Forecasting of grape production in Maharashtra state using ARIMA model

Introduction

Grape is an important table fruit in the World. It is a sub-tropical crop and is cultivated under tropical conditions. The total grape production of India was 3489.40 thousand tons during the year 2021-22 (source: website of APEDA). Grape is one of the important fruits covering an area of 161.91 thousand hectares, occupying 2.30% of the total area of fruit production in 2021-22. The country is also a major exporter of fresh grapes to the world. India exported 267,950.39 MT of grapes to the world, worth Rs. 2,543.42 crores / 313.70 USD Millions during the year 2022-23. The major export destinations are Netherlands, Bangladesh, United Arab Emirates, U.K., and Russia. Major grape-growing states are Maharashtra, Karnataka, Tamil Nadu, and Andhra Pradesh. Maharashtra ranks first in terms of production, accounting for more than 70% of total production and the highest productivity in the country during 2021-22. Karnataka is the second largest producer of Grapes with a share of 25% in 2021-22. Nasik and Sangli districts are the major grape-growing districts of Maharashtra. Apart from these two leading districts, grape is also grown in Ahmednagar, Pune, Satara, Solapur, and Osmanabad districts.

The main objective of the study is to identify the best statistical model for the production of grapes, to compare the efficiency of different statistical models, and to forecast the grape production of Maharashtra state by using the best-fitted model.

Material and Methods

The secondary data on the area, production, and productivity of grapes of Maharashtra state (1991-92 to 2022-23) were used for model construction. Agricultural production may vary from year to year due to the nature of cultivation, environmental changes, and government policies. Sometimes production of a crop can increase or decrease at a certain rate. To investigate such trends, we consider the following statistical models in the present research study:

where 𝑒 𝑡 = (𝑦 𝑡 -ŷ𝑡 ) , 𝑦 𝑡 and ŷ𝑡 are observed and estimated values of response variable for individual t. DW(d) becomes smaller as the serial correlations increase.

To test the autocorrelation at significance level α, the test statistic d is compared to lower and upper critical values (d L,α and d U,α ):

If d<d L,α , there is statistical evidence that the error terms are positively autocorrelated.

If d>d U,α , there is no statistical evidence that the error terms are positively autocorrelated.

If d L,α <d<d U,α , the test is inconclusive.

ARIMA (Autoregressive Integrated Moving Average) model

Autoregressive Integrated Moving Average (ARIMA) also known as Box-Jenkins methodology was used for the time series modeling. It includes AR and MA terms with their respective order p and q respectively. Differencing eliminates trends and seasonality and stabilizes mean of the time series. The first order differencing was used in order to make the series stationary. The non seasonal ARIMA (p,d,q) model for the grape production (y) in period t based on data up to period t -1 was used as follows

Where , 𝜇 is the constant, 𝜑 𝑝 is the autoregressive (AR) coefficient at lag p, 𝜃 𝑞 is the moving average (MA) coefficient at lag q and 𝑒 𝑡 -𝑞 = 𝑦 𝑡 -𝑝 -ŷ𝑡 -𝑝 is the forecast error that was made at period tp.

The main steps of ARIMA modeling are model identification, parameter estimation, diagnostic checking and forecasting.

Results and Discussion

The descriptive statistics of area, production, and productivity of grapes in Maharashtra are presented in , and AIC values are presented in Table 3. After applying the Durbin Watson test to the residuals of the different models, it was observed that the conventional models (linear, polynomial, compound, exponential, logarithmic, and power) exhibited positively autocorrelated residuals. Therefore, time series modeling via ARIMA was executed to address this dependency.

The results of the Augmented Dickey-Fuller (ADF) test are presented in Table 4. It indicated that grape production is non-stationary at level (d = 0, p-value = 0.25) and becomes stationary after the first difference (d = 1, p-value = 0.04). The optimal lag order and structural parameters p and q were identified from the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) plots.

Conclusion

The estimated compound annual growth rates revealed that the production of grapes has shown a significantly increasing trend of 7.41% per annum over the study period. The ARIMA model proved to be a substantial improvement over conventional models, making it more appropriate to visualize the temporal trend of grape production in Maharashtra state. It is concluded from the study that on comparing different linear and non-linear statistical models, the ARIMA (6,1,0) model performed better for describing and forecasting grape production in Maharashtra state. The predicted value of grape production for the year (2023-24) using the best-fit model ARIMA (6,1,0) is estimated to be 2703.38 thousand metric tons, lying within a confidence interval (Lower Control Limit) of 1921.17 and (Upper Control Limit) of 3485.59 thousand metric tons.

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9. How to cite this article: Bhagat A, Khandve S, Walke J, Pimparkar V. Forecasting of grape production in Maharashtra state using ARIMA model. International Journal of Statistics and Applied Mathematics. 2026;11(9):238-241. doi: https://www. doi.org/10.22271/maths.2026.v11.i9c.2707