Revista de Administração Revista de Administração
Revista de Administração 2017;52:403-18 DOI: 10.1016/j.rausp.2017.08.003
Finance and Accounting
Volatility persistence and inventory effect in grain futures markets: evidence from a recursive model
Persistência de volatilidade e efeito de inventário nos mercados de futuros de grãos: evidência de um modelo recursivo
Persistencia de volatilidad y efecto de inventario en los mercados de futuros de granos: evidencia de un modelo recursivo
Rodrigo Lanna Franco da Silveiraa,, , Leandro dos Santos Macielb, Fabio L. Mattosc, Rosangela Ballinia
a University of Campinas, Campinas, SP, Brazil
b Federal University of São Paulo, São Paulo, SP, Brazil
c University of Nebraska, Lincoln, NE, United States
Received 10 May 2016, Accepted 29 May 2017

The purpose of this paper is to investigate the volatility persistence and the inventory effect in grain futures markets during the period of 1959–2014. The innovative nature of this study lies in the evaluation of rolling estimates, using a recursive univariate TARCH(1,1)-in-mean volatility model. The daily evolution of volatility persistence and the inventory effect on corn and soybean futures contracts is analyzed using a rolling window of 1008 observations over four years. In general, the results suggest that the conditional volatility in both markets is highly persistent. There is also evidence of inventory, time-to-maturity, and seasonality effects on the volatility dynamics of corn and soybeans. In addition, the findings point to a lower short-run volatility persistence in recent years, which caused a slight decrease in long-run volatility persistence and the half-life period in both markets.


Neste artigo, os autores procuraram investigar a persistência da volatilidade e inventory effect nos mercados futuros de grãos no período entre 1959 e 2014. A inovação do estudo consistiu na aplicação de um modelo de volatilidade recursivo TARCH(1,1) com rolagem das estimativas a partir de uma janela de tempo de quatro anos. Os resultados apontaram para uma alta persistência da volatilidade condicional nos mercados de milho e soja. Além disso, observou-se a presença dos efeitos sazonalidade, inventory e time-to-maturity na dinâmica de volatilidade dos preços de ambos mercados. Verificou-se ainda uma queda na persistência de curto-prazo no período recente, o que levou a uma diminuição da persistência de longo-prazo e da meia-vida nos mercados em estudo.


El objetivo en este estudio es investigar la persistencia de la volatilidad y el efecto de inventario en los mercados de futuros de granos en el período de 1959 a 2014. La innovación del trabajo consiste en la aplicación de un modelo de volatilidad recursivo TARCH(1,1) por estimación, en un período de cuatro años. Los resultados indican una alta persistencia de la volatilidad condicional en el mercado de maíz y soja. Además, hay evidencia de efectos de inventario, tiempo hasta la expiración y estacionalidad en la dinámica de la volatilidad de los precios de ambos mercados. También se ha verificado una baja persistencia de la volatilidad a corto plazo en los últimos años, lo que ha causado una caída de la persistencia de la volatilidad a largo plazo.

Price volatility, Volatility persistence, Inventory effect, Grain futures markets
Volatilidade, Persistência da volatilidade, Inventory effect, Mercado futuro de grãos
Palabras clave
Volatilidad, Persistencia de la volatilidad, Efecto de inventario, Mercado futuro de granos

The analysis of price volatility in agricultural markets plays an important role in the decision-making process. Price variation influences decision-making in the case of production, marketing, and risk management in agriculture. High price fluctuations affect producer's profitability, even when production is very efficient. These events also affect policy makers, especially in developing countries, since price and volatility levels impact food security, balance of trade, inflation rate, tax revenue, employment, GDP, and business cycles. Additionally, in financial markets, price oscillations are relevant in portfolio allocation and derivatives pricing (Ghoshray, 2013; Naylor & Falcon, 2010).

During the 2000s, many agricultural commodities experienced a sharp and rapid rise in price. While over the second half of the 1970s and 1990s, in particular in the 1980s, the inflation-adjusted World Bank agriculture index decreased 58%, a sharp price spike of around 40% occurred during 2005–2008. Agricultural commodities, such as corn, wheat, and soybeans exhibited a price increase of more than 60% over this period.

Previous studies have investigated the factors underlying this scenario. Several explanations were given, such as an increasing demand for biofuel from grains and oilseeds, rising oil prices, a growth in demand for commodities (especially in the BRICS countries – Brazil, Russia, India, China, and South Africa), a reduction in subsidies for European farmers, adverse weather conditions, low inventory levels, depreciation of the U.S. dollar, and an increase in speculative transactions in commodities futures markets (Gilbert, 2010; Headey & Fan, 2008; Sumner, 2009).

Recent studies have explored the price fluctuations of agricultural commodities in order to verify the existence of volatility breaks in the first decade of the 2000s (Calvo-Gonzalez, Shankar, & Trezzi, 2010; Gilbert & Morgan, 2010; Huchet-Bourdon, 2011; Sumner, 2009; Vivian & Wohar, 2012). In general, no clear evidence was found to support the idea that the recent price variability was unparalleled. However, two important issues have received relatively little attention, namely the persistence of price volatility and the leverage effect (also known as the “inventory effect”, in the case of commodities). Even if agricultural markets are not experiencing unprecedented levels of volatility, it is still crucial to understand how long it takes volatility to revert to its previous level after a shock. In addition, it is important to verify the asymmetry in the volatility process. In agricultural markets, in contrast to equity markets, positive price shocks (“bad news”) tend to have a larger impact on conditional variance than negative price shocks (“good news”). This phenomenon is known as the inventory effect (Carpantier, 2010) and can be explained by the storage model.1 Volatility persistence and inventory effects affect agricultural producers’, buyers’, and traders’ exposure to risk, thus influencing risk management operations (Carpantier & Samkharadze, 2013). More broadly, these issues are relevant for countries that rely heavily on exports and imports of agricultural commodities, as well as to evaluate inflationary processes and formulate price stabilization programs (Ghoshray, 2013; Vivian & Wohar, 2012).

This paper explores the volatility persistence and inventory effect on grain futures markets over the last decades. The research uses daily futures prices of two commodities (corn and soybeans). A recursive univariate TARCH(1,1)-in-mean volatility model is applied to compute the daily evolution of the volatility persistence and the inventory effect in terms of rolling estimates. Thus, the study investigates whether there have been changes in these two measures over time and their implications for agricultural markets. The study also analyzes other determinants of agricultural commodity volatility in model specification, such as seasonality and time-to-maturity.

