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The present study was conducted in Assandh and Karnal Blocks of Karnal district, Haryana which was selected purposively on the basis of maximum production under basmati rice crop. Further, four regulated markets in Karnal district,

Market information is critical to the social and economic activities that comprise the development process. Developing economy has witnessed agricultural (green, white, yellow, blue and now rainbow), industrial and information technology revolutions. Good communication system and information system reinforce commitments to sustainable productivity. The Government of India has given more thrust on agriculture, food and information technology sectors towards achievement of economic reforms for achieving high growth rate in production (Dhankar, 2003). Marketing Information System is an interacting structure of people, equipments and procedures to arrange, analyze, evaluate, distribute, timely and right information for use by proper marketing decision makers to improve their marketing design, implementation, and control (Kotler and Keller, 2012). Singh

1.To estimate the price forecasts and long term relationship in prices among domestic markets.

The study is based on average prices of basmati rice in Haryana, data for the period of 2005 to 2016 were analyzed the time series methods. Auto Correlation Function (ACF) and Partial Auto Correlation Function (PACF) were calculated for the data. Appropriate Box-Jenkins Auto Regressive Integrated Moving Average (ARIMA) model was fitted. Validity of the model was tested using standard statistical techniques. ARIMA (0, 1, 0) and ARIMA (1, 1, 2) model were used to forecast average prices in Karnal for one leading years. The annual data on average price for the period from 2005 to 2016 were used for forecasting the future values using ARIMA models. The ARIMA methodology is also called as Box Jenkins methodology. The Box-Jenkins procedure is concerned with fitting a mixed Auto Regressive Integrated Moving Average (ARIMA) model to a given set of data. The main objective in fitting this ARIMA model is to identify the stochastic process of the time series and predict the future values accurately. These methods have also been useful in many types of situation which involve the building of models for discrete time series and dynamic systems. But, this method was not good for lead times or for seasonal series with a large random component (Granger and Newbold, 1970). Originally ARIMA models have been studied extensively by George Box and Gwilym Jenkins during 1968 and their names have frequently been used synonymously with general ARIMA process applied to time series analysis, forecasting and control. However, the optimal forecast of future values of a time-series are determined by the stochastic model for that series. A stochastic process is either stationary or non-stationary. The first thing to note is that most time series are non-stationary and the ARIMA model refer only to a stationary time series. Since, the ARIMA models refer only to a stationary time series, the first stage of Box- Jenkins model is reducing non-stationary series to a stationary series by taking first order differences.

The main steps in setting up a Box-Jenkins forecasting model are as follows:

Appropriate value of p,d and q are found first. The tools used for identification are the Autocorrelation Functions (ACF) and Partial Autocorrelation Functions (PACF).

The ARIMA process has the algebraic form:

Where,

The general functional forms of ARIMA model used are:

(i)Moving Average model of order q; MA (q)

(ii)Autoregressive model of order p; AR (p)

(iii)Autoregressive Moving Average Model ARMA (p, q)

(iv)Autoregressive Integrated Moving Average Model ARIMA (p, d, q)

(v)Seasonal ARIMA model ARIMA (p, d, q) (P,D,Q)^{s}

Where, a_{t} belongs to NID (0, σ^{2}_{a})

Where,

Y_{t} = Variable under forecasting

_{t}_{t}_{t} is the estimated value of _{t})

_{ϕp(B)} = Non-seasonal AR

ϕ*_{p}(B^{s}) = seasonal AR operator

(1-B)^{d} = Non-seasonal difference

(1-B^{s})^{d} = seasonal difference

θ_{q}(B) = Non-seasonal MA

ϕ*_{p}(B^{s}) = seasonal MA operator

The above model contains p+q+P+Q parameters, which need to be estimated. The model is non-linear in parameters.

For estimating the parameters of the ARIMA model, the algorithm is as follows:

For p, d, q, P, D and Q each = 0 to 2

Execute SPSS ARIMA with the set parameters.

Record the parameters and corresponding fitting error until all possible combinations are tried. Select the parameters that produce the least fitting error. This algorithm tries all combinations of parameters, which are limited to an integer lying between zero and two. The combination with the least fitting error will be searched. The range limitations of the parameters are set to restrict the searched to a reasonable scope. Parameters greater than two are rarely used in practices as per literature.

Having chosen a particular ARIMA model and having estimated its parameters the fitness of the model is verified. One simple test is to see if the residuals estimated from the model are white noise, if not we must start with other ARIMA model. The residuals were analyzed using Box- Ljung statics.

