1.0 - 8.00 - VARMAX Example 3: Seasonal Model, No Exogenous Model - Teradata Vantage

Teradata® Vantage Machine Learning Engine Analytic Function Reference

Product
Teradata Vantage
Release Number
1.0
8.00
Release Date
May 2019
Content Type
Programming Reference
Publication ID
B700-4003-098K
Language
English (United States)

This example models all three time series, assuming seasonality in the trends, and without any exogenous variables.

Input

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