Time-Series Modeling and Decomposition

Read this article. It provides an overview of techniques associated with decomposition. Part 4, The Business Cycle, presents how this tool is applied in business operations. Why do you think decomposition is useful in understanding seasonality costs?

THE MOVING-HOLIDAY COMPONENT

The moving-holiday or moving-festival component is attributed to calendar variations, namely the fact that some holidays change date from year to year.

For example, Easter can fall between March 23 to April 25, and Labour Day on the first Monday of September. The Chinese New Year date depends on the lunar calendar. Ramadan falls eleven days earlier from year to year. In the Moslem world, Israel and in the Far East, there are many such festivals. For example, Malaysia contends with as many as eleven moving festivals, due to its religious and ethnic diversity. These festivals affect flow and stock variables and may cause a displacement of activity from one month to the previous or the following month. For example, an early date of Easter in March or early April can cause an important excess of activity in March and a corresponding short-fall in April, in variables associated to imports, exports, tourism. When the Christian Easter falls late in April (e.g. beyond the 10-th), the effect is captured by the seasonal factor of April. In the long run, Easter falls in April eleven times out of fourteen.

Some of these festivals have a positive impact on certain variables, for examples air traffic, sales of gasoline, hotel occupancy, restaurant activity, sales of flowers and chocolate (in the case of Easter), sales of children clothing (Labour Day). The impact may be negative on other industries or sectors which close or reduce their activity during these festivals.

The festival effect may affect only the day of the festival itself, or a number of days preceding and/or following the festival. In the case of Easter, travellers tend to leave a few days before and return after Easter, which affects air traffic and hotel occupancy, etc., for a number of days. Purchases of flowers and other highly perishable goods, on the other hand, are tightly clustered immediately before the Easter date.

The effect of moving festivals can be seen as a seasonal effect dependent on the date(s) of the festival. Fig. 2 displays the Easter effect on the sales by Canadian Department Stores. In this particular case, the Easter effect is rather mild. In some of the years, the effect is absent because Easter fell too late in April.

In the case exemplified, the effect is felt seven days before Easter and on Easter Sunday but not after Easter. This is evidenced by years 1994, 1996 and 1999 where Easters falls early in April and impacts the month of March. Note that the later Easter falls in April, the smaller the displacement of activity to March; after a certain date the effect is entirely captured by the April seasonal factor. The effect is rather moderate for Department Stores. This may not be the case for other variables. For example, Imports and Exports are substantially affected by Easter, because Customs do not operate from Good Friday to Easter Monday. Easter can also significantly affect quarterly series, by displacing activity from the second to the first quarter.

Fig. 2 – Moving Holiday component of the Sales by Canadian Department Stores.


There has been cases of complete reversal on the timing of the Easter effect. For example, Marriages in Canada were performed mainly by the Church during the 1940s up to the 1960s. The Church did not celebrate marriages during the Lent period, i.e. the 40 days before Easter. Some marriages therefore were celebrated before the Lent period, potentially affecting February and March. However, if Easter fell too early, many of these marriages were postponed after Easter. Generally, festival effects are difficult to estimate, because the nature and the shape of the effect are often not well known. Furthermore, there are few observations, i.e. one occurrence per year.