Agriculture is known as the backbone of the Indian Economy, which plays a vital role for the economic development. Further, agricultural commodities have a significant weight in the GDP of our economy. Commodity prices represent an important variable in the economy. Prediction of these prices is considered to be the most important, because they can influence the government’s plan, economic and financial policies. Price volatility affects macroeconomic performance, influencing the country’s overall economy. Forecasting of agricultural prices have a major role in such countries, because macroeconomic policies are formulated considering the forecasted prices as a major factor (browman and Husain, 2004).
In order to forecast the price of commodities, Time Series Analysis is an important approach. ARIMA-Auto Regressive Integrated Moving Average Model, traditionally, have been one of the most widely used model for univariate variable.
A few risks associated with the Indian agriculturists are price risk, yield risk, monsoon risk and so on. Price risk is one such risk which can be mitigated by hedging the price of agricultural commodities in futures market. In order to explore the price risk mechanism, this study is undertaken to focus on the behavior of futures price of Maize, as India represents one of the leading country in producing Maize in the World.
REVIEW OF LITERATURE:
Literatures which were reviewed to analyse the forecasting techniques of agri commodity futures and spot market in India and abroad are as follows:
1. Rangsan, et.al.(2006), researched on fitting the best ARIMA model to forecast the wholesale price of palm oil of Thailand. Three types of price such as farm price, wholesale price and pure oil price for a period of five years from 2000-2004 were considered for this purpose. The model fitted, by considering the minimum of mean absolute percentage error (MAPE), were: for farm price of oil palm is ARIMA(2,1,0), for wholesale price of oil palm is ARIMA(1,0,1) or ARMA(1,1) and for pure oil price of oil palm is ARIMA(3,0,0) or AR(3).
2. Salvadi, et.al.(2008), examined the price discovery function of selected agri commodities (castor, cotton, peper and soya) in Indian Commodity Futures Market. Daily futures prices were collected from MCX and NCDEX for the study. Through the analysis of statistical data on price discovery of the selected agri commodities, the result showed that futures market in these commodities are not efficient. Further, the authors also studied the relationship between price, return, volume, market depth and volatility on these selected commodities, which shows that spot and futures markets are not integrated.
3. Elumalai, et.al.(2009), assessed the futures and spot price linkages for three agri commodities through Johnsen Co integration Analysis and Vector Error Correction Model. The result showed that these three commodity futures influenced the spot prices indicating its better hedge efficiency for producers to hedge their price risk in the futures market platform.
4. Vasisht, et.al. (2010), examined the volatility of maize spot and futures prices. The volatility indices were computed using the data for futures price of maize for the year 2007 and 2008 by using ARCH, co-integration, granger causality. The results had revealed that there is a long run price equilibrium relationship between the prices and it also resulted that there was volatility of spot and futures price of august month. The results also said that there is unidirectional causality from futures to spot market prices.
5. Trevor, et.al.(2011), discussed the theoretical relationship between spot and futures prices for commodities and by evaluating the empirical forecasting performance of futures prices relative to some alternative benchmarks. The results of this analysis is that futures prices have generally outperformed a random walk forecast, but not by a large margin, while both futures and a random walk noticeably outperform a simple extrapolation of recent trends. Finally concluded that futures prices, on average, outperform a random walk by a consideration margin when there is a sizeable difference between spot and future prices.
6. Moraes, et.al.(2011), using coffee spot prices from 2000 to 2010, analyzed the forecast performance of GARCH, EGACH and TGARCH. They use mean square error and Theil U to select the best model in each class. Their selected models are GARCH(2,1), EGARCH(1,1) and TGARCH(2,1). Among these models GARCH (2,1) was chosen as the best model to forecast coffee spot prices.
7. Sanjay, et.al.(2012), studied the price discovery relationship for ten agricultural commodities. Price discovery is confirmed for all commodities except Turmeric. Price discovery results are encouraging given the nascent character of commodity market in India. However, the market does not seem to be competitive.
8. Adalto, et.al.(2014), studied and estimated the models ARIMA and Volatility (GARCH, GJR and EGARCH) for forecasting the spot prices of coffee and cattle. Daily spot prices from January 2003 to December 2013 were used. Different ARIMA model and Volatility models (GARCH, GJR, EGARCH) were evaluated based on Schwarz criterion. The result says that, for cattle, ARIMA(1,1,1) with GARCH(2,2), GJR(5,6), and EGARCH(4,5) and for coffee, ARIMA(2,1,0) with GARCH(1,1), b, GJR(1,1,1) EGARCH(1,1,1) are the best fit model to forecast the price.
9. Khalid, et.al.(2014), examined the techniques that forecast the market price of grains by using ARMA and WAVELET models. A monthly data consists of 300 observations starting from July 1983 to July 2013 were considered. It contains international prices of wheat, rice, barely and maize. Result with the help of three different error tests showed that wavelet forecasting method is the most appropriate one to forecast the grain prices.
