FORECASTING OF PRICE OF MAIZE - BY AN APPLICATION OF EXPONENTIAL SMOOTHING

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1 International Journal of Current Agricultural Research, Vol. 3, No. 11, PP November Full Length Research Article FORECASTING OF PRICE OF MAIZE - BY AN APPLICATION OF EXPONENTIAL SMOOTHING 1, *Vasanth Kumar, T. and 2 Gowda, D. M. 1 College of Horticulture, UAHS, Mudigere, Karnataka College of Agriculture, UAS, Bengaluru, Karnataka Accepted 16 th October, 2015; Published 30 th November, 2015 The present study analyzes the forecasting of price of maize in selected market of Karnataka. The monthly time series data over a period of 16 years from 1999 to 2014 were collected from Agricultural Produce Marketing Committees (APMC s) located at Davanagere. Different methods viz., Single Exponential Smoothing, Double Exponential Smoothing and Triple Exponential Smoothing were carried out to know the best forecasting model during study the period. The results revealed that the R2 value to be 0.99, root mean square error to be 56.22, mean absolute percentage error was 7.49, correlation coefficient was 0.99 and the coefficient of variation was in Double Exponential Smoothing method. The results suggested that Double exponential smoothing method to be best fit for forecasting of price maize in Davanagere market by considered all the parameters. Key words: Prices of maize, Single, Double and Triple Exponential Smoothing Methods. INTRODUCTION Agriculture is one of the important activities in both developed and developing countries which provide basic raw materials to human beings and various agro-based industries. Prices play a vital role in predominantly agriculture like India. It determines not only what shall be produced but also how much to be produced. The price system is a powerful tool to transmit essential economic information and stimulate appropriate decision by producers and consumers. Price is the most important determinant of profit or loss in the farm enterprise. In farm enterprise, time factor is very important, while crops are grown in one period and are harvested in another period. This long gestation period exercise significant influence on price determination. Therefore, the prices prevailing during the marketing period are of great consequence. In a country which depends mainly on agriculture, it is absolutely necessary to modernize the age-old traditional agriculture. The transformation of agriculture into dynamic business proposition is primarily a techno-economic process, which can be accelerated by providing a suitable environment to the farmers. The upward trends in arrivals are associated with development in technology of production, input supply and infrastructure (Mundinamani et al., 1993). According to Kumar et al., (2000) the market arrivals of the selected commodities and their competing crops were the major factors influencing their prices in the market. Instability in the farm prices tends to cause inefficient allocation of resources and induce income fluctuations over time and across different categories of farmers. This results in distribution of changes in cropping pattern in the economy. On the contrary, a stable price level would provide incentive to the producers to increase the production of required commodities there by helping to achieve balanced growth of the economy. Farmers always experience with lower prices for their produce when bumper crop is harvested. *Correspondingauthor: Vasanth Kumar, T., College of Horticulture, UAHS, Mudigere, Karnataka They always commit the mistake in disposing off their produce at right time in order to get remunerative prices for their produce. Usually, they sell their produce when there is a glut in the market that is, immediately after the harvest of the crop. For this inappropriate time of sale, one can quote several reasons, but among them the most important is lack of awareness and knowledge about the proper time to sell their produce. This kind of study also helps in formulating appropriate policy measures to contain both over production as well as the forecasting of the remunerative prices for the commodity. Kumar et al., (1999) revealed that average price and production of the commodity were the major factors that determined market arrivals. Larger production and larger arrivals reflect adversely on the prices. As a result the prices usually go down. But in a mixed economy, a certain amount of direction is given to the market forces and this law may not always holds good. This control mechanism of the market forces may aim at regulating market supplies or consumption or both, particularly in the case of commodity in short reaction among the sellers and buyers. The effect of these reactions at once reflected in the supply and price position. Thus, in mixed economy it would be necessary to study the market arrivals and prices and to know the factors influencing them. The behavior of market arrivals and prices has been studied by Nahatkar et al. (1998), Khunt et al (2006), Virender kumar et al. (2006), Yogisha et al. (2007). Ramachandra et al. (2012) have studied an econometric analysis of sunflower arrivals and prices. Maize (zea mays) is an important staple food in many countries of the world and the acreage and production of maize in the world have been increasing continuously. Though the acreages have not been so erratic, the production has been a bit volatile mainly due to the variations in the yield. The area under maize is continuously increasing over the years. Maize is largely grown in north India. Highest concentration of the crop is found in Uttar Pradesh, Rajasthan, Madhya Pradesh, Bihar, Himachal Pradesh, Jammu and Kashmir and Punjab which together account for two-third of the total area and output of the crop.

