FORECAST PRICE OF BRINJAL BY HOLT WINTERS METHOD IN WEST BENGAL USING M S EXCEL ABSTRACT

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1 INTERNATIONAL JOURNAL OF BIO-RESOURCE, ENVIRONMENT AND AGRICULTURAL SCIENCES (IJBEAS) Vol. 2(): , // ISSN FORECAST PRICE OF BRINJAL BY HOLT WINTERS METHOD IN WEST BENGAL USING M S EXCEL D. S. Dhakre, K. A. Sarkar ad S Maa 2 Departmet of EES, Palli-Siksha Bhavaa (Istitute of Agriculture), Visva-Bharati, Sriiketa, WB 2 Darjeelig KVK, Uttar Baga Krishi Viswavidyalaya Received: February 206 Revised accepted: March 206 ABSTRACT The preset study coducted to kow the statistical ivestigatio of price behaviour of Brijal i West Begal. Triple expoetial smoothig (Holt witers method) was used for forecastig the mothly price of Brijal. Measures of accuracy Mea Absolute Percetage Error (MAPE), Mea Absolute Error (MAE) ad Mea Square Error (MSE) at differet levels of smoothig costats such as, ad were used for the model selectio criteria that could best describe the tred of price of Brijal durig November 2002 ad Jauary 206. Last eight moths Jue 205 to Jauary 206 price take for model validatio. Next eight moth price forecasts of Brijal i February 206 Rs.0.6 per kg whereas i September 206 Rs.2 per kg respectively alog with cofidece itervals. This paper gives us a step by step approach to doig triple expoetial smoothig (Holt witers method) aalysis usig the Microsoft office Excel software. A tool most commo to PC s based o Microsoft widows operatig systems ad its users. Keywords: Forecastig, Holt witers method, Smoothig costat, Price ad Solver INTRODUCTION Expoetial smoothig has prove through the years to be very useful i may forecastig situatios. It was first suggested by C. C. Holt i 957 ad was meat to be used for o-seasoal time series showig o tred. He later offered a procedure (958) that does hadle treds. Witers (960) geeralized the method to iclude seasoality, hece the ame "Holt-Witers Method" or Triple Expoetial Smoothig. MATERIALS AND METHODS The mothly data of Brijal price i West Begal for the period November 2002 to Jauary 206 by Directorate of Marketig & Ispectio (DMI), Miistry of Agriculture ad Farmers Welfare, Govermet of Idia were used. Triple Expoetial Smoothig (Holt Witers Method) is appropriate whe tred ad seasoality are preset i the time series. It decomposes the times series dow ito three compoets: base, tred ad seasoal compoets. Whe a actual observatio is divided by its correspodig seasoal factor, it is said to be deseasoalized (i.e. the seasoal compoet has bee removed). This allows us to make meaigful comparisos across time periods. Let L = the umber of periods i a cycle (2 moths of year) The relevat formulas for this method follow. S t = (y t / I t-l ) + (-) (S t- +b t- ) b t = (S t - S t- ) + (- ) b t- I t = (y t /S t ) + (-) I t-l F t+m = (S t + b t ) I t+m-l Overall smoothig Tred smoothig Seasoal smoothig Forecast

2 It. J. Bio-res. Ev. Agril. Sci., March 206 Where, y is the Price of Brijal S is the smoothed observatio b is the tred factor I is the seasoal idex F is the forecast at m periods ahead t is a idex deotig a time period, ad are smoothig costats betwee 0 ad that must be estimated i such a way that the MSE of the error is miimized. Step-by-step Triple Expoetial Smoothig Aalysis usig MS Excel We have the mothly price of Brijal. We kow that it is a yearly seaso where L=2. The first step is to trasform or deseasoalize the first year price data i C4:C5. So we eter the formula S t =y t /[(/L)(y +y y L )] i cell F4 which is =C4/(Average($C$4:$C$5)) i cell F4 ad fill dow tof5. Thewe assume ad eter S t =(y +y y L )/L i cell D5ad b t =0 i cell E5. Overall smoothig (base) We eter the formula S t = (y t / I t-l ) + (-) (S t- +b t- ) i cell D6 Which is =$M$3*(C6/F4)+(-$M$3)*(D5+E5) ad fill dow till D62 Tred smoothig (Tred) We eter this formula, b t = (S t - S t- ) + (- ) b t- i cell E6 which is=$m$4*(d6-d5)+(-$m$4)*e5 ad fill dow till E62. Seasoal smoothig(seasoal) We eter this formula I t = (y t /S t ) + (-) I t-l i cell F6 Which is =$M$5*(C6/D6)+(-$M$5)*F4ad fill dow till F62. Forecast Fig. 233

