Forecasting agricultural price volatility of some export crops in Egypt using ARIMA/GARCH model

Purpose – This study focuses on forecasting the price of the most important export crops of vegetables and fruits in Egypt from 2016 to 2030. Design/methodology/approach – Thestudyappliedgeneralizedautoregressiveconditionalheteroskedasticity (GARCH) model and autoregressive integrated moving average (ARIMA) model. Findings – TheresultsshowthatARIMA(1,1,1),ARIMA(2.1,2),ARIMA(1,1,0),ARIMA(1,1,2),ARIMA(0,1,0) and ARIMA (1,1,1) are the most appropriate fitted models to evaluate the volatility of price of green beans, tomatoes, onions, oranges, grapes and strawberries, respectively. The results also revealed the presence of ARCH effect only in the case of Potatoes, hence it is suggested that the GARCH approach be used instead. The GARCH (1,1) is found to be a better model in forecasting price of potatoes. Originality/value – Thestudyoffoodpricevolatilityindevelopingcountriesisessential,sinceasignificantshare of household budgets is spent on food in these economies, so forecasting agricultural prices is a substantial requirement for drawing up many economic plans in the fields of agricultural production, consumption, marketing and trade.


Introduction
Monitoring the volatility commodity prices can play a key role in a country's overall economic performance.Therefore, the commodity price forecast helps decision-makers to develop appropriate economic policies and strategies that are compatible with the future changes (Bhardwaj et al., 2014).
Commodity prices, especially the prices of agricultural commodities, are subject to high degrees of volatility; therefore, the predictable price decreases the negative impact of uncertainty, in other words, decrease producer aversion to risk (Sedghy et al., 2016).
In general, fluctuations in prices of agricultural commodity occur primarily from shocks of the supply side.These disturbances, combined with the short-term demand and supply elasticity coefficients, lead to sharp instability of the price (Sendhil et al., 2014;Piot-Lepetit and M'Barek, 2011), which lead both farmers and consumers to uncertainty and risk and so volatility of commodity prices has been studied (Apergis and Rezitis,2011;Ahmed and Serra, 2015).
More critical is the analysis of food price fluctuations in developing countries, since a significant share of household income is spent on food in these economies, so uncertainty about food prices has a direct effect on welfare.Instability of food price is particularly affecting low income people, small agricultural producers who depend on crop sales for a significant portion of their income (Ceballos et al., 2017;Sedghy et al., 2016).
The research problem is identified the most suitable models to evaluate the volatility of the most important Egyptian export crops of vegetables and fruits, so this study aims to forecast agricultural prices for green beans, potatoes, tomatoes, onions, oranges, grapes and strawberries using the ARIMA or GARCH approach.

Literature review
Various empirical studies have analyzed measuring and forecasting agricultural price volatility of different products using ARIMA-GARCH models.Felis and Garrido (2015) studied price volatility in Spain of fresh fruits and vegetables, using multivariate GARCH model.In the Spanish tomato marketing chain, Sidhoum and Serra (2016) applied the MGARCH model to test spillovers of uncertainty.Lama et al. (2015) analyzed the price volatility in agricultural market, especially for three main commodities: the international price of edible oils, the international price of cotton and the domestic price of edible oils depending on ARIMA model, GARCH model and EGARCH model.Ramirez and Fadiga (2003) and Sanjuan-Lopez and Dawson (2017) studied the volatility price of soybeans and wheat in the United States futures markets through the GARCH model.Sekhar et al. (2017) applied GARCH and EGARCH to examine volatility in agricultural price in India, while Guerrero et al. (2017) used these models to analyze agricultural price volatility in both Mexican agricultural market and international agricultural market.
For the period from January 1990 to February 2014, Ojogho and Egware (2015) studied the price volatility of sugar, meat, grain, dairy and gross food in the Nigeria.Also Kamu et al. (2010), Onour and Sergi (2011), Sukati (2013), Bhardwaj et al. (2014), Sendhil et al. (2014), Sedghy et al. (2016), Solanki and Sharma (2016) and Lama et al. (2016) applied ARIMA-GARCH model to analyze and forecast price volatility of some selected agricultural products.Yang et al. (2001) analyzed the impact of the liberalization of agricultural sector on the volatility of commodity price through GARCH application; results of the study showed that agricultural liberalization policy increases the market volatility for some grain crops.Siami and Hudson (2017) used an AR-EGARCH model to analyze the interdependent relationship between futures prices of crude oil, international prices of agricultural products and exchange rate.
Other empirical studies focused on measuring and forecasting price volatility of agricultural products using other econometric models.Corrêa et al. (2016) used a new causal forecasting approach, called (WARIMAX-GARCH) method; Benavides (2009) used an option implied approaches, GARCH model, a multivariate ARCH and composite approaches to predict futures prices of some cereal.Li et al. (2017) proved that the two-state normal mixture (NM)-GARCH approach is more accurate than the GARCH model in modeling agricultural price volatility.Jin and Frechette (2004) confirmed that the results of fractional integration (FI) GARCH model perform significantly better than traditional normal GARCH.Anggraeni et al. (2017) applied Vector Autoregressive model and an ARIMAX model to predict the price volatility of rice in Indonesia.Xiong et al. (2015) predict some of agricultural commodity prices in China with VECM-MSVR model, which is a combination of the linear and nonlinear methods.On the other hand Zou et al. (2007) ensured that the artificial neural network (ANN) model is the best model for forecasting the future price of Chinese cereal.While Haofei et al. (2007) used a multi-stage optimization approach (MSOA) to predict cereal price in China.Xiong et al. (2018) applied a hybrid STL and ELM methodology to predict the Chinese vegetable price and to evaluate the volatility of it in the short and long run.
The main contribution of this paper is that the published works regarding price volatility of agricultural prices in Egypt are so little.El-Rasoul and Tolba (2018), analyzed the price volatility in the Egyptian food markets to find the major macroeconomic factors that influence it during the period 1995-2015 through the exponential function model.The results revealed that there is some link between the seasonality of retail prices and the wholesale prices of the commodities studied.Abdelfattah et al. (2015) studied price volatility in the Egyptian markets of surge crops from 1998 to 2013 using ARIMA model.Abdel-Radi and Ahmed (2018) aims to study the price volatility of the Egyptian wheat market during the period (2008)(2009)(2010)(2011)(2012)(2013) depending on BEKK-GARCH model, and the study also examined how the shocks in the international wheat market influence the Egyptian domestic market.

