1.
Demetra+
Prototype IV
User Manual
106748842
1
2.
Contents
1. Introduction .............................................................................................................. 3
1.1. Overview of the software ................................................................................................ 3
1.2. Browsing the data ........................................................................................................... 4
1.3. Importing data from Excel ............................................................................................... 5
1.4. Displaying the data .......................................................................................................... 7
2. Application’s Menu ................................................................................................... 8
2.1. Workspace menu ............................................................................................................ 8
2.1.1.
Calendars ....................................................................................................... 8
2.1.2.
User-defined regression variables ................................................................. 9
2.2. Tools menu .................................................................................................................... 11
2.2.1.
Container...................................................................................................... 11
2.2.2.
Spectral Analysis .......................................................................................... 13
2.2.3.
Differencing.................................................................................................. 14
2.3. X-12 Doc ........................................................................................................................ 15
2.4. Window menu ............................................................................................................... 19
2.5. Interaction with other tools .......................................................................................... 20
3. Single seasonal adjustment ..................................................................................... 21
4. Multi-processing ..................................................................................................... 24
5. Changing the specification....................................................................................... 16
6. Seasonal adjustment results .................................................................................... 25
6.1. Main results ................................................................................................................... 26
6.1.1.
Pre-processing.............................................................................................. 30
6.1.2.
Decomposition ............................................................................................. 35
6.1.3.
Diagnostics ................................................................................................... 39
6.2. Editing and modifying the results ................................................................................. 46
6.3. Sending the results to external devices ........................................................................ 48
6.4. Saving and refreshing workspaces ................................................................................ 49
106748842
2
3.
Introduction
The aim of this short document is not to provide a complete description of the software but to
give a first overview of the tool and of its main functionalities.
Demetra+ is designed as an open and flexible software, which allows various uses. Instead of
describing the different functions and presentation tools of the application, we prefer, in this first
document, to describe step by step the way to solve some very basic tasks.
It is clear that such a non systematic approach is not sufficient to understand completely the
software. However, we think that it is the easiest and the most stimulating way to get some
feeling of this new product.
In a first stage, we just consider the way to visualize the data provided with the software and to
import new series from Excel.
In a second stage, we explain how we can adjust a single series.
In a third stage, we consider the processing of many series.
In a last stage, we discuss the way to save and to refresh a previous work.
1.1.
Overview of the software
When it is opened for the first time, Demetra+ appears with the following layout:
106748842
3
4.
The key parts of the application are:




the browsers panel (left panel), which presents the available time series
the workspace panel (right panel), which shows information used or generated by the
software
a central blank zone that will contain actual analyses
two auxiliary panels at the bottom of the application; the left, one (TSProperties) contains
the current time series (from the browsers’ panel) and the right one (Logs) contains
logging information.
Panels can be moved, resized, superposed, closed1... depending on needs or preferences of the
user. The presentation is saved between different sessions of Demetra+.
The application can contain multiple documents. Following the needs, you can present them in
different tabs taking the full space (default) or in floating windows (choose this one to follow
different steps). The main menu item "Window->Floating/Tabbed..." gives access to that
functionality.
1.2.
Browsing the data
The browsers’ panel presents the series available in the software. Different "time series
providers" are considered: Xml (specific schema), Excel, TSW, USCB, Text, ODBC...
The installation procedure has copied several files in different formats in the subfolders of "My
Documents\Data". We explain below the way to open Excel workbooks. The procedure is similar
for the other providers.
1. Click on the Excel tab of the browsers panel.
2. Click on the left button (see below).
3. Choose an Excel workbook (for instance "insee.xlsx") in the folder "My
Documents\Data\Excel".
1 Closed panels can be re-opened through the main menu commands: Workspace->View->...
106748842
4
5.
Different browsers show the data in trees that can be expanded by double-clicking their nodes (or
single-clicking the +/- signs)
.
Final nodes of the trees represent time series and their parents represent collections of time
series.
1.3.
Importing data from Excel
Time series from Excel can easily be integrated in Demetra+. The series must be formatted in
Excel as follows:

