Corn Future SpreadsEconometric Analysis of Seasonality
Georg Lehecka
June 8, 2010
Georg Lehecka Corn Future Spreads
Table of Content
1 Introduction: Futures and Futures Spreads
2 Description of Data
3 Application of Seasonal ModelsDeterministic ModelLinear Stationary Seasonal ModelSeasonal Unit-Root Non-Stationary Model
4 Results and Discussion
Georg Lehecka Corn Future Spreads
Introduction
Aim of this empirical analysis
Estimation and forecast of corn futures spreads based on thefact of seasonal time series
Application of different seasonal models to the time series
Georg Lehecka Corn Future Spreads
Introduction
Futures Contracts
A futures contract is an agreement between two parties to buy orsell an asset at a certain time in the future for a certain price.
Suppose that, on June 8, the July futures price of corn at theChicago Merantile Exchange (CME) is quoted as 350 $Cents perbushel (contract size is 5,000 bushels ∼127 t.). This is the price,exclusive of commissions, at which traders can agree to buy or tosell Corn for December delivery.
Georg Lehecka Corn Future Spreads
Introduction
220
230
240
250
260
270
280
July and December Corn Futures Prices 2006
2006
Fut
ure
Pric
es
Sep Nov Jan Mär Mai Jul
July Corn ContractDecember Corn Contract
Georg Lehecka Corn Future Spreads
Introduction
200
300
400
500
Corn Futures Prices
1989 − 2006
Cor
n F
utur
es P
rices
1990 1995 2000 2005
July Corn ContractDecember Corn Contract
Georg Lehecka Corn Future Spreads
Introduction
Futures Spread
A futures spread is a technique in which a trader buys one contractand sells another contract of the same commodity with anotherdelivery date.
Suppose that, on June 8, the July futures price of corn at theChicago Merantile Exchange (CME) is quoted as 350 $Cents perbushel and the December futures price of corn is quoted as 360$Cents per bushel. A trader sells July Corn and buys DecemberCorn. The spread has as value 360− 350 = 10 $Cents per bushel.The goal for the trader is that the July contract declines and thatthe December contract increases in order to increase the spreadvalue.
Georg Lehecka Corn Future Spreads
Introduction
−15
0−
100
−50
050
Corn Futures Spreads Dec−Jul (every Spread beginning with 0)
Last 250 days of both legs1989 − 2006
Spr
ead
(beg
inni
ng w
ith 0
) D
ec−
Jul i
n po
ints
1990 1995 2000 2005
Georg Lehecka Corn Future Spreads
Introduction
Economic Reasons for Seasonality in Agricultural Markets
There is obviously seasonality in the underlying agriculturalbusiness. For example the bulk of the US corn crop is plantedApril/May and harvested October/November.The seasonal patternfor the corn market should assume therefore a specific path. Priceand perceptions of supply tend to be inversely related, with priceoften lowest when supply is greatest, at harvest and with priceoften highest in May when the market is anxious about thepotential for new production.
Georg Lehecka Corn Future Spreads
Description of Data
Data are the July and December Corn Futures Contracts
At the Chicago Merantile Exchange (CME)
During the years 1989 - 2006
Unit of measurement: $Cents per bushel (contract size is5,000 bushels ∼127 t.)
Relevant time series are the last 250 days of the Dec - JulySpread
Georg Lehecka Corn Future Spreads
Description of Data
0 50 100 150 200 250
−15
0−
100
−50
050
Corn Futures Spreads Dec−Jul (in absolute numbers)
1989 − 2006Last 250 Days
Spr
eads
Dec
−Ju
l in
poin
ts
Georg Lehecka Corn Future Spreads
Description of Data
0 50 100 150 200 250
−15
0−
100
−50
050
Corn Futures Spreads Dec−Jul (in absolute numbers)
1989 − 2006Last 250 Days
Spr
eads
Dec
−Ju
l in
poin
ts
mean of spreadsmedian of spreads
Georg Lehecka Corn Future Spreads
Description of Data
0 50 100 150 200 250
05
10Mean/Median of Corn Futures Spreads Dec−Jul (in absolute numbers)
1989 − 2006Last 250 Days
Mea
n/M
edia
n of
Spr
eads
Dec
−Ju
l in
poin
ts
mean of spreadsmedian of spreads
Georg Lehecka Corn Future Spreads
Description of Data
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
●
−10
0−
500
Average Spreads over Time Classes
Days until maturity
Ave
rage
spr
ead
in ti
me
clas
ses:
mea
n(sp
read
[x[i−
1]=
>D
ays<
x[i]]
)
> 250 > 225 > 200 > 175 > 150 > 125 > 100 > 75 > 50 > 25
Georg Lehecka Corn Future Spreads
Description of Data
●
●
●
●●
●
●
●●
●
24
68
Mean of average Spread over Time Classes
Days until maturity
Mea
n of
ave
rage
spr
ead
over
tim
e cl
asse
s
> 250 > 225 > 200 > 175 > 150 > 125 > 100 > 75 > 50 > 25
Georg Lehecka Corn Future Spreads
Description of Data
−10
0−
500
Average Spreads over Time Classes
Ave
rage
spr
eads
ove
r tim
e cl
asse
s
1989 1991 1993 1995 1997 1999 2001 2003 2005
> 250> 225> 200> 175> 150> 125> 100> 75> 50> 25
Georg Lehecka Corn Future Spreads
Application of Seasonal Models
Discussion on useful Seasonal Model ClassesData follow a ’deterministic’ seasonality (’summer remainssummer’) and are non-stationary.
