Get the seasonally adjusted model from a workspace
Source:R/get_jmodel.R, R/import_workspace.R
get_model.RdGeneric functions to retrieve seasonally adjusted model(s) from workspace,
multiprocessing or sa_item object. get_model returns a "SA" object while get_jmodel returns the Java objects of the models.
Usage
get_jmodel(x, workspace, userdefined = NULL, progress_bar = TRUE)
get_model(x, workspace, userdefined = NULL, progress_bar = TRUE)Arguments
- x
the object from which to retrieve the seasonally adjusted model.
- workspace
the workspace object where models are stored. If
xis aworkspaceobject, this parameter is not used.- userdefined
a vector containing the names of additional output variables. (see
x13ortramoseats).- progress_bar
Boolean: if
TRUE, a progress bar is printed.
Value
get_model() returns a seasonally adjusted object (class c("SA", "X13") or c("SA", "TRAMO_SEATS") or a list of seasonally adjusted objects:
if
xis asa_itemobject,get_model(x)returns a"SA"object (or ajSAobject withget_jmodel(x));if
xis amultiprocessingobject,get_ts(x)returns a list of length the number of sa_items, each element containing a"SA"object (or ajSAobject withget_jmodel(x));if
xis aworkspaceobject,get_ts(x)returns list of length the number of multiprocessings, each element containing a list of"SA"object(s) (orjSAobject's) withget_jmodel(x)).
Examples
# \donttest{
spec_x13 <- x13_spec(spec = "RSA5c", easter.enabled = FALSE)
sa_x13 <- x13(ipi_c_eu[, "FR"], spec = spec_x13)
spec_ts <- tramoseats_spec(spec = "RSA5")
sa_ts <- tramoseats(ipi_c_eu[, "FR"], spec = spec_ts)
wk <- new_workspace()
mp <- new_multiprocessing(wk, "sap1")
add_sa_item(wk, "sap1", sa_x13, "X13")
add_sa_item(wk, "sap1", sa_ts, "TramoSeats")
compute(wk) # It's important to compute the workspace before retrieving the SA model
sa_item1 <- get_object(mp, 1)
get_model(sa_item1, wk) # To extract the model of the sa_item1: its the object sa_x13
#> RegARIMA
#> y = regression model + arima (2, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Phi(1) 0.02043 0.107
#> Phi(2) 0.11093 0.077
#> Theta(1) -0.58663 0.098
#> BTheta(1) -0.69921 0.041
#>
#> Estimate Std. Error
#> Monday 0.6788 0.244
#> Tuesday 0.9500 0.245
#> Wednesday 1.0053 0.246
#> Thursday -0.0656 0.245
#> Friday 1.0304 0.245
#> Saturday -1.5721 0.245
#> Leap year 2.1513 0.753
#> TC (4-2020) -36.1532 2.193
#> AO (3-2020) -20.2213 2.255
#> AO (5-2011) 13.2210 1.970
#> LS (11-2008) -12.7459 1.663
#>
#>
#> Residual standard error: 2.294 on 343 degrees of freedom
#> Log likelihood = -811.8, aic = 1656 aicc = 1657, bic(corrected for length) = 1.907
#>
#>
#>
#> Decomposition
#> Monitoring and Quality Assessment Statistics:
#> M stats
#> M(1) 0.127
#> M(2) 0.076
#> M(3) 1.139
#> M(4) 0.080
#> M(5) 1.072
#> M(6) 0.030
#> M(7) 0.084
#> M(8) 0.244
#> M(9) 0.063
#> M(10) 0.254
#> M(11) 0.239
#> Q 0.319
#> Q-M2 0.349
#>
#> Final filters:
#> Seasonal filter: 3x5
#> Trend filter: 13 terms Henderson moving average
#>
#>
#> Final
#> Last observed values
#> y sa t s i