Previous studies

Several empirical studies have employed different approaches to investigate the volatility dynamics in agricultural markets. These studies can be categorized into five main groups. The first one evaluated and compared price and volatility evolution between agricultural commodities and manufactured goods. Prebisch (1950) and Singer (1950) began this analysis and, more recently, other research has focused on price volatility, such as Jacks, O’Rourke, and Williamson (2011), Arezki, Hadri, Loungani, and Rao (2014) and Arezki, Lederman, and Zhao (2014). The second group of studies analyzed the impact of commodity price volatility on income and welfare in developing countries (Bellemare, Barrett, & Just, 2013; Blattman, Hwang, & Williamson, 2007; Naylor & Falcon, 2010; Rapsomanikis & Sarris, 2008).

A third group of studies compared commodity price volatility between the first decade of the 21st century and the previous decades of the 20th century. In general, the results showed that price variability over 2006–2010 was not higher than the volatility observed in 1970 (Gilbert & Morgan, 2010; Huchet-Bourdon, 2011). Calvo-Gonzalez et al. (2010) highlighted three periods of relevant volatility breaks – during the two world wars and during the time when the Bretton Woods system collapsed. Despite the fact that the commodity volatility level during the 2000s was not unparalleled, relevant spikes were observed from 2005 to 2008. Consequently, a number of works have evaluated the causes of the rising volatility, enumerating factors such as the fast expansion of biofuel production, increasing oil prices, depreciation of the U. S. dollar, lower level of inventories and the “financialization” of commodity markets (Arezki, Loungani, Ploeg, & Venables, 2014; Balcombe, 2009; Beckmann & Czudaj, 2014; Du, Yu, & Hayes, 2011; Mensi, Beljid, Boubaker, & Managi, 2013; Nazlioglu, Erdem, & Soytas, 2013; Power & Robinson, 2013; Serra, 2011; Wright, 2011).

In addition, a fourth group of studies analyzed the determinants of agricultural commodity price volatility. Seasonality, time-to-maturity,2 inventory level, volatility persistence, day-of-the-week, futures market trading volume, speculative activity, loan rate level, price level, among others, were analyzed in order to verify their influence on agricultural commodity price fluctuation. Table 1 present a summary of this literature and the following paragraphs address the recent studies.

Table 1.

Summary of literature reviews regarding the determinants of agricultural commodity volatility.

Reference  Method  Variables  Period (data frequency)  Seasonality effectTime-to-maturity effectInventory effectTrade effectSpeculative activity effectLoan rate effectPrice level effectVolatility persistence effect
        NS  NS  NS  NS  NS  NS  NS  NS 
Rutledge (1976)  Statistical tests  Silver, cocoa, wheat and soybean oil  1969–1971 (daily)                                 
Anderson (1985)  Tests for equality of variances and regression analysis  9 commodity futures prices (8 agricultural)  1966–1980 (daily)                                 
Milonas (1986)  Tests for equality of variances and regression analysis  11 futures prices (5 agricultural)  1972–1983 (daily)                                 
Kenyon, Kling, Jordan, Seale, and McCabe (1987)  Regression analysis  Corn, soybean, wheat, live cattle and live hog futures prices  1974–1983 (daily)                                 
Glauber and Heifner's (1986)  Regression analysis  Soybean futures price  1961–1984 (daily)                                 
Streeter and Tomek (1992)  Regression analysis  Soybean futures prices  1976–1986 (daily)                                 
Khoury and Yourougou (1993)  Regression analysis  Canola, rye, feed barley, feed wheat, flaxseed, and oats futures prices  1980–1989 (daily)                                 
Bessembinder and Seguin (1993)  Regression analysis  8 futures prices (2 agricultural)  1982–1990 (daily)                                 
Yang and Brorsen (1993)  GARCH and deterministic chaos processes  11 futures prices (7 agricultural)  1979–88 (daily)                                 
Hennessy and Wahl (1996)  Contingent claims methodology  Corn, soybeans and wheat  1985–94 (monthly)                                 
Kocagil and Shachmurove (1998)  Time-series analysis  16 futures prices (6 agricultural)  1980–1995 (daily)                                 
Malliaris and Urrutia (1998)  Time-series analysis  Corn, wheat, oats, soybean, soybean meal, and soybean oil  1981–1995 (daily)                                 
Hudson and Coble (1999)  GARCH models  Cotton futures prices (monthly)  1982–97 (monthly)                                   
Goodwin and Schnepf (2000)  GARCH and VAR models  Corn and wheat futures prices  1986–1997 (weekly)                                 
Allen and Cruickshank (2000)  Regression analysis and ARCH models  12 commodity futures prices (9 agricultural)  1979–1998 (daily)                                 
Chatrath, Adrangi, and Dhanda (2002)  Chaos tests  Corn, soybeans, wheat and cotton futures prices  1968–1995 (daily)                                 
Yang, Balyeat, and Leatham (2005)  Granger causality tests  Corn, soybeans, wheat, sugar, coffee, live cattle and cotton futures prices  1992–2001                                 
Smith (2005)  Partially overlapping time series model  Corn futures prices  1991–2000 (daily)                                 
Daal, Farhat, and Wei (2006)  Regression analysis  61 futures contracts (23 agricultural)  1960–2000 (daily)                                 
Duong and Kalev (2008)  Non-parametric and regression-based tests; GARCH model  Tick-by-tick and bid-ask quote prices for 20 futures markets (10 agricultural)  1996–2003 (intraday)                                 
Kalev and Duong (2008)  Nonparametric test and regression analysis  14 futures prices (10 agricultural)  1996–2003 (intraday)                               
Balcombe (2009)  Decomposition and panel approaches  19 agricultural spot prices  Varies (monthly–annual)                                 
Karali and Thurman (2010)  GLS estimation  Corn, soybean, wheat, and oats futures price  1986–2007 (daily)                                 
Karali, Dorfman, and Thurman (2010)  Smoothed Bayesian estimator  Corn, soybeans, and oats futures prices  Varied (daily)                                 
Carpantier (2010)  GJR-GARCH and EGARCH models  15 commodity spot prices (5 agricultural)  1994–2009 (daily)                                 
Verma and Kumar (2010)  Regression analysis  Wheat and pepper futures prices  2004–2007 (daily)                                 
Stigler and Prakash (2011)  Markov regime-switching GARCH  16 commodity spot prices  1985–2009 (daily)                                 
Carpantier and Dufays (2012)  GJR-GARCH model  16 commodity spot prices (7 agricultural)  1994–2011 (weekly)                                 
Vivian and Wohar (2012)  Iterative cumulative sum of squares and GARCH  28 commodities (13 agricultural)  1985–2010 (daily)                                 
Gupta and Rajib (2012)  GARCH, EGARCH and TGARCH  8 commodity futures prices (1 agricultural)  2008–2009 (daily)                                 
Ghoshray (2013)  Bootstrap methods  24 commodity spot prices (18 agricultural)  1900–2008 (annual)                                 
Karali and Power (2013)  Spline-GARCH model and SUR framework  11 commodity futures prices (5 agricultural)  1990–2005 (daily)                                 
Khan (2014)  GARCH model  Cotton futures prices  2001–2010 (weekly)                                 
He et al. (2014)  Time series analysis  Soybean, soy meal, corn, hard wheat, strong gluten wheat, and sugar  Until June-2010 (daily)                                 
Dawson (2015)  GARCH model  Wheat futures market  1996–2012 (daily)                                 

Y, yes; N, no; NS, not studied.