True dates in the first copied column/row,

Titles of the series in the first copied row/column,

Empty top-left cell ,

Empty cells in the data zone correspond to missing values (except at the beginning and at
the end of the series).
That format corresponds with the format used by the Excel browser (which also requires that the
input zone starts at the beginning of the sheet [A1]).
106748842
5
6.
After they have been copied in Excel, the data can be integrated in Demetra+ as follows:

Select the xml panel in the browsers,

Paste the data (they appear in the tree),

Change the names of the series/collection in the tree if necessary (click twice on the item
you would like to modify),

Save the file (if need be).
106748842
6
7.
1.4.
Displaying the data
When clicking on the one node of the trees, the basics statistics, chart and time series data are
presented in TS Properties window automatically.
106748842
7
8.
2. Application’s Menu
2.1.
Workspace menu
Workspace menu offers the following functions:

New - creates new Workspace displayed in the right panel,

Open - opens an existing project in a new window,

Save - save the project file named by the system (workspace_#number) that can be reopened at a later point in time,

Save as - save the project file named by the user that can be re-opened at a later point in
time,

View - activates or deactivates the panels chosen by user (Browsers, Workspace, Logs, TS
Properties)

Edit - allows defining countries’ calendar and regression variables. This functionalities is
described further into this instruction.

Exit - closes an open project.
2.1.1. Calendars
The calendars of Demetra+ simply correspond to the usual trading days contrasts variables, based
on the Gregorian calendar, modified to take into account some specific holidays. Those holidays
are handled as "Sundays" and the variables are properly adjusted to take into account long term
mean effects.
106748842
8
9.
Demetra+ considers three kinds of calendars:

National calendars, identified by specific days

Composite calendars, defined as weighted sum of other calendars

Chained calendars, defined by two other calendars and a break date
The calendars can be defined recursively.
The data generated by each calendar can be viewed by a double click on the corresponding item
in the workspace tree.
The regression variables can be generated for any frequency and any (reasonable) time span
through that window; the periodogram of those series are displayed when a column is selected.
Finally, the series can be copied by drag (see blue circle) and drop or through the local menu to
other places/software
2.1.2. User-defined regression variables
User-defined regression variables are simply time series identified by their name. Those names
will be used in other parts of the software (regression) as identifier of the data.
Demetra+ considers two kinds of user-defined regression variables:

Static variables, usually imported from external software

Dynamic variables, coming from some browser.
Static variables imported from external software (for instance Excel) must be formatted as
defined in the "Quick Start" document. They are imported by drag and drop or using the usual
keys (ctrl-v).
106748842
9
10.
Dynamic variables are imported by drag and drop from a browser of the application.
The figures of static variables cannot be changed. Currently, the only way to update static series
consists in removing them from the list and to re-import them with the same names as previously.
Dynamic variables are automatically updated each time the application is re-opened. So, they
should be the preferred way to handle user variables.
The names of the series can be changed as usual (selected a series and click once again when it
has been selected). The selected series can be showed in a small chart window by a double click.
106748842 10
11.
2.2.
Tools menu
2.2.1. Container
To display the data, it is also possible to open one of the available containers of Demetra+ (charts,
grids or tables, lists...)
The user can take any series or group of series from one of the browsers and drop it in a
container.
The group cannot be marked using Ctrl button. Add the series to chart or grid, by dragging and
dropping them one by one.
The chart is automatically rescaled after adding new series. Also new item “Chart” is added to
menu toolbar.
106748842 11
12.
Putting numerous time series into one chart could make it confusing. In this case it is helpful to
click on one series which is then displayed in bold.
The right-button menu offers many useful options. Chart can be edited, printed or saved as
bitmap.
106748842 12
13.
2.2.2. Spectral Analysis
Tools menu offers spectral estimators – periodogram and autoregressive spectral estimator. After
choosing it from Tools menu the empty window is displayed.
To calculate periodogram drag and drop a raw time series into the displayed window. The
methodological note about spectral analysis is available further into this instruction.
106748842 13
14.
2.2.3. Differencing
Using Differencing window from Tools menu it is possible to obtain not only table and spectral
graphs but also ACF and PACF functions for selected time series. To do it, the time series’ name
from the list should be dragged and dropped into Name box.
parameters
Estimate button
bookmarks
Autocorrelation function (AC) displayed graphically and numerically in the graph, is the serial
correlation coefficients of the current value of the series with the series lagged a certain number
of periods in a range of lags (1 through 36). Green dotted lines indicate range of two standard
errors.
Drag and drop is omnipresent in Demetra+. It is the usual way to move information between
different components. The objects that can be moved (time series, collections of time series...)
can take different forms: nodes in trees, labels in lists, headers in tables, lines in charts...
When a drag and drop operation is initiated (which means that an object is indeed "moveable"),
the cursor of the mouse changes to either a "no parking sign" or to a "+ sign", which indicates an
acceptable drop zone.
Information can also be moved by drag and drop or copy/paste to external software (for instance
Excel).
106748842 14
15.
2.3.
X-12 Doc
This item is added to the application’s menu when X-12 seasonal adjustment was done ant it
is active.
Current specification is displayed in a non modal dialog box, so the user can change any option
and inspect its impact on the results. For a detailed description of the X12 specifications, you
should refer to the "Demetra_Spec.docx" document.
For example:



