Saving and loading a model specification, SA and pre-adjustment in X13 and TRAMO-SEATS
Source:R/saveSpec.R
save_spec.Rdsave_spec saves a SA or RegARIMA model specification.
load_spec loads the previously saved model specification.
Arguments
- object
an object of one of the following classes:
c("SA_spec","X13"),c("SA_spec","TRAMO_SEATS"),c("SA","X13"),c("SA","TRAMO_SEATS"),c("regarima_spec","X13"),c("regarima_spec","TRAMO_SEATS"),c("regarima","X13"),c("regarima","TRAMO_SEATS").- file
the (path and) name of the file where the model specification will be/has been saved.
Details
save_spec saves the final model specification of a "SA_spec", "SA",
"regarima_spec" or "regarima" class object.
load_spec loads the previously saved model specification. It creates a c("SA_spec","X13"),
c("sA_spec","TRAMO_SEATS"), c("regarima_spec","X13") or c("regarima_spec","TRAMO_SEATS")
class object, in line with the class of the previously saved model specification.
References
More information and examples related to 'JDemetra+' features in the online documentation: https://jdemetra-new-documentation.netlify.app/
Examples
# \donttest{
myseries <- ipi_c_eu[, "FR"]
myreg1 <- regarima_x13(myseries, spec = "RG5c")
myspec2 <- regarima_spec_x13(myreg1, estimate.from = "2005-10-01", outlier.from = "2010-03-01")
myreg2 <- regarima(myseries, myspec2)
myreg3 <- regarima_tramoseats(myseries, spec = "TRfull")
myspec4 <-regarima_spec_tramoseats(myreg3, tradingdays.mauto = "Unused",
tradingdays.option ="WorkingDays",
easter.type = "Standard",
automdl.enabled = FALSE, arima.mu = TRUE)
myreg4 <-regarima(myseries, myspec4)
myspec6 <- x13_spec("RSA5c")
mysa6 <- x13(myseries, myspec6)
myspec7 <- tramoseats_spec("RSAfull")
mysa7 <- tramoseats(myseries, myspec7)
dir <- tempdir()
# To save the model specification of a c("regarima_spec","X13") class object
save_spec(myspec2, file.path(dir, "specx13.RData"))
# To save the model specification of a c("regarima","X13") class object
save_spec(myreg2, file.path(dir,"regx13.RData"))
# To save the model specification of a c("regarima_spec","TRAMO_SEATS") class object
save_spec(myspec4, file.path(dir,"specTS.RData"))
# To save the model specification of a c("regarima","TRAMO_SEATS") class object
save_spec(myreg4, file.path(dir,"regTS.RData"))
# To save the model of a c("SA_spec","X13") class object
save_spec(myspec6, file.path(dir,"specFullx13.RData"))
# To save the model of a c("SA","X13") class object
save_spec(mysa6, file.path(dir,"sax13.RData"))
# To save the model of a c("SA_spec","TRAMO_SEATS") class object
save_spec(myspec7, file.path(dir,"specFullTS.RData"))
# To save the model of a c("SA","TRAMO_SEATS") class object
save_spec(mysa7, file.path(dir,"saTS.RData"))
# To load a model specification:
myspec2a <- load_spec(file.path(dir,"specx13.RData"))
myspec2b <- load_spec(file.path(dir,"regx13.RData"))
myspec4a <- load_spec(file.path(dir,"specTS.RData"))
myspec4b <- load_spec(file.path(dir,"regTS.RData"))
myspec6a <- load_spec(file.path(dir,"specFullx13.RData"))
myspec6b <- load_spec(file.path(dir,"sax13.RData"))