A number of works have identified seasonality and time-to-maturity as important determinants of agricultural volatility. Kalev and Duong (2008) and Duong and Kalev (2008), using intraday data, verified the maturity effect in agricultural futures markets. In addition, Karali and Thurman (2010) identified the presence of seasonality and maturity effects in corn, soybean, wheat, and oats markets between 1986 and 2007. Karali et al. (2010) showed that the volatility of corn, soybean, and oats futures prices was affected by time-to-maturity, inventories, and progress of the crop (with, in general, a higher price fluctuation before the beginning of the harvest). Verma and Kumar (2010) and Gupta and Rajib (2012) also contributed to this debate, examining the time-to-maturity effect in Indian futures markets. On one hand, Verma and Kumar (2010) found evidence of a maturity effect in wheat and pepper futures markets. On the other hand, Gupta and Rajib (2012), focusing the analysis on eight commodities futures markets (including wheat futures contract), indicated that the futures contract trading volume has a higher effect on the volatility than time-to-maturity. He, Yang, Xie, and Han (2014) confirmed the importance of the volume effect on price volatility, by studying six commodities futures markets in China.

Many studies have also indicated the inventory effect as a relevant factor that influences agricultural price variability. Carpantier (2010) analyzed 15 commodity price series over 1994–2009 and found that there was an inventory effect in coffee, soybean, and wheat markets. A similar analysis was carried out by Carpantier and Dufays (2012), analyzing 16 commodities from 1994 to 2011. All of the estimated asymmetric coefficients for agricultural markets (corn, cotton, soybean, sugar, wheat, and coffee) were negative, however, only in the cases of sugar and coffee were the parameters statistically different from zero. Stigler and Prakash (2011) verified two distinct levels of unconditional volatility in the wheat market, where one regime oscillated between 20 and 36 times higher than the other regime. The authors showed that the higher volatility regime emerged when the United States Department of Agriculture (USDA) forecasts pointed to a low inventory level (bad news on stocks-to-disappearance). Conversely, when the USDA inventory forecasts indicated no market tightness (positive news on stocks-to-disappearance), there was no apparent relationship between wheat prices and inventory level.

Finally, the volatility persistence of agricultural commodities was evaluated by a fifth group of studies. Balcombe (2009) investigated the factors that drove the volatility of 19 agricultural commodities over the last decades. He not only found evidence of a high volatility persistence in all price series but also that oil volatility, inventory levels, and yields influence price variability. Vivian and Wohar (2012) indicated, in general, a high volatility persistence considering 28 commodities (grains, animals, metals, and energy) over the years 1985–2010. Ghoshray (2013) also examined the volatility persistence of 24 commodity prices series during the 1900–2008 period. The results suggested that the volatility persistence varies significantly over time and between different products. Using a spline-GARCH model, Karali and Power (2013) found that the volatility persistence is lower than the one estimated from standard GARCH models in the agricultural, energy, and metal futures markets. In addition, Khan (2014) and Dawson (2015) indicated a high volatility persistence in cotton and wheat futures market, respectively. Khan (2014) also verified that cotton volatility was impacted by stocks-to-use ratio, price level, and futures market concentration.

Overall, previous studies have found that the volatility increased during the 2000s financial crisis, but that it was not higher than the price variability verified in other decades. In addition, the researches, in general, stated not only the presence of volatility persistence, but also the evidence of inventory, maturity, and seasonality effects on agricultural price fluctuations. The present study contributed to this debate by exploring the evolution of the inventory effect and volatility persistence rolling estimates using a recursive univariate TARCH(1,1)-in-mean volatility model. The work also evaluates the influence of seasonality and time-to-maturity. In the following section, the methodology used to achieve these goals is described.

Research method

According to the literature, futures prices returns of agricultural commodities (Eq. (1)) do not generally follow a normal distribution, given the presence of nonzero skewness and kurtosis greater than three (Isengildina, Irwin, & Good, 2006; Karali, 2012). Thus, GARCH models are more suitable for such series (Hováth & Sapov, 2016; Pockhilchuck & Savel’ev, 2016; Watkins & Mcaleer, 2008). In addition, taking into account that markets react asymmetrically to good news and bad news, a Threshold Autoregressive Conditional Heteroskedasticity (TARCH) model is chosen to capture the volatility process (Zakoian, 1994). Eqs. (2) and (3) describe the TARCH(1,1)-in-mean model:

In Eq. (1), Rt represents the daily percentage of close-to-close futures prices returns, which is obtained by comparing the closing price of the nearest-to-maturity futures contract on day t (Pt) to the closing prices on day t1 (Pt−1). In (2), the mean equation, δ0 is a constant, Rt−1 lagged daily return to account for autocorrelation in futures returns (Isengildina et al., 2006; Karali, 2012), ht the conditional standard deviation to capture the effects of the volatility on the mean term, and ??t the error term such that ??t|Ωt−1N(0, ht2), where Ωt−1 represents the information available in t1. Finally, Eq. (3) represents the conditional variance ht2≡VAR(Rt|Ωt−1). The lagged squared residual in the mean equation, εt−12, is used to represent volatility shocks from the previous day. Additionally, a binary variable Dt−1 is included to explore asymmetric effects, such that Dt−1 equals 1 when ??t−1 is negative and 0 when ??t−1 is positive. Thus, the impact of positive volatility shocks is given by α1, while the impact of negative volatility shocks is given by (α1+γ). A statistically significant estimate for γ implies the existence of asymmetry in volatility. A negative γ provides evidence of the inventory effect, i.e. positive volatility shocks in t1 increase conditional volatility in t proportionally more than negative volatility shocks. Another variable in Eq. (3) is the lagged conditional variance, ht−12. The volatility persistence in a TARCH model is given by (α1+γ/2+β). As this sum tends to one, a given shock in return takes longer to dissipate.