The data
The study employs observations for producer prices of the most important Egyptian export crops of vegetables and fruits, including green beans, potatoes, tomatoes, onions, oranges, grapes and strawberries.All the variables are in logarithmic form.The study period 1967: 2015 except strawberries the available data only from 1991 to 2015.The main source of data was Food and Agriculture Organization (FAO) database.
3.2 Methodology 3.2.1 ARIMA model.The ARIMA is among the most common models for the study of time series forecasting.In this model, the future value of a variable is supposed to be a linear combination of past values and past errors (Guerard, 2013;Khashei and Hajirahimi, 2017;Badmus and Ariyo, 2011).
The ARIMA methodology is performed in four stages or steps, including: identification, estimation, diagnostic checking and forecasting (Kamu et al., 2010).
ARCH models permit the shocks in more recent periods to have a positive effect on current volatility; on other hand the GARCH models assume that current volatility is influenced not only by past shocks, but also by past volatilities (O'Connor and Keane, 2011;Engle, 2001Engle, , 2002;;Bauwens et al., 2006).

Results and discussions
4.1 ARIMA model 4.1.1Model identification.The stationary of variables was tested by augmented dickey fuller (ADF) test; Table 1 shows that all the variables have unit roots in levels and are stationary in first-differences as all values of ADF test are insignificant in levels, but significant at 1% level in both only intercept case, and trend and intercept case, which mean series become stationary.
Table 3 shows the parameter estimates of the ARIMA fitted model.The results show that most of the coefficients were significant at the 1% level.Lagged variables are important factors for producer decisions; Table 3 also shows that the producer response to lagged prices is statistically significant for all selected crops except green beans.

Price volatility of some export crops
4.1.3Diagnostic checking.There are no spikes outside the insignificant zone for both autocorrelation function and partial autocorrelation function residuals squared plot, we can conclude that residuals are white noise; hence, our ARIMA models are fitted.See Figure A1-A6 in appendix.
4.2 ARCH-GARCH model 4.2.1 Testing of ARCH effect.A fundamental assumption of the Box-Jenkins method is that the residuals remain constant over time (Jordaan et al., 2007).Table 4 reveals the results of the ARCH-LM tests, the results of the test revealed the presence of ARCH effect only in potatoes crop case; hence we need to apply the GARCH approach.Keep in mind that the volatility in the agricultural prices of all the other crops remains constant over time.4.2.2Applying the GARCH approaches.In this study both akaike information criterion (AIC) and bayesian information criterion (BIC) were employed to select an appropriate GARCH model for potatoes.Table 5 displays the summaries of the AIC and BIC of different GARCH models.Therefore, GARCH (1,1) model is the best volatility models for the prices of potatoes.Table 6 shows estimation results of GARCH (1,1) model for potatoes price.
4.2.3Model diagnostics GARCH (1,1) model for potatoes price.The ARCH-LM test was 1.251,189 under chi-square distribution for one lag difference of residuals squared, and the null hypothesis was not rejected.On the other hand, F-statistic was 1.230,710 and the test also not rejected the null hypothesis at the same condition.The results of the test indicated that the ARCH effect in potatoes' price series was no longer present.
Also, there are no spikes outside the insignificant zone for both autocorrelation function and partial autocorrelation function plot of the residuals squared, and we can conclude that residuals are white noise; hence, our GARCH (1,1) model is fitted.See Figure A7 in appendix.

