FORECASTING OF WHEAT PRODUCTION : A COMPARATIVE STUDY OF PAKISTAN AND INDIA

Dr. Muhammad Iqbal Ch., Muhammad Tariq Jamshaid, Asad AliandQaisar Rashid. Department of Statistics, University of Sargodha, Sargodha, Pakistan. ...................................................................................................................... Manuscript Info Abstract ......................... ........................................................................ Manuscript History

All investors are eager to know about the trend of wheat production, whether it will increase or decrease. Recently, wheat production has become a hot topic for everyone; it fluctuates rapidly from the past few years. In this study, we propose a time series model for forecasting annual wheat production of Pakistan and India by using secondary data in 1000MT from 1960 to 2015. By using Box-Jenkins methodology, Autoregressive Integrated Moving Average (ARIMA) model is selected and the model selection criterion (AIC and SBC) shows that ARIMA (1,1,1) and (0, 1,1) showing good performance in case of Pakistan where ARIMA (1, 1,0) and (0,1,1) are good for India's annual wheat production forecast.
First of all, we must know that what is wheat? Philosopher defined it as, "A cereal which is the most important kind grown in temperate countries, the grain of which is ground to make flour for bread, pasta, pastry, etc." Wheat industry is a third biggest industry of Pakistan. Along with the wheat producing country, Pakistan stands at 9th position in terms of area (8.5 million hectares) and 59th in terms of yield (21.0 m ton) annually. It occupies a highest position in the food grains of Pakistan, it covers 66% of the total area under food grains and contribute 74% of the total food grain production. Wheat only contributes 13.8% to the value other in agriculture and 3.4% towards Gross Domestic Product (GDP) of Pakistan.
Currently, India is third largest producer of Wheat in the world after China with about 12% share in total world Wheat production. Now, India is surplus and in a position to export Wheat in the International Market and can earn foreign exchange.

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Wheat is the second-most formed crop on Earth, covering behind only corn. Wheat provides a large portion of the food protein and total food supply, and is grown all throughout the world, in a broad variety of climates. Wheat is afasten crop, grown as a primary food product and for other uses as well. Wheat is perhaps the oldest cultivated plant.
If top countries in wheat production is disturbed, then in top ten countries European Union is at top, it's rate is 157.98 million metric tons. China is at number 2 and its rate is 130.19 million metric tons. Pakistan is at 9th number and its rate is 25.48 million metric tons. India is at 3 rd position and its rate is 88.94 million metric tons. As far as in top 10 countries last one is concerned...Turkey is at number ten and its rate is 19.5 million metric tons.
Today, wheat is a grass that grows between 2 and 4 feet (0.6 to 1.2 meters) tall. The physical look of the grain is recognizable to most consumers, with a long stalk that terminates in a strongly formed gather of curvy kernels with this by a beard of smooth spikes. The plant is an annual, which means that at the end of each year, fields must be plowed and prepared again to grow the grass. Inherited wheat perhaps looked very different, with much smaller kernels. The early domesticators apparently wanted to select for plants with for the most part large kernels, since more food could be eked out from each stalk. Because wheat is generally a self-pollinating plant, each plant tends to produce clones of itself. When farmers want to hybridize a twist, they must physically pollinate the different plants. Farmer's combination wheat for a variety of purposes usually unites different seeds at harvest time and extends them regularly over the field.In this study, these models were applied to forecast the production of wheat crop in Pakistan. This would enable to predict expected wheat production for the years from 2016 onward. Muhammad et al. (1992) conducted an empirical study of modeling and forecasting time series data of rice production in Pakistan. ARIMA model has been frequently employed to forecast the future requirements in terms of internal consumption and export to adopt appropriate measures. Saeed et al. (2000) investigated the study of forecasting for wheat production with considering a variable wheat production. The box Jenkins time series technique is utilized on the data from 1998-2013. The diagnostic checking shows ARIMA (2, 2, 1) is appropriate. Forecasting from this model show that these forecasts are helpful in future policy makers for agriculture and grain storage and import & export of wheat production. Shah et al. (2001) investigated the comparative study of wheat production before & after chashma right bank canal. Survey data was collected from five villages. The study has assessed variable per acre yield of wheat & area under wheat production. Two approaches used for this analysis one is t statistics and other is regression analysis. The result show that there is a significance change in per acre yields & area under wheat production. This result also show that CRBC play an important role in increasing change in wheat production. Iqbal et al. (2005) investigated the study of wheat production in Pakistan. The study of wheat production determines the forecasting of wheat production in Pakistan up to the year 2022. They used time series technique that is ARIMA model. Considering variable is wheat production. The ARIMA model show that production of wheat would be 29774.8 thousand tons in 2002-22. The possibility of higher area and production lies in enough accessibility of inputs, cultivating and guidance the agricultural group of people, soil protection and recovery, and especially the encouraging government policies concerning wheat promotion in the country. Karim et al. (2005) applied regression modeling to forecast wheat production of Bangladesh districts. Authors used seven model selection criteria's and found that different models were identified for different districts for wheat production forecasts. They have found that wheat production in Bangladesh districts i.e. Dinajpur, Rajshahi, and Rangpur would be 1.54, 0.35, 0.31, and 0.58 million tons, respectively, in 2009/10.