myspec7a <- load_spec(file.path(dir,"specFullTS.RData"))
myspec7b <- load_spec(file.path(dir,"saTS.RData"))
# To use the re-loaded specifications and models:
regarima(myseries, myspec2a)
#> y = regression model + arima (0, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Theta(1) -0.2211 0.077
#> BTheta(1) -0.6911 0.060
#>
#> Estimate Std. Error
#> Monday 1.32698 0.340
#> Tuesday 1.10991 0.346
#> Wednesday 0.68412 0.351
#> Thursday 0.04219 0.348
#> Friday 1.43827 0.348
#> Saturday -1.99253 0.345
#> Leap year 2.01847 1.152
#> Easter [8] -2.11412 0.702
#> LS (3-2020) -21.59400 2.876
#> AO (4-2020) -16.22087 2.287
#> AO (5-2011) 13.50260 2.048
#>
#>
#> Residual standard error: 2.656 on 156 degrees of freedom
#> Log likelihood = -411.2, aic = 850.3 aicc = 853.1, bic(corrected for length) = 2.346
#>
x13(myseries, myspec6a)
#> RegARIMA
#> y = regression model + arima (2, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Phi(1) 0.0003269 0.108
#> Phi(2) 0.1688192 0.074
#> Theta(1) -0.5485606 0.102
#> BTheta(1) -0.6660849 0.042
#>
#> Estimate Std. Error
#> Monday 0.55932 0.228
#> Tuesday 0.88221 0.228
#> Wednesday 1.03996 0.229
#> Thursday 0.04943 0.229
#> Friday 0.91132 0.230
#> Saturday -1.57769 0.228
#> Leap year 2.15403 0.705
#> Easter [1] -2.37950 0.454
#> TC (4-2020) -35.59245 2.173
#> AO (3-2020) -20.89026 2.180
#> AO (5-2011) 13.49850 1.857
#> LS (11-2008) -12.54901 1.636
#>
#>
#> Residual standard error: 2.218 on 342 degrees of freedom
#> Log likelihood = -799.1, aic = 1632 aicc = 1634, bic(corrected for length) = 1.855
#>
#>
#>
#> Decomposition
#> Monitoring and Quality Assessment Statistics:
#> M stats
#> M(1) 0.163
#> M(2) 0.089
#> M(3) 1.181
#> M(4) 0.558
#> M(5) 1.020
#> M(6) 0.090
#> M(7) 0.083
#> M(8) 0.244
#> M(9) 0.062
#> M(10) 0.272
#> M(11) 0.256
#> Q 0.368
#> Q-M2 0.402
#>
#> Final filters:
#> Seasonal filter: 3x5
#> Trend filter: 13 terms Henderson moving average
#>
#>
#> Final
#> Last observed values
#> y sa t s i
#> Jan 2020 101.0 102.95613 102.9586 -1.95613209 -0.002494203
#> Feb 2020 100.1 103.50876 102.9592 -3.40875640 0.549602816
#> Mar 2020 91.8 82.87617 103.1664 8.92382800 -20.290271773
#> Apr 2020 66.7 66.65243 103.5971 0.04756625 -36.944710027
#> May 2020 73.7 78.87836 104.0393 -5.17835604 -25.160905985
#> Jun 2020 98.2 87.34544 104.3804 10.85456021 -17.034985133
#> Jul 2020 97.4 92.47436 104.5319 4.92563707 -12.057551871
#> Aug 2020 71.7 97.47245 104.3751 -25.77244698 -6.902636199
#> Sep 2020 104.7 97.37717 103.9182 7.32282919 -6.541070626
#> Oct 2020 106.7 98.24194 103.3047 8.45805540 -5.062719500
#> Nov 2020 101.6 100.26862 102.7746 1.33138152 -2.506014899
#> Dec 2020 96.6 99.66730 102.5133 -3.06729670 -2.845961796
#>
#> Forecasts:
#> y_f sa_f t_f s_f i_f
#> Jan 2021 94.53021 101.0902 102.4794 -6.56002888 -1.3891608
#> Feb 2021 97.90024 101.7395 102.5246 -3.83928384 -0.7850772
#> Mar 2021 114.09983 102.3065 102.5087 11.79328397 -0.2021598
#> Apr 2021 102.16781 102.2220 102.3759 -0.05422341 -0.1538967
#> May 2021 96.01612 101.5450 102.2100 -5.52888123 -0.6650098
