AAMP Training Materials
Module 3.1: Analyzing Price Seasonality
Asfaw Negassa (CIMMYT) & Shahidur Rashid (IFPRI)
a.negassa@cgiar.org, s.rashid@cgiar.org
Objectives
• Understand the role of seasonality analysis in economic
time series data
• Review basic concepts of seasonality analysis
• Compute seasonal indices
• Forecast future prices using seasonal indices
Background
• Why Seasonality Analysis?
• Basic concepts
Why undertake seasonality analyses?
• Economic time series variables (e.g., prices, sales,
purchase, etc.) are composed of various components
• One of the critical components is seasonality, especially
in cases of:
– Agriculture production
– Marketing of goods
– Commodity pricing
Why undertake seasonality analyses?
• Understanding patterns of movement in time series
variables is useful for making better forecasts in
– Marketing decisions
• When to buy?
• When to sell?
• How long to store?
– Production decisions
• Seasonality in rainfall (timing of different operations)
• Seasonality in insect infestation (timing of insecticide application)
– Food security interventions
• Determine periods when households are most vulnerable (e.g.,
seasonal price highs)
• Monitoring changes in households food security situations (e.g.,
deviations from known seasonal price patterns)
Basic concepts
• A time series variable (e.g., prices, sales, purchases,
stocks, etc) is composed of four key components:
–
–
–
–
Long-term trends (T)
Seasonal components (S)
Cyclical components (C)
Irregular or random components (I)
• These components, when examined individually can
help to better understand the sources of variability and
patterns of time series variables – hence time series
decomposition
Basic concepts
• There are several ways of decomposing time series
variables (e.g., additive model, multiplicative model)
• The basic multiplicative model is given as:
Pt = Tt x St x Ct x It
Where:
Pt
Tt
St
Ct
It
is the time series variable of interest
is the long-term trend in the data
is a seasonal adjustment factor
is the cyclical adjustment factor
represents the irregular or random
variations in the series
Time series price variables
Include long term, cyclical, seasonal and irregular trends
45,000
40,000
35,000
30,000
25,000
20,000
15,000
10,000
5,000
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8
15
22
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43
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57
64
71
78
85
92
99
106
113
120
127
134
141
148
155
162
169
176
183
190
197
204
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DSM Maize Price
Computing seasonal indices
• There are several different techniques which are used to
isolate and examine individually the different
components of time series variables
• Here we focus on the ratio-to-moving average method,
which is commonly used
Computing seasonal indices
Step 1: Deseasonalizing
• Remove the short-term fluctuations from the data so that
the long-term and cyclical components can be clearly
identified
– The short-term fluctuations include both seasonal (St) patterns
and irregular (It) components
– The short-term fluctuations can be removed by calculating an
appropriate moving average (MA) for the series
– Assuming a 12-month period, the moving average for a time
period t (MAt) is calculated as:
MAt = (Pt – 6 + … + Pt + … + Pt + 5) / 12
Computing seasonal indices
Step 1: Continued….
• For monthly data, the number of periods (12) is even and
is not centered – need to center it
– To center the moving averages, a two-period moving average is
calculated as follows:
CMAt = (CMAt + CMAt +1) / 2………
= Tt x Ct……...
– Seasonal and irregular components are removed
Centered Moving Average (CMA)
Seasonal and irregular components removed
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204
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DSM Maize Price
CMA
Computing seasonal indices
Step 2: Measuring the degree of seasonality
• The degree of seasonality is measured by finding the
ratio of the actual value to the deseasonalized value
SFt = Pt / CMAt
= Tt x St x Ct x It / Tt x Ct
= St x It
• Where SFt is the seasonal factor and others are defined
as before.
Seasonal Factor (SF)
Actual price (P) / Deseasonalized price (CMA)
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
1
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13
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0
SF
Computing seasonal indices
Step 3: Establishing average seasonal index
• This is obtained by taking the average of seasonal
factors for each season
– Take the sum of SFs for the month of January and divide by the
number of SFs for January over the entire data period
– Pure seasonal index (S) obtained, irregular component removed
– Note: the sum of indices for all months add-up to 12.
