# Introduction n understanding of the persistence of volatility risk in grain prices most importantly, the price of wheat is crucial to help design a sustainable strategy to hedge against the attendance effects. Studies have documented several factors that could be accountable for price increases; these include: ban of export of major grain such as corn, supply shortages, reduced stock-to-use ratios and panic buying by some major importers (Gilbert, 2010;and Minot, 2014). The long shift (decline) in the prices of wheat between 2017 and 2019 with increased volatilities (see Figure 1) have generated immense concerned for investors to search for which of the volatility sources generate the highest persistence of volatility risk. Having a better comprehension of effective modeling of price returns and volatility becomes imperative considering seasonal shifts in prtrends. It is clear that this is not the first time that there is going to be a shift in commodity prices, specifically prices of grains. For instance, commodity prices rose rapidly between 2010 and 2011; and since 2007, global grain markets have witnessed an upward shift in price volatility. This is evident in the submission of Minot (2014), which provide analyses of pre-during-post of the global crises. The study shows that for these periods, the unconditional volatility of grain prices rose by 52% for corn, 87% for rice and 102% for wheat, respectfully. This indicates that price of wheat produces increased upward volatility risk to investors when compared to other grains. The paper, therefore contributes to the existing studies on commodity price volatility modeling in three folds: first, it uses the recent Narayan and Popp (2010) to model the wheat return volatility. The approach allows for structural breaks in data series. Second, the wheat return volatility analysis was performed using the volatility sources. This is an improvement to existing studies on emerging markets that had concentrated on a single source of volatility. Third, the paper considers both systematic and idiosyncratic volatility risks models. The main thrust of the paper is to identify structural breaks that occur in wheat returns; and consequently, show how intense is the volatility risk in wheat price in the international market. Our results also lend support for the consideration of the source that generates more persistence in the wheat return volatility. Comparatively, the idiosyncratic volatility models seem more appropriate in modeling wheat return volatility than the systematic ones, as it produces more persistence in volatility risk. Most importantly, the Exponential GARCH (EGARCH) model gives the best fit and therefore, propose that when modeling wheat return volatility, the EGARCH model should be considered. The implication therefore, is that investors in wheat should expect higher returns during rising volatility regardless of types and otherwise. The rest of the paper is structured as follows. Section two presents data and methods. Section three describes the analysis of empirical results and section four concludes the paper. # Data and Methods The weekly wheat price data used in this study were garnered from the Bloomberg terminal throughout January 2014 and April 2019. The pre-estimation analysis is performed in two folds: the first provides descriptive statistics for wheat returns volatility considering the two types of volatilities generatedsystematic and idiosyncratic volatilities; the second shows the unit root test using the NP unit root test with structural breaks. The wheat returns is computed with the formula i t i t i t r r ? ? ? + + = ?1 1 0 . Table 1 presents the descriptive results on wheat return volatility for both systematic and idiosyncratic volatilities. It seems evidence from the results that there are significant variations in the trends of the two volatilities. Comparatively, following the standard deviation result, the trend of the idiosyncratic volatility