Research Article

Forecasting Production and Yield of Sugarcane and Cotton Crops of Pakistan for 2013-2030

Sajid Ali1, Nouman Badar1, Hina Fatima2

1Social Sciences Division, Pakistan Agricultural Research Council, Islamabad; 2Economics Department, Fatima Jinnah Women University, Rawalpindi, Pakistan.

Editor | Tahir Sarwar, The University of Agriculture, Peshawar, Pakistan

*Correspondence | Sajid Ali. Pakistan Agricultural Research Council, Islamabad, Pakistan; E-mail | [email protected]

Citation | Ali, S., N. Badar and H. Fatima. 2015. Forecasting production and yield of sugarcane and cotton crops of Pakistan for 2013-2030. Sarhad Journal of Agriculture, 31(1): 1-9.

Keywords | Forecast, Sugarcane, Cotton, Production, Yield, ARIMA

Introduction

Sugarcane and cotton are the two major cash crops sown in Pakistan. Punjab, Sindh and Khyber Pakhtunkhwa are the major sugarcane producing provinces of the country. Total area under sugarcane crop during 2010-11 was 987.6 thousand hectares in the country. Punjab is the largest province in terms of area under sugarcane which accounts for more than 68 percent of the total area under sugarcane followed by Sindh (22.9 %) and Khyber Pakhtunkhwa (8.9 %) (GOP, 2012). However, Sindh produces highest yield (60.8 tonnes per hectare) followed by Punjab (55.8 tonnes per hectare) and Khyber Pakhtunkhwa (45.6 tonnes per hectare). Its production has increased by almost 27 percent from 43.6 million tonnes in 2000-01 to 55.3 million tonnes in 2010-11. It is primarily grown for sugar production in the country, however, other products like bio fuel, chipboard, organic fertilizer, paper, and fiber etc can also be produced from sugarcane. Its share in total value added of agriculture is approximately 3.7% (GOP, 2012).

Cotton is mainly grown in Punjab and Sindh provinces. This crop contributes significantly in Pakistan economy by providing raw material to textile industry as well as foreign exchange earnings through export of cotton lint (GOP, 2012). Its share in agriculture value added is 8.6 percent and also accounts for 1.8 percent to national GDP. During 2010-11, total area under cotton crop was 2.69 million hectares in the country. Punjab accounts for more than four-fifth of the total area under cotton in the country. In terms of yield, Sindh contributes 1354 kg/hectare whereas; cotton yield in Punjab was only 607 kg/hectare during 2010-11. Area under cotton has increased from 2.2 million in 1980-81 to 2.7 million hectares in 2010-11 (GOP, 2012).

Being two major cash crops and contributing significantly in the agricultural economy of the country, it is worthwhile to know about the production and yield status of these crops in future. If past values of crop production and yield are given, one can use past pattern of the data to forecast crop production and yield by employing forecasting model. Various models have been developed to forecast future values; however, in uni-variate time series analysis, ARIMA model technique has been used extensively in the literature for forecasting purpose. Efforts have been made to forecast production and productivity of sugarcane employing ARIMA models (Yaseen et al., 2005; Bajpai and Venugopalan, 1996). Other attempts using ARIMA models include forecasting of sugarcane production in Pakistan (Muhammad et al., 1992), forecasting of area, production and productivity of different crops for Tamilnadu State (Balanagammel et al., 2000), forecasting wheat production in Canada and Pakistan (Boken, 2000; Saeed et al., 2000), forecasting fish catches (Tsitsika et al., 2007; Venugopalan and Srinath, 1998), forecasting agricultural production at state level (Indira and Datta, 2003), forecasting sugarcane area and yield for Pakistan (Masood and Javed, 2004), forecasting production of oilseeds (Chandran and Prajneshu, 2005), forecasting and modeling of wheat yield in Pakistan (Ullah et al., 2010), sugarcane yield forecasting for Tamilnadu (Suresh and Krishnaprya, 2011), and forecasting productivity in India (Padhan, 2012).

