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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:-
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
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
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
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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.
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
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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
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RESULTS Potato Arrivals Autocorrelation plots for Potato arrivals after taking d=D=1
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Partial autocorrelation plots for Potato arrivals after taking d=D=1
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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
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Ex-ante and Ex-post forecasting of Potato arrival MSE 3110592636 MAPE 22.80 Theil’S U 0.71
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Potato Price Autocorrelation plots for Potato prices after taking d=D=1
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Partial autocorrelation plots for Potato prices after taking d=D=1
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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
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Ex-ante and Ex-post forecast of potato prices MSE 16250 MAPE 18.28 Theil’S U 0.98
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