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:-

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

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

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

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

StationaryA 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 (Yt) up to 25 lags. If the

ACF for first and higher differences drop abruptly to zero

then it indicates the series is stationary

MAIN STEPS IN BOX-JENKINS ARIMA MODEL

1) Identification

2) Estimation of parameters

3) Diagnostic checking

4) Forecasting

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

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

II) Akaike Information Coefficient (AIC) mnnAIC 2log2log1 2

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

rk = 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.

h

1k

2k

1r)kn()2n(nQ

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-δp B)(1-ΦPB)(1-Bd) (1-BD)Yt =C+ (1-qB) (1-ΘQB) et

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

2n

1ttt YY

n

1MSE

n

1t t

tt 100*Y

YY

n

1MAPE

1n

1t

2

t

t1t

1n

1t

2

t

1t1t

Y

YY

Y

YY

U

tY

tY

Where,

= Actual values

= Predicted values

RESULTS

1 3 5 7 9 11

13

15

17

19

21

23

25

Lag Number

-1.0

-0.5

0.0

0.5

1.0

AC

F

Coefficient

Upper Confidence Limit

Lower Confidence Limit

Potato Arrivals

Autocorrelation plots for Potato arrivals after taking d=D=1

1 3 5 7 9 11

13

15

17

19

21

23

25

Lag Number

-1.0

-0.5

0.0

0.5

1.0

Pa

rtia

l A

CF

Coefficient

Upper Confidence Limit

Lower Confidence Limit

Partial autocorrelation plots for Potato arrivals after taking d=D=1

Tentatively identified models for Potato arrivals

Model Q-statisticDegrees 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

tt eBCYBBBBB 11224

212

11 11111

MonthsActual value

Forecasted value

MonthsActual 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

Actual and forecasted values for arrivals of Potato (Qts)

Ex-ante and Ex-post forecasting of Potato arrival

MSE 3110592636MAPE 22.80Theil’S U 0.71

Potato Price

1 3 5 7 9 11 13 15 17 19

21 23 25

Lag Number

-1.0

-0.5

0.0

0.5

1.0

AC

F

Coefficient

Upper Confidence Limit

Lower Confidence Limit

Autocorrelation plots for Potato prices after taking d=D=1

1 3 5 7 9 11 13 15 17 19 21 23 25

Lag Number

-1.0

-0.5

0.0

0.5

1.0

Part

ial A

CF

Coefficient

Upper Confidence Limit

Lower Confidence Limit

Partial autocorrelation plots for Potato prices after taking d=D=1

Tentatively identified models for Potato prices

Model Q-statisticDegrees 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

* indicates significant at 5% level ** indicates significant at 1% and 5%

level

t12

1t12 eB1CYB1B1

MonthsActual value

Forecasted value

MonthsActual value

Forecasted value

Apr-07 1,050 812 Apr-08 - 1,007May 881 1,178 May - 1,093Jun 1,005 922 Jun - 1,147Jul 1,119 1,036 Jul - 1,191

Aug 969 951 Aug - 1,027Sep 1,065 910 Sep - 991Oct 1,075 1,192 Oct - 1,103Nov 1,113 1,158 Nov - 1,180Dec 1,038 1,107 Dec - 1,165

Jan-08 988 975 Jan-09 - 1,105Feb 925 944 Feb - 1,060Mar 888 903 Mar - 1,037

MSE=16250 MAPE=18.28 Theil,s U=0.98

Actual and forecasted values for prices of Potato (Qtls)

Ex-ante and Ex-post forecast of potato prices

MSE 16250MAPE 18.28Theil’S U 0.98

conclusionThe 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