Modeling of Tea Production in Bangladesh Using Autoregressive Integrated Moving Average (ARIMA) Model

In the present paper, different Autoregressive Integrated Moving Average (ARIMA) models were developed to forecast the tea production by using time series data of twenty-four years from 1990-2013. The performance of these developed models was assessed with the help of different selection measure criteria and the model having minimum value of these criteria considered as the best forecasting model. Based on findings, it has been observed that out of eleven ARIMA models, ARIMA (1,1,2) is the best fitted model in predicting the production of tea in Bangladesh and the forecasted value of tea production in Bangladesh, for the year 2014, 2015 and 2016 as obtained from ARIMA (1,1,2) was obtained as 65.568 Million Kilogram, 67.867 Million Kilogram and 60.997 Million Kilogram. Citation: Rahman A (2017) Modeling of Tea Production in Bangladesh Using Autoregressive Integrated Moving Average (ARIMA) Model. J Appl Computat Math 6: 349. doi: 10.4172/2168-9679.1000349


Introduction
Tea serves as the most important and popular drink for twothirds of the world population not only because of its attractive aroma and taste but also because of its many pharmacological effects, like suppressing tumor cell growth, reducing cardiovascular diseases, antiobesity and decrease the risk of atherosclerosis says Wang et al. [1] and Dhekale et al. [2]. The role of Bangladesh tea industry in global context is insignificant. It is only 1.68% of the global tea production and 0.58% of the world tea export. It seems that its export is gradually declining. If this trend continues, Bangladesh will turn into a tea importing country by 2015 discussed by Monjur [3] and Baten et al. [4]. As a result; international comparisons of the tea industry's efficiency have been of great interest to firms in the industry as well as policymakers. The large tea producing countries like India and Sri Lanka produce more than Bangladesh, where India and Sri Lanka's production level is 16 and 12 times higher than Bangladesh discussed in BCS [5]. It was found that in 1998, on an average only 1,145 kg of tea was produced per hectare in Bangladesh. Whereas, in the same year, production level per hectare in India and Sri Lanka was 1708 and 2030 kg respectively found Monjur [3] and Majumder [6].
In Bangladesh, on average the area of a tea estate is around 337 hectares. At present there are very few newly established smallholding tea gardens operating in the north-western part of Bangladesh. They have very significant contribution to the tea industry of Bangladesh. The first tea garden was established in 1857 at Malnicherra discussed Monjur [7] and Khisa and Iqbal [8], two miles away from Sylhet town, situated in the north-eastern part of Bangladesh. The British companies were the pioneer of tea plantation in Bangladesh. By 1903, there were 15 European planters in Northern Sylhet, 102 in Southern Sylhet and 26 in Habiganj district of Sylhet discussed Sana [9]. At present Bangladesh has 162 tea gardens and among them Sterlink companies operate 28 gardens and 128 gardens are operated by Bangladeshi owners (National Tea Company, Bangladesh Tea Board, Private limited companies and proprietary owners). Besides, six gardens are operated by smallholders which are situated in the north-western part of Bangladesh discussed Huque [10].
Tea cultivation in Bangladesh is spread over the hilly zones on the eastern part mainly in four districts (Sylhet, Moulvibazar, Habiganj and Chittagong). About 96% annual productions (of which 63% is of Moulvibazar district) is contributed by greater Sylhet obtained from 93% (of which 62% is of Moulvibazar district) of plantation area discussed. Islam et al. It is to be noted that Sterling companies produce about 50% of annual crop from about 42% of plantation area discussed BBS [12].

Materials
In the present study, time series secondary data on production (Million Kilogram) of tea in Bangladesh were considered for the period 1990 to 2013 from Bangladesh Tea Board (BTB) [13], Ministry of Commerce, and Government of People's Republic of Bangladesh. The time series secondary data were analyzed with the help of various ARIMA models. .

Methods
ARIMA is one of the most traditional methods of non-stationary time series analysis. In contrast to the regression models, the ARIMA model allows time series to be explained by its past or lagged values and stochastic error terms. The models developed by this approach are usually called ARIMA models because they use a combination of autoregressive (AR), integration (I)-referring to the reverse process of differencing to produce the forecast and moving average (MA) operations discussed by Box [14].
The ARIMA model is denoted by ARIMA (p,d,q) where "p" stands for the order of the auto regressive process, 'd' is the order of the data stationary and 'q' is the order of the moving average process. The general form of the ARIMA (p,d,q) can be written as which discussed Judge et al. [15] ∆ d y t =δ+θ 1 ∆ d y (t-1)+ θ 2 ∆ d y (t-2) +…………….+θ p y (t-p)+ e (t-1) αe (t-1) -α 2 e (t-2) α q e (t-2) Where, ∆ d denotes differencing of order d, i.e., ∆y t =y t -y t-1 , ∆ 2 y t =∆y t -∆y t-1 and so forth, y t-1 .......... y t-p are past observations (lags), δ,θ 1 ……… θ p are parameters (constant and coefficient) to be estimated similar to regression coefficients of the Auto Regressive process (AR) of order "p" denoted by AR (p) and is written as, Y=δ+θ 1 y t-1 +θ 2 y t-2 ………+θ p y t-p +e t (2) Where, e t is forecast error, assumed to be independently distributed across time with mean θ and variance θ 2 e, e t-1, et -2 ………. e t-q are past forecast errors, α 1 ……….α 2 are moving average (MA) coefficient. While MA model of order q (i.e.) MA (q) can be written as, Y t =e t -α 1 α t-1 -α 1 α t-2 ……….α q α t-q Seasonal ARIMA model is to be denoted by ARIMA (p,d,q) (P,D,Q), where P denotes the number of seasonal autoregressive components, Q denotes the number of seasonal moving average terms and D denotes the number of seasonal differences required to induce stationarity discussed Box et al. [16]. The steps which are followed in order to define an ARIMA model as stated by Box [17] and Rahman et al. [18].

Result and Discussion
In Figure 1, from the autocorrelation (ACF) and partial autocorrelation (PACF), it is clear that there is no significant spike in the original series which also indicates that there are no significant effects of Auto-Regressive and Moving Average in the original series, that is, the tea production series is stationary without any difference.
After making the series stationary, different parametric combinations of ARIMA (p,1,q) model were tried to analyze the twenty-four years' data (1990 to 2013) of tea production and the best fitted model is accepted on the basis of minimum value of all selection criteria as mentioned above in methodology. The results of performance of developed ARIMA (p,1,q) model is presented in Table  1. It exposed the performance of eleven ARIMA models out of which ARIMA (1,1,2) was best out of all. ARIMA (2,1,2) and ARIMA (2,1,1) ranks second and third respectively while remaining ARIMA models are not as good as these three.
Therefore, it was concluded that the appropriate model for forecasting the production of tea in Bangladesh during 2013 was ARIMA (1,1,2) having minimum value of all selection criteria as compared to remaining ten models. Table 2 shows the forecasted value of tea production using the best fitted model ARIMA (1,1,2). The forecasted value of tea production

Conclusion
This paper aimed to modeling the production of tea during 2013 in Bangladesh, by Autoregressive Integrated Moving Average (ARIMA) Approach. On basis of results obtained it is concluded that ARIMA (1,1,2) model having minimum value of all measures of selection criteria was found to be the appropriate model amongst all for predicting the tea production in Bangladesh. The model showed a good performance in case of explaining variability in the data series and also, it's predicting ability. The forecasting of tea can help tea garden owners as well as the policy makers for future planning.