A Note on Using Calendar Module in Demetra+ (UNPUBLISHED MANUSCRIPT)

A Note on Using Calendar Module in Demetra+ (UNPUBLISHED MANUSCRIPT) N. Alpay KOÇAK 1 Turkish Statistical Institute Ankara, 28 September 2011 1 Expert, alpaykocak@tuik.gov.tr The views expressed are the personal opinion of the author and do not necessarily reflect the official position of the Turkish Statistical Insitute. Last Revised : 28 September 2011 1

Contents 1. Introduction... 1 2. National Calendars... 3 2.1. Pre-specified Holidays... 3 2.1.1. An illustrative example... 5 2.2. Easter Related Days... 7 2.2.1. An illustrative example (continued)... 8 2.3. Fixed days... 9 2.3.1. An illustrative example (continued)... 10 3. Composite Calendars... 11 3.1. An illustrative example (continued)... 12 4. Chained calendars... 14 4.1. An illustrative example (continued)... 14 5. Viewing the calendar regressors... 15 6. An extension... 16 References... 20 Last Revised : 28 September 2011 2

1. Introduction Recurring day-of-week effects and leap year effects in monthly (or quarterly) economic time series are called calendar effects (Findley and Soukup, 2000). Before the description of the calendar module, it is worth to mention about basic definitions of calendar terminology. Economic time series are influenced by effects of seven days of the week and when or how often each of the seven days of the week occurs in the month (Findley and Soukup, 2000). With exports in the Turkey, for example, the volume is smaller on Saturdays and Sundays than on days later in the week. In addition, the biggest volume is on Fridays. Thus sales in June, say, will be relatively higher in a year in which June has excess of early weekdays and lower when June has five Fridays and Saturdays. Six variables have been used to model the trading day effect; These are: (N Mondays) (N Sundays), (N Tuesdays) (N Sundays),, (N Saturdays) (N Sundays) where N means the number of. The motivation for using these variables is that it is desirable that the sum of the effects of each day of the week cancel out (Gomez and Maravall, 1996). The other presentation of day of the week is the case that the days of the week are divided into week days and weekend days. The variable may be defined as (N(M,T,W,Th, F))- (N(Sat,Sun) 5 2 (Gomez and Maravall, 1996). Leap variable measures the effect of differences in the number of days in February s. This variable is equal to zero for all months different from February. In February, it takes the value -0.25 if February has 28 days, and it takes the value -0.75 if February has 29 days. The Easter variable measures a change in the movement during the d days before Easter. TRAMO&SEATS uses default number d=6 while X-12-ARIMA searches the optimal number of d. The value of d can be specified by the user, also. The variable has zeros for all months different from March and April since d days is divided into just March and April. Usually, the sum of the effects of both months, March and April, cancel out, a desirable feature (Gomez and Maravall, 1996). Tramo&Seats and X-12-ARIMA automatically create appropriate trading-day, workingday, leap year and Easter variables according to specification (RSA) used 2. But, the users need some extensions as followings: 2 To definitons of RSA, please see User Manual of Demetra+ which is available at http://www.crosportal.eu/sites/default/files/demetra+%20user%20manual.pdf Last Revised : 28 September 2011 1

To modify trading-day, working-day and leap year regressors by incorporated them with national holidays or specific days of the countries, To chain two calendar variables for two different time periods, To combine two/or more calendar variables using with proper weights, To export as user-regressor variables by changing frequency, length, start and end dates, and representation type i.e. trading day (6 regressors) or working day (1 regressor) with leap year regressor. This document aims to address how the above-mentioned requirements to be resolved with calendar module of Demetra+. We use the directions Workspace Edit Calendars to achieve the calendar module (Image 1). The User-variables is also in the same tab but it is out of the concept of this document. Image 1 When we open the calendar module, we see a properties dialog window (Image 2) which consists of three main nodes. The nodes are National Calendars, Composite Calendars and Chained Calendars. Image 2 Last Revised : 28 September 2011 2

