The TD_AUTOARIMA function can create a multilayered ART table.The function generates up to five analytical result sets:
- Primary result set containing the selected best model’s coefficients.
- Secondary result set containing “goodness of fit” metrics.
- Tertiary result set containing residuals from the fitting exercise.
- Quaternary result set containing the best model context, which is used during the forecasting process.
- Quinary result set containing the information criteria such as AIC and SBIC, and the order of the best model.
- Senary result set containing the roots information.
The first 3 layers are the same as the layers from TD_ARIMAESTIMATE and can be used with TD_ARIMAFORECAST to do the future forecast analysis. The last 3 layers are always generated and there are no options on them like fit metric or residual layers.
The primary result set are accessed using a SELECT statement. The other results sets are accessed using the TD_EXTRACT_RESULTS function.
| Name | Data Type | Description |
|---|---|---|
| derived-series-identifier | Varies | The resultant series identifying the field list. |
| INDEX | Integer | An integer index that identifies the coefficient. Index of 1 corresponds to the constant coefficient. Other indices associated with coefficients in accordance to order in which they appeared in the formula. |
| COEFF_NAME | VARCHAR (120) | Name of the coefficient. |
| COEFF_VALUE | FLOAT | The calculated value of the coefficient determined by the selection process. |
| STD_ERROR | FLOAT | The standard error associated with the calculated value for that coefficient. Only returned if COEFF_STATS(1). |
| ZSTAT_VALUE | FLOAT | The z-statistic associated with the calculated value for that coefficient. Only returned if COEFF_STATS(1). |
| ZSTAT_PROB | FLOAT | The probability associated with the z-statistic. It is the probability of obtaining an absolute value of z as large as the one that was calculated for the data, if the coefficient is 0. Only returned if COEFF_STATS(1). |
RETURNS TABLE Schema for Secondary Result Set
| Name | Data Type | Description |
|---|---|---|
| derived-series-identifier | Varies | The resultant series identifying the field list. |
| NUM_SAMPLES | Integer | Total number of sample points found in each of the original, calculated, and residual series. |
| VAR_COUNT | Integer | Number of explanatory variables, including the constant, in the original regression. |
| R_SQUARE | FLOAT | The calculated R-squared value from the original and calculated values. |
| R_ADJ_SQUARE | FLOAT | The calculated adjusted R-squared value from the original and calculated values. |
| STD_ERROR | FLOAT | The standard error or deviation associated with the model. |
| STD_ERROR_DF | FLOAT | The degrees of freedom associated with the standard error calculation. |
| ME | FLOAT | The Mean Error. |
| MAE | FLOAT | The Mean Absolute Error. |
| MSE | FLOAT | The Mean Squared Error. |
| MPE | FLOAT | The Mean Percent Error. |
| MAPE | FLOAT | The Mean Absolute Percent Error. |
| F_STAT_CALC | FLOAT | The calculated F-statistic value for the ordinary least squares (OLS) regression. |
| P_VALUE | FLOAT | The p-value corresponding to the calculated test statistic. |
| NUM_DF | FLOAT | The degrees of freedom in the numerator associated with the unexplained portion of the F-statistic. |
| DENOM_DF | FLOAT | The degrees of freedom in the denominator associated with the explained portion of the F-statistic. |
| SIGNIFICANCE_LAYER | FLOAT | Level of significance for the test. |
| F_CRITICAL | FLOAT | The chi-squared critical value extracted from the chi-squared statistic tables. |
| F_CRITCAL_P | FLOAT | The p-value corresponding to the calculated critical value. |
| NULL_HYPOTH | VARCHAR(16) | The result of the test.
|
RETURNS TABLE Schema for Tertiary Result Set
| Name | Data Type | Description |
|---|---|---|
| derived-series-identifier | Varies | The resultant series identifying the field list. |
| ROW_I | Varies | Indexing column for the one dimensional multivariate output array containing the residuals. It is incremented by 1 for each row, starting from 1. The value could be another data type based on the flowthrough feature. |
| ACTUAL_VALUE | FLOAT | The actual value of the response variable. |
| CALC_VALUE | FLOAT | The calculated value of the response variable using the model. |
| RESIDUAL | FLOAT | The difference between the calculated response value and the actual response value. |
RETURNS TABLE Schema for Quaternary Result Set
| Name | Data Type | Description |
|---|---|---|
| derived-series-identifier | Varies | The resultant series identifying the field list. |
| ROW_I | Integer | The model row number. |
| MODEL_DATA | VARBYTE (64000) | Model context in binary form. |
RETURNS TABLE Schema for Quinary Result Set
| Name | Data Type | Description |
|---|---|---|
| derived-series-identifier | Varies | The resultant series identifier inherited from the SERIES_ID. |
| ROW_I | Integer | The index of the series. |
| NUM_SAMPLES | Integer | Total number of sample points found in each of the original, calculated, and residual series. |
| VAR_COUNT | Integer | Total number of parameters involved in the model. For an ARMA(p,q) model, the calculation of VAR_COUNT is p + q + 1. |
| AIC | FLOAT | The calculated Akaike Information Criteria value. |
| SBIC | FLOAT | The calculated Schwarz Bayesian Information Criteria value. |
| HQIC | FLOAT | The calculated Hannon Quinn Information Criteria value. |
| MLR | FLOAT | The calculated Maximum Likelihood Rule value. |
| MSE | FLOAT | The calculated Mean Square Error value. |
| MODEL_ORDER | VARCHAR | The order information of final picked best model. |
RETURNS TABLE Schema for Senary Result Set
| Name | Data Type | Description |
|---|---|---|
| ROW_I | Integer | The index of the series. |
| ROOTS_NAME | VARCHAR | The type of root and its sequence in this type,, such as ARROOT1. |
| REAL | FLOAT | The real part of the inverse root. |
| IMAG | FLOAT | The imaginary part of the inverse root. |
| UNIT_CIRCLE | VARCHAR | Indicator that the root is within the unit circle. There should be no inverse roots outside the unit circle for TD_AUTOARIMA selected output model.
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