Testing of TRAMO in DemetraIIIc

Anna Ciammola - Istat

General overview

Main functionalities

Expected / Available in DemetraIIIc
Series span / Yes
Transformation / Yes
Calendar effects
- Standard regressors / Yes
- Standard holidays / Yes
- Calendar to build National holidays / No
Regression
- Pre-specified outliers / Yes
- Intervention variables / No
- User-defined variables / No
Automatic modelling / Yes
Arima model
- Specification of the model orders / Yes
- Fixing some or all ARMA parameters / No
Forecasting
- Number of multistep forecasts to compute for original series and components / No
-Out-of-sample forecast test / No
Estimation / Yes
Parameter stability
- ARMA / Yes *
- Trading-day / Yes *
- Easter / No

*Userscannot choose the period to analyse parameter stability.

Main graphs

Expected / Available in DemetraIIIc
Original series
- Plot / Yes
- Periodogram and autoregressive spectrum / Yes
- ACF and PACF / No *
Transformed and stationary series
- Plot / Yes
- Periodogram and autoregressive spectrum / Yes
- ACF and PACF / Yes
Residuals
- Plot / Yes
- Periodogram and autoregressive spectrum / Yes
- ACF and PACF / Yes
- Distribution / Yes
Forecasts
- Original, linearized series / No
- Confidence intervals / No
Parameter stability
- ARMA / Yes
- Trading-day / Yes
- Easter / No
Model
- Theoretical spectrum / Yes
- Theoretical ACF / Yes
* Yes if the original series is stationary.

Main output (data)

Expected / Available in DemetraIIIc
Residuals / Yes
Linearized series / No
Calendar adjusted series / No
Overall deterministic component / Yes
- Deterministic components / Yes
- Total outliers / Yes
- Outliers per component / Yes
- Total calendar effect / Yes
- Trading-day & Leap-Year Yes / Yes
- Easter / Yes
- Intervention and other regression effects NO / No
Forecasts
- Original, linearized series / No
- Standard errors / No
Parameter stability
- ARMA / No
- Trading-day / No
- Easter / No
Model (autoregressive roots)
- Frequency / Yes
- Modulus / No

Specific issues

Automatic treatment (Existing Spec)

The parameter RSA are first considered. All 5 options are considered.

The specifications RSA1 to RSA5 of DemetraIIIc exactly reflect the values 1 to 5 assigned to the parameter RSA in the original Tramo.

Warning about RSA=1,2

When RSA=1 or 2 the airline model is imposed and the mean is set to “True”.

Sincethe mean is often not statistically significantwith regular and seasonal difference, the mean option could be either set to “False” or automatically identified.

Tramo-Seatscan easily combine RSA and ITER and reports results in summary matrices (someexamplesaredisplayed in appendix A). They are very useful (especially when many time series are treated in an automatic way or several models are estimated for one time series) and consequently they are expected in Demetra+.

Manual treatment (New Spec)

Transformation

Series span

Specifying the series span, default dates are 01/01/1000 and 31/12/2999. The first and the last periods of the series are better. The specification of the series span could be put together the other items (Transformation, Calendar effects, …).

Selection type

Options “TO” and “BETWEEN” do not run

Calendar effects

Easter duration

This option does not run. Results do not change when it is set to a value different from 6.

Regression

Pre-specified outliers

  • Users can specify SO (Seasonal Outliers), but they are not estimated. In the figure below “Apply” does not remove the outlier SO imposed and estimatesa TC at the same date.

  • If the series span is reduced, the years displayed in the window used to impose the outliers should be reduced accordingly. In the example below 1990 is the first year of the series, but the selected series span starts from 1995.

Intervention variables

Not active

Used-defined variables

Not active

Outlier detection

Outliers detection span

Specifying the outliers detectionspan, default dates are 01/01/1000 and 31/12/2999. The first and the last periods of the selected series span are better

Selection type

Options “TO” and “BETWEEN” do not run

Critical value (when the default critical value is not used)

  • Since every real number is accepted (even negative!), a positive range should be suggested to users
  • It appears a bit instable. See figures below (moreover critical value = 2 and = 0.5 give same results!)

