The Analysis of Wheat Prices Using Multiple Structural Breakpoint Co-Integration Test

From 2005 to 2008, high volatility in the markets affected grain prices significantly. This high volatility in grain prices made many researchers curious, and many discussions aroused from this topic. This study analyzes wheat price behavior during this period of high volatility. We estimate a return index for wheat using spot and futures wheat prices with the help of a present value model. To analyze the cointegration between the wheat prices and return index, a new co-integration test with multiple structural breaks, developed by Daiki Maki (2012), is used. The long-run cointegration coefficients are estimated using the Dynamic Ordinary Least Squares methodology. The empirical results show that there is cointegration between the spot and futures wheat prices, which tends to change at breakpoints. In other words, there is an equilibrium relation between spot prices and futures prices; however, it becomes unstable during the crisis in 2008. The results may help in understanding the dynamics of wheat prices, especially during high-volatility periods. This study analyzes the presence of price breaks in the futures wheat market by using multiple breakpoint co-integration test developed by Maki (2012). Structural breaking dates are determined with this test. It is recommended to use regime-switching regression models to analyze the structural change phenomenon (Brooks and Katsaris, 2003).


Introduction
Volatility in commodities' prices, under certain limits, is helpful for the smooth and effective working of the markets. However, if it goes beyond these limits, it may have a negative impact not only on consumers and producers but also on the whole economy. High volatility increases market uncertainty. An uncertain market environment makes market manipulation easier and causes losses to market participants.
The reports of the Europen Union Commission showed that there was an increase in the overall volatility of different agricultural commodity markets from 2005to 2008and 2008to 2011(Europen Union, 2011. These developments were also on the agenda in Cannes Summit, 2011 of G-20-the leading actors of agriculture markets with a 65% market share in the global agriculture market-and it was decided to control the position limits in agriculture derivatives markets, increase transparency, and tighten the regulations in commodity markets (Hilary Till, 2011).
Especially, wheat prices showed fluctuations ranging from -40% to +280% over the period signaling speculation in the commodities market. Some researchers argued the presence of an unprecedented purchase pressure leading to several large bubbles in agricultural futures prices (e.g., Masters, W. Michael, 2008;Masters, 2009). However, academicians have previously tested the presence of bubble components at agricultural prices and found inconsistent results (Christopher L. Gilbert, 2010; Scott H. Irwin and Dwigh. R. Sanders, 2011;Luciano Gutierrez, 2013;Celso Brunetti, Bahattin Büyüksahin and Jeffrey Harris, 2016).
Wheat is the main ingredient of food production. Because households spend a relatively high portion of their income on basic food and energy, price increases negatively affect the social well-being of consumers, especially in developing countries (Chris Brooks, Prokopczuk Marcel, and Wu Yingying, 2015). Moreover, wheat is among the highly traded agricultural commodity in spot and futures markets. Therefore, it is important to determine whether the prices of this product deviate from a random walk and whether it exhibits explosive behavior.
Based on all the above-mentioned developments, this study aims to analyze the rapid rise of wheat prices in the futures market of Kansas Trade Exchange, one of the most important markets for world wheat trading.

