PRICE GENERATING PROCESS AND VOLATILITY IN THE NIGERIAN AGRICULTURAL COMMODITIES MARKET

The study examined the price generating process and volatility of Nigerian agricultural commodities market using secondary data for price series on meat, cereals, sugar, dairy and food for the period of January 1990 to February 2014. The data were analysed using both descriptive and inferential statistics. The descriptive statistics used the coefficient of variation while the inferential statistics used the linear Gaussian State-Space (SS) model. The results of the descriptive statistics showed that the coefficients of variation for cereals (39.88 %), food (32.65 %) and dairy price (43.08 %) were respectively higher during the overall time period (January 1990 to February 2014) than during the first (January 1990 to January 2002) and second (February 2002 to February 2014) subtime periods. The results of the inferential statistics showed that authoregressive moving average (ARMA) model is the most selected Nigeria agricultural commodity price generating model for the time periods, and that the final states of their unobserved component of cereals, meat, dairy and sugar prices were 6317.86, 2.06, 34.45 and 10.24 respectively. The prices of cereals, meat, dairy, sugar and food in general were generated and most fitted by the ARMA in Nigeria. Also the prices have been on the increase and have exhibited high volatility. The volatility, process and the determinants of the Nigerian food commodities prices can best be described by the simple (ARMA) model. Contact us for full article. Email: info@agrosciencejournal.com


Introduction
In a market-oriented economy with perfect information, a key variable in the food system is the price of the commodities (White & Dawson, 2005;Gortz & Weber, 1986cited in Kuwornu, Mensah-Bonsu, & Ibrahim, 2011).Prices of agricultural commodities in Nigeria have been on the increase over the years.Food price index rose by 23% in 2006 and then increased to 37% for the period between December 2006 and December 2007 while food prices rose by 55% from June 2007 to February 2008 (Food and Agriculture Organisation, FAO, 2008).These swings in agricultural commodity price cannot be attributed to international trade policies, the emergence of bio-fuels, increasing urbanization and population growth only (Abbot, Hurt, & Wallace 2008;Benson, Mugarura, & Wanda 2008;Mitchell, 2008) without recourse for the unobservable structural changes.Various studies have used different models to forecast food price and food prices volatility without concern for the time-variant parameters in such models (Kumornu et al., 2011;Gilbert, 2010;Ghysels, Santa-Clara, & Valkanov, 2006).The data on agricultural commodity prices are uncertain, are aggregated estimates rather than perfect measures, and are not easily observable, necessitating the use of proxies.Even the estimates from them are not only imperfect measures, they differ substantially among themselves and from the commodities they explain with respect to some unobservable price indicators while some contain coefficients are inherently time-varying, making economic relationships potentially unstable.Rather than the descriptive models which do not estimate directly the causal relationship between price volatility and its drivers (Clapp, 2009;Gilbert & Morgan, 2010;Wright, 2011;Anderson & Nelgen, 2012;Nissanke, 2012), mathematical modelling such as partial equilibrium models (Miao, Yu, Bao, & Tang, 2011;Babcock, 2012) and empirical models which use reduced-form (Balcombe, 2009), cointegration analysis (Pietola, Liu, & Robles, 2010), and different specifications of the GARCH(1,1) model (Zheng, Kinnucan, & Thompson, 2008;Roach, 2010;Hayo, Kutan, & Neuenkirch., 2012;Karali & Power, 2013), the nature of agricultural commodity price variability, measurement of such variability of agricultural product prices, and the effect of other unobservable impacting factors within the series are important (Ghysels & Valkanov, 2006;Mittnik & Zadrozny, 2005;Ghysels et al, 2006;Ghysels & Wright, 2008;Clements & Galvao, 2008;Marcellino & Schumacher, 2007;Schumacher & Breitung, 2008).This is in view to capturing the time-varying coefficient and extracting the unobserved components from observed series.The study, therefore, examined the price volatility in the Nigerian agricultural commodities market using the state space approach.To achieve this, the study examined the price volatility in the Nigeria agricultural commodities market, examined the time-varying variability model that best explain the price volatility, and examined the effect of other unobservable impacting factors on the price volatility in such market.This study differs in analytical approach from existing literature on agricultural commodity price volatility in general and of such studies in Nigeria in particular.The study used the state space model to capture the time-varying coefficient and in the extraction of unobserved components from observed series (Wang, 2003;Harvey, 1984Harvey, , 1989)).

