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^{*}Corresponding author : P Mishra; E-mail:

In India, white revolution was started during 1970’s with Operation flood programme. After this revolution, production of milk in India had tremendously increased. Contribution of diary sector has continuously increased in Indian Gross Domestic Product (GDP). Livestock sector has emerged as an essential growth driver of the Indian wealth. This study is associated with time series data of five major milk producing states in 2017-18 in India. The milk production projection has been made using Auto Regressive Integrated Moving average model (ARIMA) for year 2024-25. From the forecasted figures, Uttar Pradesh would be leading states of India in milk production with 37.68 MMT in year 2024-25. Whole India milk production would reach 252.948 MMT in year 2024-25. This projection helps in formulating national agricultural policy as well as proper planning for products into dairy sector.

Dairy sector in India is one of the vibrant sectors of India; it has witnessed record growth of 6.7 percent during 2017¬18 (Anonymous, 2018). This phenomenal growth record is also accompanied by its being recognized by NITI AYOG as the prime sector which can help double income of the farmers' in the country. The dairy sector has made excellent performance in exporting high value products to the tune of US $575 million compared to its imports of US $34.6 million and helped India re-emerge as the net exporter of dairy products. In 1970-71, per capita milk availability was 110 gram per day per person which rose to 378 gram per day per person in 2017-18 (Anonymous, 2018). This has significantly contributed to the betterment of food sufficiency of the nation. Despite such impressive performance, milk is luxury for many in India. The milk prices in India are comparatively higher than price prevailing in International market Bhardwaj

Time series is a branch of Statistics; the object is to study variables over time. Among its main objectives is the determination of trends within these series as well as the stability of values (and their variation) over time. Unlike traditional econometrics, the purpose of time series analysis is not to relate variables to one another, but to focus on the “dynamics” of a variable. In particular, linear models (mainly AR and MA, for Auto-Regressive and Moving Average), (Box-Jenkins, 1976)

These five states contributed nearly 53 percent of total milk production in India. The data for analysis was collected from the Department of Animal Husbandry, Dairying & Fisheries, Ministry of Agriculture and Farmers Welfare, Government of India.

In practice, it is impossible to know the probability distribution of a time series y_{t}_{t}

Conditioned on the history of the process: y_{t}_{t1}_{0}. It is therefore a necessity to model y_{t}

The conditional approach in Equation (i) provides a decomposition prediction error, according to which:

Where, E_{t}_{t}_{0}are known. And e_{f} represents unpredictable information. We suppose, e_{f}^{2}), is white noise process. The equation (2) represents an autoregressive model (AR) of order

The value y_{t}_{t}_{t1}_{-2}

The moving average processes assume that each observation y_{t}_{t}-1, e_{t}-2, ..., z_{tp}

The combination of the two models, AR (p) in equation (3) and MA(q) in equation (4) is an ARMA(p, q) process; which is the most popular models of the Box Jenkins for its flexibility and suitability for various data types. The model is designed as follow:

With:

The time series y_{t}

Definition: a time process _{t} with real values and discrete time y_{1}_{2}_{t}

When one or more stationary conditions are not met, the series is said to be non-stationary. This term, however, covers many types of non-stationary, (no-stationary in trend, stochastically non-stationary,...), we focused on the later. Thus, if y_{t}

The difference operator is given by: A(y_{t}_{t}_{t1}

With, _{t}^{d} y_{t}_{t}_{t}

Box and Jenkins (1970) proposed a prediction technique for a univariate series that is based on the notion of the ARIMA process. This technique has three stages: identification, estimation and verification. The

Generally, we use the _{t} follow a normal distribution, _{E}^{2}). The log-likelihood function of a ARMA

With:

The _{t}

We have six time series of milk production: for India at whole, Gujarat, Rajasthan, Andhra Pradesh, Madhya Pradesh and Uttar Pradesh over the period (2001-2018). ^{2}y_{t}^{2}_{t} _{t1}

Based on the selected models, and trough the theoretical part of this study, the almost objective of the Box-Jenkins method is to forecast the future dynamic of the times series. For milk production in: India, Madhya Pradesh and Rajasthan, the best model selected is an ARIMA (0,2,0), the forecast equation according to this model is :

If we order this time series according to the factor development, Rajasthan is in first place with 2.89, followed by Madhya Pradesh with 2.78 then whole India with a factor of 2.09; any can see that the milk production in India is doubled over the period (200i-20i8), with a positive yearly rate of 4.i6%. For future dynamic of milk production of these three times series, we predict that positive trend would be maintained; we expected the milk production in 2024-25 will record (respectively) 252948 miles ton in India 23589 miles ton in Madhya Pradesh and 23466 miles in Rajasthan .

Summary statistics of milk production (Million tonnes)

Models fitting for Milk production, over the period (2001-2018)

The Milk production of Andhra Pradesh time series is fitted by a random walk with drift (simply an ARIMA (0,1,0) with drift), Pincheria & Medel (2016). The model prediction equation is defined as follow:

From the Table (1), the milk production in Andhra Pradesh was factored by 2.36 times over the period 2001-2018; a higher rate compared to the national level (in India was: 2.09), the forecast estimation results indicated that the milk production in this region could reach the threshold of 17000 miles ton in 2024-25.

The mean production of milk in Gujarat and Uttar Pradesh over the period (2001-2018) was (

The forecasts details for milk production of these two time series are shown in Table (3) and Fig. (2). Statistically, an ARIMA(0,2,1) process is an equivalent to a Linear Exponential Smoothing (LES) model, Holt, (1957), Hyndman

Milk Production Forecasting: in Major states in India (In Miles tones)

Evolution of milk production in India Gujarat, Rajasthan, Andhra Pradesh, Madhya Pradesh and Uttar Pradesh over the period

Forecast results of Milk production in India Gujarat, Rajasthan, Andhra Pradesh, Madhya Pradesh and Uttar Pradesh over the period (2018-19-2024-25)

Diary sector is important activity of Agriculture sector. Milk production is having crucial role in development of dairy sector. Except the Uttar Pradesh, all major states and whole India register more than 2 percent growth rate during the study period. For all milk production data expect Andhra Pradesh, two time differencing required to make the data stationary in present investigation for forecasting purpose. From the forecasting figures, Uttar Pradesh followed by Rajasthan would play vital contribution in milk production in India. With 37.60 MMT in 2024-25 Uttar Pradesh would be leading state of India on milk production. To increase milk production need to provide quality fodder and proper health care of animals. This projection help to making strategy for future to meet our milk demand. For increasing the milk production need to make awareness to dairy owner and farmers on animal breeding program and healthcare practices.