Previous Studies
The factors causing the sudden changes in food prices during 2005 to 2008 found by previous studies can be grouped under the following five categories: Factors causing stock changes (e.g., increase in the demand of non-food items due to bio-gas programs of the USA and the EU, increase in food demand because of high growth in some developing countries like China-see Mark W. Rosegran, Tingju Zhu, Siwa Msangi and Timothy Sulser, 2008;Derek Headey and Sehenggen Fan, 2008;Teresa Serra, David Zilberman, and Jose. M. Gil, 2011;Serra et al., 2013).
The study models the wheat price behavior with the help of structural breakpoints. There are many studies analyzing price behaviors in agri-products markets using speculative movements (Martin L. Bohl and Stephan M. Stephan, 2013), mostly focusing on the changes in speculative positions and their effect on prices. Most of them find no extreme speculative movements (Sanders et al., 2010;Sanders and Irwin 2011). There are very few studies focusing directly on price bubbles. An important problem in these studies is the inability of empirical tests to answer whether there were price bubbles or not. To solve this problem, Peter Phillips and Tassos Magdalinos (2009) and Phillips and Yu (2011) developed a new unit root test for the presence of speculative bubbles. This method is developed to identify the bubbles that are even on a medium degree. Ulrich Homm and Jörg Breitung (2011) checked the success of this method using other tests. Gilbert (2010) applied this method on wheat, soya, and corn; however, except for soya, no bubbling phenomena were found in any of them. Gutierrez (2013) improved this method of Phillips et al. (2011) and tried to find price bubbles in agro-product markets using a non-parametric bootstrap method. The results of this study were exactly opposite to the results of Gilbert (2010). Bursts and crashes were found in the prices of wheat and corn but not in the prices of soya. In another study, price bubbles in wheat and corn were found using Momentum Threshold Autoregressive (MTAR) approach (Philipp Adöammer and Martin Bohly, 2015). Similar results are found in the study of Peter Liu and Ke Tang (2010). It found price bubbles in corn, soya, and sugar (wheat was not considered in this study). Liu et al. (2013) used the regime shift approach but could not find any speculative bubble except for soya. Rıza Emekter Benjamas Jirasakuldech and Peter Went (2012) took a longer period  and identified bubbles in the prices of corn, wheat, and soya. This study is conducted using a time dependence test. Recently, Phillips et al. (2013) developed a test that allows multiple bubbles. Xiaoli Etienne Irwin Scott and Philip Garcia (2014) observed bursts in cereal markets by using this test. However, their results showed that the bubbles formed in agro-products are very small and loses their significance in 2 weeks.
In this study, cointegration tests, derived from the present value model, are used. In time series analysis, the co-integration test is developed to analyze comovement between two non-stationary time series. If a linear combination of two or more non-stationary time series is stationary, then it can be said that the series are cointegrated. Many researchers in the field of finance, like Behzad Diba and Herscehel Grossman (1988) and Bohl (2003), studied the presence of price bubbles using unit root tests or co-integration between dividend and price data. These methodologies are based on the argument that if there is co-integration between the series of dividends and price, then the two series cannot move away from each other for an unlimited period and will attain equilibrium in the long run. Nowadays, the generally accepted rule is that if there is cointegration among the data, then it can be taken as an indication of a price bubble. However, three important fundamental factors determine this relationship. These are unit root tests, long period present value model, and the presence of structural breaks (Vicente Esteve, Navarra Ibáñez and Maria Asuncion. 2013). However, this topic is still being discussed in the literature. Some of the researchers think these structural breaks are formed because of the effects of future expectations on market (see Zacharias Psaradakis, Martin Sola, and Fabio Spagnolo, 2004), whereas others interpret them as result of cyclical political changes because of interest rates dynamics (see Eugene F. Fama and Kenneth R. French, 2002). Whatever the reason is, these structural changes seriously question the validity of the efficient market hypothesis. Keeping in mind the different opinions in the literature, this study focuses on explaining the price instability and its structural breaks.
There are a couple of studies analyzing the relation between spot and futures prices in commodity markets (e.g. Holly Wang and Bingfan Ke, 2005;Yunxian Yan and Michael Read, 2014). The distinguishing feature of our study is its focus on the wheat price dynamics in spot and futures markets under the structural break.
Another distinguishing feature of this study is the use of a contemporary residual-based co-integration test with multiple structural breaks, developed by Maki (2012), to analyze wheat price dynamics. This test works well both for the large and small number of breaks. This method is based on the structural breakpoint tests of Jussan Bai and Pierre Perron (1998) and the unit-root test of George Kapetanios (2005). This study uses a modified version of the code used by Maki (2012) to identify the breakpoints. Given the breakpoint dates, the coefficients of the long-run relation are estimated by the Dynamic Ordinary Least Squares (DOLS) method.

Test and Data
Monthly wheat price and storage cost data for the period of 1990:01-2012:12 are taken from the USA Kansas futures market (KBCT, 2012). Data up to 2012 is focused since it includes extraordinary movements in wheat prices both in spot and futures markets especially around 2008 and 2011. The data for wheat prices in the spot market are taken from the official website of the USA agricultural ministry (USDA, 2015). Descriptive statistics of the spot and futures wheat prices are summarized in Table 1 Table 1 shows that the average spot prices and futures prices are $418 and $452, respectively. The highest spot price is $1050, whereas the futures price is $1255 over the study period. Because the kurtosis values of both spot and futures prices are greater than 3, it shows a fat tail than the normal distribution. On the other hand, the skewness values of both spot and futures price show positively skewed distributions.
The expected price in the futures market is taken as the actual price. The prices of the first and last few days of a month, which cause high volatility, are excluded from the data set. The data of the futures contracts, whose maturities are close, are also excluded to avoid high manipulation.