Methodology
The study used data obtained from various publications of the Central Bank of Nigeria, Nigeria Statistical Bulletin, Food and Agriculture Organisation (FAO), World Trade Organisation (WTO) and the vintages of the World Bank database for price time series on meat, cereals, sugar, dairy and aggregate food for the period of January 1990 to February 2014.The entire period was divided into two sub-periods.These are the first period (January 1990 to January 2002) and the second period (February 2002to February 2014).The data were analysed using both descriptive and inferential statistics taking cue from Piot-Lepetit (2011).The descriptive statistics used the coefficient of variation while the inferential statistics fitted the Autoregressive Moving Average (ARMA), Autoregressive Conditional Heteroskedasticity (ARCH) model, the Generalised Autoregressive Conditional Heteroskedasticity (GARCH) model, the Exponential Generalised Autoregressive Conditional Heteroskedasticity (EGARCH) model and the Asymmetric Power Autoregressive Conditional Heteroskedasticity (APARCH) model version to test for the best time-varying variability model that explains the price volatility in the Nigeria agricultural commodities market ranked according to three information criteria, the Schwarz Information Criterion (SIC), Akaike Information Criterion (AIC) and the Hannan-Quinn Information Criterion (HQIC).The criteria were also used to select the appropriate lag.The data were first transformed to render them stationary by taking the first difference.The ARMA, ARCH, GARCH, EGARCH and APARCH used were ARMA (!, 1), ARCH (1), GARCH (1, 1), EGARCH (1, 1) and APARCH (1, 1), and given respectively as: Where autoregression in its squared residuals has an order of 1 Where autoregression in its squared residuals has an order of 1, and the moving average component has an order of 1.
Where  −1 2 is the ARCH term providing information about the volatility from previous period,  −1 2 is the GARCH term measuring the last forecast variance while α, β and  are parameters to be estimated from the price series for the commodities.The model with the smallest value based on the criteria was then chosen as the best-fit model.The linear Gaussian multivariate state-space (SS) model for the discrete-time 5-variate observable stochastic process was then used on the identified generating process.The state space equations, fitted into the ARMA (1, 1) models, for the five agricultural commodities were given as: Observation Equation for price of cereals   =  2  −1 + exp( 3 ) +   ,   ~(0,   ) State Equation for price of cereals   =  −1   =   +  1   +   ,   ~(0,   ) Observation Equation for price of aggregate food Observation Equation for price of meat Observation Equation for price of dairy State Equation for price of dairy   =  −1   =   +  1   +   ,   ~(0,   ) Observation Equation for price of sugar   =  2  −1 + exp( 3 ) +   ,   ~(0,   ) State Equation for price of sugar   =  −1 (5) Where the   ,   ,   ,   , and   are the measured price variables,   ,   ,   ,   , and   are the level component analogous to the intercept in the classical regression model,  1 ,  2 ,  3 ,  1 ,  2 ,  3 ,  1 ,  2 ,  3 ,  1 ,  2 ,  3 ,  1 ,  2 , and  3 are parameters measuring slope as in classical regression model while   ,   ,   ,   ,   ,   ,   ,   ,   , and   are measures of the heteroschedastic variance called hyperparameters of the model.