Forecasting values of the model's variables
The forecasted value for producer price of some export crops is given in Table 7.As seen from the table, all prices will still be increasing in the forecasted period from 2016 to 2030.Forecasted value for green beans will increase from 2589.17 pound/ton in 2016-9752.392pound/ton in 2030; forecasted value for potatoes will increase from 2399.156 pound/ton in 2016-8928.388pound/ton in 2030; forecasted value for tomatoes will increase from 1556.775 pound/ton in 2016-5052.167pound/ton in 2030; forecasted value for onion will increase from 1119.612 pound/ton in 2016-4103.752pound/ton in 2030; forecasted value for oranges will increase from 1211.640 pound/ton in 2016-4621.151pound/ton in 2030; We also note that the growth rate of forecasted prices for oranges, green beans, potatoes and onions, respectively is more than the growth rate of other selected crops, so it is expected during the forecast period the production and exports of oranges, green beans, potatoes and onions will increase at increasing rate, and will be more attractive for agricultural producers and exporters compared to tomatoes, grapes and strawberries, but this result depend on some facts which are: (1) The rise in the prices of food commodities is reflected in the cropping pattern and the orientation of agricultural resources toward the production of high-priced food crops.(FAO.1987)

Price volatility of some export crops
(2) The rewarding prices stimulate agricultural investment which is the main driver for sustainable agricultural development, where increasing investment means adding new production projects that lead to absorption a number of unemployed workers, in addition to increasing production, exports, then improving the trade balance.(Syed and Miyazako, 2013) (3) Egypt already has comparative advantage of the selected crops in many foreign markets.
(4) There are several macroeconomic factors affecting the volatility of food commodity prices that must be taken into consideration such as: productivity, climate change, (5) Future policy options will concentrate on increasing the efficiency of water usage and keeping the sustainability of both land and water.(Abdou Abdelaal and Thilmany, 2019) Then forecasting agricultural prices is an essential requirement for decision-makers to develop suitable agricultural policies in both short and long term, in the fields of production, consumption, marketing and trade (Lama et al., 2015;Solanki and Sharma, 2016).Furthermore, it is also relevant for the private sector to study the differences in price volatility among products for production and marketing decision (Heifner and Kinoshita, 1994;Jordaan et al., 2007).On the other hand, several study results indicated that agricultural price variability has a major impact on food security (El-Rasoul and Tolba, 2018), so it is extremely necessary to provide decision-makers with a database of future agricultural price to deal with any food crisis.Price volatility of some export crops

Conclusion
Commodity prices are subject to high degrees of volatility, especially the prices of agricultural commodities.Production decisions and risk-management require the producers, traders and policy-makers to have good knowledge about the trend and reasons of agricultural commodity price volatility (Riazi, 2016).This study focuses on forecasting the prices of the most important export crops of vegetables and fruits in Egypt using ARIMA model and GARCH model from 2016 to 2030.
The results show that ARIMA (1,1,1), ARIMA (2.1,2), ARIMA (1,1,0) ARIMA (1,1,2), ARIMA (0,1,0) and ARIMA (1,1,1) models are the most appropriate fitted models to evaluate the volatility of price of green beans, tomatoes, onions, oranges, grapes and strawberries, respectively.The results also revealed the presence of ARCH effect only in the case of potatoes, hence it is suggested that the GARCH approach be used instead.The GARCH (1,1) was found to be a better model in forecasting price of potatoes.The results revealed that all the forecasted prices of selected crops will still be increasing in the forecasted period from 2016 to 2030.
We also note that the growth rate of forecasted prices for oranges, green beans, potatoes and onions, respectively is more than the growth rate of other selected crops, so it is expected during the forecast period the production and exports of oranges, green beans, potatoes and onions will increase at increasing rate, and will be more attractive for agricultural producers and exporters compared to tomatoes, grapes and strawberries.
The study recommends more studies in the field of forecasting in terms of prices, production and trade, production costs for other agricultural crops that lead to have a database on the future status of Egyptian agriculture that helps agricultural producers and investors as well as it helps decision-makers in drawing different agricultural policies.
Compiled by researcher from unit root test depending on e-views.See Table A1 in appendix, http:// www.fao.org/faostat/en/#data/PP