4 pp., 5 graphsFor many crops, seasonality is often the dominant factor influencing prices within a single production period. This publication explains how to construct and use several kinds of seasonal indexes for crop marketing information

Amosson, Stephen H.

Tierney Jr., William I.

Waller, Mark L.

Texas A&amp;M Repository

How to Construct aSeasonal IndexWilliam I. Tierney, Jr., Mark L. Waller and Stephen H. Amosson*Methods of Constructing Crop SeasonalsThere are several ways to construct seasonals. Perhaps the simplest is to pro-duce a graph with the factor being studied (i.e,. price) on the vertical (or “Y”) axisand time (i.e., days, weeks or months) on the horizontal (or “X”) axis. For a sea-sonal to have any significance, a number of years’ worth of data need to be accu-mulated. They can be plotted on the chart or an average of the data can be plotted(Fig. 1). These charts are most appropriate for periods of relative stability in mar-ket conditions.If a seasonal chart consists only of an “average” (and not all of the originaldata), it is often accompanied by a plotted confidence interval of plus or minusone standard deviation. The standard deviation is a measure of the variability ofthe historical data from the calculated average. It is useful for showing how reli-able the average may be as an indicator of the expected price in a particular year.If the standard deviation is large, the average is not a very dependable indicator ofprices; however, if it is small, it is reasonable to place more confidence in theaverage as a forecasting tool (Fig. 2). For example, to calculate the average usedfor each month in Figure 2, take the prices for each month (say June 1992, 1993,1994, 1995 and 1996), add them together and divide by the number of years inthe study (in this case, 5). The answer is your June average price. If you do thesame for each of the other months, July through May, you then have your averageseries.  If you put all of your data in a spreadsheet such as Lotus or Excel, thesoftware will usually provide formula keys that will calculate the averages andstandard deviations for you.Another technique is to construct a seasonal “index.” The “base” or ”denomina-tor” for the index is generally the average for the time period being examined (365days, 52 weeks or 12 months).RiskManagement Education™L-5305RM2-6.05-99Figure 1. Wheat price seasonal (1992/93 to 1997/98).*Extension Agricultural Economist, Kansas State University Agricultural Experiment Station and CooperativeExtension Service; Associate Professor and Extension Economist, The Texas A&M University System;  Professorand Extension Economist, The Texas A&M University System.Consequently, each time period’s price (orother factor, such as exports) is expressed as apercentage of the season’s average and will havea value equal to, greater than, or less than 100. Most indices of this type use a base value of100 percent. A value of 85 (or .85) for a particu-lar period (say the month of June for wheatprices) would mean that period’s wheat pricewas 15 percent below that year’s 12-month sea-sonal average price. Conversely, if the Februaryindex value was 115, that would mean thatFebruary’s price was 15 percent above the sea-sonal average price (Fig. 3).               Example: To calculate the index in Figure 3,take your average June price for 1973-1996 andadd it together with the averages for July-May.Divide by the number of monthly averages toget an overall average price (June average + ...+ May average ÷ 12 = overall average). Thendivide each monthly average by the overall aver-age (June average ÷ overall average = Juneindex; May average ÷ overall average = Mayindex) to get the monthly indices.This method dampens the variability that mayoccur from combining data from years with highannual prices with periods of low annual prices,Figure 2. Wheat price seasonal (1992-1996).Figure 3. Wheat price seasonal index (1973-1996).because what it focuses on is the relative move-ment of prices within the season. These intra-seasonal price movements are more likely to beuniform whether annual average prices were$5.00 or $3.00 a bushel.A conditioned seasonal could be constructedusing only years in which a similar feature wasexhibited (i.e., one index for normal crop yearsand another for short crop years). Using a condi-tioned seasonal may give a better indication ofthe seasonal behavior that is likely to occur thanaveraging all years together. A variation on theseasonal index is to attach a second vertical (or“Y” axis) to the seasonal index and plot thisyear’s values. Depending on how this axis is“scaled,” the superimposing of this year’s actualprices over the seasonal index can quickly revealwhether this year’s price movements are con-forming to the expected seasonal pattern (Fig. 3).One problem with using a single season’sannual average price as a base for calculating aseasonal index is that this method will miss anytrend factors that may be affecting prices. Thiscan limit the usefulness of seasonals in periodsof significant upward or downward trends.Consequently, some seasonal indices are con-structed using a 12-month “moving average”(Fig. 4).  To explain the development of an index basedon a centered moving average would requiremore space than is available in this publication.One publication to refer to if you want to learnhow to do this is Agricultural Price andCommodity Market Analysis by John N. Ferris.Seasonals can be constructed to analyze com-ponents of crop supply/demand as well as cropprices. For wheat, one of the most influentialelements of demand is exports. On average, overthe last 10 years, exports have comprised 52 per-cent of total wheat disappearance. While wheatexports are shipped on a relatively steady sched-ule from U.S. ports, wheat grain export commit-ments (export shipments plus undelivered sales)are not so steady.Figure 5 is a seasonal index of changes incumulative wheat export commitments over a13-month period measured as a percent of totalannual wheat grain export inspections (left axis).If there was no seasonal nature in export com-mitments, the average line would be flat andwould equal 7.69 percent for each month.However, as Figure 5 suggests, above averageexport commitments tend to be booked in themonths of June, August and September, whilebookings are less than average in March, Apriland May.  The right axis has been “scaled” toreflect the assumptions that 1998/99 wheat grainexport inspections will total 1,105 millionbushels.  Given that assumption, it is clear when com-paring the April 1998/99 commitments to theseasonal index that wheat export commitmentsstarted off well below the level one wouldexpect if the market was to achieve the projec-tion for total annual exports. This might suggestthat if commitments don’t increase, USDA mayneed to lower its export forecast for the year.Figure 4. Wheat price seasonal index (1973-1996).Seasonals also can help in analyzing otheraspects of crop prices such as basis, intercom-modity spreads (corn vs. milo), intramarketspreads, option volatility, etc. While many of thegraphs shown in this publication use cashprices, it is important to understand that season-al indices also can be generated using futuresprices. Given the anticipatory nature of futuresprices, seasonals for futures prices may besomewhat different than seasonals for cashprices.  If you are using futures and options asforward pricing tools, it will be beneficial toinvestigate their seasonal behavior as well.SummaryFor many of the principal field crops grownin the U.S., seasonality is often the dominantfactor influencing crop prices within a sin-gle production period (usually 12 months).Intra-seasonal variations in supply/demand fun-damentals also have an important influence onthe pattern that is followed by crop prices (aswell as basis, spreads, and options volatility).Using the appropriate seasonal as a guide, acrop producer should have a better chance tocorrectly identify both the timing of major mar-ket moves as well as absolute price levels. Thus,seasonals can help a producer time pre-harvestsales as well as assess the prospects for prof-itable post-harvest strategies.It is unwise, however, to rely exclusively onseasonals when making crop marketing deci-sions. For one thing, seasonals are based onpast prices and may merely reflect randomeffects rather than any true predisposition inmarket performance. Also, even if seasonal pat-terns are well founded and appear to be statisti-cally reliable, seasonal effects can be over-whelmed by changing fundamental (and eventechnical) factors.ReferencesFerris, John N. “Agricultural Price andCommodity Market Analysis.” W.C.B. McGraw-Hill, 1998.Partial funding support has been provided by the Texas Wheat Producers Board, Texas Corn Producers Board,and the Texas Farm Bureau.Figure 5. Change in cumulative all wheat export commitments.

