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?

SEASONALITY

The Causes and Costs of Seasonality

Seasonality originates from climate and conventional seasons, like religious, social and civic events, which repeat from year to year.

The climatic seasons influence trade, agriculture, the consumption patterns of energy, fishing, mining and related activities. For example, in North America the consumption of heating oil increases in winter, and the consumption of electricity increases in the summer months because of air conditioning.

Institutional seasons like Christmas, Easter, civic holidays, the school and academic year have a large impact on retail trade and on the consumption of certain goods and services, namely travel by plane, hotel occupancy, consumption of gasoline.

Fig. 1 – Seasonal pattern of Sales by Canadian Department Stores.


In order to determine whether a series contains seasonality, it is sufficient to identify at least one month (or quarter) which tends to be systematically higher or lower than other months. Fig.1 exhibits the seasonal pattern of sales by Canadian Department Stores, where the values are much larger in December and much lower in January and February with respect to other months. The seasonal pattern measures the relative importance of the months of the year. The constant 100% represents an average month or a non-seasonal month. The peak month is December, with sales almost 100% larger than on an average month; the trough months are January and February with sales almost 40% lower than on an average month. The seasonal amplitude, the difference between the peak and trough months of the seasonal pattern, reaches almost 140%.

Seasonality entails large costs to society and businesses. One cost is the necessity to build warehouses to store inventories of goods to be sold as consumers require them, for example grain elevators. Another cost is the under-use and over-use of the factors of production: capital and labour.

Capital in the form of un-used equipment, buildings and land during part of the year has to be financed regardless. For example, this is the case in farming, food processing, tourism, electrical generation, accounting. The cold climate increases the cost of buildings and infrastructure, e.g. roads, transportation systems, water and sewage systems, schools, hospitals; not to mention the damage to the same caused by the action of ice.

The labour force is over-used during the peak seasons of agriculture and construction for example; and, under-used in trough seasons sometimes leading to social problems.

A more subtle unwanted effect is that seasonality complicates business decisions by concealing the fundamental trend-cycle movement of the variables of interest.

The four main causes of seasonality are attributed to the weather, composition of the calendar, major institutional deadlines, and expectations. Seasonality is largely exogenous to the economic system but can be partially offset by human intervention. For example, seasonality in money supply can be controlled by central bank decisions on interest rates. In other cases, the effects can be offset by international and inter-regional trade. For example Hydro Québec, a major Canadian electrical supplier, sells much of it excess power during the summer seasonal trough months to the neighbouring Canadian provinces and U.S. states; and imports some of it during the winter seasonal peak months of electrical consumption in Québec. The scarcity of fresh fruits and vegetables in Canada is handled in a similar manner. Some workers and businesses manage their seasonal pattern with complementary occupations: for example landscaping in the summer and snow removal in winter.

To some extent seasonality can evolve through technological and institutional changes. For example the developments of appropriate construction materials and techniques made it possible to continue building in winter. The development of new crops, which better resist cold and dry weather, have influenced the seasonal pattern. The partial or total replacement of some crops by chemical substitutes, e.g. substitute of sugar, vanilla and other flavours, reduces seasonality in the economy.

As for institutional change, the extension of the Canadian academic year to the summer months in the 1970s affected the seasonal pattern of unemployment for the population of 15 to 25 years of age. Similarly the practice of spreading holidays over the whole year impacted on seasonality.

The changing industrial mix of an economy also transforms the seasonal pattern, because some industries are more seasonal than others. In particular, economies which diversify and depend less on "primary" industries (e.g. fishing, agriculture) typically become less seasonal.

In most situations, seasonality evolves slowly and gradually. Indeed the seasonal pattern basically repeats from year to year, as illustrated in Fig. 1. Merely repeating the seasonal pattern of the last twelve months usually provides a reasonable forecast.