###### Seasonality Tool

### Question

How is the seasonality of a commodity price measured?

### Seasonality Tool

Uses monthly price data of a commodity to measure the seasonal pattern in prices. Seasonality is expressed as 12 indexes that represent the ratio of the price each month to the average annual price. The indexes are often graphed to show the seasonal pattern. This spreadsheet provides an example.

### Data Requirements

- Monthly price data over multiple years

### Background

Agricultural prices often follow a seasonal pattern because production is seasonal and storage is costly. In some cases, seasonal demand (such as holiday consumption) may also contribute to seasonality in agricultural prices. The table below shows the degree of seasonality depending on outcome under different conditions. If production and consumption are not seasonal, then prices will not be seasonal. This is the case for most non-agricultural commodities. If production or consumption are seasonal, but storage is inexpensive, then prices will not be strongly seasonal because of low storage costs from harvest period to off-season. This is the case for some cereals, such as sorghum. If production or consumption are seasonal, storage is expensive, and demand is price-elastic (consumers are not willing to pay higher prices), then the commodity will be available only during part of the year, because consumers are not willing to pay the cost of storage. This is the case of many fruits in developing countries. If production or consumption is seasonal, storage is expensive, and demand is price-inelastic (consumers are willing to pay higher prices), then the commodity will be available all year but the price will be strongly seasonal.

Seasonality in production Storage cost Price elasticity of demand Seasonality in supply

Low Not relevant Not relevant Little seasonality in prices due to steady supply, little storage

High Low Not relevant Little seasonality in prices due to inexpensive storage

High High Low Availability is seasonal, no supply in offseason

High High High High seasonality in prices. Although storage is costly, consumers are willing to pay to have it in the offseason.

The seasonality of prices can be measured by comparing the prices in a given month to the prices over the whole year. There are two methods:

The calendar-year seasonal index compares the price in each month to the average over the same calendar year and then averages this ratio over multiple years. In other words,

Variables | |
---|---|

Y |
number of years of data |

Pm |
Price in month m |

y |
index for the year |

i |
index for the month in year y |

The term in parentheses is the ratio of the price in month m to the average price over that calendar year. This is ratio is summed over the Y years and divided by Y to obtain the average.

The moving-average seasonal index is similar except that it compares the price in each month to the average over the 13-month period centered on that month.

Each method has its strengths and weaknesses: The calendar-year price index is easier to understand and to explain. However, the moving-average price index has the advantage that it is less affected by an upward or downward trend in the prices. For example, an upward trend in the prices will cause the January-February indexes in the calendar-year method to be low and the November-December indexes to be high. The moving-average seasonal index is also easier to calculate with a spreadsheet.

In practice, the two methods tend to give fairly similar results.

### Example

This spreadsheet shows the calculation of these two types of seasonal price indexes. Column A has the names of the month, which are used in the graph of the seasonal index. Column B has the month and year of the price data . Column C contains the price data for each month.

Columns D to F calculate the calendar-year seasonal index. Column D calculates the calendar-year average price, which is the denominator inside parentheses in the first equation above. Column E calculates the ratio of the price each month to the annual average (column D). This is ratio in parentheses in the first equation above. Column F calculates the average of all the January ratios, February ratios, and so on. This is the calendar-year seasonal index.

Columns G to I calculate the moving average seasonal index. Column G calculates the 13-month moving average, meaning the average price from six months before to six months after. This is the denominator in the ratio in parentheses in the second equation. Column H calculates the ratio of the price each month to the 13-month moving average (column G). This is the ratio in parentheses in the second equation above. Column I calculates the average of all the January ratios, February ratios, and so on. This is the moving-average seasonal index.

The first graph plots the two seasonal indexes. It is apparent that the two methods give almost the same results: prices climb in the first half of the year and peak in July and August. Price then fall to their lowest point in December. This suggests that the main part of the harvest is in the last three months of the year.

The moving-average index in July is 1.15, meaning that July prices are generally 15% higher than the annual average. In contrast, the moving-average index in December is 0.81, meaning that December prices are 19% below the annual average. In other words, the prices in the peak month are 42% higher than in the lowest month (1.15/0.81 = 1.42).

The second graph shows the 13-month moving average from column G in red. It also shows the moving average with seasonality added. This is obtained by multiplying the moving average (column G) and the moving-average seasonal index (column I).

The third graph shows the original price (blue line) and the price with seasonality removed (green line). This is calculated by dividing the original price by the seasonal index. If the main variation in prices was seasonal, then removing the seasonal component would result in a flat line. The fact that the green line is volatile indicates that seasonality is not the main explanation for the variation in this price.

Preview | Attachment | Size |
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Seasonality_in_prices.xls | 93.5 KB |