Results and Discussion
Table 1 shows the Dickey-Fuller (DF) and Augmented Dickey-Fuller (ADF) statistics for the variables.The DF and ADF statistic values for the variables in their first difference form were lower than the critical values at 1%, 5% and 10%, so that the null hypothesis that it has a unit root at first difference was rejected.However, the DF and ADF statistic values for the variables at level form were greater than the critical values at 1%, 5% and 10%, so that the null hypothesis that it has a unit root at level form was not rejected.Augmented Dickey-Fuller (ADF) test for the variables indicate that all variables are non-stationary at levels but stationary at first difference.This implies that the results of the econometric analysis at the level of the series may not be suitable for policy making.2 shows the estimated coefficient of variation for prices of food items in Nigeria.The results show that for aggregate food price, the dispersion was 32.65% for the entire period and 11.47% and 30.26% respectively during the first (January 1990 to January 2002) and second (February 2002 to February 2014) sub-time periods.In the second sub-time period (February 2002 to February 2014), sugar price was the most dispersed (45.23%), followed by the price of dairy products (34.45%) while meat price had the least (23.11%).The results also showed that the coefficients of variation for cereals price (39.88%), aggregate food price (32.65%) and dairy price (43.08%) were respectively higher during the overall time period (January 1990 to February 2014) than during the first (January 1990 to January 2002) and second (February 2002 to February 2014) sub-time periods while the coefficients of variation for meat price (21.40%) and sugar price (43.89%) were respectively higher only during the overall time period (January 1990 to February 2014) than during the first (January 1990 to January 2002) sub-time period that corresponds to the possible price process existing before the recent price increase.When comparing coefficients of variation values between the sub-time periods 1990-2002 and 2002-2014, the values are higher for the second (February 2002 to February 2014) sub-time period for all food items than the first (January 1990 to January 2002) sub-time period.The highest increase is shown for sugar price from 23.48% to 45.23%, followed by dairy price from 13.69% to 34.45%.It may suggest that the Nigerian agricultural commodity prices have experienced higher variability between 2002 and 2014 over the period.This is not unexpected as agricultural product markets experience not only price fluctuations from year to year but also volatile prices because of the relatively unstable conditions of supply and demand and the low elasticities of demand and supply (Schnepf, 2005;Meyers & Meyer, 2009;Robles, Torero, & von Braun, 2009;2010;2009;Christiaensen, 2009;Gilbert, 2010;FAO, 2008;Trostle, 2008).However, for an importing country like Nigeria, increasing prices would result in rising import bills and high prices with the attendant impact on the ability of poor consumers to purchase necessary food items.3 presents the model for food items prices and the selection criteria.The results show that cereals price had 6.52 AIC criterion values for the ARMA (1, 1) model as the smallest for the overall time series, and 5.32 and 7.06 respectively for the sub-time periods 1990-2002 and 2002-2014.This implies that cereals price model in Nigeria agricultural commodities market is the ARMA (1, 1) for the overall time series and the two sub-time period series, and that the future volatility of the cereals price in Nigeria is the sum of the current variance and the weighted one-period lag autoregressive moving average of the residuals.. Similarly, the model for aggregate food price is ARMA (1, 1) with the smallest AIC criteria values of 5.360 for the overall time series and 4.33 and 5.84 respectively for the sub-time periods of 1990-2002 and 2002-2014.This is also true for meat price model with the smallest AIC criterion values of 5.40 for the overall time series and 5.26 and 5.48 respectively for the sub-time periods of 1990-2002 and 2002-2014.The results are also true for dairy and sugar prices.Thus, the ARMA (1, 1) model is most selected model during the overall time periods of January 1990-February 2014.This implies that the today's timevarying agricultural commodities heteroscedastic prices variance in Nigeria is a function of the one-time lag autoregressive moving average of their residuals.This implies that, regarding the existence of a common price process in Nigeria, ARMA (1, 1) explains the price process for aggregate food in general, and the price process for cereals, dairy, sugar and meat in particular.The volatility in agricultural commodities prices in Nigeria is the result of current variability and the weighted one-period lag of their residuals.4 shows the parameter estimates of the state space model.The results show that most of the coefficients were significant at the 1% level and, at convergence, the maximum of the log likelihood was-8.16×〖10〗^9.The coefficients -0.8924, 0.0415, and 0.0408 are the log variance of the error term for state equation of the prices of cereals, sugar and aggregate food.The respective variances of the errors were 0.4097, 1.0424, and 1.0416.These imply that the volatility in price of Nigeria agricultural commodities is highest in sugar, followed by aggregate food and least in cereals.The coefficients -0.999, -0.2051, 0.1435, 0.2811 and 0.1519 are the respective marginal effects of past price state of cereals, dairy, sugar, meat and aggregate food.These imply that a unit increase in the past price state of cereals, dairy, sugar, meat and aggregate food would increase the current or future price of sugar, meat and aggregate food by N 0.14, N 0.28 and N 0.15 respectively but decrease future price of cereals and dairy by about N 1.00 and N 0.21 respectively.That the values are not zero and statistically different from zero further implies that the state variance for the slope components change with time.The maximum likelihood estimates of the level at t=1 are respectively 6317.86, 34.45, 10.24, and 2.06 for cereals, dairy, sugar and meat.The final states of seasonal and cyclical unobserved components for cereals, food aggregate, meat, dairy and sugar were respectively 22472.48, 5.14, 1704.98 240.05 and 247.06. The values 6317.86, 2.06, 34.45 and 10.24, shown in the Table are the one-step ahead predicted value for the first out-of-sample period for cereals, meat, dairy and sugar price respectively.

