O-X13-ARIMA-Output.qmd

# Output from X13-Arima {#output-chap .unnumbered}

## In this chapter

The output of X13-Arima procedure is detailed (Reg-Arima pre-processing, and X11 Decomposition).

(pre-processing or pre-adjustment or pre-treatment are used interchangeably)

This presentation is broken down by categories to make navigation easier

- series

  - final series resulting from a complete SA process, typically final series include re-allocated pre-adjustment effects

  - pre-adjustment series

  - decomposition series (based on the linearized series without pre-adjustment effects)

- parameters from

  - pre-processing

  - decomposition

- diagnostics on

  - pre-processing (eg: tests on Reg-arima model residuals)

  - decomposition (M Statistics)

  - SA process: tests for residual, seasonality, residual Trading Days effects...

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## How to generate output ?

### From Graphical User Interface

### Using the Cruncher

### With rjd3x13

### Description details

Name: name: is name in... unless difference is signalled

Fullname and how to parametrize (?)

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## Series

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### Final series from Seasonal Adjustment Process

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| Name | Description | GUI display | Fullname |
|-----------------|-----------------------|-----------------|-----------------|
| y | Original series | Main Results \> Table | y |
| y_f | Forecasts of original series | Main Results \> Table | y_f(?) |
| y_ef | Forecasts errors of original series | Main Results \> Table | y_ef(?) |
| y_b | Backcasts of original series | Main Results \> Table | y_b(?) |
| y_eb | Backcasts errors of original series | Main Results \> Table | y_eb(?) |
| sa | Seasonally adjusted series | Main Results \> Table | sa |
| sa_f | Forecasts of seasonally adjusted series | Main Results \> Table | sa_f |
| t | Trend component | Main Results \> Table | t |
| t_f | Forecasts of trend | Main Results \> Table | t_f |
| s | Seasonal component | Main Results \> Table | s |
| s_f | Forecasts of seasonal component | Main Results \> Table | s_f |
| i | Irregular component | Main Results \> Table | i |
| i_f | Forecasts of irregular component | Main Results \> Table | i_f |
| ycal | series corrected for calendar effects: y_cal = yc-/cal | Pre-Processing \> Pre-adjustment series | ycal |
| ycal_f | forecasts of the series corrected for calendar effects | Pre-Processing \> Pre-adjustment series | ycal_f(?) |
| ycal_b | backcasts of the series corrected for calendar effects | Pre-Processing \> Pre-adjustment series | ycal_b(?) |
| benchmarking.original | Unbenchmarked sa series | No | benchmarking.original |
| benchmarking.target | Series used to compute annual targets | No | benchmarking.target |
| benchmarking.result | Final benchmarked sa series | No | benchmarking.result |

### Final series with X-11 style names

Backcasts of final series can be retrieved only from this table.

GUI display: Decomposition (X11)\>D-Final-Table

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| Name        | Description                                     |
|-------------|-------------------------------------------------|
| finals.d11  | Seasonally adjusted series (=sa)                |
| finals.d12  | Trend component (=t)                            |
| finals.d13  | Irregular component (=i)                        |
| finals.d16  | Seasonal component (=s)                         |
| finals.d18  | Calendar effects (=cal)                         |
| finals.d11a | Forecasts of seasonally adjusted series (=sa_f) |
| finals.d12a | Forecasts of trend (=t_f)                       |
| finals.d16a | Forecasts of seasonal component (=s_f)          |
| finals.d18a | Forecasts of the calendar effects (=cal_f)      |
| finals.d11b | Backcasts of seasonally adjusted series         |
| finals.d12b | Backcasts of trend                              |
| finals.d16b | Backcasts seasonal component                    |
| finals.d18b | Backcasts of the calendar effects (=cal_b)      |

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### Robustified final series

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GUI display: Decomposition (X11)\> E-Table

| Name | Description |
|-------------------|-----------------------------------------------------|
| finals.e1 | Original series corrected for most important outliers |
| finals.e2 | Final seasonally adjusted series corrected for most important outliers |
| finals.e3 | Final Irregular corrected for most important outliers |
| finals.e11 | Robust estimation of final seasonally adjusted series |

### Pre-processing series

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GUI display: Pre-Processing \> Pre-adjustment series

attention couper à la fin series not displaed in GUI ? generable in GUI output ?

