Forecasting of Arecanut in India using Time Series Model

The origin of the Arecanut is debated, but it is commonly thought to be either Malaysia or the Philippines. Areca nuts are grown and consumed primarily in India, which accounts for more than half of global production. After Brazil, Bangladesh and Sri Lanka are the world’s leading producers of areca, each accounting for 14% and 10% of total production. Since half of the country’s areca nut production area is in Bangladesh, the price of areca nuts in India skyrocketed after partition and the government has since prioritised policies aimed at reducing imports. Among the many fascinating points brought up by Ullal et al., (2021), one is that consumers in the north of India tend to view themselves as autonomous, while those in the south see themselves as a much more integral part of their families and communities.
       
Therefore, there was no Areca import in the 1970s. Due to its high profitability, many farmers in southern India began cultivating Areca at this time (Viswanath and Narappanavar, 1980).
       
Karnataka is responsible for producing over 65% of India’s entire areca crop. We import roughly 18000 tonnes of areca nut annually, with our top two suppliers being Sri Lanka and Indonesia in 2017-2018 (Govt. of India, 2020). The Areca nut market has become more unstable in recent years due to fluctuations in trade volume on international and domestic marketplaces and the exchange rate of trading countries (Ramappa, 2013).
       
Areca nut traders, farmers and manufacturers all bear the brunt of the industry’s pricing risk as a result of the current market climate. However, Pinto et al., (2020) claimed that the conventional theoretical approach lends credence to the idea that risks and stock returns are directly proportional to one another. The ARIMA method is commonly used in univariate time series forecasting and a good forecasting model will help the farmers and merchants in Meghalaya and Assam make a profit (Shil et al., 2013). In econometric research, it was common practise to make forecasts by analysing past data. However, the precision of such forecasts was quite low, which is what drove the widespread use of AR, MA, ARMA and ARIMA models in time series analysis (Cortez et al., 2018).
 
Backdrop
 
Arecanut is known as Areca catechu L., belongs to the Palmaceae family. It is popularly known as supari as well as fruit of divine origin in India. Arecanut is the major crop of South East Asia. Total arecanut production in the world was 14.15 lakh tonnes in 2017 which was increased to 14.29 lakh tonnes in 2018 (Govt. of India, 2020). The area and production under Arecanuthas increased from 113 thousand hectares to 777 thousand hectares from 1960-61 to 2020-21 (Govt. of India, 2022). India contributes about 49 per cent of the area and 59 per cent of the worlds’sArecanut production (Govt of India, 2020). In the total production, around 20 per cent consumed as ripe nuts and remaining 80 per cent is unripe, processed into red boiled type (Gupta et al., 2018). In India, cultivation of Arecanut is mainly limited to the states such as Karnataka, Kerala and Assam. The area under Arecanut production has expanded to Tamilnadu, West Bengal, Maharashtra andhra Pradesh, Goa, Meghalaya and Tripura etc. The main reason for increasing the area under cultivation is high return per rupee invested (Rabha, 2021). Arecanut is used as breath-freshener as well as have various digestive properties (Winstock, 2013).Along with this, it also helps togenerate additional employment and social security (Govt. of India, 2020). There is dearth of publications in relation to forecasting and modelling of Arecanut in India.Hence there is hunger need to carry out study on Arecanut.Area, output and efficiency in India’s Arecanut industry have been projected using ARIMA, Holt’s linear and Holt’s exponential models for the period 2021-2025. The primary value of this research is that it accurately predicts what will happen in the future, allowing for proactive policymaking that will improve the area, production and productivity of Arecanut in India. Here is how the rest of the paper is structured. In Section 2, we see examples of the ARIMA and Holt-Winters linear and Exponential smoothing techniques in action. Predictions and model parameters are presented in Section 3.

In the present study, annual data on Arecanut Area, production and productivity has been collected from 1960-61 to 2019-20 from the Ministry of Agriculture and Farmer’s Welfare, GOI. As mentioned earlier, ARIMA, Holt’s winter liner and Holt’s winter exponential model is used to forecast the area, production and productivity of arecanut to find the best prediction model. Among several methodologies available for time series data, these two are well-established and pretty much applicable toour case.
       
