A hybrid time series modeling framework for banana area and production in Assam

Introduction

Application of forecasting models for crop production becomes a very trending topic now a days. A good forecasting model enables to take accurate decisions at appropriate time. Many studies had been conducted earlier in this area that provided very precise and accurate results of forecasting. A good forecasting model is not only useful for policy makers but also for farmers to take appropriate action during farming activities. In this research, area and production data of Assam of banana were attempted to fit with linear and nonlinear models. Banana is an important fruit crops of India as well as Assam. India is the leading banana producing country in the world whereas Assam is among the major banana producing state of India. The climatic condition of Assam is also suitable for banana production. However, the banana production of Assam is comparatively less than other banana producing states of the country. The main objectives of this research were to analyze the area and production series of banana through trend analysis, enumerate Compound Annual Growth Rate and at last building of forecasting model for both series. Trendline analysis helps to identify the trend pattern exhibited by the series. This was followed by forecasting model development for Assam because a region-specific model can give more accurate results as compared to a nationwide model. For forecasting model development, one linear model (ARIMA) and two non-linear model (ANN & NLSVR) were selected. Many studies have been conducted earlier that proved the usefulness of these models to get accurate forecasts. Ramadhan et. al (2024) compared the performance of ARIMA, TDNN, NLSVR model and their hybrid for forecasting banana production in Karnataka. The results revealed that hybrid ARIMA-NLSVR model performed superiorly than remaining models. Thus, in this research hybrid approach was also adopted to build good forecasting models.

Data Source:

The two-variables considered in this study are banana area, banana production. The required data of area and production of Assam was collected from "www.indiastatagri.com", "Statistical Handbook of Assam" www.extensionjournal.com (Directorate of Economics and Statistics, Assam). Banana area and production data was collected from 1961-62 to 2023-24. The whole analysis was conducted using two software-Rstudio and SPSS. 'Forecast' package of Rstudio software was utilized to build the ANN model whereas 'TSSVM' package was used to develop NLSVR models. BDS test was conducted using 'tseries' package of Rstudio software.

Research Methodology

Auto-Regressive Integrated Moving Average Model (ARIMA)-ARIMA is a linear time series model, was developed by Gorge Box and Gwilyn Jenkins in 1970 (Box and Jenkins, 1970). It mainly consists of three components namely autoregressive (AR), integrated (I) and moving average (MA). AR component explains the effect of previous lags upon current observation while MA component refers to the influence of random shocks of previous lags on current observation. On the other hand, differencing component records the times of differencing conducted on non-stationarity series to transform it to a stationary series. These three components were combined to get the typical ARIMA model is given by, Box and Jenkins put forwarded four steps of ARIMA modelling; identification stage, estimation stage, diagnostic checking stage and forecasting stage. In the identification step, appropriate orders of AR, I, MA (i.e. p, d and q) were identified. The value of 'd' was determined through Augmented Dicky Fuller (ADF) test. Values of p and q were determined through PACF (Partial Auto-Correlation Function) and ACF (Auto-Correlation Function) plot of the differenced data. In the estimation phase, coefficients of the identified model were estimated using method of maximum likelihood or iterative least square method. Here performance of selected model was compared to some other related models and best model was promoted to next step. Third stage includes the adequacy checking of model through residual analysis. If the residual series follows the characteristic of white noise, that ARIMA model is regarded as good fit and was promoted to fourth step. In the fourth step, forecasts were generated using the selected ARIMA model. ) found from the linear model are modelled using nonlinear models. Predictions of the nonlinear model are also collected and are denoted by t . Finally, the linear and non-linear series are combined to make the hybrid forecast. This relationship is given by, = + t is the required hybrid series of the initial series .

