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Paper Presentation Mohan Kumar

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  • 1. Welcome Welcome Welcome
  • 2. FORECASTING OF ARRIVALS AND PRICES OF POTATO IN BANGALORE MARKET MOHAN KUMAR, T.L. MUNIRAJAPPA, R. SURENDRA, H.S. AND VENKATA REDDY, T.N. PRESENTED BY:-
  • 3. Introduction
    • India is the second largest producer of vegetables in the world next to China.
    • India is the third largest potato producing county with production of 25 million tonnes from the area of 1.5 million ha. in 2004-05
    • Karnataka state has a prominent position in the horticultural map of India
    • Karnataka produces 7.25 lakh tonnes in 0.75 ha. of land during 2005-06
    • In Karnataka, major potato growing districts are Hassan, Kolar, Belgaum and Bangalore district
  • 4. OBJECTIVES
    • To study the trend of arrivals and prices of potato in Bangalore market
    • To forecast the arrivals and prices of potato in Bangalore market
  • 5. MATERIALS
    • The secondary data were collected for the study was monthly arrivals and prices of potato from the Bangalore urban market for 9 years (1999-2008)
    • Data on monthly arrivals recorded in quintal
    • Data on monthly prices recorded in rupees per quintal
  • 6. Methodology
    • BOX-JENKINS ARIMA MODELS
    • ARIMA (p, d, q) (P, D, Q) S
    • p = Order of non-seasonal Auto Regressive (AR)
    • d = Order of non-seasonal difference
    • q = Order of non-seasonal Moving Average (MA)
    • P = Order of seasonal Auto Regressive (SAR)
    • D = Order of seasonal difference
    • Q = Order of seasonal Moving Average (SMA)
    • S = Length of the season
  • 7. Stationary
    • A stationary process has property that the mean and variance do not change over time. Since the ARIMA model refer only to a stationary time series, the first stage of Box-Jenkins model is reducing non-stationary series data to a stationary series
    • In order to test the stationary, compute the Auto-correlation functions (ACF) of difference series (Y t ) up to 25 lags. If the ACF for first and higher differences drop abruptly to zero then it indicates the series is stationary
  • 8. MAIN STEPS IN BOX-JENKINS ARIMA MODEL
    • Identification
    • Estimation of parameters
    • Diagnostic checking
    • Forecasting
  • 9. 1) Identification of the model
    • Identification of the order of an AR process will simply be equal to the number of Partial Autocorrelations significantly different from zero
    • The order of MA can be identified by examining the Autocorrelations function, When the first Autocorrelations are significantly different from zero
    • Yet another application of the Autocorrelation function is to determine whether the data contains a strong seasonal component. This phenomenon is established if the Autocorrelation coefficients at lags between t and t-12 are significant. If not, these, coefficients will not be significantly from zero
  • 10. 2) Estimation of parameters
    • After identifying the suitable model, principle of least square estimates of the parameters used to reduce sum squares
    Fundamentally two ways of getting estimates parameters Trial and error : Examine many different values and choose set of values that minimizes the sum of squares residual Iterative method : Choose a preliminary estimate and let a computer program refine the estimate iteratively
  • 11. II) Akaike Information Coefficient (AIC) criteria is used to determine both the differencing order (d, D) required to attain stationary and the appropriate number of AR and MA parameters 3) Diagnostic checking of the model I) Ljung and Box (1978) ‘Q’ statistic h = Maximum lag considered n = Number of observation r k = ACF for lag k m =p+ q= Number of parameters to be estimated Q is distributed approximately as a Chi-square statistic with (h-m) degree of freedom.
  • 12.
    • 4) Forecasting
    • The objective of ARIMA model for a variable is to generate post sample period forecast for the same variable.
