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Double Exponential Smoothing Methods for Price Estimation of Major Pulses in Pakistan

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Double Exponential Smoothing Methods for Price Estimation of Major Pulses in Pakistan Pakistan J. Agric. Res. Vol. 25 No. 3, 2012 COMPARISON OF TREND ANALYSIS AND DOUBLE EXPONENTIAL SMOOTHING METHODS FOR PRICE ESTIMATION OF MAJOR PULSES IN PAKISTAN Saima Rani and Irum Raza* ABSTRACT: The present study was designed to find out suitable forecasting method among the two forecasting methods namely trend analysis and double exponential smoothing. Measures of accuracy (MAPE, MAD and MSD) were used as the model selection criteria that could best describe the trend of prices of major pulses such as gram, mash, masoor and mung during 1975-76 and 2009-10. Double exponential smoothing method was found to be pertinent for price estimation of major pulses in Pakistan because of smaller values of accuracy measures. Six-year's forecasts of prices of gram, mash, masoor and mung in Pakistan in 2010-11 were Rs.31.80, Rs.84.09, Rs.72.06, and Rs.47.69 per kg respectively along with 95% prediction intervals. The results showed that if the present growth rates remain the same then prices of these pulses in Pakistan would be Rs.37.64, Rs.120.26, Rs.89.55 and Rs.55.03 per kg, respectively in 2015- 16. An increasing trend in the estimated prices will turn down the demand of these pulses and consequently poor class of the economy who do not have enough resources to buy expensive livestock-based protein-rich food will be badly affected. Key Words: Pulses; Trend Analysis; Double Exponential Smoothing; Price Estimation; Pakistan. INTRODUCTION Due to low production of pulses, Pakistan imports large quantities of Pulses are the most important pulses to meet the ever increasing source of vegetable protein in gap between the domestic prod- Pakistan. They are cultivated on 5% uction and requirements (Chaudhry of the total cropped area. Their use et al., 2002). Moreover, the price of ranges from baby food to delicacies of pulses has increased much as the rich and the poor (PARC, 2012). compared to other food items such as Normally the area under pulses in wheat. This has serious implications the country is around 1395200 ha for the supply of protein to the poor out of which major pulses population who do not have resour- contributed 1298300 ha with a ces to buy expensive livestock-based production of 701800 t in 2009-2010 protein-rich food. In a failed attempt which was declining over the year. to halt this decline, the government Among major pulses, gram is the has to spend considerable foreign major winter food legume and mung exchange on the import of pulses (Ali is the major summer legume (GoP, and Abedolla, 1998). 1980, 2010). Increase in prices can be attri- * Social Sciences Research Institute, National Agricultural Research Centre, Islamabad, Pakistan. Corresponding author: [email protected] 233 SAIMA RANI AND IRUM RAZA buted to both supply and demand on the pulses in Pakistan. Therefore factors. The per capita availability of the study is designed to estimate the some of the items such as cereals prices of major pulses (gram, and pulses has been declin-ing masoor, mash and mung) but before resulting in some pressure on their esti-mating the price it is necessary prices (Sher, 2012). A farmer to estimate the forecasting model cultivated a crop on his farm keeping that best fits the time series data. in mind its price in previous year Here, an attempt is made to identify profitability and allocated his limited the best method for price estimation resources for that crop which is of major pulses in Pakistan using two stable and less risky however pulses forecasting methods on the basis of price was highly unstable. Hence accuracy measures. Therefore the instability in price was deeply goal of the study is to forecast price influenced by the production in- of major pulses in Pakistan using the stability in all the major pulses (Rani best fitted models. et al., 2012). Reliable and well-timed forecast MATERIALS AND METHOD provides essential and valuable inputs for proper foresight and The study was conducted using informed planning more so, in secondary time series data of prices agriculture which is full of uncer- of major pulses (gram, masoor, tainities. Now-a-days agriculture mung and mash) of Pakistan from has become highly input and cost 1975-76 to 2009-10 (34 years). Data intensive. Under the change scenario were collected from the various today, forecasting of various aspects issues of Agriculture Statistics of related to agriculture have become Pakistan, published by Ministry of essential (Agrawal, 2005). Because of Food and Agriculture, Islamabad. the high volatility of prices of