], [1.660449272138234, 0.6884049529205533, -0.26326075799465776]] | 3 | 3 | |||
3 | exogenous_params | 3 | 3 | ||||
3 | seasonal_ar_params | [[0.3038135044562906, -0.055637121723792274, -0.45848481298992416], [0.8796218186498189, -0.5098716183542696, -0.3679846957572214], [0.7588190526613598, -0.49764695771025447, -0.23842915354370808]] | 3 | 3 | |||
3 | seasonal_ma_params | 3 | 3 | ||||
3 | period | 4 | 3 | 3 | |||
3 | lag | 0 | 3 | 3 | |||
3 | sigma | [[0.04925768206601586, -0.06743723547426139, -0.061586897494505584], [-0.06743723547426139, 0.22449141784354268, 0.28364011938502687], [-0.061586897494505584, 0.28364011938502687, 0.41035204036308964]] | 3 | 3 | |||
3 | aic | -3.544378720752083 | 3 | 3 | |||
3 | bic | -2.567726687519719 | 3 | 3 | |||
3 | iterations | 100 | 3 | 3 | |||
3 | converged | false | 3 | 3 | |||
3 | 3 | 2255.14441988896 | 2673.97520019463 | 3 | 845.302048427789 | ||
3 | 3 | 2310.40934463343 | 2679.05646283002 | 3 | 888.074446679834 | ||
3 | 3 | 2333.56533607469 | 2727.31044779104 | 3 | 820.4016838113 |