Conclusion
Agricultural commodity price volatility requires in-depth knowledge of the commodity market prices and the tools capable of facilitating their measurement.Some econometric models can be and are used for simulation or policy analysis but not without consideration to the time-variant parameters.The study fitted the Autoregressive Moving Average (ARMA), Autoregressive Conditional Heteroskedasticity (ARCH) model, the Generalised Autoregressive Conditional Heteroskedasticity (GARCH) model, the Exponential Generalised Autoregressive Conditional Heteroskedasticity (EGARCH) model and the Asymmetric Power Autoregressive Conditional Heteroskedasticity (APARCH) model version to test for the best time-varying variability model that explains the price volatility in the Nigeria agricultural commodities market ranked according to three information criteria, the Schwarz Information Criterion (SIC), Akaike Information Criterion (AIC) and the Hannan-Quinn Information Criterion (HQIC) after a first difference transformation of the price series.The criteria were also used to select the appropriate lag.The prices of cereals, meat, dairy, sugar and aggregate food show great volatility in the period 1990-2014 with a unit increase in the past price state of cereals, dairy, sugar, meat and aggregate food increasing the future price of sugar, meat and aggregate food by N 0.14, N 0.28 and N 0.15 respectively but decreasing that of cereals and dairy by about N 1.00 and N 0.21 respectively.The estimates of the weights (slope) are not zero and statistically different from zero implies that the state variance for the slope components change with time.The Nigerian cereals, meat, dairy, sugar and aggregate food prices have experienced high variability over the period, and such volatility, price-generating process and the determinants of these Nigerian commodities prices can best be described by the simple ARMA model with timevariant hyperparameters.The volatility in agricultural commodities prices in Nigeria is the result of current variability and the weighted one-period lag of their respective residuals.

Table 2 . Estimated Coefficient of Variation for Agricultural Commodities Prices in
Computed from 1990-2014 Food and Agriculture Organisation (FAO) (2014), World Bank commodity Price Data (2014), and World Trade Organisation (WTO) price series, CP is cereals price, AFP is aggregate food price, MP is meat price, DP is dairy price and SP is sugar price Table

Table 4 . Parameter Estimates of the State Space Model and their Associated Errors.
Computed from 1990-2014 Food and Agriculture Organisation (FAO) (2014), World Bank commodity Price Data (2014), and World Trade Organisation (WTO) price series, ***Significant at 1% level, **Significant at 5% level Table