Data were analyzed in Minitab agricultural commodities over the software. Initially time series plot for past decade, the importance of prices of major pulses (gram, accurate price forecasting for deci- masoor, mung and mash) was sion makers has become even more created using MINITAB software to acute (Brandt and Bessler, 1983). evaluate trend and cyclic patterns in Traditionally different forecas- data. ting techniques such as regression models, Auto regressive integrated Analytical Technique moving average (ARIMA) model The models that are used to introduced by Box and Jenkins, describe the behavior of variables (1976) and exponential smoothing that vary with respect to time are methods have been employed to termed as growth models. In this forecast crop yield and production. study trend analysis and double These models are also helpful for exponential smoothing methods forecasting economic time series, were used inventory and sales modeling etc (Brown, 1959; Holt et al., 1960). Trend Analysis Many attempts have been made It was employed to fit a general to forecast the price of agricultural trend model to data and provide commodities but little work is done forecast. The general form of the 234 PRICE ESTIMATION OF MAJOR PULSES IN PAKISTAN trend equation as proposed by Boken thed series obtained by applying (2000), Rimi et al. (2011) is given as: simple exponential smoothing (using Yt = â0 + ât + et ------------------ (1) the same a) to series S': where: S''(t) = aS'(t) + (1-a)S''(t-1) ---- (3) Y = Price of gram/masoor Finally, the forecast Ý(t+1) is given /mash/mung by: â0 = Constant Ý(t+1) = a(t) + b(t) --------------- (4) ât = Regression coefficient where: (measure the effect of a(t) = 2S'(t) - S''(t) the esti- independent variable on the mated level at period t. dependent variable) b(t) = (a/(1-a))(S'(t) - S''(t)) t = Trend which determines the the estimated trend at tendency of time series data period t. to increase or decrease over time. Accuracy Measures The intent of using two fore- Double Exponential Smoothing casting methods was actually to Method make comparison of the estimates This method provides short- obtained and decide that which fore- term forecasts. Dynamic estimates casting method provides good fit to are calculated for two components data on the basis of three accuracy on level and trend. Double expo- measures. These accuracy measures nential smoothing-based prediction are Mean Absolute Percentage Error (DESP) models a given time series (MAPE), Mean Absolute Deviation using a simple linear regression (MAD) and Mean Squared Deviation equation where Y is the dependent (MSD). Smaller values for all these variable, intercept b0 and slope b1 are measures indicate a better fitting varying slowly over time (Bowerman model and a better model yields and Connell, 1993). Double expo- minimum forecasting error (Karim et nential smoothing technique used in al., 2010). The best-fitted method is this study (Joseph and Laviola, selected and used for estimating the 2003). prices of major pulses (gram, The algebraic form of the linear masoor, mung and mash) in exponential smoothing model, like Pakistan from 2010-11 to 2015-16. that of the simple exponential smoo- thing model, can be expressed in RESULTS AND DISCUSSION different ways. The "standard" form of this model is usually expressed as Initially time series plot (Figure follows: S' denote the singly- 1) was created to determine the smoothed series obtained by apply- trends in the price of major pulses ing simple exponential smoothing to (gram, masoor, mung and mash) series Y. That is, the value of S' at from 1976 to 2010. The prices of period t is given by: gram show an upward trend from S'(t) = aY(t) + (1-a)S'(t-1) ----- (2) 1976 to 2008 but sudden decline is (Under simple exponential smoo- apparent in 2010. An increasing thing, let Ý(t+1) = S'(t) at this point.) trend is visible in mash price during Then let S" denote the doubly-smoo- the study period. The price of masoor 235 SAIMA RANI AND IRUM RAZA 90 Table 1. Diagnostic measures for the Variable 80 Gramprices selection of the best fore- Price Mash 70 Price Masoor casting method for prices of Price Mung ) major pulses in Pakistan -1 60 50 Measures Trend Double exponential of accuracy analysis smoothing 40 Gram Mash Masoor Mung Gram Mash Masoor Mung Price (Rs kg 30 MAPE 47.21 46.91 54.32 34.76 28.19 16.72 31.22 17.91 20 MAD 2.69 5.10 6.15 3.26 2.38 2.80 4.08 2.45 10 MSD 11.40 60.13 109.61 16.22 10.65 19.18 79.26 10.69 0 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 7 7 8 8 8 8 8 9 9 9 9 9 0 0 0 0 0 tial smoothing method, suggesting 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 Year that this method provides better fit to data and is appropriate for predic- Figure 1.
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