3 It. J. Bio-res. Ev. Agril. Sci., March 206 Now we combie three formula together ad eter the formula F t+m = (S t + b t ) I t+m-l i G6 which is =(D5+E5)*F4 ad fill dow to G62 i.e. the formula. Mea Absolute Error, Mea Square Error, Mea Absolute Percetage Error The mea absolute error (MAE), mea squared error (MSE) ad mea absolute percetage error (MAPE) are etered i colum I, J ad K respectively. We eter this formula y t y t i cell P4 for Mea absolute error which is =SUMSQ (H6:H62)/(COUNT(H6:H62)) For mea square error we eter this formula =SUMSQ (H6:H62)/(COUNT(H6:H62)) Similarly we eter this formula t t t yt yt y ( y t y t ) 2 i cell P6 which is t 00i cell P5 for mea absolute percetage error which is =AVERAGE (J6:J62) Where y t y t Actual Price ad Predicted Price Solver We will use Excel Solver to miimize the MAE ad to fid a better value or optimize for Ivoke Excel Solver to miimize the MAE. We eter all the parameters i this dialogue box. It will look like Fig.2 below after all the parameters are etered. Set Target Cell: MAE (P4) Equal to: Mi By Chagig Cells: the weights at M3, M4 ad M5 Costraits are that the 0 <= M3 <=, 0 <= M4 <=, 0 <= M5 <= Click the Solve butto. Solver will start to optimize ad Keep the Solver solutio. The MAE i cell P4 has bee miimize ad is equal to 2.37 ad the i cell M3 is equal 0.3. The i cell M4= 0. The i cell M5= We have made a little improvemet after optimizig with Excel Solver. 234

4 Price (Rs kg - ) Price (Rs kg - ) It. J. Bio-res. Ev. Agril. Sci., March 206 Fig.2 If we wat to forecast m periods ahead, use the followig logic. F t+m = (S t +m b t ) I t+m-l If we wat to forecast price for st moth ahead, so we eter =(D55+*E55)*F5 i cell G63. If we wat to forecast price for 2 d moth ahead, so we eter =(D56+2*E56)*F52 i cell G63. Similarly for ext 3 rd,4 th,5 th,6 th, 7 th ad 8 th moths we forecast prices. Table. Diagostic measures for the selectio of the best forecastig Model Measure of Accuracy Triple Expoetial Smoothig Aalysis MAPE MAE 2.37 MSE 0.64 RESULTSANDDISCUSSION Iitially time series plot (Fig. 3) was created to determie the treds i the price of Brijal from November 2002 to Jauary 206.Thepricesof Brijal show upward tred durig the study. O the basis of smaller values of measures of accuracy such as i table, Triple expoetial smoothig methods were employed for the selectio of best fitted model i this study. The forecasted prices of Brijal for Feb 206 to Sep 206 were Rs.0.6, Rs.0., Rs.4.9, Rs.5.3, Rs.20.3, Rs.2.5, Rs.2.9 ad Rs.2.0 per kg, respectively alog with 95% cofidece itervals (Table 2). y = x R² = Fig. 3. Time Series plot of Prices of Brijal LCL Actual Forecast UCL 235

5 It. J. Bio-res. Ev. Agril. Sci., March 206 Fig. 4. Triple Expoetial Smoothig plots for Brijal Table 2. Forecasted Prices of Brijal i West Brijal Moths Feb- 6 Mar-6 Apr-6 May-6 Ju-6 Jul-6 Aug-6 Sep-6 LCL Forecast UCL CONCLUSION The study showed that Triple expoetial smoothig method was appropriate for price estimatio of Brijal i West Begal. The values of the accuracy measures were smaller i Triple expoetial smoothig method. Eight moths forecasted prices ted to rise i the comig moths i West Begal. The risig i the price of Brijal have become a major cocer for policy makers for West Begal. May researchers stop shut at Triple Expoetial Smoothig because they could ot estimate the smoothig costat from their data at which MAE ad MSE will be smallest. But kowig what to do ad how to do it eve with a simple tool like MS Excel whe such opportuity presets itself will eable researchers obtai further explaatios. REFERENCE Holt, C. C Forecastig Seasoal ad Treds by Expoetially Weighted Movig Averages. Office of Naval Research, Research memoradum No. 52. Holt, C. C. Modigliai, F. Muth, J. F. Ad Simo, H. A.960.Plaig, Productio, Ivetories, ad Work Force. Pretice Hall, Eglewood Cliffs, NJ,USA. Witers, P. R Forecastig Sales by Expoetially Weighted Movig Averages. Maagemet Sciece, 6, Powerful Forecastig With MS Excel a sample book by Joe Choog. 236

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