Section 2 describes the national calendars and specific holidays; Section 3 and 4 then focuses how to use composite and chained calendars properties of calendar module. Section 5 shows that how to calendar variables created be viewed. Section 6 gives an extension about creating moving holiday regressor with Excel. 2. National Calendars The user can create its own calendar regressor(s) with National Calendars. This module creates new trading/working day regressors which incorporates both country-specific holidays and default trading/working day regressors. The user may obtain new regressors in a number of types i.e. working day (1 regressor) and with leap year, trading day (6 regressors) with leap year. National calendars are divided into the three parts as in Image 3. Each part has the same object which is to determine the holiday dates to be incorporated in new regressors. The first part contains pre-specified holidays which are in most of European countries. The second is Easter related days which user can specify the offset time depending on the country/state. The last, which using this option is a controversial issue, is Fixed days option which provides feature of determining a specific day of a month. Image 3 The name of the new variable is shown at the part the Name e.g. Calendar 1 and the user can customize it. 2.1. Pre-specified Holidays Demetra+ has kept some well-known holidays in memory to use in calendar adjustment analysis. Totally 14 holidays are available with this version. When the button opposite side of the Pre-specified holidays is pressed, a pop-up window, namely pre-specified calendar, is opened (Image 4). Last Revised : 28 September 2011 3

Image 4 Here, holidays are listed which is under the Event tab. The definitions of the holidays listed are given in Table 1: Table 1. Definitions of Holidays Holidays General Definitions New Year AshWednesday falls on 1 January. is a moving holiday, occurring 46 days before Easter. Easter is a moving holiday; it varies between March 22 and April 25 depending on offset time. MaundyThursday falling on the Thursday before Easter. It is the fifth day of Holy Week, GoodFriday EasterMonday Ascension Day Pentecost WhitMonday MayDay and is preceded by Holy Wednesday and followed by Good Friday. refers to the Friday in Easter week. is the day after Easter Sunday. is traditionally celebrated on a Thursday, the 40 th day from Easter day. is celebrated seven weeks (50 days) after Easter Sunday, Pentecost falls on the tenth day after Ascension Thursday. is the holiday celebrated the day after Pentecost, a movable feast in the Christian calendar. It is movable because it is determined by the date of Easter. on May 1 is an ancient northern hemisphere spring festival and usually a public holiday. Halloween is an annual holiday observed on October 31. AllSaintsDay is a solemnity celebrated on 1 November by parts of Western Christianity, and on the first Sunday after Pentecost in Eastern Last Revised : 28 September 2011 4

Christianity. ThanksGiving currently, in Canada, Thanksgiving is celebrated on the second Monday of October and in the United States, it is celebrated on the fourth Thursday of November. Christmas Day is a holiday generally observed on December 25. Once the user adds a holiday from the list, the offset and validity period can be set if needed. Also, the user can add more pre-specified holidays using add button. Demetra+ then aggregates all holidays added by the user in a regressor. 2.1.1. An illustrative example Here, it is tried to show how the national calendar is created with an illustrative example. This example does not contain all possibilities of National Calendars. It aims to show a way of to create a calendar regressor includes public holidays for a selected country. Belgium is chosen as a sample. Then, public holidays of Belgium are listed below: Table 2 Holiday New Year's Day Easter Easter Monday Labour Day Ascension Pentecost Pentecost Monday (WhitMonday) National holiday Assumption of Mary All Saints Armistice Day Christmas The next step is to open calendar module as shown in Image 1 and Image 2. After the Properties dialog box is opened as in Image 2, you shall press the button which is the opposite side of National Calendars. Now, you shall see new dialog box called National Calendar. When the button Add is pressed, new calendar regressor, namely Calendar 1, appears. Since its name can be modified, the name is changed to Belgium (Image 5). Last Revised : 28 September 2011 5