Present Value Model and Wheat Stock Prices
The concept of efficient markets is based on rational commodity pricing. According to the present value (PV) model, the rational price of an asset can be obtained by discounting all the future cash flows of the asset at a predetermined discount rate. The PV model for a rational commodity price can be written as follows: where Pt is the rational price of a storable commodity at time t, Pt+k is the price of the commodity at time t+k, Dt+i is the convenience yield of the commodity at time t+i, β is the constant discount factor (1/1+R), and Et represents an operator for the expected future value of the asset based on the information at time t (Robert Pindyck, 1993). Convenience yield "d." which comprises carrying charges, like storage costs, insurance costs, and finance charges paid to store a physical commodity. It can also be defined as the utility, obtained by inventory holders, associated with availability in periods when supplies are scarce (Gutierrez, 2013). The use equation (1) along with the abovementioned convenience yield definition to explain the pricing of storable commodities. Because the aggregate storage cost is positive for agricultural commodities, the above PV model can be used to price a storable commodity.
The expected present value of the entity approaches zero as time t goes to infinity. It can be represented as follows If the discount rate is lower than the growth rate in the profit share, the only solution for the basic value can be written as follows: The current price of an asset reflects information about the future. The PV model is suitable for calculating a rational commodity price because it incorporates expected future cashflows given the current information. Many solutions can be made from Equation (1), which results in a difference between the market price and the base price. The base value is the present value of the future profits an asset will make. Price bubble (φt) is the deviation from this base. It can be represented as follows: P t * = P t + φ t (4)

Multiple Structural Breakpoints Co-Integration Test
Allan W. Gregory and Bruce E. Hansen (1996a) argued that standard cointegration tests, including the tests of Robert Engle and Clive Granger (1987) and Johansen (1988Johansen ( , 1991, give inadequate results under structural breaks. To overcome this problem, Gregory et al. (1996a,b) developed a test that allows a single structural break. However, the validity of the test is questionable as the number of breakpoints increases. Abdulnasser Hatemi-J (2008) developed a co-integration test with two structural breaks. However, both of the above tests lose their validity when there are 3 or more breaks. Maki (2012) developed a co-integration test that allows an infinite number of structural breaks. In our study, we applied this test to detect the presence of price bubbling phenomena in the agricultural commodity market. This residual-based test works both for a large and small number of structural breaks. This test is based on the structural breaks tests of Bai and Perron (1998) and the unit root tests of Kapetanios (2005).
In the Maki (2012) test, every period is taken as a possible breakpoint, tstatistics are calculated and the dates with the lowest t-statistics are taken as breakpoints. There are four possible model specifications.
Model 0: Model with a breakpoint in intercept and without a trend.
Ci,t denotes a dummy variable. Maki (2012) defined this variable as: Here, TBi represents the break years in the series. The hypotheses of the test are as follows: The critical values, needed for hypothesis tests, are calculated using Monte Carlo simulation and given in Maki (2012). If the calculated value is less than the critical value, H 0 is rejected, and it can be concluded that there is cointegration among the series. A necessary condition for Maki's test is that the series should be I(1), that is, stationary in their first differences. The stationarity is tested using Josep Carrion-i-Silvestre's (2009) structural breaks unit root test that allows multiple unknown breaks.

Long-Run Relationships
The logic behind cointegration is that there is a long-run relationship among some non-stationary variables. If two non-stationary variables have a stationary linear combination, then, in the long run, they tend to move together, that is, there is cointegration between them. In this study, the coefficients of a long-run relation between Dt and Pt are estimated using DOLS. To remove endogeneity and heteroskedasticity problems in the residuals, Stock and Watson (1993) propose the use of the lags and leads of the explanatory variables in the model. The estimates derived using the abovementioned methodology can be used to make statistical inferences. The above procedure is better as compared with Johansen and FMOLS methodologies. However, in Johansen's system of equations, parameter estimates of one equation may affect the residuals of other equations, whereas in DOLS, as there is only one equation, the above problem is out of the question. All the variables used in this study are stationary at I(1). Thus, the cointegration relation between them can be written as: Here, α 2 is a coefficient of a long-run relation between Dt and Pt; q represents an optimal number of lags and leads. After estimating long-run relation using DOLS, in the second step, we look for cointegration relation among the variables using a test developed by Yongcheo Shin (1994). In this test, one of the two statistics, named Cμ, is calculated assuming no trend by putting α 1 =0. Whereas the second one, named Ct, is calculated with the trend by putting α 1 ≠0. The test statistic Cμ tests the null hypothesis of the presence of cointegration relation against the alternative hypothesis of the absence of cointegration. In the equation, q represents lag structure. The optimal number of lags and lead is obtained using Akaike Information Criteria (AIC).