Two types of external effects are incorporated into the variance equation: seasonality and time-to-maturity. The seasonality effect is included using three variables SEj for quarters of the year: SE1 equals 1 for January, February, and March, and 0 otherwise; SE2 equals 1 for April, May, and June, and 0 otherwise; SE3 equals 1 for July, August, and September, and 0 otherwise. The maturity effect is expressed by the variable ME and should be negatively related to the commodity price volatility, since price variability tends to increase as the maturity date approaches.

The model is estimated recursively by the maximum likelihood method, using a rolling window of 1008 observations (4 years). This method makes it possible to analyze how volatility parameter estimates change over time. In this way, the daily evolution of the volatility persistence and the inventory effect are analyzed in terms of the rolling parameters estimate. Note that several different structures were estimated for the model using maximum likelihood, and the final specification was selected in terms of parsimony by the Schwarz Information Criteria (BIC). Since the aim of the paper is to evaluate the volatility pattern over time by means of recursive parameter estimates, a model with many parameters compromises the interpretability and requires higher computational costs, which can result in unstable time series of estimated parameters. The BIC indicated that the structure in Eqs. (1)–(3) is able to capture volatility dynamics accurately with relatively few parameters.


The data set consists of futures prices of corn and soybeans. Futures prices are daily closing quotes for nearby contracts from the Chicago Mercantile Exchange Group (CME) between July 1959 and December 2014. Fig. 1 presents the evolution of daily futures prices and returns for corn and soybeans.

Fig. 1.

Daily futures prices and percentage daily returns for soybeans and corn (July 1959–December 2014).

Descriptive statistics for corn and soybean returns are given in Table 2. Mean returns (Rt) of corn are not statistically distinguishable from zero. Mean absolute returns (|Rt|) are in the 0.96–1.02% range and are also statistically distinguishable from zero. A similar volatility in the soybean and corn futures market can be observed. Soybean returns have a daily standard deviation of 1.46% per day (23.15% per year), while corn shows 1.39% per day (22.01% per year). In addition, regarding the return series, there is no evidence of skewness, however, the distributions of absolute returns appear to be positively skewed. There is also evidence of excess kurtosis for both series. Finally, Jarque–Bera tests suggest nonnormality in all series, supporting findings given by previous studies (Isengildina et al., 2006; Karali, 2012).

Table 2.

Descriptive statistics of daily returns percentage and absolute percentage daily returns for soybeans and corn (July 1959–December 2014).

  Rt  |Rt|  Rt  |Rt| 
Observations (n13,977  13,977  13,980  13,980 
Mean (%)  0.0242a  1.0157a  −0.0064  0.9676a 
Median (%)  0.0461  0.6993  0.0000  0.6676 
Maximum (%)  12.5279  15.0626  8.6618  10.4088 
Minimum (%)  −15.0626  0.0000  −10.4088  0.0000 
Std. deviation (%)  1.4586  1.0471  1.3868  0.9916 
Skewness  −0.2465  2.4103  −0.0213  2.1846 
Kurtosis  7.9065  13.8311  6.6350  10.1911 
Jarque–Bera stat.  14,161.28  81,853.13  7697.60  41,242.95 

Statistically distinguishable from zero at 10%.


Volatility series for soybeans and corn are obtained through the estimation of the TARCH model (Eq. (3)). Results indicate the existence of volatility clusters for corn and soybean returns. In both markets, annual volatility generally ranges between 10% and 50%. In addition, the three most relevant breaks in price volatility common to corn and soybeans occurred at the end of Bretton Woods system (1973), the largest production shortfall in the U.S. grain markets in 1988, and during the subprime crisis in 2008. During these periods, the volatility in grain markets exceeded 60% a.a (Fig. 2).

Fig. 2.

Estimated conditional standard deviation for soybean and corn returns (July 1959–December 2014).

Table 3 presents the results of the estimated TARCH model for soybean futures returns. Estimated coefficients for the soybean model between July 1959 and December 2014 are reported in column I. The model was also estimated over four different periods, according to grain price evolution: 1959–1972 (column II), 1973–1988 (column III), 1989–2004 (column IV), and 2005–2014 (column V). In general, results suggest that conditional volatility is highly persistent (i.e. volatility shocks would take several days to decay) in all periods. The half-life period3 of futures price responses to a random shock is 374 days, indicating a slow adjustment process. Results also suggest a fall in half-life period during the four split periods, exhibiting 154, 93, 64 and 47 days, respectively.

Table 3.

TARCH model estimates for soybean returns.

Parameter  (I) Full sample(II) 1959–1972(III) 1973–1988(IV) 1989–2004(V) 2005–2014
  Coeff.  Prob.  Coeff.  Prob.  Coeff.  Prob.  Coeff.  Prob.  Coeff.  Prob. 
Mean equation
Constant  0.0036  0.7941  −0.0075  0.6913  0.0109  0.8965  0.0631  0.2915  0.2357  0.0510 
ht  0.0205  0.1968  0.0559  0.1302  0.0056  0.8468  −0.0479  0.3735  −0.1184  0.1617 
R(−1)  0.0017  0.8495  0.0028  0.8761  0.0013  0.9377  −0.0117  0.5004  0.0179  0.4047 
Variance equation
Constant  0.0050  0.0008  0.0017  0.2298  0.0511  0.0000  0.0394  0.0000  0.0543  0.0000 
 εt−12  0.0944  0.0000  0.0900  0.0000  0.1050  0.0000  0.0634  0.0000  0.0649  0.0000 
 Dt−1εt−12  −0.0525  0.0000  −0.0690  0.0000  −0.0512  0.0000  −0.0375  0.0000  −0.0205  0.0581 
GARCH(−1)  0.9300  0.0000  0.9400  0.0000  0.9132  0.0000  0.9446  0.0000  0.9306  0.0000 
SE1 (1° quarter)  0.0029  0.0000  0.0024  0.0003  −0.0027  0.6436  0.0046  0.0995  0.0147  0.1457 
SE2 (2° quarter)  0.0058  0.0000  0.0040  0.0000  0.0242  0.0016  0.0350  0.0000  0.0128  0.1758 
SE3 (3° quarter)  0.0029  0.0202  0.0044  0.0007  −0.0074  0.3607  −0.0063  0.1848  0.0312  0.0127 
ME  −0.0003  0.0000  −0.0001  0.0091  −0.0016  0.0001  −0.0015  0.0000  −0.0015  0.0136 
R-squared  −0.0002    −0.0005    0.0003    0.0004    0.0018   
Adjusted R-squared  −0.0004    −0.0011    −0.0002    −0.0001    0.0010   
S.E. of regression  1.4589    0.8296    1.8176    1.3408    1.6482   
Durbin–Watson stat.  1.8892    2.0438    1.7614    1.9746    2.0020   

Further, there is evidence of an asymmetric effect of volatility shocks in the soybean market (Table 3). Estimated coefficients of the term Dt−1εt−12 are negative, which means that positive shocks appear to have a greater effect on the conditional variance than negative price shocks. In addition, there is also evidence of the time-to-maturity effect, since the ME estimated coefficient is negative and statistically distinguishable from zero in all periods. Thus, when a soybean futures contract approaches its expiration, volatility increases. With respect to the seasonality effect, in general, results indicate higher volatility in the second quarter, during the planting period in the U.S.