#> Jan 2020 101.0 102.92412 102.8147 -1.9241199 0.1094395
#> Feb 2020 100.1 103.50547 102.8976 -3.4054722 0.6078825
#> Mar 2020 91.8 83.00218 103.1831 8.7978221 -20.1809275
#> Apr 2020 66.7 65.83747 103.6570 0.8625259 -37.8194996
#> May 2020 73.7 78.73548 104.1282 -5.0354792 -25.3926864
#> Jun 2020 98.2 87.26580 104.5188 10.9342001 -17.2529628
#> Jul 2020 97.4 92.53528 104.7033 4.8647224 -12.1679796
#> Aug 2020 71.7 97.64618 104.5690 -25.9461813 -6.9227978
#> Sep 2020 104.7 97.34380 104.1405 7.3562012 -6.7967236
#> Oct 2020 106.7 98.78451 103.5511 7.9154948 -4.7665946
#> Nov 2020 101.6 100.50933 103.0298 1.0906693 -2.5204281
#> Dec 2020 96.6 99.74645 102.7263 -3.1464483 -2.9798265
#>
#> Forecasts:
#> y_f sa_f t_f s_f i_f
#> Jan 2021 94.82712 101.3420 102.6158 -6.5148928 -1.27380795
#> Feb 2021 98.00197 101.8372 102.5826 -3.8352640 -0.74540432
#> Mar 2021 113.62540 101.9088 102.5235 11.7165747 -0.61463800
#> Apr 2021 103.28588 102.3855 102.3987 0.9004327 -0.01326784
#> May 2021 96.23640 101.5938 102.2898 -5.3574428 -0.69592946
#> Jun 2021 113.04727 101.6902 102.2365 11.3570720 -0.54632230
#> Jul 2021 104.27161 101.8281 102.2910 2.4435091 -0.46291753
#> Aug 2021 79.29357 102.6462 102.4831 -23.3526340 0.16311885
#> Sep 2021 109.23197 102.7863 102.7326 6.4456639 0.05371199
#> Oct 2021 108.79200 102.9386 102.9781 5.8533505 -0.03947210
#> Nov 2021 106.90616 102.9549 103.2017 3.9512094 -0.24675320
#> Dec 2021 100.22813 103.5456 103.3775 -3.3174206 0.16802658
#>
#>
#> Diagnostics
#> Relative contribution of the components to the stationary
#> portion of the variance in the original series,
#> after the removal of the long term trend
#> Trend computed by Hodrick-Prescott filter (cycle length = 8.0 years)
#> Component
#> Cycle 2.238
#> Seasonal 59.768
#> Irregular 1.203
#> TD & Hol. 2.436
#> Others 34.383
#> Total 100.028
#>
#> Combined test in the entire series
#> Non parametric tests for stable seasonality
#> P.value
#> Kruskall-Wallis test 0.000
#> Test for the presence of seasonality assuming stability 0.000
#> Evolutive seasonality test 0.059
#>
#> Identifiable seasonality present
#>
#> Residual seasonality tests
#> P.value
#> qs test on sa 1.000
#> qs test on i 0.985
#> f-test on sa (seasonal dummies) 0.916
#> f-test on i (seasonal dummies) 0.812
#> Residual seasonality (entire series) 0.902
#> Residual seasonality (last 3 years) 0.966
#> f-test on sa (td) 0.983
#> f-test on i (td) 0.998
#>
#>
#> Additional output variables
# To get all models from the multiprocessing mp:
get_model(mp, wk)
#>
|
| | 0%
|
|=================================== | 50%
|
|======================================================================| 100%
#> $X13
#> RegARIMA
#> y = regression model + arima (2, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Phi(1) 0.02043 0.107
#> Phi(2) 0.11093 0.077
#> Theta(1) -0.58663 0.098
#> BTheta(1) -0.69921 0.041
#>
#> Estimate Std. Error
#> Monday 0.6788 0.244
#> Tuesday 0.9500 0.245
#> Wednesday 1.0053 0.246
#> Thursday -0.0656 0.245
#> Friday 1.0304 0.245