    • The ultimate test for any model is whether it is capable of predicting future events accurately or not. The model is
    (1- δ p B)(1- Φ P B)(1-B d ) (1-B D )Y t =C+ (1-  q B) (1- Θ Q B) e t
  • 13. The accuracy of forecasts for both Ex-ante and Ex-post is tested 1) Mean square error (MSE) 2) Mean absolute percentage error (MAPE) 3) Theils U coefficient Where, = Actual values = Predicted values
  • 14. RESULTS Potato Arrivals Autocorrelation plots for Potato arrivals after taking d=D=1
  • 15. Partial autocorrelation plots for Potato arrivals after taking d=D=1
  • 16. Tentatively identified models for Potato arrivals Model Q-statistic Degrees of freedom(df) Akaike Information Coefficient ( 1 1 1 ) (2 1 2) 18.09 19 2357.29 ( 1 1 1 ) (1 1 2) 18.53 20 2356.81 ( 1 1 1 ) (1 1 1) 19.76 21 2357.52 ( 1 1 1 ) (1 1 3) 18.90 19 2357.32 ( 0 1 1 ) (1 1 2) 21.20 21 2357.13 (1 1 1 ) (2 1 0) 18.07 21 2355.35 ( 1 1 1 ) (2 1 1) 18.71 20 2356.56
  • 17. Actual and forecasted values for arrivals of Potato (Qts) Months Actual value Forecasted value Months Actual value Forecasted value Apr-07 180,730 218,805 Apr-08 - 144,851 May 171,207 177,026 May - 179,866 Jun 206,734 163,372 Jun - 182,840 Jul 128,501 152,538 Jul - 131,842 Aug 313,006 336,101 Aug - 283,670 Sep 411,748 358,521 Sep - 323,039 Oct 187,945 279,956 Oct - 208,778 Nov 126,790 152,987 Nov - 125,929 Dec 138,449 146,431 Dec - 125,711 Jan-08 137,870 173,380 Jan-09 - 151,543 Feb 158,944 168,181 Feb - 148,849 Mar 133,244 229,280 Mar - 162,947 MSE = 3110592636 MAPE = 22.80 Theil,s U= 0.71
  • 18. Ex-ante and Ex-post forecasting of Potato arrival MSE 3110592636 MAPE 22.80 Theil’S U 0.71
  • 19. Potato Price Autocorrelation plots for Potato prices after taking d=D=1
  • 20. Partial autocorrelation plots for Potato prices after taking d=D=1
  • 21. Tentatively identified models for Potato prices * indicates significant at 5% level ** indicates significant at 1% and 5% level Model Q-statistic Degrees of freedom(df) Akaike Information Coefficient ( 0 1 0 ) (0 1 1) 35.29 24 1196.18 ( 1 1 1 ) (0 1 1) 33.32 * 22 1199.93 ( 1 1 1 ) (1 1 1) 32.50 21 1200.88 ( 0 1 0 ) (1 1 1) 32.25 23 1197.15 ( 0 1 1 ) (1 1 1) 36.03 ** 22 1198.85 (1 1 1 ) (0 1 2) 32.17 21 1200.83
  • 22. Actual and forecasted values for prices of Potato (Qtls) Months Actual value Forecasted value Months Actual value Forecasted value Apr-07 1,050 812 Apr-08 - 1,007 May 881 1,178 May - 1,093 Jun 1,005 922 Jun - 1,147 Jul 1,119 1,036 Jul - 1,191 Aug 969 951 Aug - 1,027 Sep 1,065 910 Sep - 991 Oct 1,075 1,192 Oct - 1,103 Nov 1,113 1,158 Nov - 1,180 Dec 1,038 1,107 Dec - 1,165 Jan-08 988 975 Jan-09 - 1,105 Feb 925 944 Feb - 1,060 Mar 888 903 Mar - 1,037 MSE=16250 MAPE=18.28 Theil,s U= 0.98
  • 23. Ex-ante and Ex-post forecast of potato prices MSE 16250 MAPE 18.28 Theil’S U 0.98
  • 24. conclusion
    • The Box-Jenkins ARIMA models were suitable for both monthly arrivals and prices for potato crops under stationary as well as non-stationary situation
    • ARIMA model is best applicable under the situation of seasonality in the data
    • Box-Jenkins’s method is more applicabled for precise forecasting the arrivals and prices of potato in Bangalore market
    • Forecasted value found similar trend of actual data in both arrivals and price of potato
    • Forecasting by using ARIMA model resulting with arrivals were high during the month of harvest period and fetches high prices in the off-season.
  • 25. Thank u