| Name | Description | Fullname |
|-------------|---------------------------------------------|-------------|
| yc | interpolated series. Untransformed | yc |
| yc_f | forecasts of the interpolated series | yc_f(?) |
| yc_b | backcasts of the interpolated series | yc_b(?) |
| ylin | linearized series (series without pre-processing and regression effects). l=yc-/det. Untransformed | ylin |
| ylin_f | forcasts of the linearized series. Untransformed | ylin_f(?) |
| ylin_b | backcasts of the linearized series. Untransformed | ylin_b(?) |
| det | all deterministic effects (including pre-processing, but without trend polynomial effect). Untransformed | det |
| det_f | forcasts of all deterministic effects (including pre-processing, but without trend polynomial effect). Untransformed | det_f(?) |
| det_b | backcasts of all deterministic effects (including pre-processing, but without trend polynomial effect). Untransformed | det_b(?) |
| cal | all calendar effects (including pre-processings). cal=tde+\*mhe. Untransformed | cal |
| cal_f | forecasts of all calendar effects. Untransformed | cal_f(?) |
| cal_b | backcasts of all calendar effects. Untransformed | cal_b(?) |
| ycal | series corrected for calendar effects: y_cal = yc-/cal. Untransformed | ycal |
| ycal_f | forecasts of the series corrected for calendar effects. Untransformed | ycal_f(?) |
| ycal_b | backcasts of the series corrected for calendar effects. Untransformed | ycal_b(?) |
| tde | trading days effects (including leap year/length of period, including pre-processings). Untransformed | tde |
| tde_f | forecasts of the trading days effects. Untransformed | tde_f(?) |
| tde_b | backcasts of the trading days effects. Untransformed | tde_b(?) |
| ee | Easter effects. Untransformed | ee |
| ee_f | forecasts of the Easter effects. Untransformed | ee_f(?) |
| ee_b | backcasts of the Easter effects. Untransformed | ee_b(?) |
| omhe | other mothing holidays effects. Untransformed | omhe |
| omhe_f | forecasts of the other mothing holidays effects. Untransformed | omhe_f(?) |
| omhe_b | backcasts of the other mothing holidays effects. Untransformed | omhe_b(?) |
| mhe | all moving holidays effects. mhe=ee+\*rmde+\*omhe. Untransformed | mhe |
| mhe_f | forecats of all moving holidays effects. mhe=ee+\*rmde+\*omhe. Untransformed | mhe_f(?) |
| mhe_b | backcasts of all moving holidays effects. mhe=ee+\*rmde+\*omhe. Untransformed | mhe_b(?) |
| out | all outliers effects. Untransformed | out |
| out_f | forecasts of all outliers effects. Untransformed | out_f(?) |
| out_b | backcasts of all outliers effects. Untransformed | out_b(?) |
| reg | all other regression effects (outside outliers and calendars). Untransformed | reg |
| reg_f | forecasts of all other regression effects (outside outliers and calendars). Untransformed | reg_f(?) |
| reg_b | backcasts of all other regression effects (outside outliers and calendars). Untransformed | reg_b(?) |
| l | linearized series (transformed series without pre-processing and regression effects). Transformed) | l |
| l_f | forecasts of the linearized series. Transformed) | l_f(?) |
| l_b | backcasts of the linearized series. Transformed) | l_b(?) |
| full_res | full residuals | full_res |
| out_t | outliers effects associated to the trend | out_t |
| out_s | outliers effects associated to the seasonal | out_s |
| out_i | outliers effects associated to the irregular | out_i |
| reg_t | other regression effects associated to the trend | reg_t |
| reg_s | other regression effects associated to the seasonal | reg_s |
| reg_i | other regression effects associated to the irregular | reg_i |
| reg_sa | other regression effects associated to the sa | reg_sa |
| reg_u | other undefined regression effects (split between the components | reg_u |
| reg_y | other regression effects removed from the series (not in the components | reg_y |
| det_t | all regression effects associated to the trend | det_t |
| det_s | all regression effects associated to the seasonal | det_s |
| det_i | all regression effects associated to the irregular | det_i |
| out_t_f | outliers effects associated to the trend | out_t_f(?) |
| out_s_f | outliers effects associated to the seasonal | out_s_f(?) |
| out_i_f | outliers effects associated to the irregular | out_i_f(?) |
| reg_t_f | other regression effects associated to the trend | reg_t_f(?) |
| reg_s_f | other regression effects associated to the seasonal | reg_s_f(?) |
| reg_i_f | other regression effects associated to the irregular | reg_i_f(?) |
| reg_sa_f | other regression effects associated to the sa | reg_sa_f(?) |
| reg_u_f | other undefined regression effects (split between the components | reg_u_f(?) |
| reg_y_f | other regression effects removed from the series (not in the components | reg_y_f(?) |
| det_t_f | all regression effects associated to the trend | det_t_f(?) |
| det_s_f | all regression effects associated to the seasonal | det_s_f(?) |
| det_i_f | all regression effects associated to the irregular | det_i_f(?) |
| out_t_b | outliers effects associated to the trend | out_t_b(?) |
| out_s_b | outliers effects associated to the seasonal | out_s_b(?) |
| out_i_b | outliers effects associated to the irregular | out_i_b(?) |
| reg_t_b | other regression effects associated to the trend | reg_t_b(?) |
| reg_s_b | other regression effects associated to the seasonal | reg_s_b(?) |
| reg_i_b | other regression effects associated to the irregular | reg_i_b(?) |
| reg_sa_b | other regression effects associated to the sa | reg_sa_b(?) |
| reg_u_b | other undefined regression effects (split between the components | reg_u_b(?) |
| reg_y_b | other regression effects removed from the series (not in the components | reg_y_b(?) |
| det_t_b | all regression effects associated to the trend | det_t_b(?) |
| det_s_b | all regression effects associated to the seasonal | det_s_b(?) |
| det_i_b | all regression effects associated to the irregular | det_i_b(?) |

