X-13-ARIMA model

print_preprocessing(sa_x13)

Pre-processing (RegArima)

Summary

372 observations

Trading days effect (7 variables)

Easter [1] detected

4 detected outliers

Likelihood statistics

Number of effective observations = 359

Number of estimated parameters = 17

Loglikelihood = -799.084, AICc = 1633.964, BICc = 1.855

Standard error of the regression (ML estimate) = 2.218

ARIMA model

ARIMA coefficients
	Coefficients	Std. Error	T-stat	P (> \| t\|)
Phi(1)	0.000	0.108	0.003	0.998
Phi(2)	0.169	0.074	2.278	0.023
Theta(1)	-0.549	0.102	-5.396	0.000	***
BTheta(1)	-0.666	0.042	-15.775	0.000	***
Signif. codes: 0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1
ARIMA (2,1,1)(0,1,1)

Regression model

Regression coefficients
	Coefficients	Std. Error	T-stat	P (> \| t\|)
Monday	0.559	0.228	2.453	0.015
Tuesday	0.882	0.228	3.864	0.000	***
Wednesday	1.040	0.229	4.535	0.000	***
Thursday	0.049	0.229	0.215	0.830
Friday	0.911	0.230	3.964	0.000	***
Saturday	-1.578	0.228	-6.927	0.000	***
Leap year	2.154	0.705	3.054	0.002	**
Easter [1]	-2.380	0.454	-5.242	0.000	***
TC (4-2020)	-35.592	2.173	-16.377	0.000	***
AO (3-2020)	-20.890	2.180	-9.582	0.000	***
AO (5-2011)	13.499	1.857	7.269	0.000	***
LS (11-2008)	-12.549	1.636	-7.673	0.000	***
Signif. codes: 0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1

print_decomposition(sa_x13, caption = NULL)

Decomposition (X-11)

Mode: additive

S-I Ratio

M-statistics
	Value	Description
M-1	0.163	The relative contribution of the irregular over three months span
M-2	0.089	The relative contribution of the irregular component to the stationary portion of the variance
M-3	1.181	The amount of period to period change in the irregular component as compared to the amount of period to period change in the trend
M-4	0.558	The amount of autocorrelation in the irregular as described by the average duration of run
M-5	1.020	The number of periods it takes the change in the trend to surpass the amount of change in the irregular
M-6	0.090	The amount of year to year change in the irregular as compared to the amount of year to year change in the seasonal
M-7	0.083	The amount of moving seasonality present relative to the amount of stable seasonality
M-8	0.244	The size of the fluctuations in the seasonal component throughout the whole series
M-9	0.062	The average linear movement in the seasonal component throughout the whole series
M-10	0.272	The size of the fluctuations in the seasonal component in the recent years
M-11	0.256	The average linear movement in the seasonal component in the recent years
Q	0.368
Q-M2	0.402
Final filters: M3x5, Henderson-13 terms

Relative contribution of the components to the stationary portion of the variance in the original series, after the removal of the long term trend
	Component
Cycle	2.251
Seasonal	59.750
Irregular	1.067
TD & Hol.	2.610
Others	33.718
Total	99.395

print_diagnostics(sa_x13)

Diagnostics tests
	P (> \| t\|)
mean	0.899
skewness	0.880
kurtosis	0.034
ljung box	0.000	***
ljung box (residuals at seasonal lags)	0.212
ljung box (squared residuals)	0.024
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
Signif. codes: 0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1

TRAMO-SEATS model

Some others graphics can also be added with the ggdemetra package, for example to add the seasonally adjusted series and its forecasts:

library(ggdemetra)
ggplot(data = ipi_c_eu_df, mapping = aes(x = date, y = FR)) +
    geom_line() +
    labs(title = NULL,
         x = NULL, y = NULL) +
    geom_sa(component = "y_f", linetype = 2,
            frequency = 12, method = "tramoseats") + 
    geom_sa(component = "sa", color = "red") +
    geom_sa(component = "sa_f", color = "red", linetype = 2)

Seasonal adjustment of the French industrial production index

print_preprocessing(sa_ts)

Pre-processing (Tramo)

Summary

372 observations

Trading days effect (2 variables)

Easter [6] detected

4 detected outliers

Likelihood statistics

Number of effective observations = 359

Number of estimated parameters = 11

Loglikelihood = -816.075, AICc = 1654.912, BICc = 1.852

Standard error of the regression (ML estimate) = 2.326

ARIMA model

ARIMA coefficients
	Coefficients	Std. Error	T-stat	P (> \| t\|)
Phi(1)	0.403	0.051	7.845	0.000	***
Phi(2)	0.288	0.051	5.616	0.000	***
BTheta(1)	-0.664	0.042	-15.865	0.000	***
Signif. codes: 0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1
ARIMA (2,1,0)(0,1,1)