This paper focuses on Autoregressive Integrated Moving Average (ARIMA) model for forecasting production and yield estimates of sugarcane and cotton. The rest of paper is organized as follows. Section 2 describes data and methodology. Section 3 discusses results and discussions while, conclusion has been made in section 4.

Data and Methodology

This study is based on secondary data of cash crops for forecasting production and yield of sugarcane and cotton crops. The production and yield data for sugarcane and cotton have been taken from various issues of Economic Survey of Pakistan (GOP, Various issues), and Agricultural Statistics of Pakistan (GOP, 2007). The study covers data from 1948 to 2012. Average annual growth rate of production and yield for sugarcane and cotton crops are reported in table 1.

Various models have been used in the literature to forecast time series data; however, Auto Regressive Integrated Moving Average (ARIMA) technique is used by this study to forecast production and yield of sugarcane and cotton for Pakistan. It is the most general form of stochastic models for analyzing time series data. The ARIMA models include autoregressive (AR) terms, moving average (MA) terms, and differencing (or integrated) operations. The model is called AR model if it contains only the autoregressive terms. Model is known as MA model if it involves only the moving average terms. It is known as ARMA models when both autoregressive and moving average terms are involved. Finally when a non-stationary series is made stationary by differencing method, it is known as ARIMA model. The general form of ARIMA is denoted by ARIMA (p,d,q), where ‘p’ represents the order of autoregressive process, ‘q’ represents the order of moving average process, while ‘d’ shows the order of differencing the series to make it stationary.

Table 1: Decade-wise Average annual growth rate of Production and Yield for Sugarcane and Cotton crops in Pakistan

Decade	Sugarcane		Cotton
	Production	Yield	Production	Yield
1971-80	4.01	0.31	-1.58	-2.14
1981-90	0.26	1.03	10.27	7.78
1991-00	3.75	1.43	0.14	-1.02
2001-10	1.48	1.22	2.26	2.06

The general form of AR process of order p, denoted by AR (p) is written as follows:

Yt =Ɵ + δ1Yt-1+…+ δpYt-p+ εt ….... (1)

Where, Ytis thedependant variable at time t, Yt-1…… Yt-p are explanatory variables at time lags t-1, … t-p, εt is the error term at time t.

The general form of MA process of order q is given as follows:

Yt = εt –γ1 εt-1 –γ2 εt-2– … – γq εt-q …….. (2)

Where εt-1, εt-2 … εt-q are the forecast errors at time t-1, t-2 … t-q respectively. γ1…. γq are the coefficients to be estimated by OLS. The forecast errors represent the effects of the variable which is not explained by the model.

Finally, the general form of the ARIMA (p,d,q) can be written as follows:

∆dYt =Ɵ + δ1∆d Yt-1+ δ2∆d Yt-2+…. +δp∆d Yt-p+ εt –γ1 εt-1 –γ2 εt-2– … – γq εt-q…........ (3)

Table 2: Results of Unit Root Test(Augmented Dickey-Fuller Test: ADF)

Variables	Intercept / Intercept & Trend	Level	First difference	Order of Integration
S_P	Intercept & Trend	-3.70**	-	I(0)
S_Y	Intercept & Trend	-3.77**	-	I(0)
C_P	Intercept & Trend	-2.09	-9.73***	I(1)
C_Y	Intercept & Trend	-4.20***	-	I(0)

*** indicate the rejection of null hypothesis of unit-root at 1% level of significance. ** indicate the rejection of null hypothesis of unit-root at 5% level of significance. The variable (S_P), (S_Y), (C_P) and (C_Y) represents sugar production, sugar yield, cotton production and cotton yield, respectively. ♣As both Intercept and Trend were significant, therefore, both were used in ADF test instead of using Intercept only.

Where, ∆d represents differencing of order d, i.e., ∆Yt = Yt - Yt-1, ∆Yt = ∆Yt - ∆Yt-1 and so forth, Yt-1 …… Yt-p show lags of the variable,indicates constant term of the modeland δ1…. δp are parameters to be estimatedby using ordinary least square method (OLS).

