rjdmarkdown with HTML output

The functions developped in rjdmarkdown are:

The result is different between X-13ARIMA and TRAMO-SEATS models.

library(rjdmarkdown)
library(RJDemetra)
sa_x13 <- x13(ipi_c_eu[, "FR"])
sa_ts <- tramoseats(ipi_c_eu[, "FR"])

X-13-ARIMA model

print_preprocessing(sa_x13, format = "html")

Pre-processing (RegArima)

Summary

336 observations

Trading days effect (7 variables)

Easter [1] detected

3 detected outliers

Likelihood statistics

Number of effective observations = 323

Number of estimated parameters = 14

Loglikelihood = -624.720, AICc = 1278.803, BICc = 1.252

Standard error of the regression (ML estimate) = 1.665

ARIMA model

ARIMA coefficients
Coefficients Std. Error T-stat P (> | t|)
Theta(1) -0.527 0.048 -10.922 0.000 ***
BTheta(1) -0.487 0.051 -9.585 0.000 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1
ARIMA (0,1,1)(0,1,1)

Regression model

Regression coefficientss
Coefficients Std. Error T-stat P (> | t|)
Monday -0.134 0.164 -0.818 0.414
Tuesday -0.002 0.163 -0.015 0.988
Wednesday 0.242 0.163 1.479 0.140
Thursday -0.531 0.163 -3.252 0.001 **
Friday 0.432 0.164 2.640 0.009 **
Saturday 0.153 0.163 0.936 0.350
Leap year -0.046 0.501 -0.092 0.927
Easter [1] -1.094 0.335 -3.269 0.001 **
LS (11-2008) -8.442 1.307 -6.460 0.000 ***
LS (1-2009) -7.274 1.306 -5.568 0.000 ***
LS (5-2008) -5.020 1.257 -3.993 0.000 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1 
print_decomposition(sa_x13, format = "html", caption = NULL)

Decomposition (X-11)

Mode: additive

S-I Ratio

S-I Ratio

M-statistics
Value Description
M-1 0.061 The relative contribution of the irregular over three months span
M-2 0.034 The relative contribution of the irregular component to the stationary portion of the variance
M-3 0.840 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 0.420 The amount of autocorrelation in the irregular as described by the average duration of run
M-5 0.697 The number of periods it takes the change in the trend to surpass the amount of change in the irregular
M-6 0.236 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 0.075 The amount of moving seasonality present relative to the amount of stable seasonality
M-8 0.206 The size of the fluctuations in the seasonal component throughout the whole series
M-9 0.055 The average linear movement in the seasonal component throughout the whole series
M-10 0.166 The size of the fluctuations in the seasonal component in the recent years
M-11 0.137 The average linear movement in the seasonal component in the recent years
Q 0.272
Q-M2 0.301
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 1.646
Seasonal 49.667
Irregular 0.411
TD & Hol. 0.057
Others 49.814
Total 101.596 
print_diagnostics(sa_x13, format = "html")
Diagnostics tests
P (> | t|)
mean 0.682
skewness 0.726
kurtosis 0.018
ljung box 0.023
ljung box (residuals at seasonal lags) 0.888
ljung box (squared residuals) 0.315
qs test on sa 1.000
qs test on i 1.000
f-test on sa (seasonal dummies) 0.980
f-test on i (seasonal dummies) 0.922
Residual seasonality (entire series) 0.969
Residual seasonality (last 3 years) 0.897
f-test on sa (td) 0.980
f-test on i (td) 1.000
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

Seasonal adjustment of the French industrial production index 

print_preprocessing(sa_ts, format = "html")

Pre-processing (Tramo)

Summary

336 observations

Series has been log-transformed

Trading days effect (6 variables)

Easter [6] detected

3 detected outliers

Likelihood statistics

Number of effective observations = 323

Number of estimated parameters = 15

Loglikelihood = 875.751, AICc = 1262.750, BICc = -8.028

Standard error of the regression (ML estimate) = 0.016

ARIMA model

ARIMA coefficients
Coefficients Std. Error T-stat P (> | t|)
Phi(1) 0.352 0.256 1.376 0.170
Phi(2) 0.134 0.130 1.026 0.305
Theta(1) -0.187 0.256 -0.728 0.467
BTheta(1) -0.611 0.047 -13.010 0.000 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1
ARIMA (2,1,1)(0,1,1)

Regression model

Regression coefficientss
Coefficients Std. Error T-stat P (> | t|)
Monday -0.002 0.002 -1.385 0.167
Tuesday 0.001 0.002 0.353 0.724
Wednesday 0.003 0.002 1.938 0.054 .
Thursday -0.005 0.002 -3.342 0.001 ***
Friday 0.003 0.002 2.010 0.045
Saturday 0.002 0.002 1.128 0.260
Easter [6] -0.011 0.003 -3.201 0.002 **
LS (11-2008) -0.079 0.013 -6.143 0.000 ***
LS (1-2009) -0.071 0.013 -5.509 0.000 ***
AO (8-2001) 0.045 0.013 3.498 0.001 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1 
print_decomposition(sa_ts, format = "html", caption = NULL)

Decomposition (SEATS)

Mode: multiplicative

S-I Ratio

S-I Ratio

Model

AR: \(1+0.352B+0.134B^{2}\)

D: \(1-B-B^{12}+B^{13}\)

MA: \(1-0.187B-0.611B^{12}+0.114B^{13}\)

SA

D: \(1-2.000B+B^{2}\)

MA: \(1-1.314B+0.340B^{2}\)

Innovation variance: 0.467

Trend

D: \(1-2.000B+B^{2}\)

MA: \(1+0.040B-0.960B^{2}\)

Innovation variance: 0.049

Seasonal

AR: \(1+0.352B+0.134B^{2}\)

D: \(1+B+B^{2}+B^{3}+B^{4}+B^{5}+B^{6}+B^{7}+B^{8}+B^{9}+B^{10}+B^{11}\)

MA: \(1+0.718B+0.461B^{2}+0.310B^{3}+0.132B^{4}-0.049B^{5}-0.217B^{6}-0.355B^{7}-0.445B^{8}-0.470B^{9}-0.377B^{10}-0.166B^{11}-0.411B^{12}-0.133B^{13}\)

Innovation variance: 0.160

Irregular

Innovation variance: 0.206

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 2.181
Seasonal 66.768
Irregular 0.106
TD & Hol. 0.069
Others 30.507
Total 99.630 
print_diagnostics(sa_ts, format = "html")
Diagnostics tests
P (> | t|)
mean 0.659
skewness 0.976
kurtosis 0.901
ljung box 0.002 **
ljung box (residuals at seasonal lags) 0.882
ljung box (squared residuals) 0.484
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) 0.977
f-test on sa (td) 0.927
f-test on i (td) 1.000
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ’ ’ 1

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.