2 International Journal of Current Agricultural Research 169 In spite of such increase in price, interestingly not much effort has been made to analyze the changes scientifically and look for the reason for such variations in price. Hence it was thought that the statistical analysis of price behavior by different forecasting models would provide insight into the reasons for variation. It is hoped that the identification of the best forecasting model would help the consumers as well as suppliers in taking appropriate decisions. Naturally forecasting is one of the main objectives of time series analyses having the art of saying what will happen in the future rather than why. There are various forecasting models in use now days. Forecaster can choose his own method of forecasting based on his knowledge and available external information. As the process goes on, this procedure can be modified to meet the conditions and to satisfy the current situation. Different forecasting models may be fitted more or less equally well to the data, but they forecasts different future values. Unfortunately, there will be many occasions when analysts are not going to be certain which forecasting method or model is best one and there will be situations where it will appear that several models could do the job quite successfully. Even if we are certain of how to make a decision, we might work with different parameters and generate several forecasts, which will, again, raise the question of the best forecasts. MATERIALS AND METHODS Realizing the above mentioned facts, the present study was conducted to forecast the price of maize in Davanagere market. A time series data on monthly market on prices for the period from 1999 to 2014 were collected from the Agricultural Produce Marketing Committees (APMC s) located at Davanagere. Agricultural Produce Market Committee (APMC), Davanagere Davanagere regulated market is one of the major markets of maize in Karnataka state. The Davanagere Agricultural Produce Market Committee was established and regulated in the year It comes under the Karnataka Agricultural Produce Market Regulation Act Out of 113 notified regulated commodities, the 9 major commodities which are being marketed are cotton, paddy, groundnut, sunflower, maize, onion, coconut and areca nut. The average daily arrivals of maize for the market are about 1974 metric tons and the unit of price quotation in on quintal basis. The system of sale followed in the market is tender system. System of weighment is through electric balance and the payment is made through direct cash payment. There are a total of 652 commission agents, 516 traders, 286 importers, 543 exporters and 18 processors working in the market committee. Commodity wise processing units are present for maize, sunflower, groundnut, jowar, cotton and coconut. Market committee has information on electric boards on which the daily market arrivals and prices are being displayed. It is equipped with facilities like mechanical graders, grading and analyzing laboratory along with basic services like bank, canteen and rest room for farmers, etc. Exponential Smoothing Model (ES) Exponential Smoothing Model is one of the successful parametric nonlinear forecasting techniques to produce a smoothed time series. Exponential Smoothing assigns exponentially decreasing weights as the observation get older. In other words, recent observations are given relatively more weight in forecasting than the older observations. If the weights for exponential smoothing are available, then calculation can be carried out very simply by the formula New Estimate = W (last measurement) + (1-W) (last estimate) Exponential smoothing models are classified as either seasonal or non-seasonal. Some of the exponential smoothing models are explained as below. Single exponential smoothing method (SES) This method is also called as method of estimation of forecasts of single weight or parameter. Greater weights are assigned to recent observation and smaller weights are given distant observation. Suppose the weights in geometric series are given below. 