10. Prabhakaran, et.al.(2014), studied and forecasted the areas and production of rice in India for the time period from 1950-51 to 2011-12. ARIMA (1,1,1) model were used to forecast both the areas and production of rice for the next four years. As per the result, forecasted areas of production for the year 2015 to be about 44.75 thousand hectares with upper and lower limits 47.53 and 41.97 thousand hectares respectively and forecasted rice production to be about 104.37 thousand tonnes with upper and lower limits 115.26 and 93.48 thousand tonnes respectively.
NEED FOR THE STUDY:
In India, agricultural commodities have relevant weights in the GDP. Further, prices represent an important variable in the economy. Forecasting the prices of these commodities are considered to be the most important, because they can influence the government’s plan, economic and financial policies. Further, price risk is one of the main risk faced by Indian farmers. Traditional mechanism like MSP (Minimum support price) etc. needs to be revived and modern/market driven mechanism like commodity futures market needs to be focused. In this backdrop, the present study has been undertaken and an attempt is made to highlight the relevance of price forecasting techniques which helps the different players in the field of agri commodity futures market.
SCOPE OF THE STUDY:
The study covers only secondary data which is available at NCDEX-National Commodity and Derivatives Exchange of India. Major agri commodities are traded at this platform. Maize is one such agri commodity whose data is available at NCDEX website. Data covered for short period from October 2013 to March 2016 with the total observation of 213 for the delivery center of Nizamabad, Telangana State. The variety of Maize considered was Maize-Feed/Industrial grade (MAIZE KHRF).
OBJECTIVES OF THE STUDY:
1. To check the series are stationary series or non-stationary series.
2. To verify the suitability of appropriate ARMA Structure.
3. To propose a suitable Model for the purpose of forecasting.
Hypotheses:
Following hypotheses have been framed in accordance with the set of objectives listed above.
1. For testing the Stationarity:
H0: “Maize futures prices are not Stationary”
H1: “Maize futures prices are Stationary”
2. For testing the model adequacy:
Test of Normality:
H0: “Maize futures prices are normally distributed”
H1 “Maize futures prices are not normally distributed”
Test of Autocorrelation (Serial Correlation LM Test):
H0 “Maize futures prices have no Autocorrelation problem”
H1 “Maize futures prices have Autocorrelation problem”
Test of Heteroscedasticity:
H0 “Maize futures prices have no ARCH effect”
H1 “Maize futures prices have ARCH effect”
METHODOLOGY OF THE STUDY:
The present study is based on empirical research. It focused at studying the stationarity of Futures price of Maize commodity and its respective modeling. This paper concentrates to examine to fit a suitable ARIMA Model for the purpose of estimating the futures price of Maize. For this purpose, daily closing prices of Maize (secondary data) were collected from NCDEX website for the period starting from October 2013 to March 2016 with the total observation of 213.
Econometric Tools such as Unit root test for stationarity like Augmented Dickey Fuller (ADF) test and Phillips Perron (PP) test to check the stationary and ACF, PACF were applied and model adequacy test was done on the fitted model. Modeling was done by running various ARIMA models at differenced level of price series. All these tests were conducted and the results have been obtained by using EVIEWS software version 7.
TEST OF STATIONARITY:
In order to forecast, the series of variables should be stationary. If they are not stationary, they can be made stationary by differencing either at 1st, 2nd or 3rd difference.
The ADF test consists the following regression:
Where, ∆Yt is the first difference operator (Yt – Yt-1), α is an intercept/constant, βt is the coefficient on a time t, γ is the coefficient that allows the stationary test (if γ = 0, Y has a unitary root), p is the number of lag terms to be included in the model and εt is the random error term or the stochastic disturbance.
Test of hypotheses:
H0: “Maize prices are not stationary”
H1: “Maize prices are stationary”
In order to test for the existence of unit roots, and to determine the degree of differencing necessary to induce stationarity, we have applied the Augmented Dickey –Fuller test (ADF Test)
The following are the ADF Test results for the chosen variables.
Table No. ADF Test at Level variables:
|
|
Test without constant |
Test with intercept/ constant |
Test with constant and trend |
|
FUTURES PRICE |
p-value 0.7466 |
P-value 0.6386 |
p-value 0.4914 |
Source: Eviews output
Interpretation of results:
Futures price at their level, corresponding p values are more than 0.05 significance level, which has led us to conclude that Null Hypothesis that γ=0 or H0=1 cannot be rejected. In other words, the given price series have unit root and hence are Non-Stationary in nature.
Table No. 2 ADF Test at First Differences of Variables:
|
|
Test without constant |
Test with intercept/ constant |
Test with constant and trend |
|
FUTURES PRICE |
p-value 0.0000 |
p-value 0.0000 |
p-value 0.0000 |
Source: Eviews output
Interpretation of results: Futures price variable at their First order difference, by their corresponding p –values are less than the significance level of 0.05. This shows that the variable futures price at their First order differences do not have unit root and hence are Stationary in nature.
