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USA, Argentina and Brazil are the top three Maize producing countries in the world. They are also major exporters. The prominent importing countries include Japan, European Union, Malaysia, Taiwan, Korea, etc. India ranks top 10 producers and exports to Bangladesh, Nepal, Sri Lanka, Middle East Asian countries. Maize is an important staple food in many countries and its acreage is on the increase continuously at global level. In India, Maize is emerging as third most important crop after rice and wheat .India produces around 15 million tonnes of Maize annually. This contributes to two per cent of the total world production. Maize is grown throughout the year in India. It is predominantly a kharif crop with 85 per cent of the area under cultivation in the season. It accounts for 9 per cent of total food grain production in the country.

Maharashtra is one of the emerging Maize growing states in India, accounting for about 9 per cent of the total Maize area and equally contributing to the total Maize production in the country. Maize is grown in all the districts of the state in varying degrees. The major growing districts are Ahmednagar, Aurangabad, Buldhana, Dhule, Jalana, Nandurbar, and Nashik. The crop yield in these district has increased consistently during the past 10 years.
            The major factors influencing on prices of Maize are the arrivals in market, climatic conditions during the various growth stages, carry forward stocks, price movement over the period of time, crop condition throughout the country, export and import, global and domestic demand and supply, etc. Seasonal variations observed in prices of Maize.The markets of Maize in Maharashtra are co-integrated and they influences on prices of each other. For better marketing of any agricultural commodity the information regarding seasonality, seasonal variations, price volatility, price movement across the state and country, etc. is necessary. Analysing the past trend in the price of commodities is also useful in understanding the present scenario and to formulate appropriate strategies to improve the marketing system. The present study has undertaken with following specific objectives:
Objectives
1) To study the seasonal and cyclical variations in prices of Maize.
2) To assess the price volatility and co-integration among the selected Maize markets in Maharashtra.

MATERIALS AND METHODS

For the present study the major markets of Maize in Maharashtra namely Nashik, Sangli, Jalna and Dhule were selected. The time series data on monthly average prices of maize for the period from 2004 to 2015 were collected from AGMARKNET website for respective markets and used for present study.
Tools of Analysis
Estimation of seasonal indices
To measure the seasonal variations in prices, seasonal indices were calculated by employing twelve months ratio to moving average method.
Estimation of cyclical indices
The residual method of estimating cyclical movement in time series was used for estimating cyclical indices, after eliminating the seasonal variations and trend components.
Testing of Stationarity in Price Series of Maize
Before analysing any time series data testing for stationarity is pre-requisite. The stationarity of time series data on maize prices was tested by applying the Augmented Dickey-Fuller test (ADF). The (ADF) test is the test for the unit root in a time series sample. A stationary series is one whose parameters are independent of time, exhibiting constant mean and variance and having autocorrelations that are invariant through time.
Market Co-integration
Johansen’s Multiple Co-integration test was employed to determine the long run relationship between the price series of selected markets. The test shows whether the selected Maize markets are integrated or not. Johansen (1988) has developed a multivariate system of equations approach, which allows for simultaneous adjustment of both or even more than two variables. The multivariate system of equations approach is more efficient than single equation approach since it allows to estimating the co-integration vector with smaller variance.
Causality of price signals between selected markets
In order to know the direction of causation between the markets, Granger Causality test was employed. It is named after the first causality tests performed by Clive Granger (1969). It analyzes the extent to which the past variations of one variable explain (or precede) subsequent variations of the other. When a co-integration relationship is present for two variables, a Granger Causality Test can be used to analyze the direction of this co-movement relationship. Granger causality test come in pairs, testing weather variable xt Granger-causes variable yt and vice versa. All permutations are possible.
Presence of Price Volatility
To access the presence of price volatility the ARCH-GARCH analysis was carried out. Auto Regressive Conditional Heteroscedasticity (ARCH) models are specifically designed to forecast conditional variances. ARCH model introduced by Engel (1982) and generalized as GARCH by Bollersllev (1986).

RESULTS AND DISCUSSION

Seasonal indices for Maize prices
The seasonal indices of monthly average prices of Maize for selected markets were worked out to study seasonal variations, which are presented in Table 1.

From Table 1 it is observed that in selected markets the prices were higher from June to September except sangli market in which prices were higher from June to October. The higher prices attributed to less arrivals of Maize in the markets. All the markets recorded lower prices in the months from October to May.

