Calendar Effects

• Monthly production series are strongly affected by calendar effects.

• In particular, a close connection between production and the number of working days was always assumed

• Working day adjusted results have always been particularly important for the indices of industrial production users

Calendar effects in the Industrial Production Indices

• Length of the month

• Day-of-the-week composition

• Holidays

Public holidays in Spain vary

• From one year to another

• From one Community to another

• A straightforward use of ARIMA models is not sufficient to capture calendar variations in the indices, because they are not precisely periodic

• Regression models are used to handle calendar effects

The overall models are a sum of ARIMA and regression models

Hillmer, Bell, Tiao

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We try summarize all calendar effects using only two variables:

• Weighted working day (WDt)

• Holy week (Ht)

Weighted Working Days

Instead of the most commonly used 7 trading day variables (number of Mondays, Tuesdays, etc.), one single variable, adapted to the behaviour of the Spanish Industrial Production, is constructed

For the industrial production, the important matter is the distinction between a working day and a non-working day, and less important is the distinction within the working days (because the intensity of work is usually similar)

Weighted Working Day Variable (WDt ) (I)

Tries to measure the number of working days, subtracting Saturdays, Sundays and holidays, taking into account the different behaviour of the Communities

WDt = MFt - HOL t

MFt = Mondays to Fridays in month t

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Weighted Working Day Variable (WDt ) (II)

1 if the j th holidays is non-working the i th Community

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i : Weight of the i th Community in the

2000 industrial value added

WEIGHTED WORKING DAYS

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

1990 22,00 19,91 21,61 19,13 21,87 21,00 21,93 22,00 19,75 21,90 21,00 18,74 20,90

1991 21,79 19,91 18,53 21,40 21,78 19,75 22,58 21,00 20,74 22,90 20,00 19,52 20,83

1992 21,00 19,91 21,34 19,69 19,87 21,65 23,00 21,00 21,69 20,90 20,87 20,47 20,95

1993 19,00 20,00 22,21 20,79 19,91 21,72 21,99 21,80 21,94 20,00 21,00 20,99 20,95

1994 20,00 19,91 22,27 19,51 21,31 21,72 20,57 22,00 21,94 20,00 21,00 19,31 20,80

1995 20,81 19,91 22,76 17,78 21,80 21,97 20,69 22,00 20,69 20,90 21,00 17,74 20,67

1996 22,00 20,91 20,60 19,75 21,78 19,75 22,77 21,00 20,74 22,90 20,00 19,55 20,98

1997 21,00 19,91 18,67 21,89 20,87 20,72 22,62 20,00 21,69 22,73 20,00 20,74 20,90

1998 20,00 20,00 21,46 19,65 20,00 21,72 22,99 21,00 21,69 20,90 20,67 20,61 20,89

1999 19,00 20,00 22,31 19,76 20,91 21,72 21,98 21,74 21,94 20,00 21,00 20,99 20,95

2000 20,00 20,91 22,95 17,92 21,78 21,97 20,74 22,00 20,69 20,90 21,00 17,74 20,72

2001 22,00 19,91 21,86 18,78 21,78 21,00 21,85 22,00 19,75 21,90 21,00 18,74 20,88

2002 21,70 19,91 18,71 21,41 21,77 19,72 22,74 21,00 20,70 22,90 20,00 19,45 20,83

2003 21,06 19,92 20,62 19,84 20,96 20,77 22,79 20,00 21,69 22,74 20,00 20,80 20,93

2004 20,00 20,00 22,40 19,78 20,90 21,71 21,99 21,73 21,95 20,00 20,00 20,99 20,95

2005 20,00 19,92 20,75 21,00 20,89 21,71 20,58 22,00 21,95 20,00 21,00 19,55 20,78

2006 20,85 19,92 22,80 17,66 21,76 21,97 20,74 22,00 20,69 20,89 21,00 17,73 20,67

2007 22,00 19,92 21,86 18,79 21,76 21,00 21,94 22,00 19,74 21,89 21,00 18,73 20,89

2008 21,60 20,92 18,40 21,90 20,85 20,71 22,66 20,00 21,69 22,64 20,00 20,73 21,01

20,83 20,09 21,16 19,81 21,19 21,17 21,96 21,38 21,14 21,42 20,61 19,64 20,87