Forecasting the production of jute based on time series models in Bangladesh

Introduction

Bangladesh is currently the second largest producer of jute fiber, now over taken by India. After the country's independence, more than 80% of total foreign currency in Bangladesh was earned from jute and jute related goods. But after 80's, the earning rate of foreign currency from jute industry has gradually declined. The sector provides about 10% of the total employment in the economy and 12% of GDP. About 90% of jute products produced in Bangladesh is exported (Rahman, 2007) [7] . Foreign exchange earnings of Bangladesh come mostly from jute. Beside, jute is a good source of revenue for the governments in the form of taxes, levies, sales and custom duties on jute goods (Alam, et al., 2009) [1] . Bangladesh is famous for jute production and earned a big amount of foreign currency by exporting jute and jute products to different countries. At one stage, Jute was only the vital sector in Bangladesh from which major portion of foreign currency is to come and help Bangladesh's economy and a large number of manpower were employed there. Bangladesh was recognized as one of the best jute producing and exporting countries of the world (Bangladesh Bank, 2014) [6] . Over the last 20-25 years it did slide down to the seventh position. Now it regained to come to the forth position (Rahman & Salim, 2013) [8] . Jute is called the Golden Fiber of Bangladesh. The Jute Area, popular for highest quality of jute fiber is located in Bangladesh. Therefore, Bangladesh is able to supply the highest quality of jute fiber in the world. Jute is grown mainly in Bangladesh for fiber rather than for seed. In Jute, use of quality seeds of improved variety alone contributes 223.54kg of extra fiber per hectare i.e. an increase of about 17% (BBS, 2010) [5] . It is one of the cheapest and the strongest of all natural fibers and considered as fiber of the future. Jute is second only to cotton in world's production of textile fibers. India, Bangladesh, China and Thailand are the leading producers of Jute. It is also produced in southwest Asia and Brazil. India is the largest producer of jute goods in the world, while Bangladesh is the largest cultivator of raw jute (Ministry of Finance, 2010) [4] . In Bangladesh, almost 3 million farming households are involved in jute cultivation. Jute harvesting takes place at a time when marginal farmers and farm workers are faced with shortage of their food stocks. The cash derived from sales of jute fiber and the wages received by workers are an important contribution to food security for this vulnerable segment of the population. Rapid employment generation is vital to poverty reduction in Bangladesh. Economic growth driven by sectors that are labor-intensive by nature has greater potential for job creation. The fact that the jute sector is so labor-intensive has played important strength, given the country's large rural underemployment. The global demand for jute and allied products has seen a steady increase driven by a fresh comeback for biodegradable fiber as people now look for ecofriendly products replacing synthetics. Bangladesh produces around 30% of the total world production of jute and exports around 40% of its total produce as raw jute. Thus, it is necessary to estimate the behaviors of jute production and forecast the future production of jute in Bangladesh.

Objectives of the study

The main objective of this study is to forecast the future production of Jute in Bangladesh. Here we study time series analysis on production of Jute. On the basis of this analysis the study attempts to-1. To fit accurate model of Jute production of Bangladesh.

To check the model adequacy for different fitted model

for Jute production of Bangladesh. 3. To forecast future production, obtain form Jute of Bangladesh. 4. To see the forecasting performances of the selected ARIMA models.

Materials and Methods

For forecasting purposes, one of the important types of data used in empirical analysis is time series data. The empirical work based on time series data assumes that the underlying time series is stationary. The time series analysis based on the stationary time series data. In this section we briefly discuss on stationary and non-stationary time series. A stochastic process is said to be stationary if its mean and variance are constant over time. Otherwise it will be non-stationary. Why are stationary time series so important? Because if a time series is non-stationary, we can study its behavior only for the time period under consideration. Each set of time series data will therefore be for a particular episode. As a consequence, it is not possible to generalize it to other time periods. [2,3] .

Auto correlation function (ACF)

For a stationary process, auto correlation function (ACF) is the process of k and the parameter of the process. The ACF is a useful device for describing a time series process. One of the characteristics of a stationary process is an autocorrelation function. Mathematically the auto-correlation function is,

Partial Auto-correlation function (PACF)

Alternative valuable technique to scrutinize serial dependencies is to observe the partial autocorrelation function (PACF) -an extension of autocorrelation, where the dependence on the intermediate elements (those within the lag) is removed. Mathematically the partial auto-correlation function is,

Augmented dickey-fuller test

For theoretical and practical reasons the Dickey Fuller test is applied to regression model of the following form:

Where t is the time or trend variable. In each case the null hypothesis is that δ = 0, that is there is a unit root. The difference between (a) and the other two regression lines are in the inclusion of the constant (intercept) and the trend term.