Table No.3 PP Test at Level variables:
|
|
Test without constant |
Test with intercept/ constant |
Test with constant and trend |
|
FUTURES PRICE |
p-value 0.7408 |
p-value 0.5858 |
p-value 0.4360 |
Source: Eviews output
Interpretation of results: Futures price at their level, corresponding p values are more than 0.05 significance level, which has led us to conclude that Null Hypothesis that γ=0 or H0=1 cannot be rejected. In other words, the given price series have unit root and hence are Non-Stationary in nature.
Table No.4 PP Test at First Differences of Variables:
|
|
Test without constant |
Test with intercept/ constant |
Test with constant and trend |
|
FUTURES PRICE |
p-value 0.0000 |
p-value 0.0000 |
p-value 0.0000 |
Source: Eviews output
Interpretation of results: Futures price variable at their First order difference, by their corresponding p –values are less than the significance level of 0.05. This shows that the variable futures price at their First order differences do not have unit root and hence are Stationary in nature.
MODELLING OF MAIZE FUTURES PRICE SERIES BY USING ARIMA:
Broadly speaking, there are different approaches to economic forecasting based on time series data. They are, Exponential Smoothening Method, Single-Equation Regression Model, Simultaneous-Equation Model, ARIMA-Auto Regressive Integrated Moving Average Model, VAR-Vector Autoregression Model. The general ARMA model was introduced by Peter Whittle, and it became common after book by George E. P. Box and Gwilym Jenkins.
The present study is based on ARIMA, one such approach among the above mentioned important approaches for forecasting. ARIMA popularly known as Box-Jenkins Methodology.
• We begin by determining the order of differencing (d) which requires to stationarize the series by examining ACF and PACF functions of Futures price series with the help of correlogram.
• After identifying the probable models, the Akaike Information Criteria (AIC)and Schwartz Bayesian Criteria (SBC/BIC) are used to select that ARIMA(p,d,q) model for the AIC and BIC are minimum.
Figure No. 1 ACF and PACF of FUTURES PRICE:
Source: Eviews output
The above correlogram clearly suggest that the FUTURES PRICE variable has unit root and PACF graph reveals that there is one significant spike in lag 1 of the variable futures price. It means significant information is available (at lag 01) in the previous day. Further, it also indicates that, today’s futures price is influenced by previous day’s futures price.
AR(1) Process: (Yt−δ)=α1(Yt−1−δ)+ut
This model says that the forecast value of Y at time t is simply some proportion (=α1) of its value at time (t−1) plus a random shock or disturbance at time t.
AR (2) Yt follows a second-order autoregressive, or AR (2) process. That is, the value of Y at time t depends on its value in the previous two time periods, the Y values being expressed around their mean value δ.
Notice that in all the preceding models only the current and previous Y values are involved; there are no other regressors. In this sense, we say that the “data speak for themselves.”
Moving Average (MA) Process: Here Y at time t is equal to a constant plus a moving average of the current and past error terms. Thus, in the present case, we say that Y follows a first-order moving average, or an MA(1), process. But if Y follows the expression:
Yt=μ+β0ut+β1ut−1+β2ut−2
The next focus of the study is to analyze the auto regressive nature of the chosen Futures price series by applying ARIMA models.
The acronym ARIMA stands for Auto-Regressive Integrated Moving Average. Lags of the stationarized series in the forecasting equation are called "autoregressive" terms, lags of the forecast errors are called "moving average" terms, and a time series which needs to be differenced to be made stationary is said to be an "integrated" version of a stationary series. Random-walk and random-trend models, autoregressive models, and exponential smoothing models are all special cases of ARIMA models.
A non-seasonal ARIMA model is classified as an "ARIMA (p,d,q)" model, where:
· p is the number of autoregressive terms,
· d is the number of non-seasonal differences needed for stationarity, and
· q is the number of lagged forecast errors in the prediction equation.
The forecasting equation is constructed as follows. First, let y denote the dth difference of Y, which means:
If d=1: yt = Yt - Yt-1
If d=2: yt = (Yt - Yt-1) - (Yt-1 - Yt-2) = Yt - 2Yt-1 + Yt-2
In terms of y, the general forecasting equation is:
ŷt = μ + ϕ1 yt-1 +…+ ϕp yt-p - θ1et-1 -…- θqet-q
To identify the appropriate ARIMA model for Y, i…e AR(1), AR(2), …, and MA(1), MA(2), … etc..we begin by determining the order of differencing (d) needed to stationarize the series by examining ACF and PACF functions of Futures price series with the help of correlogram .
After identifying the probable models the Akaike Information Criteria (AIC)and Schwartz Bayesian Criteria (SBC/BIC) are used to select that ARIMA(p,d,q) model for which the AIC and BIC are minimum.
RESULT OF ARIMA (1,1,1) FOR MAIZE FUTURES:
Fitting the most appropriate ARIMA model mainly aims at forecasting the price for a single time series (Rahulamin and Razzaque 2000). ARIMA models are developed basically to forecast the corresponding price of the variable.