Select in the output window the 'Main results -> Charts" window,
Modify the span of the series in the "Basic" panel:
o Click on the Basic item in the left panel of the specification dialog box,
o Expand the "series span" node in the right panel,
o Choose the "excluding" selection type,
o Write "12" in the "last" node,
Press the "Apply" button.
The processing is computed on the series without the last 12 observations. A visual comparison of
the forecasts of X12 and of the actual figures is displayed on the chart.
Some other examples are explained below. They are based on series coming from the "prod.xml"
file, which provide more eloquent results. The next snapshots use the series named "Industries
manufacturières"
106748842 15
16.
Suppressing of trading days
The trading days regression variables can be suppressed by setting the "Trading days -> Type" to
"None" in the "Calendar effects" panel of the specification dialog box.
Meaningful information is provided in the "Pre-processing -> Arima" panel or in the different
panels of the spectral analysis
Changing the specification
The user is able to modify the used specification and to see immediately the result of changes
made.
The specification is edited through the main menu: TramoSeatsDocxxx / X12Docxxx ->
Specification... It is possible to edit the specification used to generate the processing (current
specification) or the specification that corresponds to the results (result specification).
106748842 16
17.
Changing X11 options
The X11 panel of the specification dialog box contains a rich set of options on the X11
decomposition. Their effects appear - for instance - in the SI-ratio chart
The previous snapshot was realized by setting the "Use forecasts" option on false and the
"Seasonal filter" on "S3x15"
User-defined regression variables
Once calendar variables and/or user-defined regression variables have been defined (see general
features), they can be integrated in the regression model of X12 using several ways.
Calendars can be chosen in the trading days node of the calendar effects panel of the specification
dialog box:
106748842 17
18.



Select the option "Calendar" in the "Type" field,
Choose the holiday in the list that is automatically displayed (it corresponds to the
calendars defined in the workspace; calendars must be defined to get access to that
option),
The corresponding calendar variables are computed "on the fly".
Trading days effects can also be defined in a free way as pure user-defined regression variables:


Select the option "UserDefined" in the "Type" field,
Choose the variables in the list that is displayed after a click on the dots on the right of the
"Details -> Items" row (it corresponds to the user variables defined in the workspace; user
variables must be defined to get access to that option).
Regression variables that are not considered as trading days can be integrated in a quite similar
way through the regression panel of the specification dialog box.
106748842 18
19.
2.4.
Window menu
Window menu offers the following functions:

Floating,

Tabbed - arranges all windows in central zone as tabs,

Tile vertically -arranges all windows in central zone vertically,

Tile horizontally -arranges all windows in central zone vertically,

Skinning – allows to custom graphical appearance of Demetra+.
The window menu includes also the seasonal adjustment processing done and not closed by the
user during the current session.
“Documents” option offers some additional options helpful for organising windows.
106748842 19
20.
2.5.
Interaction with other tools
The different series that appear in the results can be dropped in other windows of Demetra+
Useful examples are described below:




Open auto-regressive spectrum windows using the following main menu item: "Tools ->
Spectral Analysis -> Auto-regressive spectrum",
Drop meaningful series of the results in those tool windows (for example "A1" and "B1"
from the "Decomposition (X11)" sub-nodes,
Open a "growth chart" using the following main menu item: "Tools -> Tool Windows ->
Growth chart",
Drop D11 (for example) in it.
The different tool windows are dynamically updated when:


A new series is selected, through a double click in the browsers panel or when a series is
dropped in the left zone of the X12 window,
The specification is changed, by means of the specification dialog box or when another
specification, coming from the workspace, is dropped in the left zone of the X12 window.
Many other combinations are of course possible.
It should be noted that the current implementation is not able to detect recursive processing,
obtained for instance by dropping a series like "D11" in the left zone of the same X12 window.
Such an attempt will generate a crash of Demetra+.
106748842 20
21.
3. Single seasonal adjustment
The seasonal adjustment of a single series can be done in different ways. Below, we present the
simplest solution (also known as the short –cut).
The first step to produce a fast seasonal adjustment consists in choosing a specification from the
list displayed in the workspace panel. The procedure is as follows:

Select in the tree the specification you want to select,

Open the local menu by means of the right button of the mouse,

Choose the "Active" menu item.
That specification, called active specification, will be used to generate the processing. It can be
changed at any time.
106748842 21
22.
Specifications correspond to the terminology used in TSW2.
Name
Content
RSA1
log/level, outliers detection, Airline model
RSA2
log/level, working days, Easter effect, outliers detection, Airline model
RSA3
log/level, outliers detection, automatic model identification
RSA4
log/level, working days, Leap year, Easter effect , outliers detection, automatic
model identification
RSA5
log/level, trading days, Leap year, Easter effect, outliers detection, automatic model
identification
Once the active specification is chosen, the user has just to make a double click on the series in
the browsers’ panel that he wants to adjust. The processing is immediately initiated, with the
selected specification and the chosen series.
double click on the time series
results of seasonal adjustment are
presented in the central panel
mark the specification
Demetra+ provides a multiple documents interface (MDI). The user can display and compare
many documents.
One can process as follows:




Select another active specification (for instance, "RSA1"), following the procedure
described above,
Double click on a series in the browsers panel,
Make some place by clicking on either the "Auto Hide" and "Close" buttons of the system
windows ("Workspace", "Logs", "TSProperties"),
Tile the output windows through the "Window" sub-menu,
2 Description from G. Caporello, A. Maravall “PROGRAM TSW, REVISED REFERENCE MANUAL,” July 2004. TSW program
be downloaded form webpage http://www.bde.es.
106748842 22
23.

New double click in the browsers will update the different processing (that feature can be
disabled by locking a given processing, through the "X12Doc-xxx" -> "Lock" main menu
item.

This procedure can be used with any specification (Tramo-Seats and X12).
The figure below shows how to use the "Auto Hide" (red) button or the "Close" (blue) button:
As an example, the following chart presents the comparison of the results for “Tile vertically”
option.
The user can inspect the different facets of the results through the exploring tree displayed in the
left panel of the output window. The results contain many detailed panels. The user can go
through them by selecting a node in the navigation tree of the X12 processing. The current
specification and the current series are displayed on the top of the window.
106748842 23
24.
4. Multi-processing
The seasonal adjustment of many series can also be done using various ways. The short way is
explained below.
Multi-processing needs the following steps:

Create a new multi-processing window, through the main menu (Seasonal adjustment ->
Multi-processing -> New),

Choose an active specification (see above),

Import by drag and drop the series (or collection of series) you want to process; they can
come from different providers.
If you want to mix different specifications (from TramoSeats and X12), you can change at any time
the active specification; the series added after that change will be associated with the new active
specification.
Start the processing (through the main menu "SAProcessing XXX-> Start"); it should be noted that
the processing runs in a multi-threaded environment; so, the user can continue his work without
waiting for the end of the action.
106748842 24
25.
5. Seasonal adjustment results
The exact content of the panel depends on the seasonal adjustment methods chosen by the user.
The basic output structure is as follows:




Main results,
o
Charts,
o
Table,
o
S-I ratio,
Pre-processing,
o
Pre-adjustment series,
o
Arima,
o
Residulas,
Decomposition,
o
Stochastic series,
o
WK analysis,
Diagnostics,
o
Seasonality tests,
o
Spectral analysis,
o
Revision history,
o
Sliding spans,
o
Model stability.
Detailed description of the seasonal adjustment outcomes is presented below.
106748842 25
26.
5.1.
Main results
This section includes basic information about seasonal adjustment and the quality of the
outcomes. Left panel presents the results from Tramo Seats, right panel - the results from X-12ARIMA
In Charts section the top panel presents the original series with forecasts, the final seasonally
adjusted series, the final trend with forecasts and the final seasonal component with forecasts.
The second panel shows the final irregular component and the final seasonal component with
forecasts.
106748842 26
27.
The charts in main results section (and many other charts available in Demetra+) provide zooming
features. Select the zone you want to zoom with your mouse (from the top-left corner to the
bottom-right one). Select any rectangle from bottom-right to top-left to un-zoom the chart.
You can move (red) or resize (blue) the selected zooming window with the scroll bars. You can
also highlight any series by clicking on it.
106748842 27
28.
Table presents the original series with forecasts and forecast error, the final seasonally adjusted
series, the final trend with forecasts, the final seasonal component with forecasts, the final
irregular component.
S-I ratio chart presents the final estimation of the seasonal-irregular component and final
seasonal factors for each of the period in time series (months or quarters). The combined
seasonal-irregular component (dots) is obtained by subtracting trend-cycle from Original Series
Adjusted for Trading-day and Prior Variation (additive model) or division the trend-cycle by
Original Series Adjusted for Trading-day and Prior Variation (multiplicative model). Curves
represents the final seasonal factors and the straight line represents the average for the these
values in each period.
106748842 28
29.
You can enlarge a specific period in the SI-ratio chart by clicking in its zone. The details are
displayed in a resizable pop-up window.
106748842 29
30.
5.1.1. Pre-processing
Pre-adjustment series
Table presented in pre-processing section contains series estimated in TRAMO or Reg-ARIMA
part. It includes interpolated series, series adjusted for calendar effects, deterministic component,
calendar effects, trading days effect, outliers effect on irregular component, total outliers effect,
total regression effect (X-12ARIMA only).
Arima
This section demonstrates spectrum linearised series and ARIMA model parameters’ values.
106748842 30
31.
Residuals
Residuals are calculated as a difference between the one-step-predicted output from the model
and the measured output from the validation data set. They represent the portion of the
validation data which is not explained by the model. One-step ahead residuals from the model are
presented in the graph and in the numbers.
Analysis of the residuals consist of several tests.
Normality test
Jarque-Berra test on normality checks if skewness and kurtosis in the sample is like in the normal
distribution. The assumption of normality is used to calculate the confidence intervals from
standard errors. If this assumption is rejected, the estimated confidence intervals will be distorted
even if the standard forecast errors are reliable. A significant value of one of these statistics
indicates that the standardised residuals do not follow a standard normal distribution; because of
that the reported confidence intervals might not represent the actual ones.
106748842 31
32.
Independence of the residuals
This statistic measures the probability of the autocorrelation function occurring under the
hypothesis that the model has accounted for all serial correlation in the series up to the lag. Pvalues greater than 0.05, up to lag 12 for quarterly data and lag 24 for monthly data, indicate that
there is no significant residual autocorrelation and that, therefore, the model is adequate for
forecasting.
Durbin-Watson test
The Durbin-Watson statistic is a test for first-order serial correlation. This statistic verified the
linear association between residuals from a regression model, testing if   0 in the following
specification:
T
DW 
 (e  e
i2
i 1
i
T
e
i 1
)2
,
2
i
Where:
et - residuals.
If there is no serial correlation, the DW statistic will be around 2. The Durbin-Watson statistic
ranges in value from 0 to 4. If there is no serial correlation, the DW statistic will be near 2. The
values lower than 2 indicates positive autocorrelation, while the values higher than 2 indicates
negative autocorrelation.
Randomness of residuals
The runs test implemented in Demetra+ is used to test for randomness of residuals. To conduct
the test a up-down series is created. The observations in this series indicate if the given value in is