appears more volatile than the systematic volatility. The statistical distribution of the series, indicates that both idiosyncratic and systematic volatilities are negatively skewed which shows that there exist extreme right tails in both series. Other descriptive statistics show that wheat return volatility series are leptokurtic (both possess fat tails than the normal distribution); the Jarque Bera statistic reveals evidence of non-normality for both systematic and idiosyncratic volatilities. Since the descriptive results show that wheat return volatilities are negatively skewed and not normally distributed, therefore, the inferential statistics that is most appropriate must follow non-normal distributions (see Wilhelmsson, 2006). The alternatives available consist of the generalized error distribution (GED), the Student-t distribution, the Student-t distribution with fixed degree of freedom and GED with fixed parameter. All these non-normality procedures are conducted for each of the volatility models and the model selection criteria are used to determine the most appropriate models. Only results that are best fit in each of the techniques is reported in the report. Results of the unit root test are presented in Table 2. The estimations follow the NP test that allows for the inclusion of two structural breaks in the series. The NP test is based on two assumptions on the deterministic components. The first allows for the two breaks in the intercept of the data series, which we tagged model 1 (M1). The second allows for two structural breaks both in levels and in slope of trend of the series. It is named model 2 (M2). Therefore, the two models are specified differently to consider for the deterministic component. The models are specified as follows: is the polynomial lag operator that allows breaks to occur slowly over time (see Narayan et al., 2010). The procedure follows the innovative outlier framework and it allows for changes to the trend to occur gradually rather than been instantaneous. The assumption behind the framework is that the series reacts to shocks from the innovation process (i.e. a Moving Average representation of the shocks). ( )[ ] ( ) 1 * , 2 2 , 1 1 2 1 1 t t M t U D U D L t d ? + ? + + = ? ? ? ? ? ( )[ ] ( ) 2 * , 2 2 , 1 1 , 2 2 , 1 1 2 1 2 t t t t M t T D T D U D U D L t d ? + ? + ? + ? + + = ? ? ? ? ? ? ? Where ( ) ( )( ) . 2 , 1 ; 1 ; 1 , , , , , = ? ? ? = ? ? = ? i T t T t T D T t U D i g i g t i i g t i ? ? Also, Following the assumption on the deterministic component ( ) t d and stochastic component ( ) t ? of Ri t ( ) ( ) ( ) ( ) 3 * * 1 1 , 2 2 1 , 1 1 , 2 2 , 1 1 2 1 1 1 t R j t m j j t t t B t B R t M R t U D U D T D T D t ? ? ? ? ? ? ? ? ? ?? ? + ? + ? + ? + ? + ? + + + = ? = ? ? ? ? ( ) ( ) ( ) ( ) 4 * * * * * * * 1 1 , 2 2 1 , 1 1 1 , 2 2 1 , 1 1 , 2 2 , 1 1 2 1 1 2 t R j t m j j t t t t t B t B R t M R t T D T D U D U D T D T D t ? ? ? ? ? ? ? ? ? ? ? ?? ? + ? + ? + ? + ? + ? + ? + ? + + + = ? = ? ? ? ? ? ? Where ( ) ( ) . 2 , 1 ; 1 1 , . = + ? = = ? i T t T D i B t i B In this case, to test the unit root of null hypothesis of 1 = ? against the alternative hypothesis of . 1 ? ? The NP test suggests the use of t-statistics of ? ?obtained after equations ( 3) and ( 4) have been estimated. The break dates are selected using the sequential procedure proposed by the NP test and appropriate critical values as indicated in the work of Narayan et al (2010). In Table 2, the unit root test results are presented with the optimal break point dates for both volatility types. As presented in Table 2, the two types of return volatility series are non-stationary after accounting for structural breaks and thus, adequate cognizance should be taken to recognize these breaks when dealing with wheat returns volatility modeling. Expectedly, the break dates (TB1 and TB2) for the two volatilities considered are not far apart. The first break was experienced in 2015 for both considered volatility