Findings and Discussion
The stationarity of the series is tested using Augmented Dickey-Fuller (ADF) unit root test. Unit roots are found in all the series at level as the calculated test statistics are found to be greater than the critical values (Table 2). In other words, series are not stationary at their levels. They become stationary at the first difference, that is, all the series are I(1).  (Table 3). In other words, the series is not stationary at their levels. They become stationary at the first difference, that is, all the series are I(1). To study the cointegration relation among the variables, Maki's (2012) cointegration test is used. This study analyzes the presence of price breaks in the futures wheat market by using multiple breakpoint co-integration test developed by Maki (2012). Structural breaking dates are determined with this test. It is recommended to use regimeswitching regression models to analyze the structural change phenomenon (Brooks and Katsaris, 2003).
Model (2), which is called the regime-shifts model, allows for structural breaks of β in addition to μ.
So, model 2 and model 3 of Maki's test are used in this study. The results of the test are presented in Table 4. The test has obtained a minimum t-statistic using a simple structure.
The results show for all the models that the calculated test statistics are greater than the critical values, and thus under structural breakpoints, there is cointegration between the series. The abovementioned results show that at a 5% level of significance, a regression model with two breakpoints is significant for model 2 ( > ~ −5.37/−5.36). However, at the same level of significance, a regression model with one breakpoint is significant for model 3 ( > ~ −5.99/−4.62). Thus, in the Kansas futures market, there is a structural breakpoint in June 2008. However, according to the two breaks model, there are structural breaks in March 2008 and June 2008 in the same exchange. Furthermore, in model 2, with three breaks, another statistically significant breakpoint (at a 10% level of significance) is found in December 2007, along with the other two breaks. In model 3 with two breaks, statistically significant breaks (at a 10% level of significance) are found in April 2008 and July 2010. It needs to be mentioned that no statistically significant breaks are found after July 2010, even at a 10% level of significance (Table 4).
The main reason for not choosing the findings of model 3 is that the results are not statistically significant at a 5% significance level. Although the two breaks version of Model 2 is significant at a 5% significance level, it shows structural breaks in the 3rd and 6th months of 2008. Moreover, both the single-break and two-break versions of model 2 point to June 2008. It is difficult to predict a long-term relationship over such a short regime with reasonable accuracy. Therefore, it is logical to focus on only one break with a smooth transition that started in March 2008. Wheat prices exploded in June 2008.
The coefficients of a long-run relation between Pt and Dt are estimated using a test, based on DOLS methodology. We do this using a test developed by James Stock and Mark Watson (1993) and Shin (1994) based on DOLS methodology. We use two sub-periods: 1990:1 to 2008:6 and 2008:7 to 2012:12. The results of cointegration tests are shown in Table 5.
According to the results, we do not reject the null hypothesis of the presence of cointegration relation between the series, because test statistic Cμ calculated for the whole period (1990:1-2012:12) is lesser than the critical value at 5% level of significance (Table 5). So, we can say the series are cointegrated.
To check whether the cointegration relation is strong or weak, the Wald test is used to test whether the coefficient α 2 is equal to one or not. The null hypothesis of strong cointegration (α 2 =1) is rejected because the test statistic (WDOLS) of the Wald test is greater than the critical value (3.841), taken from the Chi-square table, at a 5% level of significance. If we do not consider the structural breaks, the relation for the whole period (1990:1 to 2012:12) is found as [1, 2.47]. And if we consider structural breaks, the whole period is divided into two regimes because of the breakpoint identified in 2008:06. In the first regime (1990:01 to 2008:06), the null hypothesis of the presence of cointegration relation cannot be rejected because the calculated test statistic, Cμ, is lesser than the critical value (0.314) at 5% level of significance. The coefficient α 2 is also found to be different than 0 at a 5% level of significance for the said period. The null hypothesis of α 2 =1, in the Wald test, is rejected, implying weak cointegration. In the second regime (2008:07 to 2012:12), statistically significant cointegration is found between wheat price and return index. Analyzing both regimes shows there is a decreasing trend [2.90, 1.52] in the coefficients (α2) of the long-run relation between Pt and Dt. The null hypothesis of strong cointegration, in the Wald test, is rejected for the said period also as the calculated test statistic WDOLS is greater than the critical value (3.841) at a 5% level of significance. The empirical results show that the cointegrating relationship has changed over time, that is, it is not stable. There is cointegration between the spot and futures wheat prices, which tends to change at breakpoints. The empirical results also show, in particular, the Maki tests for testing multiple structural breaks in cointegrated regression models suggest a model of three regimes, with the dates of the breaks estimated at 2018:M3 and 2008:M6, and a model of two regimes, with the date of the break estimated at 2008:M6. Accordingly, Kansas futures market wheat prices exploded in June. Besides, the intrinsic bubble concept explains the asset prices deviating from the intrinsic/base value and the response of these deviations to the shocks (Kenneth Froot and Maurice Obstfeld, 1991). Therefore, it is stated that tests with regime change are suitable for periodically exploding bubbles (Stephan Hall, Zacharias Psaradakis, and Martin Sola, 1999). Based on the evidence, it can be said that the wheat price bubble, which originated in March 2008, collapsed in June 2008. The total duration of the wheat price exuberance was 3 trading months.
In another study, conducted on the wheat prices in the Chicago Board of Trade, the bubbles are identified in August 2007 and April 2008 (see Gutierrez, 2013). Our results are in line with other studies indicating the presence of speculative bubbles in wheat prices (Liu and Tang, 2010;Emekter et al., 2012;Roberto Espostia and Giulia Listorti, 2013;Adämmer and Bohl, 2015). Figure 1 shows the breakpoint relation in the spot and futures wheat prices in the Kansas Trade Market. This study provides important evidence about the deviation of wheat prices from their market-based internal values from 2007 to 2008. In general, structural breaks are a problem for the analysis of economic series, because they are affected by either internal shocks or changes in policy regimes.
The sub-prime credit crisis, starting in 2007, began to affect all the financial system of the USA rapidly, by March 2007, New Century Financial Corporation, the second-largest credit firm of the United States, along with many other finance and insurance companies had gone bankrupt. In 2008, the effect of the crisis increased further. The turbulence in the world market increased as the news that Bear Stearns, the world's largest investment and consultancy firm, was facing financial problems. So the crisis, starting from the United States, moved to the rest of the world. The financial crisis also affected the other sectors of the economy.
Overall, weak expectations in stocks and the housing sector can make a speculative investment in food products an attractive opportunity. Only part of the wheat production can be stored, the rest is sold quickly. Particularly low wheat stock levels encourage speculation on price increases more easily. It is observed that the stock levels are at very low levels (Piesse and Thirtle, 2009) when the breaks are formed. Although this study determines where and when price breaks have occurred, further research is needed to understand which factors affect price dynamics.