up or down in value from the prior value in sequence. The runs test is performed on the up-down
series rather than upon the original quantitative variable.
106748842 32
33.
Linearity of the residuals
Residual autocorrelation is verified using two tests: Ljung-Box test and Box Pierce test.
For Ljung –Box the test statistic is:
nk2
,
k 2 ( N  k )
L
QLB  N ( N  2)
where:
N - the sample size,
n k2 - the squared sample autocorrelation at lag k
L - the number of lags being tested.
Null hypothesis is: The data are random.
The test statistic for Box-Pierce test is:
S
Qs  T  rk2
k 1
where:
rk2 - k th sample autocorrelation,
The p-value marked in red indicates that null hypothesis was rejected.
106748842 33
34.
Demetra+ also presents residuals’ distribution. In this section autocorrelation and partial
autocorrelation functions are presented.
106748842 34
35.
5.1.2. Decomposition
The contain of Decomposition section depends on the seasonal adjustment method chosen by
user.
Tramo/Seats
The decomposition made by Seats assumes that all components in time series - trend, seasonal
and irregular - are orthogonal and could be modeled using ARIMA model. Identification of the
components requires that only irregular components include noise. ARIMA models estimated for
each components are presented below:
Additional information presented by Demetra is set of stochastic series (seasonally adjusted
series, trend, seasonal component, irregular component, trend-forecast, seasonal componentforecast) and Wiener-Kolmogorow analysis.
106748842 35
36.
X-12-ARIMA
In the decomposition section all important tables from X-11 procedure are available:
Part A - Raw Series
Table A1- Time Series Data
Table A1a Table A2 Table A6 Table A8 -
Part B - Preliminary Estimation of Extreme Values and Calendar Effects
Table B1 - Raw Series Adjusted a Priori
Table B2 - Trend-Cycle
Table B3 - Unmodified Seasonal-Irregular Component
Table B4 - Replacement Values for Extreme SI Values
Table B5 - Seasonal Component
Table B6 - Seasonally Adjusted Series
Table B7 - Trend-Cycle
Table B8 - Unmodified Seasonal-Irregular Component
Table B9 - Replacement Values for Extreme SI Values
Table B10 - Seasonal Component
Table B11 - Seasonally Adjusted Series
Table B13 - Irregular Component
Table B17 - Preliminary Weights for The Irregular
Table B20 - Adjustment Values for Extreme Irregulars
Part C - Final Estimation Of Extreme Values And Calendar Effects
Table C1 - Modified Raw Series
Table C2 -Trend-Cycle
106748842 36
37.
Table C4 - Modified SI
Table C5 - Seasonal Component
Table C6 - Seasonally Adjusted Series
Table C7 - Trend-Cycle
Table C9 - SI Component
Table C10 - Seasonal Component
Table C11 - Seasonally Adjusted Series
Table C13 - Irregular Component
Table C20 - Adjustment Values For Extreme Irregulars
Part D - Final Estimation of the Different Components
Table D1 - Modified Raw Series
Table D2 -Trend-Cycle
Table D4 - Modified SI
Table D5 - Seasonal Component
Table D6 - Seasonally Adjusted Series
Table D7 - Trend-Cycle
Table D8 - Unmodified SI Component
Table D9 - Replacement Values for Extreme SI Values
Table D10 - Final Seasonal Factors
Table D10A Table D11 - Final Seasonally Adjusted Series
Table D11A - Final Seasonally Adjusted Series with Revised Annual Totals
Table D12 - Final Trend-Cycle
Table D12A Table D13 - Final Irregular Component
Table D13U Table D16 - Seasonal and Calendar Effects
Table D16A 106748842 37
38.
Table D18 - Combined Calendar Effects Factors
Part E - Components Modified For Large Extreme Values,
Table E1 - Raw Series Modified for Large Extreme Values
Table D2 - SA Series Modified for Large Extreme Values
Table E3 - Final Irregular Component Adjusted for Large Extreme Values
Table E11 - Robust Estimation of the Final SA Series
right-clock on the column's header or
table name to open the context menu
106748842 38
39.
5.1.3. Diagnostics
Seasonality tests
Several seasonality tests are available in Demerta+.
Friedman test
Friedman's test is a non-parametric method for testing that samples are drawn from the same
population or from populations with equal medians. In the regression equation the significance of
the month (or quarter) effect is tested. Friedman test requires no distributional assumptions. It
uses the rankings of the observations. Therefore it is not as sensitive to outliers in small samples
as regression analysis. The test statistic is approximately distributed as chi-squared with 11
degrees of freedom. The null hypothesis is: The months (quarters) have identical effects.
Kruskal-Wallis test
Kruscal-Wallis test is used to compare samples from two or more groups. The null hypothesis
states that all months (or quarters, respectively) have the same mean.
106748842 39
40.
Spectral analysis
Demetra+ provides spectral plots to alert the user to the presence of remaining seasonal and
trading day effects. Two spectrum estimators are implemented.
Periodogram has the following form3:
^
2
j ( )  10 log 10 (
N
N
x e
t 1
2
i 2t
t
)
Where:
 - frequency, 0    0.5
xt - time series, 1  t  N .
The second spectrum estimator is an autoregressive spectrum estimator4:

^

2
^


m
s ( )  10 log 10 
m ^

2

1

 j ei 2j


j 1



 i 2j
e
2



Where:
 - frequency, 0    0.5
^
 m2 - the sample variance of the residuals

^

 j - coefficients from regression xt  x on xt  j  x , 1  j  m .
Seasonal frequencies are marked as grey, vertical lines, while violet lines correspond to tradingdays frequencies. The X-axis shows the different frequencies. The periodicity of phenomenon at
frequency f is
2
. It means that for monthly time series the seasonal frequencies are:
f
   2 5
, , , ,
. Horizontal yellow line corresponds to a significance level of 0.5% and delimits
6 3 2 3 6
highly suspect peaks.
3 D. Findley, B. Monsell, W. Bell, M.Otto, B. Chen, New Capabilities and Methods of the X-12-ARIMA Seasonal
Adjustemnt Program, pp.22.
4 Definition taken from: X-12-ARIMA Reference Manual, p. 55, http://www.census.gov/srd/www/x12a/
106748842 40
41.
At seasonal and trading days frequencies, a peak in model residuals indicates that the need for a
better fitting model. A peak in the spectrum from the seasonally adjusted series or irregulars
reveals inadequacy of the seasonal adjustment filters for the time interval used for spectrum
estimation. In this case different model specification or data span length should be considered.
Revision histories
Revision histories deal with the revisions associated with continuous seasonal adjustment over a
period of years. Revisions are calculated as a difference between the first (earliest) adjustment of
an observation computed when that observation is the final period of the time series (concurrent
adjustment, denotes as At |t ) and a later adjustment based on all data span (most recent
adjustment, denotes as At | N ).
The revision history of the seasonal adjustment from time N 0 to N1 is a sequence of RtA| N
calculated in a following way5:
RtA| N  100 
At | N  At |t
At |t
Demetra+ calculates revision history for both SA series and trend-cycle component. Revision
history is done for last 12 (monthly series) or 4 (quarterly) observations.
5 D. Findley, B. Monsell, W. Bell, M.Otto, B. Chen, New Capabilities and Methods of the X-12-ARIMA Seasonal
Adjustemnt Program, pp.26.
106748842 41
42.
Red line represents the final estimation of the seasonally adjusted time series, while dots denote
the initial estimation. The history analysis plot is accompanied by information about the relative
difference between initial and final estimation. Values which absolute value are too large are
marked in red and provide information about the stability of the outcome.
In the revisions history panels the user can have a complete overview of the different revisions for
a given time span by selecting with the mouse (just like for zooming) the considered periods. The
successive estimation are displayed in a separate pop-up window
One can also get all the revisions for a specific period by clicking on the point that corresponds to
the first estimate for that period. The results of those popup-up windows can be copied or drag
and dropped to other software (Excel...)
106748842 42
43.
By default, the revisions are obtained with the same model, but in re-estimating its parameters.
That option can be changed through the local menu of the revision history node (left panel), at
the expense of the speed of the processing and for results that are usually very similar.
Sliding spans
The sliding spans analysis means the comparison of the correlated seasonal adjustments of a
given observation obtained by applying the adjustment procedure to a sequence of three or four
overlapping spans of data, all of which contain this observation. The procedure of withdrawing
spans from time series is described in Findley, Monsell, Shulman and Pugh (1990)6. Each period
(month or quarter) which belongs to more than one span is examined to see if its seasonal
adjustments vary more than a specified amount across the spans.
Seasonal factor is regarded to be unreliable if the following condition is fulfilled:
SSt 
max kN t St k   min kN t S t k 
min kN t S t k 
 0.03 ,
(16)
Where:
St k  - the seasonal factor estimated from span k for month t .
N t = { k : period t is in the k -th span}; .
For seasonally and trading days adjusted series the following statistic is being calculated:
6 Findley, Monsell, Shulman and Pugh (1990), Sidings Spans Diagnostics for Seasonal and Related Adjustments, Bureau
of the Census.
106748842 43
44.
max j At j  min j At j
min j At j
The value is considered to be unreliable if it is higher than 0.03 .
Similarly, the seasonally adjusted changes are unstable if :
max j
At j
At j