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Results and Discussion

Initially trend analysis was conducted on the two series namely banana area, banana production. Method of curve fitting was adopted using four different curves namely linear, quadratic, logarithmic and exponential. Each curve represents different types of relationship. As for example, those variables that increases approximately at a constant rate generally follows a linear trend, whereas variables increasing at a moderate or slightly higher growth rate (increasing) than linear model is well explained by a quadratic model. Similarly, the growth rate of a variable (increasing) following an exponential model is generally considered as faster than both linear and quadratic model. On the other hand, if trendline of a variable is logarithmic, then it indicates that the variable acquired an increasing trend with a faster decreasing rate. Each series were fitted with all the aforesaid functions, then performance of each model was recorded through coefficient of determination (R 2 ) and root mean square error (RMSE) value. Finally, the trendline model possessing lowest error and highest Rsquare value were selected as best model. The best trendline model of variables are given in Table-1. Trendline analysis was followed by calculation of Compound Annual Growth Rate of both the series. The CAGR percent of banana area was found 1.82 while 2.48% was found for banana production during the assessed period of 63 years. This was succeeded by forecasting model development. All the four series were fitted with ARIMA initially. In the identification step, orders of ARIMA model were identified. Stationarity of each series was tested through ADF test and ACF-PACF plot. Results revealed that second differenced series of the two variables (banana area, banana production) are stationary in nature. Therefore, the order of differencing 'd' is taken as 2. To determine the order of AR and MA, the ACF-PACF plot of second differenced series was observed to get the number of significant spike present in each plot. Value of 'p' was determined through PACF plot while value of 'q' was selected through ACF plot. One significant lag was found both in ACF and PACF plot. Therefore, from all the visual observation ARIMA (1,2,1) was identified as the potential model for banana area and production series. In the estimation step, coefficients of potential ARIMA models were estimated. After this, the performances of the selected models were compared to some other related ARIMA model to examine the validity of selection. The best models were subsequently promoted to next step of diagnostic checking.

Here, residual analysis was conducted using Ljung box test and residual ACF-PACF plot. The results of Ljung box test of all the models were given in table-4. These results (pvalue > 0.05) depicted that the residual series of each model is white noise (no autocorrelation), thus the respective models were regarded as good fit. Similar result was also found in residual ACF-PACF plot where no significant lags www.extensionjournal.com were observed. Therefore, both the good fit models were promoted to the final step of forecasting. In this step, forecasts were generated for the upcoming five years using the models. ANN modelling was followed by NLSVR modelling. 'TSSVM' package of Rstudio software was used to build the NLSVR model for each series. It is an automated package that used the training data to develop the model.

Testing data set was used to get the idea of performance of the suggested NLSVR model by the package. At last forecasts were generated for each variable using their respective best NLSVR model.

Conclusion

The trendline analysis results disclosed that the banana area series is following a downward parabolic quadratic trendline (negative coefficient) whereas banana area series is following an upward parabolic quadratic trendline (positive coefficient). Thus, it could be concluded that the banana area is following an increasing trendline with a moderately decreasing growth rate (i.e. growth is slowing gradually). Alternatively, banana production is acquiring an increasing trendline with a moderate increasing growth rate. CAGR results disclosed that the cultivable banana area was growing by 1.82% on average per year since the values were found positive. Similarly, results signified that the banana production of Assam was growing annually at a rate of 2.48% on average. Therefore, it could be concluded that the area of banana cultivation was growing at a comparatively slower rate than the banana production. Results of forecasting models revealed that among the individual models, ANN model performed much better than other models for explaining banana area whereas in case of banana production variable, the ARIMA (1, 2, 1) model performed better than individual ANN and NLSVR model. Regarding the hybrid models, ARIMA-ANN model outperformed the ARIMA-NLSVR model in case both area and production variables. Comparing the all developed model, it was observed that hybrid ARIMA-ANN model showed superior results for both area and production variable and therefore this model was declared as best forecasting model. Thus, all best models were recommended for forecasting generation. At the end, predictions were generated for subsequent five years. It was expected from the forecast results that production of banana will increase in the future if the series continues to follow the similar trendline. Although the rate of growth was found slower for banana area as suggested by the results of trend analysis, however the forecast results reflected that the area under banana cultivation would also increase in future even though the rate of growth is moderate. However, much scope is still available for enhancing the area of banana cultivation.

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