#> Saturday -1.5721 0.245
#> Leap year 2.1513 0.753
#> TC (4-2020) -36.1532 2.193
#> AO (3-2020) -20.2213 2.255
#> AO (5-2011) 13.2210 1.970
#> LS (11-2008) -12.7459 1.663
#>
#>
#> Residual standard error: 2.294 on 343 degrees of freedom
#> Log likelihood = -811.8, aic = 1656 aicc = 1657, bic(corrected for length) = 1.907
#>
#>
#>
#> Decomposition
#> Monitoring and Quality Assessment Statistics:
#> M stats
#> M(1) 0.127
#> M(2) 0.076
#> M(3) 1.139
#> M(4) 0.080
#> M(5) 1.072
#> M(6) 0.030
#> M(7) 0.084
#> M(8) 0.244
#> M(9) 0.063
#> M(10) 0.254
#> M(11) 0.239
#> Q 0.319
#> Q-M2 0.349
#>
#> Final filters:
#> Seasonal filter: 3x5
#> Trend filter: 13 terms Henderson moving average
#>
#>
#> Final
#> Last observed values
#> y sa t s i
#> Jan 2020 101.0 102.92412 102.8147 -1.9241199 0.1094395
#> Feb 2020 100.1 103.50547 102.8976 -3.4054722 0.6078825
#> Mar 2020 91.8 83.00218 103.1831 8.7978221 -20.1809275
#> Apr 2020 66.7 65.83747 103.6570 0.8625259 -37.8194996
#> May 2020 73.7 78.73548 104.1282 -5.0354792 -25.3926864
#> Jun 2020 98.2 87.26580 104.5188 10.9342001 -17.2529628
#> Jul 2020 97.4 92.53528 104.7033 4.8647224 -12.1679796
#> Aug 2020 71.7 97.64618 104.5690 -25.9461813 -6.9227978
#> Sep 2020 104.7 97.34380 104.1405 7.3562012 -6.7967236
#> Oct 2020 106.7 98.78451 103.5511 7.9154948 -4.7665946
#> Nov 2020 101.6 100.50933 103.0298 1.0906693 -2.5204281
#> Dec 2020 96.6 99.74645 102.7263 -3.1464483 -2.9798265
#>
#> Forecasts:
#> y_f sa_f t_f s_f i_f
#> Jan 2021 94.82712 101.3420 102.6158 -6.5148928 -1.27380795
#> Feb 2021 98.00197 101.8372 102.5826 -3.8352640 -0.74540432
#> Mar 2021 113.62540 101.9088 102.5235 11.7165747 -0.61463800
#> Apr 2021 103.28588 102.3855 102.3987 0.9004327 -0.01326784
#> May 2021 96.23640 101.5938 102.2898 -5.3574428 -0.69592946
#> Jun 2021 113.04727 101.6902 102.2365 11.3570720 -0.54632230
#> Jul 2021 104.27161 101.8281 102.2910 2.4435091 -0.46291753
#> Aug 2021 79.29357 102.6462 102.4831 -23.3526340 0.16311885
#> Sep 2021 109.23197 102.7863 102.7326 6.4456639 0.05371199
#> Oct 2021 108.79200 102.9386 102.9781 5.8533505 -0.03947210
#> Nov 2021 106.90616 102.9549 103.2017 3.9512094 -0.24675320
#> Dec 2021 100.22813 103.5456 103.3775 -3.3174206 0.16802658
#>
#>
#> Diagnostics
#> Relative contribution of the components to the stationary
#> portion of the variance in the original series,
#> after the removal of the long term trend
#> Trend computed by Hodrick-Prescott filter (cycle length = 8.0 years)
#> Component
#> Cycle 2.238
#> Seasonal 59.768
#> Irregular 1.203
#> TD & Hol. 2.436
#> Others 34.383
#> Total 100.028
#>
#> Combined test in the entire series
#> Non parametric tests for stable seasonality
#> P.value
#> Kruskall-Wallis test 0.000
#> Test for the presence of seasonality assuming stability 0.000
#> Evolutive seasonality test 0.059
#>
#> Identifiable seasonality present
#>
#> Residual seasonality tests
#> P.value
#> qs test on sa 1.000
#> qs test on i 0.985
#> f-test on sa (seasonal dummies) 0.916
#> f-test on i (seasonal dummies) 0.812