min
 0.03
j
At j1
At j1
Where:
At k  - the seasonally (or trading day) adjusted value from span k for month t
N1(t ) = { k : period t and t  1 are in the k -th span} .
Results of sliding spans analysis are presented in three graphs. Upper panel shows the sliding
spans statistic for each period, the bottom-left panel presents the distribution of sliding spans
statistics and bottom-left panel contains information about the percentage of values for which
sliding spans condition is not fulfilled.
106748842 44
45.
One can also change the series and/or the specification by importing new elements7 by drag and
drop (in the exploring tree).
Model stability
The diagnostics output window provides some purely descriptive features to analyze the stability
of some part of the model, like trading days, Easter and Arima. For instance, the coefficients of
the trading days variables computed by means of a moving window (by default on 8 years, using
the same model but with re-estimated parameters) are displayed in the panel corresponding to
the "Model stability -> Trading days" node.
7 It is not possible to drop a TramoSeats specification in an X12 output and vice versa.
106748842 45
46.
5.2.
Editing and modifying the results
It is possible to edit any item of the processing by double clicking it.
The complete output, with the used specification is displayed. The user can modify it, apply the
new specification to see its effects and save the results to the multi-processing window, if need
be.
It is not necessary to close the details window to get information on another series; that window
is updated by a simple click on another series of the multi-processing view.
106748842 46
47.
5.3.
Changing the specification
The user is able to modify the used specification and to see immediately the result of changes
made.
The specification is edited through the main menu: TramoSeatsDocxxx / X12Docxxx ->
Specification... It is possible to edit the specification used to generate the processing (current
specification) or the specification that corresponds to the results (result specification).
106748842 47
48.
5.4.
Sending the results to external devices
When the processing is finished, it is possible to generate several outputs (Excel workbook, csv
files...), through the main menu command: "SAProcessingXXX -> Generate output...". It should be
noted that Excel and .csv outputs will be put in the temporary folder if their target folders are not
specified
106748842 48
49.
5.5.
Saving and refreshing workspaces
By default, single and multi-processing generated through the so-called "short-ways" are not put
in the current workspace. To be able to save and to refresh them, the user must first add them to
the workspace. That can be done, for instance, through the main menu "SAProcessingXXX -> Add
to Workspace".
The user still has to save the workspace, using the usual menu command (Save/Save as).
When Demetra+ is re-opened, it will automatically open at the last used workspace. The software
also maintains a list of the most recently used workspace, which can be easily accessed.
A saved item of a workspace can be opened by a double click or by its local menu. It is then
showed in its previous state. Demetra+ proposes several options to refresh it8:
8 For the moment, those options are only available for multi-processing.
106748842 49
50.
Parameters
Only the parameters are refreshed. The structure of the model is
unchanged
Outliers (+ params)
Outliers (and of course parameters) are re-estimated
Arima and outliers (+params)
Stochastic component, outliers (and of course parameters) are
re-estimated
Complete
The model is completely re-estimated
Obviously, other options could be added in the future (for instance, identification of new outliers
on the last period(s)).
When the refresh option has been selected, Demetra+ automatically goes to the suitable time
series provider(s) to ask for the updated observations; the new estimations are done on those
series (using the previous models, modified by the chosen option).
In next papers, we will describe in details and in a more formal way all the features of Demetra+.
106748842 50