Image 5 Now, next step is to enter holidays given in Table 1 to Belgium calendar regressor. To do this, you shall need to press on the button which is opposite side of Pre-specified holidays. Then, new dialog box called Belgium-Pre-specified calendar day is appeared. You shall enter the holiday listed in the Table 1 by selecting the appropriate holidays and the Add button, consecutively 3. After the holidays entered to the dialog box, you shall see a view as in Image 6, then press OK buttons, which is coming one after the other, to complete the session. Offset and validity period are not adjusted to keep the exercise the illustrations. Thus, the calendar variable called Belgium which is covering eight public holidays of Belgium is appeared under the Default calendar in Calendars node on the Workspace as in Image 7 4. Image 6 3 National Holiday, Assumption of Mary and Armistice Day holidays are not available in Pre-specified holidays and they will be considered as Fixed days. Please, see Section 2.3 and, the current version of Demetra+ has a bug in Labour Day to be corrected in the next version. 4 Trading day, working day and leap year regressor without any holidays are already presented in the node of Calendars on Workspace. Its name is Default as seen in Image 7. Last Revised : 28 September 2011 6

Image 7 2.2. Easter Related Days The dates of the Easter Related Days (e.g. Pentecost, Whit Mondays etc.) also vary over years since the Easter is a moving holiday and the dates of Easter varies year by year. In addition, the number of the days between the Easter and the Easter Related Days may vary by countries. So, it is a tough work to collect all Easter Related Days in Demetra+. Therefore, Easter Related Days feature is provided for the user to design its own country-specific Easter related days. When the button opposite side of the Easter related days is pressed as in Image 8, a pop-up called Easter Related Days window is opened as in Image 9. Then, the button Add in the window is used to enter a/more Easter related days. You shall see two option; the first is Offset and the second is Validity period. Relationship between Easter and it related days is determined by the number Offset. If the users want this event to valid for a specific period range or specific starting/lasting date, validity period option may be adjusted, optionally. Image 8 Image 9 Last Revised : 28 September 2011 7

2.2.1. An illustrative example (continued) It has been shown that the Pentacost and WhitMonday holidays are moving holidays because their dates determined by the date of Easter (Table 1). Let s assume that these two holidays are not available in pre-specified holidays to show how to use Easter Related Days option. Remember the definitions of Pentacost and Whitmonday from Table 3: Table 3 Holidays Pentecost General Definitions is celebrated seven weeks (50 days) after Easter Sunday, Pentecost falls on the tenth day after Ascension Thursday. WhitMonday is the holiday celebrated the day after Pentecost, a movable feast in the Christian calendar. It is movable because it is determined by the date of Easter. The Belgium calendar regressor is already created in previous example by entering prespecified holidays. Now, Pentecost and Whit-Monday holidays will be entered into as Easter related days using by its option. But, it should be note that these two holidays have to be removed from the event list of Belgium calendar regressor, before. Assuming that Pentecost and Whit-Monday holidays are removed from pre-specified holidays event list, the user shall to press the button opposite side of the Easter related days as shown in Image 10. Please note that the number of pre-specified holidays declined to six since Pentecost and Whit-Monday are dropped from the event list of pre-specified holidays. Image 10 Last Revised : 28 September 2011 8

The new dialog box called Easter related day is opened, and then the user shall to press the button Add to enter Pentecost holidays as a holiday related with Easter. Since the Pentecost holiday is 50 days after the Easter, the offset is set 50 (Image 11). If it was before the Easter, the user would enter 50 with (-) minus sign. Image 11 Finally, for the Whit-Monday, the offset value is set 51 since it is the holiday celebrated the day after Pentecost (Image 12). Validity period option is omitted to take the example simple. Image 12 2.3. Fixed days Countries have the holidays occurring in moving days as well as fixed days in a year. Whether the fixed-date holidays are considered in the scope of seasonality is a questionable issue. The answer of this question depends on whether the day(s) of the fixed holidays overlap with the weekend days or week-days. Since this dependency is a deterministic process in terms of calendar, adding this knowledge to the calendar regressor may make seasonal adjustment process more powerful. When the button opposite side of the Fixed days is pressed, a pop-up called Fixed day window is opened as in Image 13. Then, the button Add in window to enter a/more fixed days. You shall see three options; the first is Month option used to determine which month Last Revised : 28 September 2011 9