types. Correspondingly, the second break (TB2) appears during the 2018 trading bout. In this period, the wheat market witnessed tremendous negative sentiments, rising speculations and huge divestment and the volatility risks were rising against falling wheat price trajectories. # III. Wheat Return Volatility Estimates In this section, the paper makes use of different plausible models to estimate wheat return volatility. This is conducted by considering both systematic and idiosyncratic volatility sources and consequently, the paper compares the performance of the estimations by bearing in mind varying wheat portfolios, equal and value weighted volatility. Model selection criteria used for the selection of appropriate model of return volatility of wheat are Schwarz Information Criterion (SIC), Akaike Information Criterion (HIC) and HQC. The volatility results also present some post-estimation analyses using ARCH LM test to validate the presence of heteroscedasticity in the selected volatility estimates. The paper estimated the volatility of wheat returns through the symmetric and asymmetric models. The symmetric volatility models consist of the GARCH (1, 1) and GARCH in mean (GARCH-M (1, 1)), while the asymmetric volatility models are Threshold GARCH (TGARCH (1, 1)) and Exponential GARCH (EGARCH (1, 1)). A significant contribution of this paper as far as modeling of corn return volatility is concerned, is that it considers structural breaks. Apart from this, the volatility modeling approach adopted has made it possible to accommodate the time-varying conditional heteroscedasticity of wheat price return and also evaluate the mean-reverting property of the wheat return volatility. The mean and variance equations for the GARCH (1, 1) model are presented as follows: ( ) 5 , 2 2 , 1 1 1 t t t R t R t B B ? ? ? ? µ ? + + + ? + = ?( ) 7 2 2 1 1 1 2 2 1 0 t R t t R t B B ? ? ? ? ? ? ? ? ? + + + + + = ? As said earlier, the asymmetric volatility models considered are TGARCH (1, 1) and EGARCH (1, 1). The two models have their mean equation as shown in equation ( 5) and the variance equations are specified as follows: ( ) ( ) ( ) 8 2 1 2 1 2 1 2 1 2 1 2 ? ? ? ? ? + + + = t t t t t t In In ? ? ? ? ? ? ? ? µ ? The variance of the EGARCH model is specified in equation ( 8), while the variance of the TGARCH model is expressed as: ( ) 3 and 4 show the results of the several volatility models for both systematic and idiosyncratic volatility forms. The implication of the results is that, the variance process reverts to its mean slowly for all the models and irrespective of the volatility form. This is inferred from the addition of the ARCH and GARCH effects of the variance equations that are close to one, therefore indicating that the variance process reverts slowly although the systematic volatility form reverts quickly than the idiosyncratic one. The slow mean reverting process is an indication of high level of volatility persistence in the price of wheat. In this case, price of wheat with intense idiosyncratic volatility appear more persistent than that with systematic volatility. The findings are consistent with the descriptive statistics presented in Table 1. 9 1 2 1 2 1 2 2 1 1 0 2 ? ? ? ? + + + = t t t t t I ?? ? ? ? ? ? ? Where 1 1 = ? t I if 0 1 ? ? t Comparing the performance of the two volatility forms given the models, the GARCH (1, 1) model appears to produce a better fit over the GARCH in mean (GARCH-M (1, 1)) model for the symmetric volatility models. This is reached with the SIC value. This is not striking as such, as the inclusion of the coefficients on the standard deviation of the wheat price returns in the conditional mean equation, is statistically not significant and therefore, does not provide any useful information as to the volatility models (i.e. systematic and idiosyncratic models). Similarly, the estimates of TGARCH (1, 1) provide an inferior result when compared to the EGARCH (1, 1) for the case of asymmetric. In all, the