Table 4 shows the results of the estimated TARCH model for corn futures returns. Again, estimated coefficients for the model, considering the complete sample, are reported in column I, and for the model considering different periods in columns II (1959–72), III (1973–88), IV (1989–2004), and V (2005–2014). Estimated coefficients for εt−12 and ht−12 are statistically distinguishable from zero during all periods, implying that previous shocks and the volatility forecast impact the conditional variance in corn.

Table 4.

TARCH model estimates for corn returns.

Parameter  (I) Full sample(II) 1959–1972(III) 1973–1988(IV) 1989–2004(V) 2005–2014
  Coeff.  Prob.  Coeff.  Prob.  Coeff.  Prob.  Coeff.  Prob.  Coeff.  Prob. 
Mean equation
Constant  0.0093  0.4471  0.0073  0.8301  −0.0106  0.8189  0.1604  0.0084  −0.1031  0.4503 
ht  −0.0146  0.5967  −0.0137  0.8078  0.0133  0.7641  −0.1603  0.0043  0.0564  0.4735 
R(−1)  0.0401  0.0000  0.0294  0.1227  0.0585  0.0004  0.0481  0.0024  0.0247  0.2085 
Variance equation
Constant  0.0197  0.0000  0.0415  0.0000  0.0365  0.0000  0.0221  0.0000  0.0259  0.2201 
 εt−12  0.0875  0.0000  0.1516  0.0000  0.0917  0.0000  0.0477  0.0000  0.0436  0.0000 
 Dt−1εt−12  −0.0192  0.0000  −0.0778  0.0000  −0.0074  0.5349  −0.0200  0.0008  0.0243  0.0199 
GARCH(−1)  0.9210  0.0000  0.8513  0.0000  0.8992  0.0000  0.9528  0.0000  0.9245  0.0000 
SE1 (1° quarter)  −0.0026  0.0877  −0.0123  0.0000  −0.0046  0.4464  0.0012  0.6981  0.0554  0.0001 
SE2 (2° quarter)  0.0012  0.5344  −0.0108  0.0013  0.0066  0.2759  0.0328  0.0000  0.0858  0.0000 
SE3 (3° quarter)  0.0026  0.2613  0.0044  0.3236  0.0231  0.0231  −0.0067  0.1177  0.0477  0.0139 
ME  −0.0005  0.0000  −0.0005  0.0000  −0.0007  0.0000  −0.0005  0.0001  0.0002  0.7026 
R-squared  0.0025    −0.0009    0.0081    0.0047    0.0007   
Adjusted R-squared  0.0024    −0.0015    0.0076    0.0042    −0.0001   
S.E. of regression  1.3852    0.7851    1.4314    1.2752    1.9821   
Durbin–Watson stat.  1.9715    2.0547    1.9181    1.9834    1.9958   

In addition, in the variance equation, the model shows high volatility persistence. For the years 1959–2014, the half-life period is 630 days, indicating a very slow adjustment process. Regarding the split periods, the models show a half-life of 19 days for 1959–1972, 54 days for 1973–1988, 73 days for 1989–2004, and 35 days for 2005–2014.

There is also evidence of inventory and time-to-maturity effects in all periods (except during 2005–2014). Furthermore, results suggest higher volatility in the second quarter compared to the rest of the year.

Overall, results suggest changes in the estimated parameters. In both markets, we can verify a slightly lower short-run persistence (εt−12) and a slightly higher asymmetric effect (Dt−1εt−12), particularly between 2005 and 2014. Furthermore, there is evidence of maturity and seasonality effects. Rolling coefficient estimates, which are discussed as follows, provide a more comprehensive analysis of these issues and shed more light on the analysis.

Fig. 3 shows the evolution of rolling α1, β and γ coefficient estimates with a rolling window of 1008 observations for corn and soybeans and their corresponding t-ratios from July 1963 to December 2014. In general, rolling β coefficient estimates for corn and soybean models are in the 0.8–1.0 range and are statistically distinguishable from zero, which indicates greater long-run shock persistence. For corn, β coefficient estimates present lower levels and higher instability than the respective soybean parameter (Table 5).

Fig. 3.

Rolling coefficient estimates for soybeans and corn.

Table 5.

Descriptive statistics for rolling α1, β and γ coefficient estimates and half-life period.

  Summary statistics
  Mean  Median  SD 
Alpha (α1)
Soybeans  0.0796  0.0786  0.0265 
Corn  0.0792  0.0774  0.0458 
p-Value  0.3689  0.0000  0.0000 
Beta (β)
Soybeans  0.9314  0.9329  0.0262 
Corn  0.9004  0.9012  0.0453 
p-Value  0.0000  0.0000  0.0000 
Gamma (γ)
Soybeans  −0.0480  −0.0524  0.0279 
Corn  −0.0228  −0.0285  0.0526 
p-Value  0.0000  0.0000  0.0000 
Half-life (ϑ)
Soybeans  65.94  21.24  2276.53 
Corn  98.47  56.52  2827.86 
p-Value  0.3123  0.0000  0.0000 

With respect to rolling α1 coefficient estimates, which indicate short-run persistence, the values oscillated between 0–0.15 for soybean and 0–0.20 for corn (Fig. 3). In addition, rolling α coefficient estimates for corn and soybeans seemed to present similar levels, along with higher variability for corn (Table 5). Finally, rolling γ coefficient estimates for soybeans (corn) vary between −0.10 and 0.02 (−0.15 and 0.15). The γ estimates from the corn model also show higher values and greater variability than the estimates from the soybean model. In general, since the coefficient is usually negative, there is evidence of an inventory effect.

Furthermore, Appendices A–C present the rolling coefficient estimates for seasonality and time-to-maturity effects for the soybean and corn markets. Results point to the existence of greater volatility during the planting period and before the harvest in the U.S. (second and third quarters). The evolution of time-to-maturity coefficient indicates higher futures price variability when the futures contract approaches its expiration for both markets.