#> Residual seasonality (entire series) 0.902
#> Residual seasonality (last 3 years) 0.966
#> f-test on sa (td) 0.983
#> f-test on i (td) 0.998
#>
#>
#> Additional output variables
#>
#> $TramoSeats
#> RegARIMA
#> y = regression model + arima (2, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Phi(1) 0.02572 0.108
#> Phi(2) 0.16988 0.075
#> Theta(1) -0.53992 0.102
#> BTheta(1) -0.67459 0.042
#>
#> Estimate Std. Error
#> Monday 0.56114 0.231
#> Tuesday 0.89966 0.231
#> Wednesday 1.06703 0.232
#> Thursday 0.02403 0.232
#> Friday 0.86378 0.234
#> Saturday -1.55222 0.231
#> Leap year 2.19751 0.712
#> Easter [6] -2.31734 0.461
#> TC (4-2020) -20.83317 2.183
#> TC (3-2020) -20.98304 2.183
#> AO (5-2011) 13.28128 1.872
#> LS (11-2008) -12.57486 1.631
#>
#>
#> Residual standard error: 2.221 on 342 degrees of freedom
#> Log likelihood = -799.8, aic = 1634 aicc = 1635, bic(corrected for length) = 1.858
#>
#>
#>
#> Decomposition
#> Model
#> AR : 1 + 0.025720 B + 0.169879 B^2
#> D : 1 - B - B^12 + B^13
#> MA : 1 - 0.539919 B - 0.674594 B^12 + 0.364227 B^13
#>
#>
#> SA
#> D : 1 - 2.000000 B + B^2
#> MA : 1 - 1.531766 B + 0.545834 B^2
#> Innovation variance: 0.5502022
#>
#> Trend
#> D : 1 - 2.000000 B + B^2
#> MA : 1 + 0.032214 B - 0.967786 B^2
#> Innovation variance: 0.02623268
#>
#> Seasonal
#> AR : 1 + 0.025720 B + 0.169879 B^2
#> D : 1 + B + B^2 + B^3 + B^4 + B^5 + B^6 + B^7 + B^8 + B^9 + B^10 + B^11
#> MA : 1 + 1.245052 B + 0.658623 B^2 + 0.593270 B^3 + 0.481574 B^4 + 0.366624 B^5 + 0.304938 B^6 + 0.184553 B^7 + 0.190108 B^8 + 0.095090 B^9 + 0.221559 B^10 + 0.186281 B^11 - 0.207005 B^12 - 0.348481 B^13
#> Innovation variance: 0.1464012
#>
#> Irregular
#> Innovation variance: 0.3257068
#>
#>
#>
#> Final
#> Last observed values
#> y sa t s i
#> Jan 2020 101.0 102.72726 103.1221 -1.7272634 -0.3948220
#> Feb 2020 100.1 102.95124 103.1797 -2.8512352 -0.2284534
#> Mar 2020 91.8 82.31999 103.3030 9.4800115 -20.9830366
#> Apr 2020 66.7 66.85029 103.5340 -0.1502858 -36.6836970
#> May 2020 73.7 79.46771 103.9124 -5.7677083 -24.4446419
#> Jun 2020 98.2 87.82311 104.2371 10.3768872 -16.4139594
#> Jul 2020 97.4 92.74114 104.3260 4.6588650 -11.5848433
#> Aug 2020 71.7 97.04194 104.1300 -25.3419376 -7.0880934
#> Sep 2020 104.7 97.32774 103.6918 7.3722629 -6.3640867
#> Oct 2020 106.7 98.66536 103.2317 8.0346351 -4.5663227
#> Nov 2020 101.6 100.05441 102.8519 1.5455901 -2.7974884
#> Dec 2020 96.6 99.35191 102.5735 -2.7519144 -3.2215659
#>
#> Forecasts:
#> y_f sa_f t_f s_f i_f
#> Jan 2021 94.55690 101.0346 102.4680 -6.477689 -1.43341231
#> Feb 2021 97.86506 101.4506 102.4540 -3.585540 -1.00338862
#> Mar 2021 113.01303 101.7376 102.4400 11.275402 -0.70237203
#> Apr 2021 103.19842 101.9344 102.4260 1.264068 -0.49166042
#> May 2021 96.00309 102.0679 102.4120 -6.064764 -0.34416230
#> Jun 2021 112.77599 102.1571 102.3980 10.618882 -0.24091361
#> Jul 2021 104.03135 102.2154 102.3840 1.815959 -0.16863953
#> Aug 2021 79.09787 102.2520 102.3700 -23.154116 -0.11804767