#> Jun 2021 112.76658 101.3438 102.0725 11.42275939 -0.7286526
#> Jul 2021 104.13805 101.6681 102.0297 2.46989932 -0.3615193
#> Aug 2021 79.13003 102.3617 102.1360 -23.23171595 0.2257112
#> Sep 2021 109.06438 102.4772 102.3249 6.58713572 0.1523168
#> Oct 2021 108.64207 102.1329 102.5185 6.50921416 -0.3856588
#> Nov 2021 106.46022 102.5908 102.6996 3.86943752 -0.1088338
#> Dec 2021 99.79901 103.0831 102.8580 -3.28410831 0.2251086
#>
#>
#> 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 2.251
#> Seasonal 59.750
#> Irregular 1.067
#> TD & Hol. 2.610
#> Others 33.718
#> Total 99.395
#>
#> 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 0.034
#>
#> Identifiable seasonality present
#>
#> Residual seasonality tests
#> P.value
#> qs test on sa 0.985
#> qs test on i 0.865
#> f-test on sa (seasonal dummies) 0.958
#> f-test on i (seasonal dummies) 0.893
#> Residual seasonality (entire series) 0.876
#> Residual seasonality (last 3 years) 0.906
#> f-test on sa (td) 0.987
#> f-test on i (td) 0.993
#>
#>
#> Additional output variables
tramoseats(myseries, myspec7a)
#> RegARIMA
#> y = regression model + arima (2, 1, 0, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Phi(1) 0.4032 0.051
#> Phi(2) 0.2883 0.051
#> BTheta(1) -0.6641 0.042
#>
#> Estimate Std. Error
#> Week days 0.6994 0.032
#> Leap year 2.3231 0.690
#> Easter [6] -2.5154 0.436
#> AO (5-2011) 13.4679 1.787
#> TC (4-2020) -22.2128 2.205
#> TC (3-2020) -21.0391 2.217
#> AO (5-2000) 6.7386 1.794
#>
#>
#> Residual standard error: 2.326 on 348 degrees of freedom
#> Log likelihood = -816.1, aic = 1654 aicc = 1655, bic(corrected for length) = 1.852
#>
#>
#>
#> Decomposition
#> Model
#> AR : 1 + 0.403230 B + 0.288342 B^2
#> D : 1 - B - B^12 + B^13
#> MA : 1 - 0.664088 B^12
#>
#>
#> SA
#> AR : 1 + 0.403230 B + 0.288342 B^2
#> D : 1 - 2.000000 B + B^2
#> MA : 1 - 0.970348 B + 0.005940 B^2 - 0.005813 B^3 + 0.003576 B^4
#> Innovation variance: 0.7043507
#>
#> Trend
#> D : 1 - 2.000000 B + B^2
#> MA : 1 + 0.033519 B - 0.966481 B^2
#> Innovation variance: 0.06093642
#>
#> Seasonal
#> 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 + 1.328957 B + 1.105787 B^2 + 1.185470 B^3 + 1.067845 B^4 + 0.820748 B^5 + 0.632456 B^6 + 0.404457 B^7 + 0.245256 B^8 + 0.001615 B^9 - 0.055617 B^10 - 0.203557 B^11
#> Innovation variance: 0.04290744
#>
#> Transitory
#> AR : 1 + 0.403230 B + 0.288342 B^2
#> MA : 1 - 0.260079 B - 0.739921 B^2
#> Innovation variance: 0.05287028
#>
#> Irregular
#> Innovation variance: 0.2032994
#>
#>
#>
#> Final
#> Last observed values
#> y sa t s i
#> Jan 2020 101.0 102.93775 103.0182 -1.9377453 -0.08043801
#> Feb 2020 100.1 103.53944 103.2312 -3.4394383 0.30818847
#> Mar 2020 91.8 82.47698 103.4998 9.3230241 -21.02286361
#> Apr 2020 66.7 65.77310 103.9608 0.9268969 -38.18766871
#> May 2020 73.7 79.43342 104.7269 -5.7334221 -25.29345247
#> Jun 2020 98.2 88.07766 105.3319 10.1223443 -17.25422206
#> Jul 2020 97.4 92.71048 105.4216 4.6895154 -12.71111705
#> Aug 2020 71.7 97.32129 104.9801 -25.6212858 -7.65880696
