Partial concurrent adjustment • pickmdl3

In accordance with the best practice defined in ESS Guideluines on seasonal adjustment, model identification should be done once a year and the sARIMA model order should be kept in line with the chosen refreshment policy. With the pickmdl package, it is easy to implement this best practice in a production process. A date for model selection can be set in the x13_pickdmlfunction by the options identification_end or identification_estimate.to. The x13_pickmdl function will then do the model selection based on data only up to and including this date.

For the sake of illustration, let us say that model selection is to be done each January, based on data until the preceding December. We use the Norwegian rti of nace 47.6 and the standard specification rsa5c, with outliers turned off to illustrate this option.


library(pickmdl3)

rti_476 <- pickmdl3::pickmdl_data("norwegian_rti")$rti_476

spec_now <- x13_spec("rsa5c") |>
  set_outlier(outliers.type= NULL) 

last_year <- stats::end(rti_476)[1] - 1 

model_now <- x13_pickmdl(rti_476,spec=spec_now,identification_end = c(last_year,12),output="all")

# or equivalently 

model_now <- x13_pickmdl(rti_476,spec=spec_now,identification_estimate.to = paste0(last_year,"-12-01")) 

ok(model_now)
#> $ok
#> [1] TRUE
#> 
#> $ok_final
#> [1] FALSE
#> 
#> $mdl_nr
#> [1] 2

Based on the model identification set at the preceding December, the second model on the pickmdl list is chosen by the pickmdl procedure. Compare this to what would have happened if model selection was done with all available data up toJuly 2026. In this case the chosen model is the fifth model, of order $(2,1,2)(0,1,1)_s$ . Model change is thus prevented in the middle of the year when we specify identification date for model selection.

model_now_b <- x13_pickmdl(rti_476,spec=spec_now)

model_now_b
#> Serie span: All 
#> 
#> Model: X-13
#> Log-transformation: yes 
#> SARIMA model: (2,1,2) (0,1,1)
#> 
#> SARIMA coefficients:
#>    phi(1)    phi(2)  theta(1)  theta(2) btheta(1) 
#>   -0.1296   -0.4386   -0.6958   -0.3040   -0.4697 
#> 
#> Regression model:
#>      mon      tue      wed      thu      fri      sat 
#> -0.01104  0.00689  0.01277 -0.01275  0.01792  0.01595 
#> 
#>  Seasonal filter: FILTER_S3X5;  Trend filter: H-13 terms
#>  M-Statistics: q Good (0.501); q-m2 Good (0.547)
#>  QS test on SA: Good (1.000);  F-test on SA: Good (0.972)
#> 
#> For a more detailed output, use the 'summary()' function.

Notice that there now is a difference between $ok and ok_final in the output above. Now $ok tells us that the selected model satisfied the pickmdl criteria at the identification date, i.e. December 2025. The ok_final gives information about whether the selected model still passes the criteria when the new data is taken into account. That is, whether the model selected based on data until December 2025 still fits the data in July 2026. We see that that is no longer the case, which is an indication that model change should be expected when the model is to be re-identified in January 2027.

Outliers

In the example above, we didn’t consider outliers. The default option in x13_pickmdl is that outliers are identified by the shortened series. That is, the outliers identified by the shortened series are kept throughout the year, and only new ouliers after the identification date are selected throughout the year.

In the example below, we manipulate the series to forace an outlier in June 2026, after model selection is done based on data up to and including December 2025.