1, (1-W), (1-W) 2,..., (1-W) n-1... (1) Where weights lies between zero to one and n = Number of observations St= ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ).. (2) Similarly, St = ( ) ( ) ( ) ( ) ( ) ( ) ( )... (3) Where Xt = Current observation values Xt-1, Xt-2,...,Xt-(n-1) = Previous observed values St+1 = Current forecasting value St = last estimate value Taking n large value and neglecting higher power of weights (W) and (1-W). Smoothed or new forecast = W (observed value) + (1-W) old forecast OR St+1 = W Xt+1 + (1-W) St... (4) In relation of equation number 4, St+1, the smoothed value at the next period of time is W times the previous period observed values plus (1- W) times the preceding smoothed value, which is itself an average smoothed value. Now to make a forecast for each successive period, these, smoothed value are used to find out a change in each period, W is called the smoothing coefficient. In this particular method only one smoothing constant (W) is used assuming prices are random. The single parameter exponential smoothing is used in estimating forecast price value of groundnut and maize form the selected markets. The first smoothed value is taken as average of first four observed price values. Choice of Weight (W1) The value of W1 can obtained in two ways, one is by trial and error method and another by Pricey time series forecasting software, such as MINITAB, E-Views etc, which use an algorithm to select the value of the W that minimizes mean square error for in-sample forecasts. In the present study MINITAB package is used to the obtain value of appropriate value of W1. Double exponential smoothing method (DES) This method is also called as trend adjusted exponential smoothing. Single exponential smoothing can be improved by the introduction of a second equation with a second smoothing constant/ second weight (W2) assuming price is influenced by the trend component and this represents the double exponential smoothing. This must be chosen in conjunction with W1. The two equations associated Double Exponential Smoothing given by

3 International Journal of Current Agricultural Research 170 St = W1Xt + (1-W) (St-1 + t-1).. (1) t = W2 ( St - St-1) + (1-W2) t-1.. (2) Where, St = smoothened value at time period t St-1 = smoothened value at time period t-1 W1 = level smoothing constant Xt = actual price at time period t bt = trend estimate of the time period t bt-1 = trend estimate of the period t-1 W2 = trend smoothing constant Taking different value for both W1 and W2 by trial and error method both trend factor and level factor is estimated. Hence by using both trend estimate and level estimate, forecast value for the period m is obtained by t + m = St + m t.. (3) In relation of equation 3, forecast value for the m period ahead is m times the trend estimate of the time period t plus the level estimate of the time period t. initial value of the trend estimate (b1) and level estimate (S1) or first smoothened value is taken as follows, S1 = X1 1 = ( ) ( ) Where, X1, X2, X3 and X4 are observed prices for the initial first four season of the time series data set. The current value of the series is used to calculate its smoothed value in double exponential smoothing. The second smoothing equation then updates the trend, which is expressed as the difference between the last two values. The equation is similar to the basic form of single smoothing, but here applied to the updating of the trend. Triple exponential smoothing method To handle seasonality present in the time series data, the third parameter is added. Assuming price is influenced by seasonal factor, third equation being introduced along with new weight (W3) in order to take care of seasonality and to forecast price. The resulting set of equations is called the Holt-Winters (HW) method after the names of the inventors. There are two main HW models, depending on the type of seasonality Holt-winters multiplicative model: Where, = + (1 )( + ) W1 = level smoothing constant SI = seasonality estimate l = length of seasonal cycle. Trend estimate given by Seasonality estimate given by Forecast equation for additive seasonality: = ( + + ) Selection of weights (W1, W2, W3) The value of all three smoothing constant is obtained by trial and error method. Time series are analysed by giving different weights and the best triple exponential model in each case is selected, based on the minimum MAPE and MSD value under different weights. Determination of Estimators The method for obtaining the optimal values of parameters is an iterative process in which the data were smoothed by using different combinations of weights. The combination that produces the smallest mean squared error (MSE) is the optimal set of weights. Theoretically, each of these weights range from 0 to 1. Thus weights are iteratively chosen either by trial and error method or by some software s like MINITAB, E-Views, SPSS etc. which use an algorithm to select the value of the weights that minimizes Mean Square Error for out of sample forecasts. In the present study, MINITAB software is used to obtain appropriate values of all three parameters. RESULTS AND DISCUSSION Under exponential smoothing, the weights (W1, W2, and W3) assigned in geometric progression. All three techniques of Exponential smoothing methods are considered for forecasting timber prices from selected timber depots and results are presented as under. Table 1. Validation measures for forecasted maize prices at Davanagere market Measures SES DES TES R-Square RMSE MAPE Correlation C V Trend estimate is given by Seasonality estimate given by = + (1 )( ) Where, W3 = seasonal smoothing constant Then m period ahead forecast is given by = ( + )( ) Holt-winters additive model: Smoothing equation is given by = ( ) + (1 )( + ) Fig.1. Maize price forecasting by double exponential smoothing of Davanagere market