#> Sep 2021 109.04546 102.2734 102.3560 6.772048 -0.08263337
#> Oct 2021 108.59337 102.2842 102.3421 6.309157 -0.05784336
#> Nov 2021 106.47776 102.2876 102.3281 4.190193 -0.04049035
#> Dec 2021 99.77303 102.2857 102.3141 -2.512692 -0.02834325
#>
#>
#> Diagnostics
#> Relative contribution of the components to the stationary
#> portion of the variance in the original series,
#> after the removal of the long term trend
#> Trend computed by Hodrick-Prescott filter (cycle length = 8.0 years)
#> Component
#> Cycle 1.887
#> Seasonal 58.928
#> Irregular 0.509
#> TD & Hol. 2.598
#> Others 33.908
#> Total 97.830
#>
#> Combined test in the entire series
#> Non parametric tests for stable seasonality
#> P.value
#> Kruskall-Wallis test 0.000
#> Test for the presence of seasonality assuming stability 0.000
#> Evolutive seasonality test 0.064
#>
#> Identifiable seasonality present
#>
#> Residual seasonality tests
#> P.value
#> qs test on sa 1.000
#> qs test on i 1.000
#> f-test on sa (seasonal dummies) 1.000
#> f-test on i (seasonal dummies) 1.000
#> Residual seasonality (entire series) 1.000
#> Residual seasonality (last 3 years) 0.968
#> f-test on sa (td) 0.984
#> f-test on i (td) 1.000
#>
#>
#> Additional output variables
#>
# To get all models from the workspace wk:
get_model(wk)
#> Multiprocessing 1 on 1:
#>
|
| | 0%
|
|=================================== | 50%
|
|======================================================================| 100%
#> $sap1
#> $sap1$X13
#> RegARIMA
#> y = regression model + arima (2, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Phi(1) 0.02043 0.107
#> Phi(2) 0.11093 0.077
#> Theta(1) -0.58663 0.098
#> BTheta(1) -0.69921 0.041
#>
#> Estimate Std. Error
#> Monday 0.6788 0.244
#> Tuesday 0.9500 0.245
#> Wednesday 1.0053 0.246
#> Thursday -0.0656 0.245
#> Friday 1.0304 0.245
#> Saturday -1.5721 0.245
#> Leap year 2.1513 0.753
#> TC (4-2020) -36.1532 2.193
#> AO (3-2020) -20.2213 2.255
#> AO (5-2011) 13.2210 1.970
#> LS (11-2008) -12.7459 1.663
#>
#>
#> Residual standard error: 2.294 on 343 degrees of freedom
#> Log likelihood = -811.8, aic = 1656 aicc = 1657, bic(corrected for length) = 1.907
#>
#>
#>
#> Decomposition
#> Monitoring and Quality Assessment Statistics:
#> M stats
#> M(1) 0.127
#> M(2) 0.076
#> M(3) 1.139
#> M(4) 0.080
#> M(5) 1.072
#> M(6) 0.030
#> M(7) 0.084
#> M(8) 0.244
#> M(9) 0.063
#> M(10) 0.254
#> M(11) 0.239
#> Q 0.319
#> Q-M2 0.349
#>
#> Final filters:
#> Seasonal filter: 3x5
#> Trend filter: 13 terms Henderson moving average
#>
#>
#> Final
#> Last observed values
#> y sa t s i
#> Jan 2020 101.0 102.92412 102.8147 -1.9241199 0.1094395
#> Feb 2020 100.1 103.50547 102.8976 -3.4054722 0.6078825
#> Mar 2020 91.8 83.00218 103.1831 8.7978221 -20.1809275
#> Apr 2020 66.7 65.83747 103.6570 0.8625259 -37.8194996
#> May 2020 73.7 78.73548 104.1282 -5.0354792 -25.3926864
#> Jun 2020 98.2 87.26580 104.5188 10.9342001 -17.2529628
#> Jul 2020 97.4 92.53528 104.7033 4.8647224 -12.1679796
#> Aug 2020 71.7 97.64618 104.5690 -25.9461813 -6.9227978