EGARCH (1, 1) model offers a better fit when compare to the GARCH (1, 1) in the symmetric case. In addition, the results of the EGARCH model suggest that there are leverage effects in both volatility models -idiosyncratic and systematic volatility forms. This is inferred from the findings, as the variable measuring the leverage effects is negative for both return volatility forms. The implication therefore, is that negative shocks have tendency of reducing volatility more than positive shocks in the wheat market. It also show that investors in the wheat market react more to bad news, as bad news has immense potential of increasing volatility than good news. In the descriptive statistics, it is evident that there is presence of ARCH effects in the return volatility series (i.e. systematic and idiosyncratic volatility); thus, necessitating the estimation of the post-estimation diagnostic tests to ascertain if the volatility models have accommodated the effects. These is the reason why the ARCH tests is conducted using both F-test and chisquare distributed ( ) 2 nR test. The results show that in all the estimations the acceptance of the null hypothesis of no ARCH effects is appropriate. All the values are statistically not significant. Summarily, the findings show that with structural breaks in volatility series, the exponential GARCH (EGARCH (1, 1)) is superior to other GARCH variants considered in the paper. Hence, more appropriate to model volatility of wheat returns, more specifically in period of structural shifts. IV. # Concluding Remarks Modeling volatility of wheat returns provides crucial information to investors and actors, more particularly; it reveals the level of persistence in volatility risk in the price of wheat. In essence, variability in wheat prices implies significant losses (gains) in investments and therefore, decreases (increases) returns of investors in wheat prices. As a profit maximizing investor, with a risk averse investment interest, the incidence of persistent high volatility will impact on the diversification of investor's portfolio either to a less risky assets or to more volatile asset class. Therefore, testing for persistence in wheat returns volatility has major policy relevance for investors and investors in agricultural produces. The NP unit root test procedure shows that there are two structural breaks in wheat returns volatility. These occur in 2016 and 2018, respectively. These two seasonal shifts substantially affected wheat prices and consequently its volume of investment. The estimations show that there is persistence in the wheat returns volatility irrespective of volatility types. However, the idiosyncratic volatility type appears more persistent than systematic volatility. The results also show the evidence of leverage effects in both volatility types, and therefore, investors in wheat prices react to news differently. More importantly, the findings show that bad news has the possibility of increasing volatility in the returns of wheat prices than good news. Furthermore, relatively, the asymmetric models seem more appropriate in modeling stock return volatility than the symmetric approach. Particularly, the exponential GARCH (EGARCH) model produces the best fit and therefore, the paper proposes that the EGARCH should be considered when dealing with wheat return volatility modeling. In sum, the paper recommends the consideration of asymmetric effects as well as structural shifts when modeling wheat return volatility. 1Panel A: Summary StatisticsDetailsMeanMedianStdDevCoef.VSkewnessJBSVolew 0.02010.02030.01120.2783-0.10451.0123SVolvw 0.01570.01840.00830.3674-0.08271.0104IVolew0.01130.01460.00780.3106-0.05492.0112IVolvw0.07860.00730.00490.2984-0.03782.0062Panel B: Correlation StatisticsSVolewSVolvwIVolewIVolvwSVolew1SVolvw 0.80161IVolew0.84390.55331IVolvw0.71550.79210.73091Panel C: Autocorrelation TableSVolewSVolvwIVolewIVolvw1 ?0.5240.4570.7230.689?30.4460.3430.6820.622?60.2080.1980.5140.595?90.1950.1240.4830.47912 ?0.1830.1530.430.374Source: Author's computation and compilation 2?2 t=?0+?1 ?2 ? 