4 International Journal of Current Agricultural Research 171 Table 2. Forecasting of maize price at Davanagere market by Double Exponential Smoothing Month Actual Value Forecast Month Actual Value Forecast Month Actual Value Forecast Jan Jul Jan Feb Aug Feb Mar Sep Mar Apr Oct Apr May Nov May Jun Dec Jun Jul Jan Jul Aug Feb Aug Sep Mar Sep Oct Apr Oct Nov May Nov Dec Jun Dec Jan Jul Jan Feb Aug Feb Mar Sep Mar Apr Oct Apr May Nov May Jun Dec Jun Jul Jan Jul Aug Feb Aug Sep Mar Sep Oct Apr Oct Nov May Nov Dec Jun Dec Jan Jul Jan Feb Aug Feb Mar Sep Mar Apr Oct Apr May Nov May Jun Dec Jun Jul Jan Jul Aug Feb Aug Sep Mar Sep Oct Apr Oct Nov May Nov Dec Jun Dec Jan Jul Jan Feb Aug Feb Mar Sep Mar Apr Oct Apr Month Actual Value Forecast Month Actual Value Forecast Month Actual Value Forecast May Nov May Jun Dec Jun Jul Jan Jul Aug Feb Aug Sep Mar Sep Oct Apr Oct Nov May Nov Dec Jun Dec Jan Jul Jan Feb Aug Feb Mar Sep Mar Apr Oct Apr May Nov May Jun Dec Jun Jul Jan Jul Aug Feb Aug Sep Mar Sep Oct Apr Oct Nov May Nov Dec Jun Dec Jan Jul Jan Feb Aug Feb Mar Sep Mar Apr Oct Apr May Nov May Jun Dec Single Exponential Smoothing (SES) Method In the present study single parameter exponential smoothing model was used for forecasting maize price from Davanagere market. Equal weight has been given to all the observations; the weight is assigned by trial and error method. The weight (W1) i.e., the alpha (level) was found to be 0.2 was found to be performing best for Davanagere market with a minimum MAPE value of 9.87 per cent. Double Exponential Smoothing (DES) Method This method is also called as trend adjusted exponential smoothing and is improved by the introduction of a second smoothing constant i.e., trend constant, (W2); assuming the timber price value is influenced by the trend component. This must be chosen in conjunction with W1. By applying double exponential option in MINITAB package for maize price. The two weights (level smoothing

5 International Journal of Current Agricultural Research 172 constant and trend smoothing constant) obtained by trial and error method for Davanagere market are (W1 = 0.9 and W2 = 0.1) which are found to be producing minimum MAPE value of 7.49 per cent. Triple Exponential Smoothing (TES) Method To handle seasonality present in the maize price series data, the third parameter (W3) is added. Values of the softening constants W1, W2 and W3, was obtained by trial and error method based on the minimization of the mean absolute percentile error (MAPE) of the forecasting. By applying triple exponential option in MINITAB package for maize price. The three weights obtained by trial and error method for Davanagere market are (W1 = 0.4, W2 = 0.2 and W3 = 0.1) found to be producing minimum MAPE value of 9.32 per cent. Conclusion This study has demonstrated that the double exponential smoothing to be best among all different methods of exponential smoothing for forecasting of price of maize at Davanagere market. Kumar, T. V., Bhat, A. R. S., and Patil, S. J., 2005, Price forecasting of different classes of teak by the application of exponential smoothing model, Kar. J. Agric. Sci., 18(3): Mundinamani, S.M., Sastry, N. R. and Murthy Shankar, H. G., 1993, Market structure for oilseeds in Karnataka - a case study of groundnut. Ind. J. Agric. Mktg., 7(2): Nahatkar, S.B., Kiradiya, B.S., and Sharma, H.O., 1998, Price variation of cotton: A case study of Kukshi regulated market of Dhar district of Madhya Pradesh. Indian J. Agri. Econ., 53(3): Ramachandra, V. A., Pavithra, B. S., and Yeledahalli, R. A., 2012, An econometric analysis of sunflower arrivals and prices in Karnataka, India. Plant Archives, 12(2): Virender Kumar, H.R., Sharma and Sharma, R.K., 2006, Market arrivals and price behavior of potato - a study of four metropolitan markets. Ind. J. Agric. Mktg., 20(1): Yogisha, G.M., Karnool, N.N., Vijaya Kumar, H.S., AND Basavaraja, H., 2007, Trends and seasonal variation in arrivals and prices of potato in Kolar district. Agric. Mktg., 69(4): REFERENCES Khunt, K, A., Gajipara, H. M., and Vekariya, S. B., 2006, Price behaviour of major vegetables in Gujarat state. Indian. J. Agric. Mktg., 20(1): *******