Table 6 shows the descriptive statistics for rolling α1, β and γ coefficient estimates for each separate period. The findings confirm previous results related to lower α estimates over the last two periods, resulting in a decrease in the importance of short-run volatility persistence in soybean and corn markets. Consequently, it can be largely verified that the long-run persistence (α1+γ/2+β) and half-life period tend to be lower in the recent period, especially during 2005–2014, despite increasing values for γ.

Table 6.

Descriptive statistics for rolling α, β and γ coefficient estimates and half-life period during 1959–1972, 1973–1988, 1989–2004, and 2005–2014.

  Alpha (α)Beta (β)Gamma (γ)Half-life
  Mean  Med  SD  Mean  Med  SD  Mean  Med  SD  Mean  Med  SD 
1959–72  0.0920  0.0942  0.0212  0.9402  0.9382  0.0177  −0.0689  −0.0682  0.0182  141.22  137.56  6233.85 
1973–88  0.0899  0.0921  0.0252  0.9209  0.9245  0.0264  −0.0441  −0.0520  0.0255  135.90  50.48  2042.34 
1989–04  0.0768  0.0830  0.0276  0.9329  0.9310  0.0320  −0.0611  −0.0622  0.0180  57.22  46.44  678.03 
2005–14  0.0572  0.0578  0.0112  0.9383  0.9380  0.0126  −0.0155  −0.0146  0.0190  68.25  60.68  30.67 
Comparison between periods (p-value)a
1959–72×1973–88  0.0010  0.0151  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.9605  0.0000  0.0000 
1959–72×1989–04  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.5399  0.3974  0.0000  0.0000 
1959–72×2005–14  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0247  0.5570  0.0000  0.0000 
1973–88×1989–04  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0203  0.0000  0.0000 
1973–88×2004–14  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0966  0.0000  0.0000 
1989–04×2004–14  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0012  0.4151  0.0000  0.0000 
1959–72  0.1504  0.1467  0.0298  0.8458  0.8440  0.0351  −0.0832  −0.0802  0.0225  14.62  13.96  210.93 
1973–88  0.0747  0.0751  0.0310  0.9195  0.9309  0.0316  −0.0181  −0.0215  0.0417  137.54  30.21  4036.63 
1989–04  0.0693  0.0757  0.0271  0.9053  0.8954  0.0474  −0.0216  −0.0270  0.0203  45.84  24.18  166.50 
2005–14  0.0418  0.0425  0.0349  0.9084  0.9110  0.0298  0.0189  0.0098  0.0723  27.05  18.66  22.29 
Comparison between periods (p-value)a
1959–72×1973–88  0.0000  0.0000  0.0330  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.1596  0.0000  0.0000 
1959–72×1989–04  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 
1959–72×2005–14  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0033  0.0000  0.0000 
1973–88×1989–04  0.0000  0.4668  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.1496  0.0001  0.0000 
1973–88×2004–14  0.0000  0.0000  0.0000  0.0000  0.0000  0.0014  0.0000  0.0000  0.0000  0.1695  0.0000  0.0000 
1989–04×2004–14  0.0000  0.0000  0.0000  0.0029  0.0029  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 

p-Value for the hypothesis test that the population statistics are equal.


Agricultural markets are largely characterized by high price volatility, due to the low price elasticity of supply. This characteristic highlights the risk of this activity, which represents a susceptibility factor for primary producing countries. During the first decade of the 2000s, major agricultural commodities experienced a sharp and rapid rise in price and volatility, thus stimulating discussions and research in order to understand the reasons that led to such a scenario. With the increase in biofuel production from grains and oilseeds and restriction of acreage growth due to environmental issues, the pressure on agricultural areas will intensify, which may be reflected in increasing food prices.

Studies that investigate price volatility patterns in agricultural markets have significant importance, since they can help to improve decision-making processes related to production, risk management and marketing. In addition, policy makers can also benefit from these studies as they analyze the impacts of energy policies on agricultural price and food security. This paper contributes to the recent debate about volatility in agricultural markets by focusing the analysis on grain volatility persistence and the inventory effect. Using a conditional volatility model to generate rolling estimates, this work provides evidence on the evolution of volatility, its persistence and the inventory effect over the last 40 years. In addition, the study evaluates the maturity and seasonality effects through model estimates.

Results indicate that the three most significant volatility peaks in grain markets occurred in 1973 (collapse of the Bretton Woods system), 1988 (large production shortfall in U.S. grain markets) and 2008 (subprime crisis). High persistence from shocks on the conditional variance was found in corn and soybean markets between 1959 and 2014. There is also evidence of an asymmetric effect of volatility shocks in the grain markets, with negative shocks exhibiting a larger impact on conditional variance. In addition, the evolution of rolling coefficient estimates indicates decreasing short-run volatility persistence in both markets in recent years. Consequently, long-run persistence and the half-life period fall slightly. Further, seasonality and time-to-maturity effects are also found in both markets.

In terms of future works, this topic can be further explored with the inclusion of other commodities, along with the use of other volatility models. Volatility spillover effects over time could also be analyzed by means of recursive parameter estimates of multivariate GARCH models. In addition, other variables can be included in the model, such as futures contract trading volume and crop report announcements.

Conflicts of interest

The authors declare no conflicts of interest.


The authors would like to thank FAPESP (São Paulo Research Foundation) for the financial support given to this research.