has the holiday and the second is Day of the month option used to determine which day has the holiday, and the last is Validity period is as explained before (Image 14). Image 13 Image 14 2.3.1. An illustrative example (continued) It has been stated before that the National Holiday, Assumption of Mary and Armistice Day holidays are not available in Pre-specified holidays for Belgium. But, it is know that these holidays are on a fixed date in the year as shown in Table 4. So, the user can modify Belgium calendar regressor entering these dates by fixed day option. Table 4 Holiday Date National holiday July 21 Assumption of Mary August 15 Armistice Day November 11 The user shall to press the button opposite side of the Easter related days as shown in Image 13. And then, you shall enter the holiday listed in the Table 4 by selecting the appropriate dates and the Add button, consecutively. As seen the Image 15, all three fixeddays holidays are entered respectively. Final view of National calendar window is given in Image 16. Last Revised : 28 September 2011 10

Image 15 3. Composite Calendars Image 16 Previously, it is examined that how to create a calendar regressor for a specific country. The users can create more calendar variables for different countries or sectors using by national calendars module. But, calendar regressors may be need to aggregate when the time series to be analyzed is aggregated by horizontal (countries) or by vertical (sectoral). For instance, industrial production indexes for each of EU member countries can be analyzed with each calendar regressor of them, separately. But, aggregation of calendar regressors already created for each of member countries is requested to analyze the aggregate industrial production index series for EU-27. On this request, Demetra+ offers an application called Composite Calendars to users. With this application, the users can combine the calendar regressors previously created with appropriate weights. When the button opposite side of the Composite calendars is pressed, a pop-up called Composite calendar blank window is opened. Then, the button Add in window to enter a/more composite calendars as shown in Image 17. The user can change the name of the composite calendar to be created from corresponding option. Then, the technical options for the composite calendar can be specified from the node Calendars in the window. To see the options, the user shall press the button opposite side of the Calendars. After pressing Add Last Revised : 28 September 2011 11

button in the new window called weighted calendar, the user can select the calendar regressors to be combined and can give proper weights to them (Image 18). Image 17 Image 18 3.1. An illustrative example (continued) In this exercise which is a continuation of the exercise given previous section, two calendar regressors created before for Belgium and France are aggregated with proper weights. It should be note that France calendar regressor is created using the same way as Belgium. Just for information, France holidays are given in Table 5. Table 5 Holidays Date Type New Year s Day - Pre-specified holidays Good Friday - Pre-specified holidays Easter Monday - Pre-specified holidays Ascension - Pre-specified holidays Whit Monday - Pre-specified holidays All Saints Day - Pre-specified holidays Christmas - Pre-specified holidays Victory in Europe Day 8 May Fixed days Bastille Day 14 July Fixed days Assumption of Mary 15 August Fixed days Armistice Day 11 November Fixed days St Etienne 26 December Fixed days Last Revised : 28 September 2011 12

By coming to composite calendar window and pressing the button Add, new blank composite calendar appears. In this example, the name is preferred to change to Composite (Image 19). Image 19 Then, the user shall press to the button opposite side of the calendars to modify the properties of composite calendars. Now, the calendars to be aggregated have to be selected and proper weight have to be given for each of the calendars selected (Image 20). Image 20 After selecting calendar regressors of Belgium and France, the equally weights are given e.g. 0.5 for each of them to avoid any inconvenience (Image 21). At the end of the day, an item called Composite is placed under the node Calendars on Workspace. Image 21 Last Revised : 28 September 2011 13

4. Chained calendars In a rare situation, the users may need to chain two different calendar regressors. This request may arise in case of, for example, a holiday being removed which exists before a certain date. In addition, two calendar regressors may be asked to chain based on a certain date at which happened an increase in the number of working days in a sector. Chain calendars application proposed by Demetra+ is offered to benefit to users with this regard. Chained calendar regressor can be easily obtained by selecting regressors to be chained and a break date. When the button opposite side of the Chained calendars is pressed, a pop-up blank window called Chained calendar is opened. Then, the button Add in window to enter a/more composite calendars as shown in Image 22. Image 22 The user can change the name of the chained calendar to be created by the name option. Then, there are three options to determine the properties of chained calendar. The user should select the calendar series created before to be used in the first part of the chained series. Afterwards, the user shall enter the date which represents starting position of chaining process. The last step is to select the calendar series created before to be used in the last part of the chained series. 4.1. An illustrative example (continued) In this exercise, the calendar regressors, which are created in previous steps of this example, namely Belgium and France, are chained based on the break date 01.01.2005. The Belgium calendar regressor represents the first part of the chained series while the France calendar regressor represents the second part of the chained series which means that the part is Last Revised : 28 September 2011 14

