1. Ketty Attal-Toubert Dominique Ladiray Régina Soares Specifications for TD&MH regressors SA User’s Group – Luxembourg, April 2013

2. Luxembourg, April 2013 Specifications for TD&MH Regressors Outline › A reminder –Basic models for TD effect detection and correction –Why should we use contrasts? › A very general model taking into account National calendars › Specifications for TD effects › Moving holiday effects –Examples: Easter, Ramadan › Specifications for MH effects –Constant and linear models

3. Luxembourg, April 2013 Specifications for TD&MH Regressors Basic models for TD effects › Fixed TD effect › We take contrasts to avoid some problems (stability, saisonnality, global effect equal to 0) › The Weekday model

4. Luxembourg, April 2013 Specifications for TD&MH Regressors Why should we use contrasts? › N it is seasonal (always more Mondays in January than in February) › But in a 400-year cycle of the Gregorian calendar, there are the same number of Monday, Tuesday … per month.

5. Luxembourg, April 2013 Specifications for TD&MH Regressors Spectrum of the Weekday Series

6. Luxembourg, April 2013 Specifications for TD&MH Regressors Spectrum of the centered Weekday Series

7. Luxembourg, April 2013 Specifications for TD&MH Regressors Why should we use contrasts? › Open question: is there an easier way to seasonally adjust the regressors? Annual difference? › Contrasts increase the stability of the model: (-1, 0 or 1) instead of (0 or 1) –This is a very serious problem › You assure that the sum of the coefficients is equal to 0: the reference day coefficients is derived as minus the sum of the 6 others.

8. Luxembourg, April 2013 Specifications for TD&MH Regressors A more general model › We specify a 15-variable model introducing a difference between Monday off and Monday in. › Where the N it are the # of Mondays in, Tuesdays in, …, Sundays in, Mondays off, Tuesdays off, …., and Sundays off. › Then you make hypothesis on the days.

9. Luxembourg, April 2013 Specifications for TD&MH Regressors An example › All days off are equivalent to a Sunday. › And we get the model › But the contrasts do not remove seasonality anymore. –You have to SA the regressors removing the long-term monthly averages you can compute using the 400-year periodicity of the Gregorian calendar.

10. Luxembourg, April 2013 Specifications for TD&MH Regressors Specifications (1) › You must precise the reference day, usually the second day of the week-end: Tunisia vs Algeria. This day will be the core of the “reference group” for the contrasts. › You have to specify which group a day belongs to –Monday in, Tuesday in, in Group 1 –Wednesday in, Thursday in, Friday in, in Group 2 –All other days (in or off) in Group 0 which will be the reference group –In this case, you have 2 regressors: Group1 vs Group0 and Group2 vs Group0

11. Luxembourg, April 2013 Specifications for TD&MH Regressors Specifications (2) › For each “fixed” or moving holiday, you have to specify –The date (day, month) or the calendar –The type of holiday (fixed or moving) –The “starting year” –The “ending year” –The weight –If the holiday can be “reported” when it falls during a “week-end” (Canada, Serbia etc.) › Warning: a moving holiday can fall on the same date than a “fixed” holiday. Avoid duplicates. –Usually moving holidays are religious holidays which are considered more important.

12. Luxembourg, April 2013 Specifications for TD&MH Regressors Moving Holidays › They are expressed in another calendar and therefore, they “move” in the Gregorian calendar › Easter is linked to a lunar calendar –Easter Sunday is the first Sunday after the first full moon after vernal equinox. › BUT, its date is expressed: –In the Gregorian Calendar for Catholic and Protestant churches –In the Julian Calendar for Orthodox churches (Greece, Romania, Bulgaria, Cyprus etc.)

13. Luxembourg, April 2013 Specifications for TD&MH Regressors An algorithm to compute Easter dates

14. Luxembourg, April 2013 Specifications for TD&MH Regressors Holidays linked to Easter › Easter is periodic of period 5 700 000 years in the Gregorian calendar.

15. Luxembourg, April 2013 Specifications for TD&MH Regressors The Islamic Calendar (1) › This is a Lunar calendar. › A year contains 12 months of 29 or 30 days. The length of the year is 354 or 355 days (a day is added to the last month). › The names of the 12 months that comprise the Islamic year are:

16. Luxembourg, April 2013 Specifications for TD&MH Regressors The Islamic Calendar (2) › Each month starts when the lunar crescent is first seen (by a human being) after a new moon. And the length of a month can change across years. › Thus, the Islamic calendar is not purely deterministic and can slightly varie from a country to another. › Some approximative algorithms exist, useful to forecast the calendar. › For example, the length of the year follows a 30-year cycle where « leap years » are the years {2, 5, 7, 10, 13, 16, 18, 21, 24, 26, or 29}

17. Luxembourg, April 2013 Specifications for TD&MH Regressors Important dates › Ras El Am is the first day of the year › The Islamic calendar is periodic with period 5 400 000 years in the Gregorian calendar › Measuring the impact of the Ramadan

18. Luxembourg, April 2013 Specifications for TD&MH Regressors A General Constant Effect Model › The regressor for month m is the “% of days in the month m”

19. Luxembourg, April 2013 Specifications for TD&MH Regressors A General Linear Effect Model

20. Luxembourg, April 2013 Specifications for TD&MH Regressors Specifications › You must specify –The date of the event –The starting day of the effect before the event (8 days before) –The ending day of the effect before the event –The starting day of the effect after the event –The ending day of the effect after the event –The kind of effect (constant or linear) › Warning: the seasonal adjustment of the effects › Examples