#> Sep 2020 104.7 97.34380 104.1405 7.3562012 -6.7967236
#> Oct 2020 106.7 98.78451 103.5511 7.9154948 -4.7665946
#> Nov 2020 101.6 100.50933 103.0298 1.0906693 -2.5204281
#> Dec 2020 96.6 99.74645 102.7263 -3.1464483 -2.9798265
#>
#> Forecasts:
#> y_f sa_f t_f s_f i_f
#> Jan 2021 94.82712 101.3420 102.6158 -6.5148928 -1.27380795
#> Feb 2021 98.00197 101.8372 102.5826 -3.8352640 -0.74540432
#> Mar 2021 113.62540 101.9088 102.5235 11.7165747 -0.61463800
#> Apr 2021 103.28588 102.3855 102.3987 0.9004327 -0.01326784
#> May 2021 96.23640 101.5938 102.2898 -5.3574428 -0.69592946
#> Jun 2021 113.04727 101.6902 102.2365 11.3570720 -0.54632230
#> Jul 2021 104.27161 101.8281 102.2910 2.4435091 -0.46291753
#> Aug 2021 79.29357 102.6462 102.4831 -23.3526340 0.16311885
#> Sep 2021 109.23197 102.7863 102.7326 6.4456639 0.05371199
#> Oct 2021 108.79200 102.9386 102.9781 5.8533505 -0.03947210
#> Nov 2021 106.90616 102.9549 103.2017 3.9512094 -0.24675320
#> Dec 2021 100.22813 103.5456 103.3775 -3.3174206 0.16802658
#>
#>
#> Diagnostics
#> Relative contribution of the components to the stationary
#> portion of the variance in the original series,
#> after the removal of the long term trend
#> Trend computed by Hodrick-Prescott filter (cycle length = 8.0 years)
#> Component
#> Cycle 2.238
#> Seasonal 59.768
#> Irregular 1.203
#> TD & Hol. 2.436
#> Others 34.383
#> Total 100.028
#>
#> Combined test in the entire series
#> Non parametric tests for stable seasonality
#> P.value
#> Kruskall-Wallis test 0.000
#> Test for the presence of seasonality assuming stability 0.000
#> Evolutive seasonality test 0.059
#>
#> Identifiable seasonality present
#>
#> Residual seasonality tests
#> P.value
#> qs test on sa 1.000
#> qs test on i 0.985
#> f-test on sa (seasonal dummies) 0.916
#> f-test on i (seasonal dummies) 0.812
#> Residual seasonality (entire series) 0.902
#> Residual seasonality (last 3 years) 0.966
#> f-test on sa (td) 0.983
#> f-test on i (td) 0.998
#>
#>
#> Additional output variables
#>
#> $sap1$TramoSeats
#> RegARIMA
#> y = regression model + arima (2, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Phi(1) 0.02572 0.108
#> Phi(2) 0.16988 0.075
#> Theta(1) -0.53992 0.102
#> BTheta(1) -0.67459 0.042
#>
#> Estimate Std. Error
#> Monday 0.56114 0.231
#> Tuesday 0.89966 0.231
#> Wednesday 1.06703 0.232
#> Thursday 0.02403 0.232
#> Friday 0.86378 0.234
#> Saturday -1.55222 0.231
#> Leap year 2.19751 0.712
#> Easter [6] -2.31734 0.461
#> TC (4-2020) -20.83317 2.183
#> TC (3-2020) -20.98304 2.183
#> AO (5-2011) 13.28128 1.872
#> LS (11-2008) -12.57486 1.631
#>
#>
#> Residual standard error: 2.221 on 342 degrees of freedom
#> Log likelihood = -799.8, aic = 1634 aicc = 1635, bic(corrected for length) = 1.858
#>
#>
#>
#> Decomposition
#> Model
#> AR : 1 + 0.025720 B + 0.169879 B^2
#> D : 1 - B - B^12 + B^13
#> MA : 1 - 0.539919 B - 0.674594 B^12 + 0.364227 B^13
#>
#>
#> SA
#> D : 1 - 2.000000 B + B^2
#> MA : 1 - 1.531766 B + 0.545834 B^2
#> Innovation variance: 0.5502022
#>
#> Trend
#> D : 1 - 2.000000 B + B^2