spec_now <- x13_spec("rsa5c") |>
   set_outlier(outliers.type= c("AO","LS"))
  

last_year <- stats::end(rti_476)[1] - 1 

rti_476_fix <- rti_476
rti_476_fix[length(rti_476)-1] <- 10

model_now <- x13_pickmdl(rti_476_fix,spec=spec_now,identification_end = c(last_year,12))

model_now
#> Serie span: All 
#> 
#> Model: X-13
#> Log-transformation: yes 
#> SARIMA model: (0,1,1) (0,1,1)
#> 
#> SARIMA coefficients:
#>  theta(1) btheta(1) 
#>   -0.6243   -0.4483 
#> 
#> Regression model:
#>             mon             tue             wed             thu             fri 
#>      -0.0124209       0.0047325       0.0119882      -0.0072352       0.0179482 
#>             sat AO (2020-01-01) AO (2020-03-01) LS (2020-05-01) LS (2020-08-01) 
#>       0.0004963      -0.1773416      -0.2213182       0.2261907      -0.1732089 
#> LS (2021-05-01) LS (2021-08-01) AO (2026-06-01) 
#>       0.1943734      -0.1435998      -2.4332986 
#> 
#>  Seasonal filter: FILTER_S3X5;  Trend filter: H-13 terms
#>  M-Statistics: q Good (0.768); q-m2 Good (0.492)
#>  QS test on SA: Good (0.909);  F-test on SA: Good (0.499)
#> 
#> For a more detailed output, use the 'summary()' function.

We see that seven outliers are identified in total. Six of these have a date before the model selection date in December 2025 and was therefore identified in the model selection step. If we take a closer look at the estimation specification for the model in June 2026, we see that the six outliers have been defined as pre-specfied outliers and that the detection span for new outliers is now from January 2026:

model_now$estimation_spec
#> Specification
#> 
#> Series
#> Serie span: All 
#> Preliminary Check: Yes
#> 
#> Estimate
#> Model span: All 
#> 
#> Tolerance: 1e-07
#> 
#> Transformation
#> Function: LOG
#> AIC difference: -2
#> Adjust: LEAPYEAR
#> 
#> Regression
#> Calendar regressor: TradingDays
#> with Leap Year: No
#> AutoAdjust: FALSE
#> Test: NO
#> 
#> Easter: No
#> 
#> Pre-specified outliers: 6
#>  - AO (2020-01-01), coefficient: -0.177667511131776 (INITIAL)
#>  - AO (2020-03-01), coefficient: -0.220168845662991 (INITIAL)
#>  - LS (2020-05-01), coefficient: 0.224423169320979 (INITIAL)
#>  - LS (2020-08-01), coefficient: -0.174401233307672 (INITIAL)
#>  - LS (2021-05-01), coefficient: 0.195195660086895 (INITIAL)
#>  - LS (2021-08-01), coefficient: -0.143382952057627 (INITIAL)
#> Ramps: No
#> 
#> Outliers
#> Detection span: From 2026-01-01 
#> Outliers type: 
#>  - AO, critical value : 0 (Auto)
#>  - LS, critical value : 0 (Auto)
#> TC rate: 0.7 (Auto)
#> Method: ADDONE (Auto)
#> 
#> ARIMA
#> SARIMA model: (0,1,1) (0,1,1)
#> 
#> SARIMA coefficients:
#>  theta(1) btheta(1) 
#>         0         0 
#> 
#> Specification X11
#> Seasonal component: Yes
#> Length of the Henderson filter: 0
#> Seasonal filter: FILTER_MSR
#> Boundaries used for extreme values correction : 
#>   lower_sigma:  1.5 
#>   upper_sigma:  2.5
#> Nb of forecasts: -1
#> Nb of backcasts: 0
#> Calendar sigma: NONE
#> Mode X-11: UNKNOWN
#> Bias: RATIO
#> 
#> Benchmarking
#> Is enabled: No

It is possible to let the outlier span be the whole series, even though the model order is identified at a specific date. This is done by setting the option identify_outliers = FALSE. Comparing outliers with the model above, we see that they are somewhat different, as they now all were identified based on the whole available time series.


rar <- x13_pickmdl(rti_476_fix,spec=spec_now,identification_end = c(last_year,12),
                   identify_outliers = FALSE)

Refreshment policy

The specification at the identification time is the reference specification for the following year. Estimation specification is refreshed according to refreshment policy, as defined in x13_refresh(). Default refreshment policy in the pickmdl package is Outliers, where the model order is set, but parameters estimated anew. (Obs: only Outliers available pro tempora) To be extended.