1 t+?2?2 ? 1 t;?0?, 0?1?, 0?2?0( ) 6TB i( i=Where ) 2 , 1 represented the selected breaks (see 1 , = t i B if i TB t ? and zero otherwise;mean shows the effect of the conditional variance in the mean equation, and therefore, the mean equation is modified by including the conditional variance the returnTable 2). Note thatt ? =?it eand t e is standardmodel:normally distributed with unit variance. The GARCH in 3VariableAsymmetric ModelsSymmetric ModelsValue Weighted EstimatesEGARCH (1, 1)TGARCH (1, 1)GARCH (1,1)GARCH-M (1, 1)Mean EquationAlpha0.0041 (0.8322)0.0005 (0.5722)0.0002 (0.4276)-0.0002 (-0.3081)Beta-0.0089 (-1.6149)-0.0208 (-1.9803)-0.0112 (-1.2102)-0.0039 (-1.0527)Delta3.29*10^7 (3.2984)**0.0008 (3.2097)**0.0001 (2.7812)**0.0003 (2.8133)**Theta0.0003 (0.4282)0.0003 (0.4435)0.0003 (0.4219)0.0004 (0.2172)Conditional Variance---0.0259 (1.0056)Variance EquationAlpha-0.2064 (-8.1508)*4.29*10^5 (3.8923)* 4.98*10^5 (3.2091)* 4.88*10^5 (3.8730)*Beta-0.0592 (6.9831)*0.0278 (10.5470)*0.0309 (12.7760)*Lamda-0.8217 (9.0023)*0.7437 (8.6727)*0.8014 (10.0598)*Phile-0.0049 (0.7638)--Rho0.1472 (10.2086)*---Tau-0.0142 (-2.6591)**---Sigma0.7739 (5.4028)*---Diagnostic StatisticsAIC-4.9935-4.9320-4.9109-4.9106SIC-4.8931-4.8856-4.9086-4.9083HQC-4.8826-4.8811-4.9101-4.9078ARCH LM Test (7)F-Test1.80691.55721.72091.7091nR^21.86096.09825.80447.2206No of Observation884884884884Equal Weighted EstimatesEGARCH (1, 1)TGARCH (1, 1)GARCH (1,1)GARCH-M (1, 1)Mean EquationAlpha0.0027 (0.7062)0.0004 (0.2092)0.0002 (0.4276)-0.0002 (-0.3081)Beta-0.0089 (-1.7140)-0.0318 (-1.2803)-0.0112 (-1.2102)-0.0039 (-1.0527)Delta2.42*10^6 (3.5491)**0.0006 (2.9473)**0.0001 (2.7812)**0.0003 (2.8133)**Theta0.0002 (0.5009)0.0008 (0.3851)0.0003 (0.4219)0.0004 (0.2172)CVariance---0.0259 (1.0056)Variance EquationAlpha-0.1424 (-8.2398)*3.11*10^6 (3.0243)* 3.88*10^6 (4.9501)* 4.32*10^6 (3.8609)*Beta-0.0616 (5.1131)*0.0678 (9.1573)*0.0579 (10.3860)*Lamda-0.5231 (7.2323)*0.7238 (7.0085)*0.8009 (9.1738)*Phile-0.0052 (0.6447)--Rho0.2097 (9.8160)*---Tau-0.0112 (-3.0191)**---Sigma0.6506 (3.9988)*--- 4Testing for Volatility Persistence in Wheat Prices: Is Idiosyncratic Source Matters?VariableAsymmetric ModelsSymmetric ModelsYear 2019Value Weighted EstimatesEGARCH (1, 1)TGARCH (1, 1)GARCH (1,1)GARCH-M (1, 1)35Mean Equation Alpha Beta Delta Theta Conditional Variance Variance Equation Alpha-0.0001 (-0.7082) 0.0375 (3.1091)* 0.0007 (2.2004)** 0.0003 (0.5089) --0.2117 (-10.1218)*-0.0002 (-0.4278) 0.0402 (3.0803)* 0.0005 (2.0192)** 0.0004 (0.7058) -5.28*10^5 (5.2203)*4.02*10^6 (0.2246) 0.0204 (3.0214)* 0.0007 (2.8503)** 0.0006 (0.6739) -4.58*10^5 (6.6201)*0.0007 (1.1031) 0.0339 (2.8793)** 0.0014 (2.0103)** 0.0004 (0.6544) -0.0518 (-1.1576) 4.37*10^5 (5.9030)*Volume XIX Issue II Version IBeta Lamda--0.0849 (4.1991)* 0.7907 (9.1241)*0.0583 (12.6220)* 0.8828 (9.8932)*0.0679 (15.3260)* 0.8812 (12.1438)*( ) GPhile Rho Tau Sigma Diagnostic Statistics AIC SIC HQC ARCH LM Test F-Test nR^2 No of Observation Equal Weighted Estimates-0.1784 (7.0056)* -0.0125 (-3.6071)* 0.5639 (3.4918)* -4.9735 -4.9383 -4.9306 0.0372 0.0369 884 EGARCH (1, 1)0.0209 (3.7855)* ----4.9180 -4.8836 -4.8902 0.2682 0.2676 884 TGARCH (1, 1)-----4.9310 -4.9196 -4.9275 0.2147 0.2134 884 GARCH (1,1)-----4.9192 -4.9190 -4.9107 0.3421 0.3586 884 GARCH M (1, 1)Global Journal of Management and Business ResearchMean EquationAlpha-0.0002 (-0.6983)-0.0003 (-0.5308)4.02*10^6 (0.2246)0.0007 (1.1031)Beta0.0328 (3.0119)*0.0396 (3.0874)*0.0204 (3.0214)*0.0339 (2.8793)**Delta0.0006 (2.3204)**0.0004 (2.1196)**0.0007 (2.8503)**0.0014 (2.0103)**Theta0.0002 (0.6129)0.0003 (0.8858)0.0006 (0.6739)0.0004 (0.6544)© 2019 Global JournalsNote: *, ** indicate 1% and 5% levels of significance. © 2019 Global Journals * Does inflation has an impact on stock returns and volatility? Evidence from Nigeria and Ghana URAliyu International Conference on Economics and Finance Research IPEDR 4 2011. 