#> Sep 2020 104.7 97.44274 104.0807 7.2572622 -6.63793072
#> Oct 2020 106.7 98.20925 103.1711 8.4907485 -4.96183772
#> Nov 2020 101.6 99.98044 102.4813 1.6195550 -2.50088282
#> Dec 2020 96.6 98.99458 101.9735 -2.3945790 -2.97892307
#>
#> Forecasts:
#> y_f sa_f t_f s_f i_f
#> Jan 2021 93.22264 100.1984 101.7578 -6.975740 -1.55946363
#> Feb 2021 96.81455 100.8845 101.7113 -4.069924 -0.82679910
#> Mar 2021 111.72198 100.8668 101.6647 10.855228 -0.79795880
#> Apr 2021 102.76178 101.0716 101.6181 1.690178 -0.54654378
#> May 2021 95.52744 101.2474 101.5716 -5.719910 -0.32422597
#> Jun 2021 111.44221 101.2711 101.5250 10.171157 -0.25395653
#> Jul 2021 103.57813 101.2947 101.4784 2.283395 -0.18370915
#> Aug 2021 78.21363 101.3135 101.4319 -23.099833 -0.11841662
#> Sep 2021 108.57631 101.3000 101.3853 7.276282 -0.08528380
#> Oct 2021 107.32040 101.2771 101.3387 6.043321 -0.06166933
#> Nov 2021 105.33458 101.2505 101.2922 4.084088 -0.04168414
#> Dec 2021 98.79675 101.2164 101.2456 -2.419656 -0.02920922
#>
#>
#> 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 6.087
#> Seasonal 80.528
#> Irregular 0.965
#> TD & Hol. 3.590
#> Others 8.102
#> Total 99.271
#>
#> Combined test in the entire series
#> Non parametric tests for stable seasonality
#> P.value
#> Kruskall-Wallis test 0.00
#> Test for the presence of seasonality assuming stability 0.00
#> Evolutive seasonality test 0.01
#>
#> 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) 0.974
#> f-test on sa (td) 0.152
#> f-test on i (td) 0.224
#>
#>
#> Additional output variables
regarima(myseries, myspec4a)
#> y = regression model + arima (0, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Theta(1) -0.6221 0.043
#> BTheta(1) -0.6720 0.042
#>
#> Estimate Std. Error
#> Mean 0.001332 0.016
#> Monday 0.577428 0.239
#> Tuesday 0.842975 0.238
#> Wednesday 1.073966 0.240
#> Thursday 0.030442 0.239
#> Friday 0.872297 0.241
#> Saturday -1.555483 0.238
#> Leap year 2.136324 0.726
#> Easter [6] -2.170391 0.484
#> TC (4-2020) -21.181047 2.222
#> TC (3-2020) -21.228566 2.217
#> AO (5-2011) 12.919433 1.907
#> LS (11-2008) -12.465765 1.648
#>
#>
#> Residual standard error: 2.243 on 343 degrees of freedom
#> Log likelihood = -803.2, aic = 1638 aicc = 1640, bic(corrected for length) = 1.861
#>
x13(myseries, myspec6b)
#> RegARIMA
#> y = regression model + arima (2, 1, 1, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Phi(1) 0.0003269 0.108
#> Phi(2) 0.1688192 0.074
#> Theta(1) -0.5485606 0.102
#> BTheta(1) -0.6660849 0.042
#>
#> Estimate Std. Error
#> Monday 0.55932 0.228
#> Tuesday 0.88221 0.228
#> Wednesday 1.03996 0.229
#> Thursday 0.04943 0.229
#> Friday 0.91132 0.230
#> Saturday -1.57769 0.228
#> Leap year 2.15403 0.705
#> Easter [1] -2.37950 0.454
#> TC (4-2020) -35.59245 2.173
#> AO (3-2020) -20.89026 2.180
#> AO (5-2011) 13.49850 1.857
#> LS (11-2008) -12.54901 1.636
#>
#>
#> Residual standard error: 2.218 on 342 degrees of freedom
#> Log likelihood = -799.1, aic = 1632 aicc = 1634, bic(corrected for length) = 1.855
#>
#>
#>
