Thesis_Presentation

Modelling Commodity Price Volatility with Mixtures of
GARCH Processes
Jinrui Wang1 Alan P. Ker2
1M.Sc. Student
Food, Agricultural and Resource Economics
University of Guelph
jinrui@uoguelph.ca
2Chair and Professor
Food, Agricultural and Resource Economics
University of Guelph
aker@uoguelph.ca
CAES Joint Annual Meeting, 2014
Jinrui Wang, Alan P. Ker (UoGuelph) Modelling Commodity Price Volatility CAES Joint Annual Meeting 1 / 20

Outline
1 Introduction
Background Introduction
Commodity Price Volatility Eﬀects
Modeling Commodity Price Volatility
Previous Studies on Price Volatility
2 Data & Methodologies
Data
Diﬀerent Methodologies
3 Results & Conclusions
Estimation Results
Conclusions

Background Introduction
Figure 1: World Commodity Prices (2006-2012)

Commodity Price Volatility Eﬀects
Why Is It A Concern?
Commodity Price Volatility Create Risks for:
Producers & Consumers:
Increasing prudcution and investment risks; Diﬃcult to make
consumption decisions;
Reduce the accuracy of producers and consumers price forecasts, and
causing welfare losses
(Bingswanger & Rosenzweig, 1986; Saha & Delgado 1989)
Governments:
Negative impacts on economic growth (Rodrick, 1999);
Lead to economic crisis (Acemoglu et al.,2003)

Modeling Commodity Price Volatility
Why Is It Important?
Forecast the absolute magnitude, quantiles, and the entire
distribution of price changes
Widely used in risk management, derivative pricing, and hedging,
portfolio selection;
Help producers & traders: Make proper production and investment
decisions under conditions of price change uncertainty

Previous Studies on Price Volatility
Literature Review
Generalized Autoregressive Conditional Heteroscedasticity (GARCH)
Engle (1982) frist proposed
Measure and forecast changes in volatility of time series agricultural
commodity prices
Bollerslev (1986) developed
The usual assumption in the proposed volatility models applied to
commodity prices is that: error process is conditionally normally distributed

Previous Studies on Price Volatility (Cont’d)
Literature Review -- Importance of modeling commodity price volatilities
Shively (1996)
Fitted a single-equation ARCH model to monthly wholesale maize
prices in Ghana
Higher past prices are found to lead to higher current price volatility
Accurate measurement of the stochastic component in the prices may
contribute to policy decisions regarding the possible implementation of
commodity price stabilisation programmes
Serra & Gil (2013)
Reseached price volatility in food markets, by using multivariate
GARCH models
U.S corn price volatility could be explained by volatility clustering, the
inﬂuence of biofuel prices, corn stocks and global economic conditions

Literature Review -- Extension of GARCH Methods
GARCH model do not adequately capture heavy tails, large kurtosis, and
occurrence of extreme events
Bollerslev (1987) proposed modelling the innovations via GARCH
model with a Student’s t-distribution
Haase et al (2004) introduced the general symetric Normal Mixture
(NM) GARCH model
Alexander and Lazard (2006) further modiﬁed the general class of
NM-GARCH(p,q) model, to the NM-GARCH(1,1)

Literature Review -- Extension of GARCH Methods
NM-GARCH model accommodates the possibility of distinct types of
responses to heterogeneous market shocks (Haas et al. 2004)
In NM-GARCH model, component with low variance represent
”usual” state (generally occurs); component with high variance
represent ”crash” state (rarely occurs) (Alexander and Lazar (2009))

Data
County level daily cash prices in harvest periods of three crops, corn,
soybeans, and winter wheat, in ON
Covering period from 2006-2012,obtained from Ridgetown College
data resource center

Data
Figure 2: Ontario daily cash crop prices (2006-2012)

Diﬀerent Methodologies
Compare 3 Diﬀerent Methods
GARCH (1,1)
NM(2)-GARCH (1,1)
NM(3)-GARCH (1,1)

Methodologies
Conceptual Framework
εt|Ωt−1 ∼ NM(p1, . . . , pk, µ1, . . . , µk, δ2
1t, . . . , δ2
kt) (1)
Error term : εt
Mean : µt
Component variance : δ2
it
Ωt : the information set at time t
pi ∈ (0, 1), i = 1, . . . , k are mixing weight
k
i=1
pi = 1
k
i=1
pi µi = 0

Methodologies (Cont’d)
Condiser diﬀerent possibilities for the conditional variance of k
components:
NM(k) - Garch(1,1):
δ2
it = ωi + αi ε2
t−1 + βi δ2
it−1 for i = 1, . . . , k, (2)
αi : the volatility reaction parameter
βi : the volatility persistence parameter

Methodologies (Cont’d)
For each commodity, ﬁt the continuously compounded percentage
changes of prices with an autoregressive-moving-average
(ARMA(p,q)) model :
γt = 100 ∗ (logPt − logPt−1) (3)
γt = c + εt +
p
i=1
ai γt−i +
q
j=1
bj εt−j (4)
An Akaike Information Criterion (AIC) is used to select the
appropriate values of p and q

Estimation Results
Summary of GARCH Results
Table : Summary of Estimation Results

Estimation Results
Summary of AIC Results
Table: AIC for Diﬀerent Methodologies
Method Corn Soybean Winter Wheat
GARCH -6.842659 -6.835264 -6.709625
NM(2) -7.145738 -7.170853 -6.806431
NM(3) -7.227868* -7.176558* -6.814145*

Conclusions
Relationship between component mean and component volatility dynamics
Expected negative price change corresponds to a larger volatility
persistence parameter (βi ), and a smaller volatility reaction parameter
(αi ) indicating volatility tends to be more persistent when shocks are
negative;
Expected positive price change corresponds to a higher volatility
reaction parameter (αi ) suggesting volatility is more reactive to price
rises than prices drops

Conclusions
NM-GARCH model:
A lower-volatility component that occurs with a high probability;
A high-volatility component that occurs with a low probability;
(Alexander & Lazar(2006), Bauwens et al. (2007))
NM(3) performs better than GARCH(1,1) and NM(2)

Happy to Ask Any Questions

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