after 01.01.2005. The new chained series is called Chained as seen in Image 23. At the end of the process, an item called Chained is placed under the node Calendars on Workspace. Image 23 5. Viewing the calendar regressors The regressor created can be viewed in detail by a double click on the Belgium item on the Workspace (as shown in Image 4, previously). After double clicking, the user shall see an auxiliary window which has three panels like in Image 24. The upper-left panel, namely Misc, is used to set up the properties of calendar regressor. The upper-right panel is used to examine spectral properties of selected series which is the one of the series presented at the bottom grid panel. Actually, Misc panel is a tool to generate different representation types of calendar regressor by the user. There are four dimensions to do this. Frequency: The user can transform its regressor into different frequencies. The options are Year, HalfYear, QuadriMonth, Quarter, Bimonth, Month 5. Length (in years): The user can define a length in terms of year for calendar regressor. Start: The user can define a start date for calendar regressor. Variable type: The user can transform its regressor into three types of variables. If the option None is selected, only leap year variable is shown on the grid panel. If the option Trading days is selected, calendar regressor is represented by six day variables and leap year variable. The last option WorkingDays is used to represent calendar regressor by working day (single) and leap year variables. Spectrum panel is useful to see at which frequencies the variables show regular movements. But, it does not give so easy-interpretable information. year. 5 Half year means 2 observation per year, QuadriMonth means 3 obs per year, Bimonth means six obs per Last Revised : 28 September 2011 15

Image 24 Finally, the variables generated in grid panel can be copied by drag and drop into Excel as well as XML browser to use another application. But, it is important to say that this presentation module does not affect the seasonal adjustment analysis and it may be used to just see the properties of calendar regressor. Because, the user already can define the type of the calendar regressor created to be used in seasonal adjustment at the single or multi processing stages. 6. An extension Demetra+ provides an easy way to create calendar regressor using with Calendar module. The calendar regressor created can include not only trading/working day but also country or sector specific holidays. These holidays may be fixed or moving. Last Revised : 28 September 2011 16

However, the users may want to put an exogenous variable which includes solely fixed and/or moving holidays into Reg-Arima model in pre-adjustment process. So, week-day regressors 6 and holiday regressors are separately entered to the Reg-ARIMA model. Moreover, some moving holidays such as Ramadan Feast or Sacrifice Feast which can not to be created by calendar module may be required for an economic time series to be seasonally adjusted. In such cases, the best way is to create the regressor in Excel and export to Demetra+ as a user variable. In this section, it is shown that how to operate this process with the example of Ramadan and Feast Sacrifice for Turkey. It should be note that to create moving holiday regressor is tough task. First, the dates of Ramadan and Sacrifice should be determined day-by-day for a specific date length. In this example, this length is between 01/01/1974 and 31/12/2015. An Excel sheet is designed as give in Table 6. The columns between A and F represent the official holidays in Turkey. Then, two different options are considered. The first option is that moving holidays are excluded Saturday, Sunday and official holidays. The second is that moving holidays are excluded Sunday and official holidays. The second step is to aggregate the columns G, H, J and K for monthly as given in Table 7. (Quarterly table is omitted here). The third step is to extract the variables from its long term averages. But, the average value is calculated for each of months, not for all period (Table 8). The user can directly take sum of the Ramadan and Sacrifice holiday regressors to obtain total moving holiday regressor. Afterwards, the user can drag and drop it into Demetra+ XML Workspace for making it static variable or directly be read it from Excel file for making it dynamic variable. 6 They are trading day, working day, leap Year and Easter regressors. Last Revised : 28 September 2011 17