In this study we follow Box-Jenkins (1976) procedure of ARIMA modeling i.e. identification, estimation, diagnostic checking, and forecasting time series data of sugarcane and cotton crops of Pakistan. The ARIMA modeling procedure starts with identification of the model, however, stationarity of variables of interest is also required. The stationarity can be tested both through graphics and through other formal techniques i.e. Partial Autocorrelation Function (PACF), Autocorrelation Function (ACF), and Augmented Dickey-Fuller test (ADF) of unit root. If the variables of interest are found non-stationary at level, the data need transformationin such a way to make them stationary. The model can be identified through PACF and ACF. After identification of the model, the next step is the estimation of model parameterswhich is done through Ordinary Least Square (OLS) method. Moving further, various diagnostic tests are used on residual of the model. If the model passes successfully through these diagnostics tests, then the estimated coefficients of forecasting can be used for future values.

Results and Discussions

The results of unit root test for sugarcane and cotton crop production and yield are given in table 2. The results indicate that production and yield of sugarcane crop are stationary at level i.e. both series are integrated of order zero I (0). So it is not needed to make these series stationary by taking difference. Similarly, the yield series of sugarcane was stationary at level. On the other hand, production series of cotton crop is non-stationary at level and therefore, it was made stationary by taking first order differencing. Therefore, ARMA model was used for forecasting production and yield of sugarcane crop, yield of cotton crop, whereas, ARIMA model was employed to forecast production of cotton crop of Pakistan.

Table 3: Estimates of Sugarcane Production Parameters

Type	Coefficients	S.E	t-statistic	Prob.
AR(1)	0.979	0.028	34.884	0.0000
MA(4)	0.534	0.118	4.520	0.0000
MA(2)	-0.443	0.113	-3.922	0.0002

Table 4: Estimates of Sugarcane Yield Parameters

Type	Coefficients	S.E	t-ratio	Prob.
AR(1)	0.997	0.027	36.623	0.0000
MA(1)	-0.477	0.123	-3.868	0.0003

Using diverse values of p and q, a range of ARMA and ARIMA models have been fitted in order to choose appropriate models. Appropriate models were selected based on certain selection criterion, for example, Schwarz-Bayesian Information Criteria (SBC) and Akaike Information Criteria (AIC). Consequently, ARMA (1, 4) and ARMA (1, 1) were found appropriate for production and yield of sugarcane respectively. Similarly, ARMA (0, 1) was found appropriate for production of cotton crop. Finally, ARIMA (2, 1, 1) was the appropriate model to be used for forecasting cotton yield. The parameters estimates for sugarcane production and yield are given in table 3 and table 4 respectively along with their standard errors and t-ratios. Likewise, parameters estimates for cotton production and yield are given in table 5 and table 6 respectively.

Table 5: Estimates of Cotton Production Parameters

Type	Coefficients	S.E	t-statistic	Prob.
MA(1)	-0.486	0.113	-4.284	0.0001

Table 6: Estimates of Cotton Yield Parameters

Type	Coefficients	S.E	t-ratio	Prob.
AR(2)	-0.516	0.119	-4.353	0.0001
AR(1)	1.515	0.117	12.953	0.0000
MA(1)	-0.984	0.030	-32.619	0.0000

Once the models were fitted and estimated, the next step in Box-Jenkins (1976) procedure was diagnostic checking of the fitted models. For this purpose, we used ACF and PACF of plotted residuals of the fitted models. The ACF and PACF of the plotted residuals of production and yield of both sugarcane and cotton crops were found within the limits which indicated that models were well fitted (see Appendix-C). Using parameter estimates of the fitted models, forecast for production and yield of sugarcane and cotton crops of Pakistan for the years 2013 to 2030 were estimated and presented in Appendix-A, whereas, the graphical presentation are given in Appendix-B.

The forecasted values of sugarcane crop reveal that it will reach 71,414 thousand tonnes and its yield will attain 60,765 kg/ha by 2030. On the other hand, the forecast of cotton production is 15,479 thousand tonnes and its yield is 870 kg/ha for 2030.