Allen and Cruickshank, 2000
D.E. Allen,S.N. Cruickshank
Empirical testing of the Samuelson hypothesis: An application to futures markets in Australia, Singapore and the UK. Working paper
School of Finance and Business Economics, Edith Cowan University, (2000)
Anderson, 1985
R.W. Anderson
Some determinants of the volatility of futures prices
Journal of Futures Markets, 5 (1985), pp. 331-348
Arezki et al., 2014a
R. Arezki,D. Lederman,H. Zhao
The relative volatility of commodity prices: A reappraisal
American Journal of Agricultural Economics, 96 (2014), pp. 939-951
Arezki et al., 2014b
R. Arezki,K. Hadri,P. Loungani,Y. Rao
Testing the Prebisch–Singer hypothesis since 1650: Evidence from panel techniques that allow for multiple breaks
Journal of International Money and Finance, 42 (2014), pp. 208-223
Arezki et al., 2014c
R. Arezki,P. Loungani,R. Ploeg,A.J. Venables
Understanding international commodity price fluctuations
Journal of International Money and Finance, 42 (2014), pp. 1-8
Balcombe, 2009
K. Balcombe
The nature and determinants of volatility in agricultural prices: An empirical study from 1962–2008. A report to the Food and Agriculture Organization of the United Nations
Beckmann and Czudaj, 2014
J. Beckmann,R. Czudaj
Volatility transmission in agricultural futures markets
Economic Modelling, 36 (2014), pp. 541-546
Bellemare et al., 2013
M.F. Bellemare,C.B. Barrett,D.R. Just
The welfare impacts of commodity price volatility: Evidence from rural Ethiopia
American Journal of Agricultural Economics, 95 (2013), pp. 877-899
Bessembinder and Seguin, 1993
H. Bessembinder,P.J. Seguin
Price volatility, trading volume, and market depth: Evidence from futures markets
Journal of Financial and Quantitative Analysis, 28 (1993), pp. 21-39
Blattman et al., 2007
C. Blattman,J. Hwang,J.G. Williamson
Winners and losers in the commodity lottery: The impact of terms of trade growth and volatility in the Periphery 1870–1939
Journal of Development Economics, 82 (2007), pp. 156-179
Calvo-Gonzalez et al., 2010
O. Calvo-Gonzalez,R. Shankar,R. Trezzi
Are commodity prices more volatile now? World Bank Policy Research Working Paper 5460
Carpantier, 2010
J.-F. Carpantier
Commodities inventory effect. Discussion Paper 2010/40
Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, (2010)
Carpantier and Dufays, 2012
J.-F. Carpantier,A. Dufays
Commodities volatility and the theory of storage. Discussion Paper 2012/37
Center for Operations Research and Econometrics, Université Catholique de Louvain, Louvain-la-Neuve, (2012)
Carpantier and Samkharadze, 2013
J.-F. Carpantier,B. Samkharadze
The asymmetric commodity inventory effect on the optimal hedge ratio
Journal of Futures Markets, 33 (2013), pp. 868-888
Chatrath et al., 2002
A. Chatrath,B. Adrangi,K.K. Dhanda
Are commodity prices chaotic?
Agricultural Economics, 27 (2002), pp. 123-137
Daal et al., 2006
E. Daal,J. Farhat,P.P. Wei
Does futures exhibit maturity effect? New evidence from an extensive set of US and foreign futures contracts
Review of Financial Economics, 15 (2006), pp. 113-128
Dawson, 2015
P.J. Dawson
Measuring the volatility of wheat futures prices on the LIFFE
Journal of Agricultural Economics, 66 (2015), pp. 20-35
Du et al., 2011
X. Du,C.L. Yu,D.J. Hayes
Speculation and volatility spillover in the crude oil and agricultural commodity markets: A Bayesian analysis
Energy Economics, 33 (2011), pp. 497-503
Duong and Kalev, 2008
H.N. Duong,P.S. Kalev
The Samuelson hypothesis in futures markets: An analysis using intraday data
Journal of Banking & Finance, 32 (2008), pp. 489-500
Ghoshray, 2013
A. Ghoshray
Dynamic persistence of primary commodity prices
American Journal of Agricultural Economics, 95 (2013), pp. 153-164
Gilbert, 2010
C.L. Gilbert
How to understand high food prices
Journal of Agricultural Economics, 61 (2010), pp. 398-425
Gilbert and Morgan, 2010
C.L. Gilbert,C.W. Morgan
Food price volatility
Philosophical Transactions of the Royal Society B: Biological Sciences, 365 (2010), pp. 3023-3034
Glauber and Heifner, 1986
J.W. Glauber,R.G. Heifner
Forecasting futures price variability. Applied commodity price analysis, forecasting, and market risk management
Proceedings of the NCR 134 conference, pp. 153-165
Goodwin and Schnepf, 2000
B.K. Goodwin,R. Schnepf
Determinants of endogenous price risk in corn and wheat futures markets
Journal of Futures Markets, 20 (2000), pp. 753-774
Gupta and Rajib, 2012
S.K. Gupta,P. Rajib
Samuelson hypothesis & Indian commodity derivatives market
Asia-Pacific Financial Markets, 19 (2012), pp. 331-352
Hasan et al., 2013
M.Z. Hasan,S. Akhter,F. Rabbi
Asymmetry and persistence of energy price volatility
International Journal of Finance and Accounting, 2 (2013), pp. 373-378
He et al., 2014
L.-Y. He,S. Yang,W.-S. Xie,Z.-H. Han
Contemporaneous and asymmetric properties in the price–volume relationships in China's agricultural futures markets
Emerging Markets Finance and Trade, 50 (2014), pp. 148-166
Headey and Fan, 2008
D. Headey,S. Fan
Anatomy of a crisis: The causes and consequences of surging food prices
Agricultural Economics, 39 (2008), pp. 375-391
Hennessy and Wahl, 1996
D.A. Hennessy,T.I. Wahl
The effects of decision making on futures price volatility
American Journal of Agricultural Economics, 78 (1996), pp. 591-603
Hováth and Sapov, 2016
R. Hováth,B. Sapov
GARCH models, tail indexes and error distributions: An empirical investigation
North American Journal of Economics and Finance, 37 (2016), pp. 1-15
Huchet-Bourdon, 2011
M. Huchet-Bourdon
Agricultural commodity price volatility: An overview. OECD food, agriculture and fisheries papers, no. 52
OECD Publishing, (2011)
Hudson and Coble, 1999
D. Hudson,K. Coble
Harvest contract price volatility for cotton
Journal of Futures Markets, 19 (1999), pp. 717-733
Isengildina et al., 2006
O. Isengildina,S.H. Irwin,D.L. Good
The value of USDA situation and outlook information in hog and cattle markets
Journal of Agricultural and Resource Economics, 31 (2006), pp. 262-282
Jacks et al., 2011
D.S. Jacks,K.H. O’Rourke,J.G. Williamson
Commodity price volatility and world market integration since 1700
Review of Economics and Statistics, 93 (2011), pp. 800-813
Kalev and Duong, 2008
P.S. Kalev,H.N. Duong
A test of the Samuelson hypothesis using realized range
Journal of Futures Markets, 28 (2008), pp. 680-696
Karali, 2012
B. Karali
Do USDA announcements affect comovements across commodity futures returns?
Journal of Agricultural and Resource Economics, 37 (2012), pp. 77-97
Karali and Power, 2013
B. Karali,G.J. Power
Short- and long-run determinants of commodity price volatility
American Journal Agricultural Economics, 95 (2013), pp. 724-738
Karali and Thurman, 2010
B. Karali,W.N. Thurman
Components of grain futures price volatility
Journal of Agricultural and Resource Economics, 35 (2010), pp. 167-182
Karali et al., 2010
B. Karali,J.H. Dorfman,W.N. Thurman
Delivery horizon and grain market volatility
Journal of Futures Markets, 30 (2010), pp. 846-873
Kenyon et al., 1987
D. Kenyon,K. Kling,J. Jordan,W. Seale,N. McCabe
Factors affecting agricultural futures price variance
Journal of Futures Markets, 7 (1987), pp. 73-92
Khan, 2014
B.F. Khan
Determinants of futures price volatility of storable agricultural commodities: The case of cotton
Texas Tech University, (2014)
(Thesis in Agricultural and Applied Economics)
Khoury and Yourougou, 1993
N. Khoury,P. Yourougou
Determinants of agricultural futures price volatilities: Evidence from Winnipeg Commodity Exchange
Journal of Futures Markets, 13 (1993), pp. 345-356
Kocagil and Shachmurove, 1998
A.E. Kocagil,Y. Shachmurove
Return-volume dynamics in futures markets
Journal of Futures Markets, 18 (1998), pp. 399-426
Malliaris and Urrutia, 1998
A.G. Malliaris,J.L. Urrutia
Volume and price relationships: Hypotheses and testing for agricultural future
Journal of Futures Markets, 18 (1998), pp. 399-426
Mensi et al., 2013
W. Mensi,M. Beljid,A. Boubaker,S. Managi
Correlations and volatility spillovers across commodity and stock markets: Linking energies, food, and gold
Economic Modelling, 32 (2013), pp. 15-22
Milonas, 1986
N.T. Milonas
Price variability and the maturity effect in futures markets
Journal of Futures Markets, 6 (1986), pp. 443-460
Naylor and Falcon, 2010
R.L. Naylor,W.P. Falcon
Food security in an era of economic volatility
Population and Development Review, 36 (2010), pp. 693-723
Nazlioglu et al., 2013
S. Nazlioglu,C. Erdem,U. Soytas
Volatility spillover between oil and agricultural commodity markets
Energy Economics, 36 (2013), pp. 658-665
Pockhilchuck and Savel’ev, 2016
K.A. Pockhilchuck,S.A. Savel’ev
On the choice of GARCH parameters for efficient modelling of real stock price dynamics
Physica A: Statistical Mechanics and Applications, 448 (2016), pp. 248-253
Power and Robinson, 2013
G.J. Power,J.R.C. Robinson
Commodity futures price volatility, convenience yield and economic fundamentals
Applied Economics Letters, 20 (2013), pp. 1089-1095
Prebisch, 1950
R. Prebisch
The economic development of Latin America and its principal problems
Economic Bulletin for Latin America, 7 (1950), pp. 1-22
Rapsomanikis and Sarris, 2008
G. Rapsomanikis,A. Sarris
Market integration and uncertainty: The impact of domestic and international commodity price variability on rural household income and welfare in Ghana and Peru
Journal of Development Studies, 44 (2008), pp. 1354-1381
Rutledge, 1976
D.J.S. Rutledge
A note on the variability of futures prices
Review of Economics and Statistics, 58 (1976), pp. 118-120
Serra, 2011
T. Serra
Volatility spillovers between food and energy markets: A semiparametric approach
Energy Economics, 33 (2011), pp. 1155-1164
Singer, 1950
H. Singer
The distribution of gains between investing and borrowing countries
American Economic Review, 11 (1950), pp. 473-485
Smith, 2005
A. Smith
Partially overlapping time series: A new model for volatility dynamics in commodity futures
Journal of Applied Econometrics, 20 (2005), pp. 405-422
Stigler and Prakash, 2011
M. Stigler,A. Prakash
The role of low stocks in generating volatility and panic
Safeguarding food security in volatile global markets, pp. 314-328
Streeter and Tomek, 1992
D.H. Streeter,W.G. Tomek
Variability in soybean futures prices: An integrated framework
Journal of Futures Markets, 12 (1992), pp. 705-728
Sumner, 2009
D.A. Sumner
Recent commodity price movements in historical perspective
American Journal of Agricultural Economics, 91 (2009), pp. 1250-1256
Verma and Kumar, 2010
A. Verma,C.V.R.S.V. Kumar
An examination of the maturity effect in the Indian commodities futures market
Agricultural Economics Research Review, 23 (2010), pp. 335-342
Vivian and Wohar, 2012
A. Vivian,M.E. Wohar
Commodity volatility breaks
Journal of International Financial Markets, Institutions and Money, 22 (2012), pp. 395-422
Watkins and Mcaleer, 2008
C. Watkins,M. Mcaleer
How has volatility in metals markets changed?
Mathematics and Computers in Simulation, 78 (2008), pp. 237-249
Wright, 2011
B.D. Wright
The economics of grain price volatility
Applied Economic Perspectives and Policy, 33 (2011), pp. 32-58
Yang et al., 2005
J. Yang,R.B. Balyeat,D.J. Leatham
Futures trading activity and commodity cash price volatility
Journal of Business Finance & Accounting, 32 (2005), pp. 297-323
Yang and Brorsen, 1993
S.R. Yang,B.W. Brorsen
Nonlinear dynamics of daily futures prices: Conditional heteroskedasticity or chaos?
Journal of Futures Markets, 13 (1993), pp. 175-191
Zakoian, 1994
J.M. Zakoian
Threshold heteroskedasticity models
Journal of Economic Dynamics and Control, 18 (1994), pp. 931-955