The dataset is divided into two parts, comprising 80 per cent and 20 per cent of data for model specification and model validation. Thus, data from 1960-61 to 2015-16 is used for model building and annual data from 2016-17 to 2019-20 is used for model validation. Suitable statistical tools are used to estimate errors in test data. Finally, the Diebold-Mariano Test results were compared to find any significant differences between the two forecasts from different models. The schematic flow of forecasting of area, production and productivity is presented in Fig 1.
 

 
Autoregressive integrated moving average (ARIMA)
 
The Box-Jenkins technique is another name for the autoregressive integrated moving average (ARIMA) model established by Box and Jenkins (1976). When an autoregressive (AR) model is combined with a moving average (MA), the resulting model is known as the autoregressive moving average model (ARMA). Although these models work well with stationary series, the ARIMA approach is used for analysing non-stationary data. First, the differences of the data from the stabilisation process at degree d are taken and then the ARMA (p, d, q) model is added. p indicates the AR model’s degree, q the MA model’s degree and d the number of differences to be used to stabilise the data in the ARIMA. The ARIMA (p, d, q) model can be defined as follows (equation 1):
   
Where,
Y^t = Represents the value of the time series at time t.
φ₁, φ₂, ...,φ_p = Autoregressive (AR) coefficients of lag p.
α₁, α₂, ..., α_p = Coefficients of the exogenous variables (if any) at lag p.
ε_t = Represents the error term at time t.
θ₁, θ₂‚ ..., θ_p = Moving average (MA) coefficients of lag q.
       
This equation demonstrates how the current value of the time series (Y_t) can be predicted based on its past values (lagged terms), the error terms (ε_t) and potentially the influence of exogenous variables (α₁, α₂,..., α_p). The autoregressive component captures the dependency on past values, the moving average component accounts for the dependency on past error terms and the exogenous variables can introduce additional explanatory factors.
       
Yt is the data with the difference of d degree from the original data (Brockwell et al., 2016; Gujarati and Porter 2012). The following steps can be applied for fitting a time series data to an ARIMA model (Hyndman and Khandakar 2007).
 
Step 1
 
Plotting the data, detecting any outlier and transforming the data (using the function of the log, sqrt…) to stabilise the variance if necessary.
 
Step 2
 
Taking differences of the data until the data are stationary.
 
Step 3
 
Finding the optimal values for the ARIMA model’s p and q parameters by examining the Autocorrelation function (ACF) and Partial autocorrelation function (PACF) and then applying Akaike’s Information Criterion with correction (AICc) to the set of candidate models.
 
Step 4
 
Examining residuals from the best model selected by plotting the ACF and PACF for residuals. A different model should be tried if the results do not resemble white noise (Mishra et al., 2021c).
 
Step 5
 
Calculating forecasts once the residuals look like white noise.
 
Holt’s linear trend method
 
The exponentially weighted moving average is similar to the averages of smoothing random variability, but it has the added benefits of being (1) easy to calculate, (2) ever less weight is given to older data and (3) most importantly for data sets, requiring only a small initial sample. After Holt (1957) provided three equations for forecast, level and trend, Mishra et al., (2021a, b). Forecast equation:  
Level equation:  
Trend equation:  
Where,
Y_t = Forecasted value at time t.
χ_t = Level component at time t.
ρ = Weight for the level component in the forecast equation.
M_t = Level component at time t.
υ = Weight for the current observation in the level equation.
ω = Weight for the previous level in the level equation.
θ_t  = Trend component at time t.
b_t = Trend component at time t.
γ = Weight for the difference between current and previous levels in the trend equation.
 

Descriptive statistics regarding the mean, median, mode and skewness are reported in Table 1. As Table 1 is examined, we find the area of Arecanut increased by 558 per cent from 1960 to 2020. During the same duration, production increased by 1160 per cent. It shows a significant productivity improvement too. Productivity as bled during the study period with more than 100 per cent increase. The positive skewness of area, Production and productivity indicates the scope of future improvements in production too. A negative value of Kurtosis in productivity indicates a mesokurtic curve thatemphasises relatively stable productivity throughout the study period.
 

       
After seeing the arecanut area, production and productivity through descriptive statistics in Table 1, next step is model specification validation and forecast the area, production and productivity of Arecanut using the time series data. For projection purposes, we used different time series models. ARIMA, Holt’s winter linear and Holt’s winter exponential models were estimated and compared for best projection. The model selection for ARIMA Holt’s winter linear and exponential for area, production and productivity of arecanut was obtained using some goodness of fit criteria like AIC and BIC. Following the autocorrelation function and partial autocorrelation Function charts, we were able to determine the various p and q values for the ARIMA model. (Fig 2 and 3).
 