Conclusions

One of the main objectives of this study was to forecast production and yield of sugarcane and cotton crops of Pakistan. Auto Regressive Moving Average (ARMA) and Auto Regressive Integrated Moving Average (ARIMA) models were used for this purpose. Time series data for 65 years (1948 to 2012) have been used in this study. All the essential steps of ARMA and ARIMA modeling have been systematically followed to forecast productions and yields of selected crops from 2013 onward to 2030. These forecast values could be used for formulating agriculture policy especially for sugarcane and cotton crops by policy makers at national level.These models use the historical time series data for forecasting, however, there could be some other factors affecting production and yield of these crops. For example, availability of high yielding varieties, applying best management practices, judicious use of pesticides etc. Consequently, the future thrust of this study is to apply other available models of forecasting which have features of incorporating more agriculture related information to forecast production and yields of these crops.

The study used univariate analysis for forecasting; however, this does not mean that the technique supersedes multivariate techniques. ARIMA does not perform well in case of volatile series. Moreover, ARIMA models of forecasting are ‘backward looking’ and do not perform better during forecasting at turning points.

References

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APPENDIX-A

A-I: Forecast of Sugarcane Production and Yield from 2013-2030 with 95% confidence interval

Year	Production (000 t)			Yield (kg/ha)
	Forecast	95 % Limit		Forecast	95 % Limit
		Lower	Upper		Lower	Upper
2013	55859	50103	61615	54689	49575	59803
2014	58287	52531	64043	54874	49760	59988
2015	57927	52171	63683	55103	49990	60217
2016	58302	52546	64058	55370	50256	60484
2017	59865	54110	65621	55667	50553	60781
2018	61060	55305	66816	55989	50875	61103
2019	62073	56317	67829	56332	51218	61445
2020	62995	57239	68751	56691	51577	61805
2021	63872	58116	69628	57065	51951	62179
2022	64727	58971	70483	57450	52336	62564
2023	65571	59815	71327	57845	52731	62959
2024	66410	60654	72166	58247	53134	63361
2025	67246	61490	73001	58657	53543	63770
2026	68080	62324	73836	59071	53957	64185
2027	68914	63158	74670	59490	54376	64604
2028	69747	63992	75503	59912	54798	65026
2029	70581	64825	76337	60337	55223	65451
2030	71414	65658	77170	60765	55651	65879

Source: Authors’ estimation

A-2: Forecast of Cotton Production and Yield from 2013-2030 with 95% confidence Interval

Year	Production (000 b)			Yield (kg/ha)
	Forecast	95 % Limit		Forecast	95 % Limit
		Lower	Upper		Lower	Upper
2013	12472	10301	14643	728	601	855
2014	12649	10478	14819	734	607	861
2015	12826	10655	14996	741	614	868
2016	13002	10832	15173	749	622	876
2017	13179	11008	15350	757	631	884
2018	13356	11185	15527	766	639	893
2019	13533	11362	15704	775	648	901
2020	13710	11539	15881	783	657	910
2021	13887	11716	16057	792	665	919
2022	14064	11893	16234	801	674	928
2023	14240	12070	16411	810	683	936
2024	14417	12247	16588	818	692	945
2025	14594	12423	16765	827	700	954
2026	14771	12600	16942	836	709	963
2027	14948	12777	17119	844	718	971
2028	15125	12954	17296	853	726	980
2029	15302	13131	17472	862	735	989
2030	15479	13308	17649	870	744	997

Source: Authors’ estimation

APPENDIX-B

Figure B1: Production and Yield Forecast of Sugarcane Crop in Pakistan (2013-2030)

Figure B2: Production and Yield Forecast of Cotton Crop in Pakistan (2013-2030)

APPENDIX-C: Correlogram of Residuals

1. d(c_p) c ma(1)

2. c_y c ma(1) ar(2) ar(1)

3. s_p c ar(1) ma(4) ma(2)

4. s_y c ar(1) ma(1)