#> Decomposition
#> Monitoring and Quality Assessment Statistics:
#> M stats
#> M(1) 0.163
#> M(2) 0.089
#> M(3) 1.181
#> M(4) 0.558
#> M(5) 1.020
#> M(6) 0.090
#> M(7) 0.083
#> M(8) 0.244
#> M(9) 0.062
#> M(10) 0.272
#> M(11) 0.256
#> Q 0.368
#> Q-M2 0.402
#>
#> Final filters:
#> Seasonal filter: 3x5
#> Trend filter: 13 terms Henderson moving average
#>
#>
#> Final
#> Last observed values
#> y sa t s i
#> Jan 2020 101.0 102.95613 102.9586 -1.95613209 -0.002494203
#> Feb 2020 100.1 103.50876 102.9592 -3.40875640 0.549602816
#> Mar 2020 91.8 82.87617 103.1664 8.92382800 -20.290271773
#> Apr 2020 66.7 66.65243 103.5971 0.04756625 -36.944710027
#> May 2020 73.7 78.87836 104.0393 -5.17835604 -25.160905985
#> Jun 2020 98.2 87.34544 104.3804 10.85456021 -17.034985133
#> Jul 2020 97.4 92.47436 104.5319 4.92563707 -12.057551871
#> Aug 2020 71.7 97.47245 104.3751 -25.77244698 -6.902636199
#> Sep 2020 104.7 97.37717 103.9182 7.32282919 -6.541070626
#> Oct 2020 106.7 98.24194 103.3047 8.45805540 -5.062719500
#> Nov 2020 101.6 100.26862 102.7746 1.33138152 -2.506014899
#> Dec 2020 96.6 99.66730 102.5133 -3.06729670 -2.845961796
#>
#> Forecasts:
#> y_f sa_f t_f s_f i_f
#> Jan 2021 94.53021 101.0902 102.4794 -6.56002888 -1.3891608
#> Feb 2021 97.90024 101.7395 102.5246 -3.83928384 -0.7850772
#> Mar 2021 114.09983 102.3065 102.5087 11.79328397 -0.2021598
#> Apr 2021 102.16781 102.2220 102.3759 -0.05422341 -0.1538967
#> May 2021 96.01612 101.5450 102.2100 -5.52888123 -0.6650098
#> Jun 2021 112.76658 101.3438 102.0725 11.42275939 -0.7286526
#> Jul 2021 104.13805 101.6681 102.0297 2.46989932 -0.3615193
#> Aug 2021 79.13003 102.3617 102.1360 -23.23171595 0.2257112
#> Sep 2021 109.06438 102.4772 102.3249 6.58713572 0.1523168
#> Oct 2021 108.64207 102.1329 102.5185 6.50921416 -0.3856588
#> Nov 2021 106.46022 102.5908 102.6996 3.86943752 -0.1088338
#> Dec 2021 99.79901 103.0831 102.8580 -3.28410831 0.2251086
#>
#>
#> 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 2.251
#> Seasonal 59.750
#> Irregular 1.067
#> TD & Hol. 2.610
#> Others 33.718
#> Total 99.395
#>
#> 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 0.034
#>
#> Identifiable seasonality present
#>
#> Residual seasonality tests
#> P.value
#> qs test on sa 0.985
#> qs test on i 0.865
#> f-test on sa (seasonal dummies) 0.958
#> f-test on i (seasonal dummies) 0.893
#> Residual seasonality (entire series) 0.876
#> Residual seasonality (last 3 years) 0.906
#> f-test on sa (td) 0.987
#> f-test on i (td) 0.993
#>
#>
#> Additional output variables
tramoseats(myseries, myspec7b)
#> RegARIMA
#> y = regression model + arima (2, 1, 0, 0, 1, 1)
#> Log-transformation: no
#> Coefficients:
#> Estimate Std. Error
#> Phi(1) 0.4032 0.051
#> Phi(2) 0.2883 0.051
#> BTheta(1) -0.6641 0.042
#>
#> Estimate Std. Error
#> Week days 0.6994 0.032
#> Leap year 2.3231 0.690
#> Easter [6] -2.5154 0.436
#> AO (5-2011) 13.4679 1.787
#> TC (4-2020) -22.2128 2.205
#> TC (3-2020) -21.0391 2.217
#> AO (5-2000) 6.7386 1.794
#>
#>
#> Residual standard error: 2.326 on 348 degrees of freedom