“TC rate”

It is expected to represent the dampening factor of the temporary change outliers (in fact it is given the default value of 0.7). Every real value (even negative or greater than one!) is allowed with consequent doubtful results.

Arima modelling

Automatic modelling

TSIGappears to serve no purpose (this also happens with TSW)

Arima model

User can only specify the order of the polynomials. There is no possibility to fix some parameters (one fixed value, for example 0, could be entered for a coefficient that is not statistically significant or all the coefficients could be fixed for simulation purposes).

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APPENDIX

Some summarymatrices from Tramo-Seats (version of March 2009 available on the web site of Bank of Spain)

Residuals Diagnostics

Model Nz Lam Mean P D Q BP BD BQ SE(res) BIC Q-val N-test SK(t) KUR(t) QS Q2 RUNS

Model1 236 0 0 0 1 1 0 1 1 0.0332541 -6.74796 379.3 0.364 -0.42 -0.44 26.6 69.20 2.83

Model2 236 0 0 0 1 1 0 1 1 0.0198818 -7.67846 32.50 4.47 -0.36 2.08 0.526 76.17 0.408

Model3 236 0 1 3 0 0 0 1 1 0.0256389 -7.17038 60.26 1.80 -0.54 -1.23 7.48 32.05 -1.35

Model4 236 0 1 2 0 0 0 1 1 0.0199868 -7.64894 24.94 12.8 -0.33 3.56 1.38 23.45 0.272

Model5 236 0 1 2 0 0 0 1 1 0.0190843 -7.64409 26.73 2.05 1.37 0.399 1.71 53.52 0.

Trading-Day, Leap Year and Easter coefficients

Model TD1 (t) TD2 (t) TD3 (t) TD4 (t) TD5 (t) TD6 (t) LY (t) EE (t)

Model1 - ( -) - ( -) - ( -) - ( -) - ( -) - ( -) - ( -) - ( -)

Model2 0.007077 ( 21.) - ( -) - ( -) - ( -) - ( -) - ( -) 0.024839 ( 3.5) - ( -)

Model3 - ( -) - ( -) - ( -) - ( -) - ( -) - ( -) - ( -) - ( -)

Model4 0.007157 ( 22.) - ( -) - ( -) - ( -) - ( -) - ( -) 0.028042 ( 4.0) - ( -)

Model5 0.002142 ( 0.94) 0.008781 ( 3.9) 0.013832 ( 6.2) 0.003782 ( 1.7) 0.002214 ( 1.0) -0.01324 ( -6.0) 0.028884 ( 4.5) - ( -)

Outliers

Model1 TC01(1007, 3.61);

Model2 AO01(0707, -5.28); AO02(0606, -3.41); TC01(1007, 4.59); TC02(0608, -4.23);

Model3 TC01(1007, 4.87); TC02(0707, -5.73); TC03(0608, -4.68);

Model4 AO01(0706, 5.22); AO02(0608, -3.72); TC01(1007, 4.69);

Model5 AO01(0706, 5.68); AO02(0608, -3.56); TC01(1007, 5.11);

ARMA parameters

Model PHI1 (t) PHI2 (t) PHI3 (t) BPHI (t) TH1 (t) TH2 (t) TH3 (t) BTH (t)

Model1 - ( -) - ( -) - ( -) - ( -) -0.89618 ( -29.) - ( -) - ( -) -0.56257 ( -8.5)

Model2 - ( -) - ( -) - ( -) - ( -) -0.64326 ( -12.) - ( -) - ( -) -0.46124 ( -7.0)

Model3 0.154122 ( 2.8) -0.20012 ( -3.9) -0.63747 ( -12.) - ( -) - ( -) - ( -) - ( -) -0.52946 ( -7.7)

Model4 -0.35804 ( -5.3) -0.32793 ( -4.9) - ( -) - ( -) - ( -) - ( -) - ( -) -0.43574 ( -6.2)

Model5 -0.34566 ( -5.3) -0.37620 ( -5.7) - ( -) - ( -) - ( -) - ( -) - ( -) -0.36715 ( -5.3)

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