How to Construct a Seasonal Index

Texas A&M University

How to Construct a
Seasonal Index
William I. Tierney, Jr., Mark L. Waller and Stephen H. Amosson*
Methods of Constructing Crop Seasonals
There are several ways to construct seasonals. Perhaps the simplest is to pro-
duce a graph with the factor being studied (i.e,. price) on the vertical (or “Y”) axis
and time (i.e., days, weeks or months) on the horizontal (or “X”) axis. For a sea-
sonal to have any significance, a number of years’ worth of data need to be accu-
mulated. They can be plotted on the chart or an average of the data can be plotted
(Fig. 1). These charts are most appropriate for periods of relative stability in mar-
ket conditions.
If a seasonal chart consists only of an “average” (and not all of the original
data), it is often accompanied by a plotted confidence interval of plus or minus
one standard deviation. The standard deviation is a measure of the variability of
the historical data from the calculated average. It is useful for showing how reli-
able the average may be as an indicator of the expected price in a particular year.
If the standard deviation is large, the average is not a very dependable indicator of
prices; however, if it is small, it is reasonable to place more confidence in the
average as a forecasting tool (Fig. 2). For example, to calculate the average used
for each month in Figure 2, take the prices for each month (say June 1992, 1993,
1994, 1995 and 1996), add them together and divide by the number of years in
the study (in this case, 5). The answer is your June average price. If you do the
same for each of the other months, July through May, you then have your average
series.  If you put all of your data in a spreadsheet such as Lotus or Excel, the
software will usually provide formula keys that will calculate the averages and
standard deviations for you.
Another technique is to construct a seasonal “index.” The “base” or ”denomina-
tor” for the index is generally the average for the time period being examined (365
days, 52 weeks or 12 months).
Ri
sk
Ma
nagement Education
™
L-5305
RM2-6.0
5-99
Figure 1. Wheat price seasonal (1992/93 to 1997/98).
*Extension Agricultural Economist, Kansas State University Agricultural Experiment Station and Cooperative
Extension Service; Associate Professor and Extension Economist, The Texas A&M University System;  Professor
and Extension Economist, The Texas A&M University System.
Consequently, each time period’s price (or
other factor, such as exports) is expressed as a
percentage of the season’s average and will have
a value equal to, greater than, or less than 100. 
Most indices of this type use a base value of
100 percent. A value of 85 (or .85) for a particu-
lar period (say the month of June for wheat
prices) would mean that period’s wheat price
was 15 percent below that year’s 12-month sea-
sonal average price. Conversely, if the February
index value was 115, that would mean that
February’s price was 15 percent above the sea-
sonal average price (Fig. 3).               
Example: To calculate the index in Figure 3,
take your average June price for 1973-1996 and
add it together with the averages for July-May.
Divide by the number of monthly averages to
get an overall average price (June average + ...
+ May average ÷ 12 = overall average). Then
divide each monthly average by the overall aver-
age (June average ÷ overall average = June
index; May average ÷ overall average = May
index) to get the monthly indices.
This method dampens the variability that may
occur from combining data from years with high
annual prices with periods of low annual prices,
Figure 2. Wheat price seasonal (1992-1996).
Figure 3. Wheat price seasonal index (1973-1996).
because what it focuses on is the relative move-
ment of prices within the season. These intra-
seasonal price movements are more likely to be
uniform whether annual average prices were
$5.00 or $3.00 a bushel.
A conditioned seasonal could be constructed
using only years in which a similar feature was
exhibited (i.e., one index for normal crop years
and another for short crop years). Using a condi-
tioned seasonal may give a better indication of
the seasonal behavior that is likely to occur than
averaging all years together. A variation on the
seasonal index is to attach a second vertical (or
“Y” axis) to the seasonal index and plot this
year’s values. Depending on how this axis is
“scaled,” the superimposing of this year’s actual
prices over the seasonal index can quickly reveal
whether this year’s price movements are con-
forming to the expected seasonal pattern (Fig. 3).
