6.3: Seasonal Component

A seasonal pattern is observed with regularity within a given period of time, usually within a year. Typically, the interest is in seasonal patterns over a calendar or marketing year, but there may be contexts in which we could see regular patterns over shorter periods. For example, shopping traffic in a supermarket is seasonal through a week (with higher traffic on weekends) or even on a weekday (with more traffic around the end of the workday).

Seasonal patterns can be demand-induced or supply-induced. For example, demand for products like Christmas trees, carving pumpkins, and whole turkeys are highly seasonal. In these examples, demand is driven by consumption around holidays. In volume, although not so much in price, there are clear demand-induced seasonal patterns in wine consumption (Anez 2005). White and rose wines are traditionally served chilled. These have higher volume sales in the summer months. Red wines, traditionally served at room temperature, have higher volume sales in the winter months. There are volume spikes for all wines regardless of color around holidays.

Supply-induced seasonal patterns are observed in the market for perishable commodities like fruits and vegetables. For example, Sobekova, Thomsen and Ahrendsen (2013) show seasonal price patterns for strawberries, blueberries, blackberries and raspberries. For each of these crops, there is a clear relationship between available supply at different points in the year and price. This is because berries are sourced from different regions of the country or world during different parts of the year. The costs of producing and shipping berries to market differ depending on the supply region. Essentially, the supply curve for berries differs depending on the season of the year and this leads to seasonality in the prices of these berries.

Storage costs can result in supply-induced seasonal price patterns for storable commodities like grains and oilseeds. These crops are harvested once a year, but demand is spread over the year. It is often the case that prices are lowest around the harvest season but then increase in the following months. The increase in price is necessary to provide incentives to store commodities and make them available for use in non-harvest months. Figure 1 shows average cash prices for corn by month over the 2001 to 2016 period. The marketing year for corn runs from September 1 through August 31. Notice that prices are lowest during the harvest months (September through November) and increase consistently until July, about the time when there are good expectations of what the upcoming corn crop will be and when elevators are under pressure to make room for wheat and other small grains harvested in the summer.

Figure \(\PageIndex{1}\): Average cash price for corn by month of the marketing year (2001-2016). Source: Based on cash prices reported by Top Flight Grain Cooperative (Illinois) via https://www.quandl.com/data/TFGRAIN/CORN-Cash-Price-of-Corn.

An n-period moving average is an average of the n most recent time series observations. If one chooses n to correspond to the periodicity of the data, a moving average can be used to remove the seasonal component of a time series, which may help you better see the trend or cyclical components. The data presented in Table \(\PageIndex{1}\) are quarterly (four periods per year). Verify that the four-period moving average is simply the average of the four most recent observations. Note also that these price data show a very strong seasonal pattern. The moving average, however, removes that seasonality. This can be seen in Figure \(\PageIndex{2}\), which charts the data in Table \(\PageIndex{1}\) along with the four-period moving average.

Table \(\PageIndex{1}\). Computing a Four-period Moving Average

t	Quarter	Price	Four-pd. Moving Avg.
1	1	3	-
2	2	8	-
3	3	4	-
4	4	8	5.75
5	1	11	7.75
6	2	16	9.75
7	3	12	11.75
8	4	16	13.75
9	1	19	15.75
10	2	24	17.75
11	3	20	19.75
12	4	24	21.75
13	1	27	23.75
14	2	32	25.75
15	3	28	27.75
16	4	32	29.75

Figure \(\PageIndex{2}\): Table \(\PageIndex{1}\) Data with a Four-period Moving Average (in Red)

In the example above, a four-period moving average was used because we had quarterly data. Every point in our moving average included one each of quarter 1 through 4. If, instead, we were interested in removing seasonality from monthly data or weekly data, we would use 12-period or 52-period moving average instead. The 12-period moving average would be used for monthly data because there are 12 months per year. The 52-period moving average would be used for weekly data since there are 52 weeks per year.