Table 6 Date Sacrifice Ramadan New Year 23 April 01.May 19.May 30 Agu 29 Oct Saturday Sunday If it is Sacrifice day,1 ; othewise 0 (Excluding Sat, Sun and official holiday) If it is Sacrifice day,1 ; othewise 0 (Excluding Sun and official holiday) If it is Ramadan day,1 ; othewise 0 (Excluding Sat, Sun and official holiday) If it is Ramadan day,1 ; othewise 0 (Excluding Sun and official holiday) A B C D E F G H J K 1 Jan 1974 Tue 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 Jan 1974 Wed 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 Jan 1974 Thu 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 Jan 1974 Fri 1 0 0 0 0 0 0 0 0 0 1 1 0 0 5 Jan 1974 Sat 1 0 0 0 0 0 0 0 1 0 0 1 0 0 6 Jan 1974 Sun 1 0 0 0 0 0 0 0 0 1 0 0 0 0 7 Jan 1974 Mon 1 0 0 0 0 0 0 0 0 0 1 1 0 0 8 Jan 1974 Tue 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 Oct 1974 Wed 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17 Oct 1974 Thu 0 1 0 0 0 0 0 0 0 0 0 0 1 1 18 Oct 1974 Fri 0 1 0 0 0 0 0 0 0 0 0 0 1 1 19 Oct 1974 Sat 0 1 0 0 0 0 0 0 1 0 0 0 0 1 20 Oct 1974 Sun 0 0 0 0 0 0 0 0 0 1 0 0 0 0 21 Oct 1974 Mon 0 0 0 0 0 0 0 0 0 0 0 0 0 0 26 Dec 2015 Sat 0 0 0 0 0 0 0 0 1 0 0 0 0 0 27 Dec 2015 Sun 0 0 0 0 0 0 0 0 0 1 0 0 0 0 28 Dec 2015 Mon 0 0 0 0 0 0 0 0 0 0 0 0 0 0 29 Dec 2015 Tue 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30 Dec 2015 Wed 0 0 0 0 0 0 0 0 0 0 0 0 0 0 31 Dec 2015 Thu 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Last Revised : 28 September 2011 18

Table 7 Total Sacrifice Holiday Days (Exc. Sat, Sun and Official Holidays) Total Ramadan Holiday Days (Exc. Sat, Sun and Official Holidays) Total Sacrifice Holiday Days (Exc. Sun and Official Holidays) Total Ramadan Holiday Days (Exc. Sun and Official Holidays) Date Jan.74 2 0 3 0 Feb.74 0 0 0 0 Mar.74 0 0 0 0 Apr.74 0 0 0 0 May.74 0 0 0 0 Jun.74 0 0 0 0 Jul.15 0 1 0 2 Agu.15 0 0 0 0 Sep.15 3 0 4 0 Oct.15 0 0 0 0 Nov.15 0 0 0 0 Dec.15 0 0 0 0 Table 8 Date Total Sacrifice Holiday Days (Exc. Sat, Sun and Official Holidays) Average values for 1974 2015 Sacrifice Holiday Regressor (Exc. Sat, Sun and Official Holidays) Jan.74 2 0.2381 1.7619 Feb.74 0 0.2143 0.2143 Mar.74 0 0.2143 0.2143 Apr.74 0 0.1905 0.1905 May.74 0 0.1429 0.1429 Jun.74 0 0.2143 0.2143 Agu.15 0 0.2143 0.2143 Sep.15 3 0.2619 2.7381 Oct.15 0 0.3333 0.3333 Nov.15 0 0.4048 0.4048 Dec.15 0 0.2857 0.2857 Last Revised : 28 September 2011 19

References Findley, D. F. and Soukup R. J. (2000), Detection and Modeling of Trading Day Effects, ICES Proceedings, un published version available at http://www.census.gov/ts/papers/ices00_td.pdf Gomez, V., and Maravall, A. (1996), Programs TRAMO (Time Series Regression with ARIMA Noise, Missing Observations and Outliers) and SEATS (Signal Extraction in ARIMA Time Series), Instruction for the user, Working Paper 9628, Bank of Spain, Madrid. Grudkowska, S. (2011) Demetra+ User Manual, unpublished version, available at http://www.cros-portal.eu/sites/default/files/demetra+%20user%20manual.pdf Last Revised : 28 September 2011 20