Deterministic model class: non-stationary → maybe a goodmodel for data
Linear stationary model class: stationary → not such a goodmodel for data
Unit-root model class: non-stationary but ’summer maybecome winter’ → maybe only a good model withdeterministic parts
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Deterministic Model
Simple Model for Deterministic Seasonality
yt =S∑
s=1
δstms + εt
δst = 1 if t falls to season s, and δ = 0 otherwise; ms is the meanfor season s; S is the numer of seasons and in the example 250; εt
is zero-mean stationary; t = 1, ...,T = 4500
Estimation:SSE 1.508 · 106
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Deterministic Model
−15
0−
100
−50
050
Corn Futures Spreads Dec−Jul
Last 250 days of both legs1989 − 2006 ( 2007 estimate)
Spr
ead
Dec
−Ju
l in
poin
ts
1990 1995 2000 2005
Seasonality Estimation
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Linear Stationary Model
Simple Stationary Seasonal Model
yt = φSyt−S + εt , |φS | < 1
S is the numer of seasons and in the example 250; εt is zero-meanstationary; t = 1, ...,T = 4500
Estimation:Estimate t value p-value
φ̂S 0.10872 −6.846 < 10−3
AIC 37, 197 SSE 1.642 · 106
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Linear Stationary Model
−15
0−
100
−50
050
Corn Futures Spreads Dec−Jul
Last 250 days of both legs1989 − 2006 ( 2007 estimate)
Spr
ead
Dec
−Ju
l in
poin
ts
1990 1995 2000 2005
Seasonality Estimation
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Linear Stationary Model
Another Stationary Seasonal Model
yt =5∑
i=1
φiSyt−iS + εt
S is the numer of seasons and in the example 250; εt is zero-meanstationary; t = 1, ...,T = 4500; |φiS | < 1 for each i
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Linear Stationary Model
Another Stationary Seasonal Model
Estimation:Estimate t value p-value
φ̂1S 0.22493 −11.808 < 10−3
φ̂2S 0.11821 −6.039 < 10−3
φ̂3S 0.09586 −5.007 < 10−3
φ̂4S 0.01669 −0.865 0.387
φ̂5S −0.01464 0.790 0.429
AIC 28, 957 SSE 1.695 · 106
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Linear Stationary Model
−15
0−
100
−50
050
Corn Futures Spreads Dec−Jul
Last 250 days of both legs1989 − 2006 ( 2007 estimate)
Spr
ead
Dec
−Ju
l in
poin
ts
1995 2000 2005
Seasonality Estimation
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Unit-Root Model
Seasonal Unit-Root Model (SWR)
yt = yt−S + εt
S is the numer of seasons and in the example 250; εt is zero-meanstationary; t = 1, ...,T = 4500
Estimation:SSE 3.376 · 106
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Unit-Root Model
−15
0−
100
−50
050
Corn Futures Spreads Dec−Jul
Last 250 days of both legs1989 − 2006 ( 2007 estimate)
Spr
ead
Dec
−Ju
l in
poin
ts
1990 1995 2000 2005
Seasonality Estimation
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Unit-Root Model
Another more general seasonal unit-root model
yt = φyt−S +S∑
s=1
δstms + εt ,
assuming φ to be well behaved (all roots outside unit circle). S isthe numer of seasons and in the example 250; ms is the mean for
season s; εt is zero-mean stationary; t = 1, ...,T = 4500
Estimation:Estimate t value p-value
φ̂ 0.19682 −13.11 < 10−3
AIC 36, 721 SSE 1.632 · 106
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Unit-Root Model
−15
0−
100
−50
050
Corn Futures Spreads Dec−Jul
Last 250 days of both legs1989 − 2006 ( 2007 estimate)
Spr
ead
Dec
−Ju
l in
poin
ts
1990 1995 2000 2005
Seasonality Estimation
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Unit-Root Model
A third general seasonal unit-root model
yt =5∑
i=1
φiSyt−iS +S∑
s=1
δstms + εt ,
assuming φiS to be well behaved (all roots outside unit circle). S isthe numer of seasons and in the example 250; ms is the mean for
season s; εt is zero-mean stationary; t = 1, ...,T = 4500
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Unit-Root Model
A third general seasonal unit-root model
Estimation:Estimate t value p-value
φ̂1S 0.30125 −16.678 < 10−3
φ̂2S 0.20608 −11.104 < 10−3
φ̂3S 0.19126 −10.535 < 10−3
φ̂4S 0.12277 −6.708 < 10−3
φ̂5S 0.07595 −4.325 < 10−3
AIC 28, 612 SSE 1.920 · 103
Georg Lehecka Corn Future Spreads
Application of Seasonal Models: Unit-Root Model
−15
0−
100
−50
050
Corn Futures Spreads Dec−Jul
Last 250 days of both legs1989 − 2006 ( 2007 estimate)
Spr
ead
Dec
−Ju
l in
poin
ts
1995 2000 2005
Seasonality Estimation
Georg Lehecka Corn Future Spreads
Results and Discussion
Model comparisonModel AIC SSE
Simple Deterministic Model
yt =∑S
s=1 δstms + εt - 1.508 · 106
Simple Stationary Seasonality Model
yt = φSyt−S + εt 37, 197 1.642 · 106
Another Stationary Seasonality Model
yt =∑5
i=1 φiSyt−iS + εt 28, 957 1.695 · 106
Seasonal Unit-Root Model(SRW)
yt = yt−S + εt - 3.376 · 106
Another Seasonal Unit-Root Model
yt = φyt−S +∑S
s=1 δstms + εt 36, 721 1.632 · 106
A third Seasonal Unit-Root Model
yt =∑5
i=1 φiSyt−iS +∑S
s=1 δstms + εt 28, 612 1.920 · 106
Georg Lehecka Corn Future Spreads
End
Thank you for the attention!
Georg Lehecka Corn Future Spreads