One problem with using a single season’s
annual average price as a base for calculating a
seasonal index is that this method will miss any
trend factors that may be affecting prices. This
can limit the usefulness of seasonals in periods
of significant upward or downward trends.
Consequently, some seasonal indices are con-
structed using a 12-month “moving average”
(Fig. 4).  
To explain the development of an index based
on a centered moving average would require
more space than is available in this publication.
One publication to refer to if you want to learn
how to do this is Agricultural Price and
Commodity Market Analysis by John N. Ferris.
Seasonals can be constructed to analyze com-
ponents of crop supply/demand as well as crop
prices. For wheat, one of the most influential
elements of demand is exports. On average, over
the last 10 years, exports have comprised 52 per-
cent of total wheat disappearance. While wheat
exports are shipped on a relatively steady sched-
ule from U.S. ports, wheat grain export commit-
ments (export shipments plus undelivered sales)
are not so steady.
Figure 5 is a seasonal index of changes in
cumulative wheat export commitments over a
13-month period measured as a percent of total
annual wheat grain export inspections (left axis).
If there was no seasonal nature in export com-
mitments, the average line would be flat and
would equal 7.69 percent for each month.
However, as Figure 5 suggests, above average
export commitments tend to be booked in the
months of June, August and September, while
bookings are less than average in March, April
and May.  The right axis has been “scaled” to
reflect the assumptions that 1998/99 wheat grain
export inspections will total 1,105 million
bushels.  
Given that assumption, it is clear when com-
paring the April 1998/99 commitments to the
seasonal index that wheat export commitments
started off well below the level one would
expect if the market was to achieve the projec-
tion for total annual exports. This might suggest
that if commitments don’t increase, USDA may
need to lower its export forecast for the year.
Figure 4. Wheat price seasonal index (1973-1996).
Seasonals also can help in analyzing other
aspects of crop prices such as basis, intercom-
modity spreads (corn vs. milo), intramarket
spreads, option volatility, etc. While many of the
graphs shown in this publication use cash
prices, it is important to understand that season-
al indices also can be generated using futures
prices. Given the anticipatory nature of futures
prices, seasonals for futures prices may be
somewhat different than seasonals for cash
prices.  If you are using futures and options as
forward pricing tools, it will be beneficial to
investigate their seasonal behavior as well.
Summary
For many of the principal field crops grown
in the U.S., seasonality is often the dominant
factor influencing crop prices within a sin-
gle production period (usually 12 months).
Intra-seasonal variations in supply/demand fun-
damentals also have an important influence on
the pattern that is followed by crop prices (as
well as basis, spreads, and options volatility).
Using the appropriate seasonal as a guide, a
crop producer should have a better chance to
correctly identify both the timing of major mar-
ket moves as well as absolute price levels. Thus,
seasonals can help a producer time pre-harvest
sales as well as assess the prospects for prof-
itable post-harvest strategies.
It is unwise, however, to rely exclusively on
seasonals when making crop marketing deci-
sions. For one thing, seasonals are based on
past prices and may merely reflect random
effects rather than any true predisposition in
market performance. Also, even if seasonal pat-
terns are well founded and appear to be statisti-
cally reliable, seasonal effects can be over-
whelmed by changing fundamental (and even
technical) factors.
References
Ferris, John N. “Agricultural Price and
Commodity Market Analysis.” W.C.B. McGraw-
Hill, 1998.
Partial funding support has been provided by the Texas Wheat Producers Board, Texas Corn Producers Board,
and the Texas Farm Bureau.
Figure 5. Change in cumulative all wheat export commitments.


English

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How to Construct a Seasonal Index

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Texas A&M Repository

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How to Construct a Seasonal Index

Abstract

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Full text

Available Versions

Texas A&amp;M Repository

Texas A&M University

Texas A&M Repository