1.0 - 8.00 - VARMAX Example 1: 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 uses three time series as response columns modeled by the autoregression (AR) and moving average (MA) parameters. Because the model uses no exogenous variables, it is equivalent to the VARMA model.

Input

The input table, finance_data3, has seasonally adjusted quarterly financial data from West Germany between 1960 and 1982, in billions of Deutsche Marks. The table has three time series—consumer expenditures, disposable income, and fixed investmen—partitioned by the column id, which indicates the decade.

finance_data3
id period expenditure income id investment
1 1960Q1 415 451 1 180
1 1960Q2 421 465 1 179
1 1960Q3 434 485 1 185
1 1960Q4 448 493 1 192
1 1961Q1 459 509 1 211
1 1961Q2 458 520 1 202
1 1961Q3 479 521 1 207
1 1961Q4 487 540 1 214
1 1962Q1 497 548 1 231
1 1962Q2 510 558 1 229
1 1962Q3 516 574 1 234
1 1962Q4 525 583 1 237
1 1963Q1 529 591 1 206
1 1963Q2 538 599 1 250
... ... ... ... ... ...

SQL Call

Three values are predicted (StepAhead (3)) for each time series with PDQ (1, 1, 1).

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')
  IncludeMean ('false')
  StepAhead (3)
) AS dt ORDER BY id;

Output

Series id = 2 does not converge. You might improve convergence by adding more orders or more models.

id coef coef_value stepahead id predict_expenditure predict_income predict_investment
1 coef 1, 1, 1, 0, 0, 0, 0   1      
1 ar_params [[0.5401142443401908, -0.22144696209085052, -0.8658134069625404], [0.46112845524514406, -0.3141400396767603, 0.5401312499458767], [-0.5436170410196307, 0.3550487442187296, 0.11840800979913536]]   1      
1 ma_params [[0.9418274466713232, 0.47136752532237564, -3.5912652252354267], [0.6921921561542808, 1.1978201256969616, -3.1537918114389636], [-0.4072848688634932, 0.5456117174031574, -1.0037912602351198]]   1      
1 exogenous_params     1      
1 seasonal_ar_params     1      
1 seasonal_ma_params     1      
1 period 0   1      
1 lag 0   1      
1 sigma [[9303.34637558586, 8911.919784323425, 2489.9006735815274], [8911.919784323425, 11603.406279896304, 2608.8269629048896], [2489.9006735815274, 2608.8269629048896, 1873.3459372621583]]   1      
1 aic 25.17173031402279   1      
1 bic 25.939527996851854   1      
1 iterations 90   1      
1 converged true   1      
1     1 1 1938.76079858415 2252.24766189307 744.997964522574
1     2 1 1925.43436379877 2283.39702101694 740.419046284062
1     3 1 1915.30312439615 2264.99334498778 758.180883573926
2 coef 1, 1, 1, 0, 0, 0, 0   2      
2 ar_params [[-2.068628487877914, 1.4352819442850229, 0.5040312926651062], [-1.7033511912858643, 1.4975506746058223, 0.5074485754476421], [0.02390658218391805, 0.09069981493533767, 0.6323254473495666]]   2      
2 ma_params [[1.1099224166373396, -1.4699745679694927, -0.13597198353294757], [2.0484118200773467, -1.461011739772329, -0.966987021587989], [1.215189995141357, -0.48167519587064467, -0.7805184850752649]]   2      
2 exogenous_params     2      
2 seasonal_ar_params     2      
2 seasonal_ma_params     2      
2 period 0   2      
2 lag 0   2      
2 sigma [[20710.85970757356, 19488.49092866746, 3238.838942282427], [19488.49092866746, 23099.4579527159, 7096.235865937958], [3238.838942282427, 7096.235865937958, 4997.15664809357]]   2      
2 aic 26.28445013189386   2      
2 bic 27.052247814722925   2      
2 iterations 100   2      
2 converged false   2      
2     1 2 1647.53805974095 1992.4468446864 677.020182217684
2     2 2 1797.20517373109 2154.41616652847 744.891590184598
2     3 2 1754.28047469318 2176.47902609351 806.077025266635
3 coef 1, 1, 1, 0, 0, 0, 0   3      
3 ar_params [[2.356733508164794, -0.5621044042754211, -1.4440215700897763], [1.3690594672816452, -0.374171671178873, 0.145908702245906], [-0.46084660401307126, 0.5119208015206022, 0.5487744352179722]]   3      
3 ma_params [[1.4346653216242653, 1.2117554668497033, -1.3437736962000293], [2.4823004009827208, 0.7810702841064198, 0.9249544231941549], [1.2614528273336505, 0.46230687456647834, 0.8258407892382512]]   3      
3 exogenous_params     3      
3 seasonal_ar_params     3      
3 seasonal_ma_params     3      
3 period 0   3      
3 lag 0   3      
3 sigma [[3350.0872240469225, 2079.903284457588, -57.80956553330401], [2079.903284457588, 1813.642959968383, 53.094810167970195], [-57.80956553330401, 53.094810167970195, 545.3242237694398]]   3      
3 aic 23.919079900514713   3      
3 bic 24.570181256002957   3      
3 iterations 96   3      
3 converged true   3      
3     1 3 2349.23362243522 2735.7962811932 863.755002444903
3     2 3 2437.20210713965 2816.0995450051 889.634165862864
3     3 3 2562.01149424731 2910.26242054004 904.404922890561