#> Log likelihood = -816.1, aic = 1654 aicc = 1655, bic(corrected for length) = 1.852
#>
#>
#>
#> Decomposition
#> Model
#> AR : 1 + 0.403230 B + 0.288342 B^2
#> D : 1 - B - B^12 + B^13
#> MA : 1 - 0.664088 B^12
#>
#>
#> SA
#> AR : 1 + 0.403230 B + 0.288342 B^2
#> D : 1 - 2.000000 B + B^2
#> MA : 1 - 0.970348 B + 0.005940 B^2 - 0.005813 B^3 + 0.003576 B^4
#> Innovation variance: 0.7043507
#>
#> Trend
#> D : 1 - 2.000000 B + B^2
#> MA : 1 + 0.033519 B - 0.966481 B^2
#> Innovation variance: 0.06093642
#>
#> Seasonal
#> 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 + 1.328957 B + 1.105787 B^2 + 1.185470 B^3 + 1.067845 B^4 + 0.820748 B^5 + 0.632456 B^6 + 0.404457 B^7 + 0.245256 B^8 + 0.001615 B^9 - 0.055617 B^10 - 0.203557 B^11
#> Innovation variance: 0.04290744
#>
#> Transitory
#> AR : 1 + 0.403230 B + 0.288342 B^2
#> MA : 1 - 0.260079 B - 0.739921 B^2
#> Innovation variance: 0.05287028
#>
#> Irregular
#> Innovation variance: 0.2032994
#>
#>
#>
#> Final
#> Last observed values
#> y sa t s i
#> Jan 2020 101.0 102.93775 103.0182 -1.9377453 -0.08043801
#> Feb 2020 100.1 103.53944 103.2312 -3.4394383 0.30818847
#> Mar 2020 91.8 82.47698 103.4998 9.3230241 -21.02286361
#> Apr 2020 66.7 65.77310 103.9608 0.9268969 -38.18766871
#> May 2020 73.7 79.43342 104.7269 -5.7334221 -25.29345247
#> Jun 2020 98.2 88.07766 105.3319 10.1223443 -17.25422206
#> Jul 2020 97.4 92.71048 105.4216 4.6895154 -12.71111705
#> Aug 2020 71.7 97.32129 104.9801 -25.6212858 -7.65880696
#> Sep 2020 104.7 97.44274 104.0807 7.2572622 -6.63793072
#> Oct 2020 106.7 98.20925 103.1711 8.4907485 -4.96183772
#> Nov 2020 101.6 99.98044 102.4813 1.6195550 -2.50088282
#> Dec 2020 96.6 98.99458 101.9735 -2.3945790 -2.97892307
#>
#> Forecasts:
#> y_f sa_f t_f s_f i_f
#> Jan 2021 93.22264 100.1984 101.7578 -6.975740 -1.55946363
#> Feb 2021 96.81455 100.8845 101.7113 -4.069924 -0.82679910
#> Mar 2021 111.72198 100.8668 101.6647 10.855228 -0.79795880
#> Apr 2021 102.76178 101.0716 101.6181 1.690178 -0.54654378
#> May 2021 95.52744 101.2474 101.5716 -5.719910 -0.32422597
#> Jun 2021 111.44221 101.2711 101.5250 10.171157 -0.25395653
#> Jul 2021 103.57813 101.2947 101.4784 2.283395 -0.18370915
#> Aug 2021 78.21363 101.3135 101.4319 -23.099833 -0.11841662
#> Sep 2021 108.57631 101.3000 101.3853 7.276282 -0.08528380
#> Oct 2021 107.32040 101.2771 101.3387 6.043321 -0.06166933
#> Nov 2021 105.33458 101.2505 101.2922 4.084088 -0.04168414
#> Dec 2021 98.79675 101.2164 101.2456 -2.419656 -0.02920922
#>
#>
#> 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 6.087
#> Seasonal 80.528
#> Irregular 0.965
#> TD & Hol. 3.590
#> Others 8.102
#> Total 99.271
#>
#> Combined test in the entire series
#> Non parametric tests for stable seasonality
#> P.value
#> Kruskall-Wallis test 0.00
#> Test for the presence of seasonality assuming stability 0.00
#> Evolutive seasonality test 0.01
#>
#> 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) 0.974
#> f-test on sa (td) 0.152
#> f-test on i (td) 0.224
#>
#>
#> Additional output variables
# }