Methodology:-
A mystery to know, what happened in the future, the index rises or fall, a forecasting methodology was planned by Box and Jenkins in 1970 named as Box-Jenkins methodology. It is most suitable model selection method for forecasting of time series variable. The Box-Jenkins methodology is valid only when the variable fulfills some assumptions. First of all, variable should be stationary and there is no seasonality, but if the variable violated the assumption or any pattern according to scale or location then the first mission is to make it stationary for applying Box-Jenkins model. Practice shows that most variables are non-stationary in real life so to convert non-stationary variables into stationary variables we obtain the difference of variables and the new variables are known as integrated variable. The Box-Jenkins methodology may be followed by this way: 701 For testing the null hypothesis "data is not stationary", we use Augmented Dickey Fuller (ADF) test. If the significant value of ADF test is less than desired level of significance which is mostly 0.05, we conclude that data is stationary.
The linear relationship between two values of the similar variable is terms as autocorrelation (ACF). If we determine ACF after removing any linear dependency from the lag values, it will have called partial autocorrelation (PACF). ACF and PACF both ranges from -1 to +1. The graphical representation of ACF and PACF is called Correlogram. In the correlogram ACF show the order of autoregressive model (p) and PACF show the order of moving average model (q).

Results and Discussion:-
For the forecasting purpose, data is taken from the site of Index mundi and it consists of the yearly wheat production in Pakistan and India (1000MT) from 1960 to 2015.

Stationary Test:-
When the variable is without any modification of its average value and variation for a long time, is said stationary. For using the Box-Jenkins methodology, variable must be stationary. In the literature numerous charts and empirical methods, available to verify stationary. In this study, both graphics and empirical methods were used for these purposes. Figure 1 shows the line chart of wheat production of Pakistan and India from 1960 to 2015. Figure 2 shows correlogram for yearly wheat production.

Figure 1.
Yearly wheat production Figure 1 shows time on x-axis and wheat production on y axis. The pattern reveals that there are many ups and downs in the wheat production in both countries. Long term increasing pattern of wheat production indicates that it is non stationary. It also shows that long run increase in production is rapid in India as compare to Pakistan. In Figure 2, Correlogram shows that there is high correlation between the values, but with the passage of time it decreases but still shows significant behavior.
In empirical methods, ADF (Augmented-Dickey Fuller) test has been utilized. On the basis of its ADF values 0.580382, 0.073287 for Pakistan and India respectively, we don't reject our H0 at the 5 % level of significance. In this study, differenced technique is utilized to make variable stationary. Line chart, Correlogram and ADF test have been utilized again after taking 1st difference of variable.
704 Figure 3:-Line chart of wheat production in Pakistan and India at 1st Difference.
Line chart of the yearly wheat production by using the 1st difference is shown in Figure 3. It shows that the mean of wheat production has no change so it has constant variation throughout the time period. We may say that series is stationary at 1st difference. Correlogram of the yearly wheat production by using the 1st difference is shown above in Figure 4. It clearly indicates that all spikes are random and very small in magnitude, so, our data is stationary.

Pakistan India
When we apply ADF test on 1st difference data it shows ADF values -8.365612, -10.53668 for yearly wheat production of Pakistan and India respectively. So we reject our H0 at the 5 % level of significance. We conclude that our data is stationary at the 1st difference.    Table 2 shows that MAE, MAPE, and RMSE of ARIMA (1,1,0) model are less than ARIMA (0,1,1) model. So, there is less error in forecast values of ARIMA (1,1,0) than ARIMA (0,1,1).

Analysis of Forecast Results:-
The yearly wheat production from 1960 until 2015 are used for forecasting the next 10 values of the yearly wheat production by using both ARIMA (1,1,1) and ARIMA (1,1,0) models. The forecasted results are following: 707 Model (1,1,1)

Residuals Analysis:-
In the Box-Jenkins methodology, best equipped model residues should be independently identical normally distributed (IID). To justify this hypothesis, normality plot and correlogram are utilized. India Pakistan

India
The normality plot shows that residuals of ARIMA (1,1,1) and ARIMA (1,1,0) are normally distributed as the residuals close to the line. So, Normality plot and Correlogram tells that the selected model ARIMA (1,1,1) and ARIMA (1,1,0) are best for the forecasting purpose of yearly wheat production of Pakistan and India respectively.

Conclusion:-
As the population increases over time regularly, therefore it is necessary to plan to meet the requirements of nation. For this purpose, forecasting is the key tool to alarm about the need of nation in advance. Wheat is the basic need of any country all over the world. In this study, we developed time series models to forecasts wheat production of Pakistan and India on the basis of historical data i.e. 1960-2015. We have developed different time series models on wheat production of Pakistan and India on this data. Best model is selected on the basis of model selection criteria i.e. AIC and SBC. Main interest of developing time series model is that the model fitted is also satisfied residual assumptions i.e. normality, independence and no autocorrelation. On the basis of these model selection criteria, we have found that best model for wheat production forecasting of Pakistan and India are ARIMA (1, 1, 1), (0,1,1) respectively because these models have lower AIC and SBC as compared to other fitted time series models. On the basis of these models, we have found that wheat production of Pakistan would become 27623.5 thousand tons in 2020 and would become double in 2060 as compared in 2010 under the assumption that there is no irregular movement or variation is occurred.