View
6.121
Download
3
Embed Size (px)
DESCRIPTION
Citation preview
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