Conclusion
This study analyzes price behavior in the KCBT wheat futures market based on bubbling phenomena. For this, the wheat price-return relation, taken from a present value model, is analyzed by using a new multiple structural breakpoint test of Maki (2012). The relation between structural breaks and cointegration is also considered to avoid the problems observed in the empirical literature. Furthermore, to estimate the cointegration coefficients of the relation between futures prices, taken from Kansas Trade Market, and returns, DOLS regression is used.
A significant cointegration relation is found in model 2 with one and two structural breaks. According to the results, in March 2008, the wheat prices in the Kansas futures market burst; and in June 2008, they crash. These structural breaks can be attributed to the global subprime crisis of 2007 to 2008.
The results obtained in our study are consistent with the existence of linear cointegration between the wheat prices and the returns, with a vector [1, 2.47]. Thus, the cointegration vector is not [1, 1], as predicted by the theory. The empirical results show the cointegration relation between the series tends to change over time because of the structural breaks.
The results suggest that ignoring structural changes in the cointegration relationship may understate the extent of correlation between the spot prices and the return index because the response of the present-value future price to changes in returns increases over time. Summing up, there is cointegration between the spot and futures wheat prices; and the equilibrium relation, that is, the cointegration vector, changes over time. In other words, the relation between spot prices and futures prices becomes unstable during the crisis.
The academic research for speculative bubbles in the agricultural commodity markets is still limited as compared to stock markets. The results of the study will enrich the literature and broaden the view of the researcher studying the dynamics of commodity markets.