Table 1: Seasonal index for Maize prices in selected markets of Maharashtra

Month	Dhule	Jalna	Nashik	Sangli
Jan	97.08	99.75	93.37	88.35
Feb	97.53	98.30	93.59	94.12
Mar	97.55	78.92	96.09	94.25
Apr	94.64	96.33	98.67	97.24
May	94.00	95.63	98.59	98.40
Jun	100.22	103.81	103.11	101.85
Jul	110.96	110.05	109.03	109.26
Aug	111.91	109.73	112.52	110.32
Sep	115.25	113.10	106.62	110.14
Oct	95.92	98.34	99.47	101.86
Nov	90.11	98.02	96.18	97.83
Dec	94.79	98.03	92.76	96.37

 

Cyclical indices for Maize prices

The cyclical indices for Maize prices are presented in Table 2. From Table 2 it is observed that the cyclical variations were observed in the prices of Maize in the selected markets. The higher prices were recorded during the years 2004, 2012 and 2013 in all markets.

Table 2: Cyclical index for Maize prices in selected markets of Maharashtra

Testing of stationarity in price series

The Augmented Dickey Fuller (ADF) test based on unit root test procedure was carried out to check whether Maize prices are stationary in the selected markets and the results are presented in Table 3.

Table 3: ADF test results of Maize prices in selected markets of Maharashtra

From Table 3, it is observed that at level with lag 1, the ADF values are lesser than the critical value at 1% level of significance indicating the nonexistence of unit root implied that the price series in all markets are stationary. This implied that the Maize prices series of all selected markets are stationary at level.
Presence of price volatility

To assess the presence of price fluctuations in the prices of Maize, ARCH-GARCH analysis was carried out and the results are presented in Table 4.

Table 4: Results of ARCH-GARCH analysis for Maize prices in selected markets of Maharashtra

The sum of Alpha and Beta (α+β), indicated ARCH and GARCH effect for the given market. It was observed that among the markets, the sum of Alpha and Beta is nearer to 1 i.e. 1.006, 1.010, 2.077 and 1.004 for Dhule, Jalna, Nashik and Sangli markets, respectively, indicated that the volatility shocks in the prices of Maize are  persistent in these markets.
Market Co-integration

Johansen’s Multiple Co-integration test is employed to determine the long run relationship between the price series of Maize. The test shows whether the selected Maize markets are integrated or not. The results of the test were presented in Table 5.

Table5.  Results of multiple co-integration analysis for Maize prices in selected markets of Maharashtra

Presence of at least one co-integration equation at 5 per cent level of significance confirms that there exists long run equilibrium relation in the markets. The results of Co-integration test showed four co-integration equations were significant at 5% level of significance. It indicated that the selected Maize markets having long run equilibrium relationship and there existed co-integration between them.
Causality of price signals between selected markets
Granger Causality Test is a statistical tool which used F-test to know the cause and effect relationship between the two time series and this technique is employed to know the relationship between the prices of selected Maize markets. When a co-integration relationship is present for two price series, a Granger Causality Test (Granger, 1969) is used to analyse the direction of this co-movement relationship. The results of the test showing the relationship between selected Maize markets were presented in Table 6.

Table 6: Results of pair wise Granger causality test for Maize prices in selected markets of Maharashtra

From Table 6 It is observed that there was bidirectional causality in Maize prices between Nashik and Dhule, Nashik and Jalna, Sangli and Jalna and Sangli and Nashik. The prices of Dhule market exhibited unidirectional causality and affects prices of Jalna market. The prices of Sangli market exhibited unidirectional causality and affects prices of Dhule market. So the influence of Nashik and Sangli  markets prices plays a significant role over the other selected markets. Thus a strong market integration of the selected markets are established through the results of the analysis.

REFERENCES

Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroscedasticity. Journal of  Econometrics 31, 307–27.
Engle, R. F., & Granger, C. W. J.  (1987). “Cointegration and Error Correction:  Representation, Estimation and Testing,” Econometrica, 55(2), 251-276.
Madhusudan, G. (2011). Agricultural policy reforms and spatial integration of food grain  markets in India. Jour. of Econ. Development 36(2), 15-36.
Granger C. J. (1969). Investigating Causal Relationships by Econometrics Models and Cross Spectral Methods, Econometrica, 37, pp. 425-435.
Johansen, S. (1988). “Statistical Analysis of Cointegration Vectors,” Journal of Economic Dynamics and Control, 12, 231-254.
Mukim, M., Singh, K., Kanakaraj, A. (2009). Market Integration, Transaction Costs and the Indian Wheat Market: ASystematic Study. Economic & Political Weekly XLIV (22), 149-155.
Sekhar, C. S. C. (2003). Volatility of agricultural prices – an analysis of major international and domestic markets. Working Paper No. 103 (Indian Council For Research On International Economic Relations).