One of the reasons for the popularity of the ARIMA modeling is its success in forecasting. In many cases, the forecasts obtained by this method are more reliable than those obtained from the traditional econometrics modeling, particularly for short-term forecasts. An Autoregressive Integrated Moving Average process model is a way of describing how a time series variable is related to its own past value. Mainly an ARIMA model is used to produce the best weighted average forecasts for single time series (Rahulamin and Razzaque 2000). The accuracy of forecasts for both Ex-ante and Ex-post were using the following test (Markidakis and Hibbon, 1979) such as Mean absolute percentage error (MAPE).

In this study, we used the data average prices for the period 2005 to 2016. As we have earlier stated that development of ARIMA model for any variable involves four steps: Identification, Estimation, Verification and Forecasting. Each of these four steps is now explained for basmati rice average prices as follows.

For forecasting Basmati rice average price, ARIMA model estimated only after transforming the variable under forecasting into a stationary series. The stationary series is the one whose values over time only around a constant mean and constant variance. In this difference of order 1 was sufficient to achieve stationarity in mean. The newly constructed variable X_{t}can now be examined for stationary. The graph of X_{t} was stationary in mean. The next steps are to identify the values of p, _{t} are computed. The model statistics showing goodness fit for Root Mean Square Error (RMSE), Mean Absolute Percentage Error (MAPE), Normalized Bayesian Information Criterion (Normalized BIC), Ljung-Box statistics are depicted in

Basmati rice average prices model parameters were estimated using SPSS package. Results of estimation are reported in

Model statistics of different markets in Karnal district of Haryana

Model parameters of different markets in Karnal district of Haryana

From Assandh market the data set only first order differentiation was found to be fit and seasonal AR(p) of Lag 1 were fitted with on degree of differentiation. The tentative models were identified based on Autocorrelation functions (ACF) and Partial Autocorrelation functions (PACF) at fixed interval, showing significant for price of basmati rice crop in Karnal district markets (

ARIMA models are developed basically to forecast the corresponding variable. To judges the forecasting ability of the fitted ARIMA model important measure of the sample period forecasts accuracy was computed. Forecasting performance of the model was judged by computing Mean Absolute Percent Error (MAPE). The model with less MAPE was preferred for forecasting purposes. Forecasting was done through indentified models for the variable prices of Basmati rice crop in selected district markets. Using the obtained model, the expost forecasted values, considering the January 2005 to December 2016 were computed and have been presented in Fig. 1 to 4. The figs. observed that the forecasted of price in Karnal, Gharunda, Assandh and Taraori markets moved in same direction with observed values.

Autocorrelation and partial autocorrelation functions of average monthly prices in Gharunda market of Karnal district

Autocorrelation and partial autocorrelation functions of average monthly prices in Gharunda market of Karnal district

Autocorrelation and partial autocorrelation functions of average monthly prices in Assandh market of Karnal district

Autocorrelation and partial autocorrelation functions of average monthly prices in Taraori market of Karnal district

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The price forecasts in main market of Karnal district,

Co-integration is a statistical property obtained by given time series data set that is defined by the concepts of stationarity and the order of integration of the series. The stationary series is one with a mean value which will not change during the sampling period. For an illustration, the mean of a subset of a given series does not vary significantly from the mean of any other subset of the same series. Further, the series will constantly return to its mean value as fluctuations occur. In other words, a non-stationary series will shows a time-varying mean. The order of integration of a series is given by the number of times the series must be differenced in order to produce a stationary series. Co-integration analysis was carried out to study the long run relationship of average price of basmati rice for Karnal districts in all four markets. The Dickey-Fuller test was used to study the order co-integration of prices among different markets.

Forecasting of Basmati rice for average monthly price of Kamal market for Karnal district (Main market)

Forecasting of Basmati rice for average monthly price of Gharunda market for Karnal district (Reference market)

Forecasting of Basmati rice for average monthly price of Assandh market for Kamal district (Main market)

Forecasting of Basmati rice for average monthly price of Taraori market for Karnal district (Reference market)

Co-integration between selected markets for basmati rice selected agricultural commodities in Haryana

The

In our study, the developed model for average prices for basmati rice in Karnal district was found to be ARIMA (0, 1, 0) (1, 1, 2) respectively. From the forecast variable by using the developed model, it can be seen that forecasted average price increases the next years. The validity of the forecasted value can be checked when data for the lead periods become available. The model can be used by researchers for forecasting average prices in Karnal. However, it should be updated from time to time with incorporation of current data.

In this study the development model for average prices for basmati rice in Karnal district was found to be ARIMA (0,1,0) (1,1,2) respectively. From the forecast variable by using the developed model, it can be seen that forecasted value can be checked when data for the lead periods become available. The model can be used by researchers for forecasting average prices in Karnal. However, it should be updated from time to time with incorporation of current data.

Authors are thankful to Department of Agricultural Economics, Chaudhary Charan Singh Haryana Agricultural University, Hisar, 123005.