If the error term 𝑢 𝑡 is auto correlated, one modified (c) as follows:

Where 𝑓𝑜𝑟 𝑒𝑥𝑎𝑚𝑝𝑙𝑒, ∆𝑦 𝑡-1 = (𝑦 𝑡-1 -𝑦 𝑡-2 ), ∆𝑦 𝑡-2 = (𝑦 𝑡-2 -𝑦 𝑡-3 ) 𝑒𝑡𝑐. i.e. one uses lag difference terms.

The null hypothesis is still that δ = 0 or δ = 1, i.e., a unit root exists in y (i.e. is non-stationary) when the Dickey Fuller test is applied to models like (d), it is called augmented Dickey-Fuller (ADF) test. The ADF the test statistic has same asymptotic distribution as the DF statistic, so the same critical values can be used.

Model selection

Here, we applied Box-Jenkin's Methodology to identify the appropriate model for analyzing and forecasting the production of Aman rice in Bangladesh. The Box-Jenkin's Methodology is shown below:

Forecasting

A planning tool that helps management in its attempts to cope with the uncertainty of the future, relying mainly on data from the past and present and analysis of trends. Predictions of future events and conditions are called forecasts, and the act of making such predictions is called forecasting (Brockwell, et al., 2002 & Box, 1994) [2,3] .

Result and Discussion

We have used the secondary data regarding Jute production in Bangladesh which are collected over the period 1972-1973 to 2016-2017. From Department, Bangladesh Bank. Here we applied different techniques for analyzing the data and the results of this data are shown below: After the period 2003-04 there was an upward trend in the jute production in Bangladesh, i.e., the variance is unstable which indicates the jute production data series is not stationary. From Figure 3 & 4 we observed that the series is non-stationary. From Table 1 we showed that the calculated values are garter than the tabulated values. Therefore we conclude that the series is non-stationary. From Table 2 we observed that -1.85(ADF value) >-1.94 (Negative Critical Value) accept the null hypothesis. So, the production is non-stationary. From Table 3 we showed that the calculated values are garter than the tabulated values. Therefore we conclude that the series is non-stationary. From the above Table 4 we observed that -0.802 (ADF value) >-1.94(Negative Critical Value) accept the null hypothesis. So, the production of natural log is non-stationary. From Figure 8-10, we observed that the series of jute production based on 1 st difference of natural log is stationary. From Table 5 we showed that the calculated values are less than the tabulated values. Therefore we conclude that the series is stationary. From Table 6 we showed that -6.85(ADF value) < -1.94 (Negative Critical Value). We can reject the null hypothesis. So, the production is stationary.

Checking non-stationary of original jute production by time series plot

Checking stationary by time series plot of Jute production with natural log

Model Selection of Jute Production

Let us consider the different types of tentative models as much as possible from which we select the best model using the model selection criterion. Since the characteristics of a good ARIMA model is parsimonious ignoring the higher order of p and q, the tentative models on the basis of model selection criterion are as follows: We have already fitted an ARIMA (1, 1, 1) model for the forecasting of yearly data of jute. Now to see the performance of this model in the out of sample forecasting, the forecasted value of jute production data for the year 2017-18 to 2026-2027 will be derived using this model. Then we compare the forecasted value with the actual value, which is available from 2017-18 to 2026-2027. The Table 9 gives the forecasted value obtained by ARIMA (1,1,1) model along with the forecasting errors in the test set. The following table contains the forecasted values under the period 2017-18 to 2026-27.

Conclusion

The best selected Box-Jenkins ARIMA model for forecasting the jute productions in Bangladesh is ARIMA (1, 1, 1). From the comparison between the original series and forecasted series shows the same manner indicating fitted model are statistically well behaved to forecast jute productions in Bangladesh i.e., the models forecast well during and beyond the estimation period which reached at a satisfactory level. Thus, this model can be used for policy purposes as far as forecasts the jute production in Bangladesh.

References

1. Alam GM, Hoque KE, Khalifa MTB, Siraj S, Ghani MF. The Role of Agriculture Education and Training on Agriculture Economics and National Development of Bangladesh, African Journal of Agricultural Research. 2009; 12:1334-1350.
2. Brockwell PJ, Davis RA. Introduction to Time Series and Forecasting. 2nd.ed. Springer-Verlang, 2002.
3. Box GEP, Jenkins GM, Reinsel GC. Time Series Analysis, Forecasting and Control. 3rd ed. Prentice Hall, Englewood Clifs, NJ, 1994.
4. Ministry of Finance, Bangladesh Economic Review. 2010. Finance Division, Government of the People's Republic of Bangladesh, Dhaka, 2010.
5. Bangladesh Bank, Annual Report. Bangladesh Bank, Dhaka, 2014.
6. Rahman S. Regional productivity and convergence in Bangladesh agriculture, Journal of Developing Areas. 2007; 41:221-236.
7. Rahman S, Salim R. Six Decades of Total Factor Productivity Change and Sources of Growth in Bangladesh Agriculture (1948-2008). Journal of Agricultural Economics. 2013; 64(2):275-294.