A decrease in the commodity inventory levels, originating from a scenario of supply shortages and/or demand expansion related to this commodity, tend to cause an increase in its price. The inventory effect considers that the reaction to commodity returns is higher for positive price shocks than to negative shocks (Hasan, Akhter, & Rabbi, 2013; Stigler and Prakash, 2011).

Peer Review under the responsibility of Departamento de Administração, Faculdade de Economia, Administração e Contabilidade da Universidade de São Paulo – FEA/USP.

The time-to-maturity effect is also known as the Samuelson effect. According to the Samuelson hypothesis, futures price volatility tends to increase as the futures contract maturity date approaches. When a futures contract approaches its expiration, “the price of an expiring contract must virtually equal the prevailing spot price, nearer contracts tend to respond strongly to new information so that the price of an expiring futures contract will converge to the spot price” (Milonas, 1986, p. 445).

The half-life, ϑ, is the expected time for a shock to decay by 50%. It is a measure of the speed of adjustment and is calculated using: ϑ=log(0.5)/log(α1+0.5γ+β1).

Corresponding author at: Unicamp/Instituto de Economia, CP 6135, sala 68, CEP 13085-970 Campinas, SP, Brazil. (Rodrigo Lanna Franco da Silveira
Copyright © 2017. Departamento de Administração, Faculdade de Economia, Administração e Contabilidade da Universidade de São Paulo ¿ FEA/USP
Revista de Administração 2017;52:403-18 DOI: 10.1016/j.rausp.2017.08.003