 

       
The combination with least AIC and BIC criteria were selected for model validation and forecasting. After estimating all the possible combinations, the best model for area and production was Holt’s exponential model (Table 2) with least AIC and BIC values. However, we did consider ARIMA (2, 2, 1) for area and production validation and forecasting as it was having least AIC and BIC values among all combinations of ARIMA. In case of productivity, ARIMA (0, 1, 1) is the best model for forecasting as it possessleast AIC and BIC values (Table 2).
 

       
However, in all these three cases, finally we proceed with ARIMA, Holt’s linear and exponential models and tried to capture the best forecasts possible for area, production and productivity of arecanut. 
       
We estimated the errors on the forecasted values of testing data using some well-established measures like RMSE (root mean square errors), MAPE (mean absolute percentage errors), MAE (Mean Absolute Error) and MSE (Mean Square Error) to obtain the best model which is presented in Table 3.
 

       
In case of area, all the indicators suggest Holts Exponential as the best suited model for forecasting. In the case of production, two indicators suggest ARIMA (2, 2, 1) and rest two suggests Holts exponential as best fit model for prediction. Again, in case of productivity, both ARIMA (0, 1, 1) and Holt’s Linear model was found to be best fit for future prediction. The models predicted values are reported later in Table 6. To further verify our models, we ran a Ljung box q test on the data we had collected as residuals. Based on the results of the tests, we know that the residuals are white noise series and so lack autocorrelation. The detailed results of the model parameter of the best fit models and Ljung box Q test are presented in the Table 4.
 

       
The mathematical model for Area prediction using ARIMA (2, 2, 1) is specified as: Where,
 
Y_t = Value of the time series at time t.
c = Constant term or the intercept.
(-0.032) and (-0.2416) = Autoregressive (AR) coefficients for the lagged terms Y_t-1 and Y_t-2, respectively.
(-0.848) = Moving average (MA) coefficient for the lagged = error term e_t-1.
e_t = Error term at time t.
       
The mathematical model for prediction of production  using ARIMA (2,2,1) is specified as:  
Where,
Y_t = Value of the time series at time t.
c = Constant term or the intercept.
(-0.341) and (-0.332) = Autoregressive (AR) coefficients for the lagged terms Y_t-1 and Y_t-2 respectively.
(-0.718) = Moving average (MA) coefficient for the lagged error term e_t-1.
e_t = Represents the error term at time t.
       
The mathematical model for prediction of Productivity using ARIMA (0, 1, 1) is specified as: Where,
Y_t = The differenced value of the time series at time t.
c = Constant term or the intercept.
(-0.373) = Moving average (MA) coefficient for the lagged differenced value ΔY_t-1.
e_t = Represents the error term at time t.
       
The selected model lead to fewer errors in predicting the future and the difference in the accuracy among the selected models were tested with the help of DM test (Table 5). The DM test results show that there is a significant difference among the predicted values of ARIMA and Holt’s Exponential in case of arecanut area.
 

       
No significant differences were found in the predicted values of production and productivity when we used ARIMA v/s Halt’s Exponential and ARIMA v/s Holt’s linear model. Either of the models give forecast with least errors. The final forecasts for the next five years, starting from 2021 to 2025 is presented in Table 6.
 

The study uses arecanut area, production, annual data from 1960-61 to 2019-20 to forecast Area, Production and Productivity for India. Autoregressive Integrated Moving Average (ARIMA), Holt’s winter linear model and Holt’s winter exponential model was used for forecasting. Based on suitable selection criteria, Holt’s exponential model was found best for predicting both Area, Production whereas ARIMA (0, 1, 1) model was found best for predicting productivity. Only in case of Area prediction, the two alternative models gave significantly different whereas in case of production and productivity, the forecasts were found non-significantly different to each other. The forecasts of area, production and productivity suggests that all three variables will increase in future in India but the productivity growth will be subtle as compared to area and production. The limitation of the study is that it uses annual data for autocorrelated time series modelling. Increasing the frequency of the dataset by either increasing the number of years or by incorporating monthly data may lead to decreased results’ robustness. However, incorporating more advanced methodology like machine learning technique may increase the accuracy of the forecasts and future studies can aim in this direction. The methodology of Arecanut forecasts can even be utilized for other crops and in other countries.

None.