2011 IACSIT Press * The cross section of volatility and expected returns AAng RJHodrick YXing XZhang Journal of Finance 61 1 2006 * Aggregate idiosyncratic risk and market returns TGBali NCakici Journal of Investment Management 4 4 2006 * Is there a trend in idiosyncratic volatility? Paper presented at the AFA 2009 San Francisco meetings GBekaert RJHodrick XZhang 2009 San Francisco * Aggregate idiosyncratic volatility GBekaert RJHodrick X&zhang 2010 Columbia University Unpublished Working Paper * The idiosyncratic volatility puzzle: Time trend or speculative episodes? MWBrandt ABrav JGraham AKumar Review of Financial Studies 23 2 2009 * Is idiosyncratic volatility prices? The international evidence PBrockman MGSchutte W&yu 2010 Michigan Tech University * The time series behavior and pricing of idiosyncratic volatility: Evidence from 1926 to 1962. Working Paper series PBrockman Yan XS 2008 University of Missouri -Columbia * Have individual stocks become more volatile? An empirical exploration of idiosyncratic risk JYCampbell MLettau BGMalkiel Y&xu Journal of Finance 56 2001 * The econometrics of financial markets JYCampbell AWLo CAMackinlay 1997 Princeton University Press Princeton -New Jersey * Are beta, firm size, liquidity and idiosyncratic volatility related to stock returns? Australian Evidence LClayton MDempsey MVeeraraghavan Working Paper Series 2006 * Idiosyncratic risk and Australian equity returns MDempsey MEDrew MVeeraraghavan Working Paper series 2001 Griffin University * Equity premium: Does it exists? Evidence from Germany and United Kingdom MEDrew MMallin TNaughton MVeeraraghavan Studies in Economics and Finance 23 2 2006 * Systematic factors and returns on equities in the Nigerian Securities Market CAEmenuga 1994 Nigeria Department of Economics, University of Ibadan Unpublished PhD Thesis * Expected stock returns and volatility KFrench GWSchwert RStambaugh Journal of Financial Economics 19 1987 * Risk and the cross section of expected stock returns FFu Journal of Financial Economics 91 2009 * Investor sentiment and idiosyncratic risk puzzle XGao JYu Y&yuan 2010 Hong Kong University of Hong Kong Working paper series * How to understand high food prices CLGilbert Journal of Agricultural Economics 61 2010 * Idiosyncratic risk matters! AGoyal PSanta-Clara Journal of Finance 58 2003 * Idiosyncratic risk and creative destruction in Japan YHamao JMei YXu 2003 Unpublished Working Paper, NBER * Modelling stock returns volatility in Nigeria using GARCH models EOKalu 2008 Nigeria Department of Banking and Finance, University of Nigeria, Enugu Campus, Enugu State * RLiu PKNarayan A new structural break unit root test based on a GARCH model 2010 * The risk return tradeoff in the long run CLundblad Journal of Financial Economics 85 2007 * Idiosyncratic risk and security returns BGMalkiel YXu 2006 Princeton University & The University of Texas at Dallas * Food price volatility in sub-Saharan Africa: Has it really increased? NMinot Food Poicy 45 2014 * SAMustapha Asset Volatility and Pricing in the Nigerian Stock Market Benin City, Nigeria 2015 Department of Economics and Statistics, University of Benin PhD Thesis * Stock (Mis) Pricing and Investment Dynamics in Africa" Evidence from African Equities SAMustapha 2017 African Development Bank Headquarters Cote D'Ivoire, Abidjan African Development Bank Working Paper Series * A new unit root test with two structural breaks in level and slope at unknown time PKNarayan SPopp Journal of Applied Statistics 37 9 2010 * Does idiosyncratic risk matter? Evidence from the Philippine Stock Market GVNartea BDWard Asian Journal of Business and Accounting 2 1&2 2009 * NSE factbook Nigerian Stock Exchange 2012. 2012 Edition * Why did individual stocks become more volatile? SXWei CZhang Journal of Business 79 1 2005 * GARCH forecasting performance under different distribution assumptions AWilhelmsson Journal of Forecasting 25 2006