#> MA : 1 + 0.032214 B - 0.967786 B^2
#> Innovation variance: 0.02623268
#>
#> Seasonal
#> AR : 1 + 0.025720 B + 0.169879 B^2
#> D : 1 + B + B^2 + B^3 + B^4 + B^5 + B^6 + B^7 + B^8 + B^9 + B^10 + B^11
#> MA : 1 + 1.245052 B + 0.658623 B^2 + 0.593270 B^3 + 0.481574 B^4 + 0.366624 B^5 + 0.304938 B^6 + 0.184553 B^7 + 0.190108 B^8 + 0.095090 B^9 + 0.221559 B^10 + 0.186281 B^11 - 0.207005 B^12 - 0.348481 B^13
#> Innovation variance: 0.1464012
#>
#> Irregular
#> Innovation variance: 0.3257068
#>
#>
#>
#> Final
#> Last observed values
#> y sa t s i
#> Jan 2020 101.0 102.72726 103.1221 -1.7272634 -0.3948220
#> Feb 2020 100.1 102.95124 103.1797 -2.8512352 -0.2284534
#> Mar 2020 91.8 82.31999 103.3030 9.4800115 -20.9830366
#> Apr 2020 66.7 66.85029 103.5340 -0.1502858 -36.6836970
#> May 2020 73.7 79.46771 103.9124 -5.7677083 -24.4446419
#> Jun 2020 98.2 87.82311 104.2371 10.3768872 -16.4139594
#> Jul 2020 97.4 92.74114 104.3260 4.6588650 -11.5848433
#> Aug 2020 71.7 97.04194 104.1300 -25.3419376 -7.0880934
#> Sep 2020 104.7 97.32774 103.6918 7.3722629 -6.3640867
#> Oct 2020 106.7 98.66536 103.2317 8.0346351 -4.5663227
#> Nov 2020 101.6 100.05441 102.8519 1.5455901 -2.7974884
#> Dec 2020 96.6 99.35191 102.5735 -2.7519144 -3.2215659
#>
#> Forecasts:
#> y_f sa_f t_f s_f i_f
#> Jan 2021 94.55690 101.0346 102.4680 -6.477689 -1.43341231
#> Feb 2021 97.86506 101.4506 102.4540 -3.585540 -1.00338862
#> Mar 2021 113.01303 101.7376 102.4400 11.275402 -0.70237203
#> Apr 2021 103.19842 101.9344 102.4260 1.264068 -0.49166042
#> May 2021 96.00309 102.0679 102.4120 -6.064764 -0.34416230
#> Jun 2021 112.77599 102.1571 102.3980 10.618882 -0.24091361
#> Jul 2021 104.03135 102.2154 102.3840 1.815959 -0.16863953
#> Aug 2021 79.09787 102.2520 102.3700 -23.154116 -0.11804767
#> Sep 2021 109.04546 102.2734 102.3560 6.772048 -0.08263337
#> Oct 2021 108.59337 102.2842 102.3421 6.309157 -0.05784336
#> Nov 2021 106.47776 102.2876 102.3281 4.190193 -0.04049035
#> Dec 2021 99.77303 102.2857 102.3141 -2.512692 -0.02834325
#>
#>
#> Diagnostics
#> Relative contribution of the components to the stationary
#> portion of the variance in the original series,
#> after the removal of the long term trend
#> Trend computed by Hodrick-Prescott filter (cycle length = 8.0 years)
#> Component
#> Cycle 1.887
#> Seasonal 58.928
#> Irregular 0.509
#> TD & Hol. 2.598
#> Others 33.908
#> Total 97.830
#>
#> Combined test in the entire series
#> Non parametric tests for stable seasonality
#> P.value
#> Kruskall-Wallis test 0.000
#> Test for the presence of seasonality assuming stability 0.000
#> Evolutive seasonality test 0.064
#>
#> Identifiable seasonality present
#>
#> Residual seasonality tests
#> P.value
#> qs test on sa 1.000
#> qs test on i 1.000
#> f-test on sa (seasonal dummies) 1.000
#> f-test on i (seasonal dummies) 1.000
#> Residual seasonality (entire series) 1.000
#> Residual seasonality (last 3 years) 0.968
#> f-test on sa (td) 0.984
#> f-test on i (td) 1.000
#>
#>
#> Additional output variables
#>
#>
# }