• Issues:
– Predictability of seasonal patterns
– Changes in seasonal patterns
Seasonal index (S): Multiple years
Pure seasonal component (S) without irregular component
1.600
1.400
1.200
1.000
0.800
0.600
0.400
0.200
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S
Seasonal Index (S): One year
The seasonal Index helps predict price extremes
Seasonal Index (S)
1.4
Seasonal High
1.2
Seasonal Low
1.0
0.8
0.6
0.4
0.2
0.0
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Computing seasonal indices
Month
Seasonal Index
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
0.965522624
0.921371556
0.942636238
0.945834259
1.011026204
1.101787997
1.110037521
Aug
Nov
Sum of indices
Seasonal High
Seasonal Low
11.99961488
1.170524076
1.093278943
0.959423752
0.883398512
0.8947732
Completing the price decomposition
• In order to complete the price decomposition, three
components must be computed
– Long term time trend of deseasonalized data (CMAT)
– Cyclical Factor (CF)
– Irregular Factor (I)
• The combination of CMAT and S is a useful method for
forecasting future prices
Computing other components
Step 4: Finding the long-term trend
• The long-term trend is obtained from the deseasonalized
data using OLS as follows:
CMAt = a + b (Time)
Where Time = 1 for the first period in the dataset
and increases by 1 each month thereafter
• Once the trend parameters are determined, they are
used to generate an estimate of the trend value for CMAt
for the historical and forecast period.
Long term trend (CMAT)
OLS on deseasonalized price (CMA)
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CMA
CMAT
Computing other components
Step 5: Finding the cyclical component (CF)
• The CF is given as the ratio of centered moving average
(CMAt) to the centered moving average trend (CMATt)
as follows:
CF = CMAt / CMATt
= Tt x Ct x It / Tt
=Ct
Cyclical Factor (CF)
Deseasonalized price (CMA) / Long-term trend (CMAT)
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
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CF
Computing other components
Step 6: Finding the irregular component (It)
• The It is given as the ratio of seasonal factor (SF) to pure
seasonal index (S) as follows:
It = St It / St
= It
• This completes the decomposition
Irregular component (I)
Seasonal Factor (SF) / Seasonal Index (S)
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
1
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25
31
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0
I
Forecasting using seasonality analysis
• Forecasting time series variables
– Prices for the next year can be forecasted
– Timing of price changes
• When will prices be low?
• When will prices be high?
– Magnitude of price level at specific future dates
– Magnitude of temporal price differential (between seasonal high
and low)
• Is storage profitable?
Forecasting using seasonality analysis
• Two main ways of forecasting
1. Forecast monthly values by multiplying estimated average
value for the next year by the seasonal index for each month–
this assumes no significant trend,
2. First estimate the 12-month trend for deseasonalized data and
then apply the seasonal index to forecast the actual prices for
the next year
Forecast Pt = Tt x St
Forecasting using method 2
CMAT x S
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Forecast DSM Maize Price
DSM Maize Price
Forecasting limitations
• The seasonal analysis is used under normal conditions
and there are several factors which alter the seasonal
patterns
– Drought, floods, earthquake, etc.
– Government policy changes
• Abnormal years should not be included in the
computation of seasonal indices
Exercises
• Open Module 3.1 Excel workbook
• Read over the notes in the [NOTES] sheet
• In [Dar Maize Price Analysis] sheet, replicate the
outcomes in the [Tanzania Example]
– First, calculate seasonality indices (MA, CMA, SF and S)
– Then, forecast future prices (CMAT, CF, predicted price)
• Make sure to understand what each component does
• Don’t just copy and paste the formulas.
References
• Tschirley, David. 1995. Using microcomputer
spreadsheets for spatial and temporal price analysis: an
application to rice and maize in Ecuador. In Prices,
Products, and people: Analyzing agricultural markets in
developing countries (Scott, G., editor) International
Potato Centre, Lima, Peru.