Regression model

Regression coefficients
	Coefficients	Std. Error	T-stat	P (> \| t\|)
Week days	0.699	0.032	22.016	0.000	***
Leap year	2.323	0.690	3.367	0.001	***
Easter [6]	-2.515	0.436	-5.773	0.000	***
AO (5-2011)	13.468	1.787	7.535	0.000	***
TC (4-2020)	-22.213	2.205	-10.072	0.000	***
TC (3-2020)	-21.039	2.217	-9.492	0.000	***
AO (5-2000)	6.739	1.794	3.757	0.000	***
Signif. codes: 0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1

print_decomposition(sa_ts, caption = NULL)

Decomposition (SEATS)

Mode: additive

S-I Ratio

Model

AR: 1 + 0.403B + 0.288B²

D: 1 − B − B¹² + B¹³

MA: 1 − 0.664B¹²

SA

AR: 1 + 0.403B + 0.288B²

D: 1 − 2.000B + B²

MA: 1 − 0.970B + 0.006B² − 0.006B³ + 0.004B⁴

Innovation variance: 0.704

Trend

D: 1 − 2.000B + B²

MA: 1 + 0.034B − 0.966B²

Innovation variance: 0.061

Seasonal

D: 1 + B + B² + B³ + B⁴ + B⁵ + B⁶ + B⁷ + B⁸ + B⁹ + B¹⁰ + B¹¹

MA: 1 + 1.329B + 1.106B² + 1.185B³ + 1.068B⁴ + 0.821B⁵ + 0.632B⁶ + 0.404B⁷ + 0.245B⁸ + 0.002B⁹ − 0.056B¹⁰ − 0.204B¹¹

Innovation variance: 0.043

Transitory

AR: 1 + 0.403B + 0.288B²

MA: 1 − 0.260B − 0.740B²

Innovation variance: 0.053

Irregular

Innovation variance: 0.203

Relative contribution of the components to the stationary portion of the variance in the original series, after the removal of the long term trend
	Component
Cycle	6.087
Seasonal	80.528
Irregular	0.965
TD & Hol.	3.590
Others	8.102
Total	99.271

print_diagnostics(sa_ts)

Diagnostics tests
	P (> \| t\|)
mean	0.988
skewness	0.413
kurtosis	0.095	.
ljung box	0.010	**
ljung box (residuals at seasonal lags)	0.192
ljung box (squared residuals)	0.000	***
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
Signif. codes: 0 ‘*’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1

Directly create a R Markdown file

A R Markdown can also directly be created and render with the create_rmd function. It can take as argument a SA, jSA, sa_item, multiprocessing (all the models of the multiprocessing are printed) or workspace object (all the models of all the multiprocessing of the workspace are printed).

The print of the pre-processing, decomposition and diagnostics can also be customized with preprocessing_fun, decomposition_fun and diagnostics_fun arguments. For example, to reproduce the example of the previous section:

preprocessing_customized <- function(x){
  library(ggdemetra)
  y <- get_ts(x)
  data_plot <- data.frame(date = time(y), y = y)
  p <- ggplot(data = data_plot, mapping = aes(x = date, y = y)) +
    geom_line() +
    labs(title = NULL,
         x = NULL, y = NULL) +
    geom_sa(component = "y_f", linetype = 2,
            frequency = 12, method = "tramoseats") +
    geom_sa(component = "sa", color = "red") +
    geom_sa(component = "sa_f", color = "red", linetype = 2)
  plot(p)
  cat("\n\n")
  print_preprocessing(sa_ts)
}
decomposition_customized <- function(x){
  print_decomposition(x, caption = NULL)
}

output_file <- tempfile(fileext = ".Rmd")

create_rmd(sa_ts, output_file, output_format = "html_document",
           preprocessing_fun = preprocessing_customized,
           decomposition_fun = decomposition_customized,
           knitr_chunk_opts = list(
             fig.pos = "h", results = "asis", 
             fig.cap =c("Seasonal adjustment of the French industrial production index",
                        "S-I Ratio"),
             warning = FALSE, message = FALSE, echo = FALSE)
)
# To open the file:
browseURL(sub(".Rmd",".html", output_file, fixed= TRUE))

Several models can also be printed creating a workspace:

wk <- new_workspace()
new_multiprocessing(wk, "sa1")
add_sa_item(wk, "sa1", sa_x13, "X13")
add_sa_item(wk, "sa1", sa_ts, "TramoSeats")
# It's important to compute the workspace to be able to import the models
compute(wk)

output_file <- tempfile(fileext = ".Rmd")
create_rmd(wk, output_file, output_format = "html_document",
           output_options = list(toc = TRUE,
                                 number_sections = TRUE))
# To open the file:
browseURL(sub(".Rmd",".html", output_file, fixed= TRUE))

Reproductibility

To produce this document, the knitr options were set as followed:

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>", out.width = "100%",
  fig.dim = c(7, 5),
  warning = FALSE, message = FALSE
)

And the options results='asis', fig.cap = "S-I Ratio" were used in the chunks.

rjdmarkdown with HTML output

X-13-ARIMA model

TRAMO-SEATS model

Directly create a R Markdown file

Reproductibility