### Pre-processing series in X11 A-Table

GUI display: Decomposition (X11)\>A-Table

| Name | Description | GUI dsiplay |
|----------------|----------------------------------------|-----------|
| preadjustment.a1 | original series | yes |
| preadjustment.a1a | forecasts of the original series (=y_f) | yes |
| preadjustment.a1b | backcasts of the original series (=y_b) | no |
| preadjustment.a6 | trading days effects (=tde) | yes |
| preadjustment.a7 | moving holidays effects (including easter) (=tde+ee) | yes |
| preadjustment.a8 | outliers effects (=out) | yes |
| preadjustment.a8t | outliers effects associated to the trend (=out_t) | yes |
| preadjustment.a8i | outliers effects associated to the irregular (=out_i) | yes |
| preadjustment.a8s | outliers effects associated to the seasonal (=out_s) | yes |
| preadjustment.a9 | other regression effects (=reg) | yes |
| preadjustment.a9cal | other regression effects, associated to the calendar component | yes |
| preadjustment.a9u | other regression effects, split in the different components (allocation = "undefined") | yes |
| preadjustment.a9sa | other regression effects, associated to the SA series (allocation= "sa") | yes |
| preadjustment.a9ser | other regression effects, removed from the series and not integrated in the final components (allocation ="series") | yes |

- allocation: brief explanation and link

## Diagnostics

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remark: stand alone tests: - in GUI - in R (rjd3toolkit)

### Tests on residuals

ONE TEST example : LB TEST, link to M chap what do we describe here

### Seasonality tests

ONE TEST example : Friedman TEST, link to M chap what do we describe here

## Parameters and other estimation results

### char

| Name                     | Description                                                                 | GUI display                     |
| ------------------------ | --------------------------------------------------------------------------- | ------------------------------- |
| period                   | number of observations per year                                             |                                 |
| span.start               | start date of SA estimation                                                 |                                 |
| span.end                 | end date of SA estimation                                                   |                                 |
| span.n                   | number of observations in the original series                               |                                 |
| span.missing             | number of missing values in the original series                             |                                 |
| regression.espan.start   | start date of pre-processing model estimation                               | Main Results and Pre-processing |
| regression.espan.end     | end date of pre-processing model estimation                                 | Main Results and Pre-processing |
| regression.espan.n       | number of observations in pre-processing model estimation                   | Main Results and Pre-processing |
| regression.espan.missing | number of missing values in series used for pre-processing model estimation |                                 |