Jordan Journal of Mathematics and Statistics (JJMS) 8(3), 2015, pp
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1 Jordan Journal of Mahemaics and Saisics (JJMS) 8(3), 015, pp FORECASTING THE TEA PRODUCTION OF BANGLADESH:APPLICATION OF ARIMA MODEL ** MD. MOYAZZEM HOSSAIN (1) AND FARUQ ABDULLA () ABSTRACT: Bangladesh is he world s 10 h larges ea producer and fifeen number exporers and sixeen number consumers in he world. The consumpion is increasing day by day mainly due o he rapid increase in populaion. The main purpose of his research is o idenify he Auo-Regressive Inegraed Moving Average (ARIMA) model ha could be used o forecas he producion of ea in Bangladesh. This sudy considered he published secondary daa of yearly ea producion in Bangladesh over he period 197 o 013. According o AIC, AIC C and BIC, he mos suiable model o forecas he ea producions in Bangladesh is ARIMA (0,,1). Adequacy of he fied model has been esed using Run es and Jarque and Bera es crieria followed by residual analysis. The comparison beween he original series and forecased series shows he same manner indicaing he fied model behaved saisically well and suiable o forecas he Tea producions in Bangladesh i.e., he models forecas well during and beyond he esimaion period. 1. INTRODUCTION Tea Camellia sinensis L. [8] is a unique crop relaive o any ohers ypical crop due o is culivaion and harvesing sysem. I is a ype of crop which shows wide adapabiliy and grows in a range of climaes and soils in various pars of he world Hamid [1]. Mondal e al. [3] menioned in his research ha Tea is he oldes non alcoholic caffeine conaining beverage in he world. Khisa and Iqbal [9] said ha now-a-days ea is he mos popular drink all over he world. Modern man canno hink of saring a day wihou having a cup of 000 Mahemaics Subjec Classificaion. 6E05, 6E99. Keywords and phrases. Tea, ARIMA Model, Forecasing, Bangladesh Copyrigh Deanship of Research and Graduae Sudies, Yarmouk Universiy, Irbid, Jordan. Received: April 0, 015 Acceped: Oc. 6,
2 58 MD. MOYAZZEM HOSSAIN AND FARUQ ABDULLA ea. I refreshes he mind and gives energy. Almos all people ake ea once or wice a day. Bekhi [8] said ha he Chinese were he firs o use ea as medicinal drink, laer as beverage and have been doing so for he pas 3000 years. Redowan and Kanan [7] menioned ha he ar of ea culivaion in Bangladesh began over a cenury and a half ago in he 1840s near he Chiagong Club and firs ea garden for commercial purpose was esablished a Malnicherra in Sylhe in Is commercial producion began shorly hereafer in 1857 and his same year Bangladesh Tea Board was esablished in Dhaka and Bangladesh Tea Research Insiue (BTRI) was founded in Srimangal see Nasir and Shamsuddhoa [33]. The ea culivaion in Bangladesh has been expanding since hen. A presen here are 163 ea gardens in he counry see BTD [5]. In Bangladesh, ea grows well a only f. above from sea level mainly in he hilly regions norheas of Sylhe (Sylhe, Moulvibazar and Habibgonj disrics) and souheas of Chiagong see BTRI [6]. Bu few ea gardens also presen in Brahmanbaria and Panchagar disrics. From oal annual producion, 94% comes from Sylhe (63% Moulvibazar disric) from and res from ohers par of he counry. Bangladesh is he world s 10h larges ea producer and fifeen number exporers and sixeen number consumers in he world BTD [5]. Rahman [5] has invesigaed he impac of price and oher facors on he supply of ea in Bangladesh by he modified form of he Cobweb supply model. The relaionship beween ea drinking and human healh has become a subjec of inense sudy by scieniss hroughou he world in he pas wo decades. These sudies sugges ha ea may be beneficial o human healh for deails see Weisburger [0]; Chen [37]; Yang e al. [9]; Blumberg [18]. Researcher like Weisburger [0][1]; Yang e al. [8]; McKay and Blumberg [10]; Blumberg [18]; Chen [38]; Huang and Xu [16] conclude ha Tea may have grea poenial for he developmen of medicaion and in he prevenion of a number of human diseases including cancer. Yong-xing Zhu e al. [36] showed ha ea and ea consiuens have various biological aciviies and suggesed ha ea drinking migh be beneficial o human healh. Tea has poenial in he prevenion or adjuvan reamen of several diseases including cancer, cardiovascular diseases and obesiy. Kamah e al. []
3 FORECASTING THE TEA PRODUCTION OF BANGLADESH menioned ha Researchers from Brigham and Women s Hospial and Harvard Universiy published novel daa indicaing ha ea conains a componen ha can help he body ward of infecion and disease and ha drinking ea may srenghen he immune sysem. ADA [3] said ha Type diabees is considered a global epidemic. Soe and Baer [4]; Anderson and Polansky [30] said ha Caechins in ea have been shown o help reduce blood sugar and provide insulinboosing aciviy, which may be benefiial for people wih boh ype 1 and ype diabees. Linke and LeGeros [15] said ha a recen sudy conduced a he New York Universiy Denal Cener examined he effecs of Black Tea exrac on denal caries formaion in hamsers. Compared o hose who were fed waer wih heir food, hamsers ha were fed waer wih Black Tea exrac developed up o 63.7 percen fewer denal caries. Hazarika [19] has been developed an Auoregressive Inegraed Moving Average (ARIMA) model wih he help of Box- Jenkins approach for he ea producion of Assam. He has shown ha he seleced ARIMA model is quie appropriae for he ea producion of Assam, India. Gijo, E.V. [11] was modelled by Box-Jenkins seasonal auo regressive inegraed moving average (ARIMA) model for a ea packaging company in India and shown ha his model has helped he organisaion o plan he producion aciviies more efficienly. Dhekale, B. S., e al. [4] analyze he growh and rend behavior of ea producion scenario in Wes Bengal. They used ARIMA model o forecas ea producion. Ahammed [] analyzed he rends in Bangladesh ea using polynomial models. Borodoloi [3] analyzed global ea producion and expor rend of India using linear regression analysis. Dissanayake [6] was forecased Tea producion in Sri Lanka using ARIMA models. Dua e al. [31] sudied he linear relaionship beween rainfall and ferilizer wih norh eas ea producion. Nasir and Shamsuddoha [33] menioned ha In Bangladesh he producion has increased by 1.84 % and conribues 1.37 in expor in he word ea rade and earns near abou 1775 million Taka (Taka 69 = USD 1.00) every year. Kamal and Bhuiyan [35] said ha he ea indusry of Bangladesh is no only provides a huge amoun of foreign currency, bu also provides a lo of employmen.
4 60 MD. MOYAZZEM HOSSAIN AND FARUQ ABDULLA Taking ea is an inegral par of social life in Bangladesh. The consumpion is increasing day by day mainly due o he rapid increase in populaion. The ea producing indusry has been radiionally regarded as one of he major agro-based labor inensive indusry and occupies an imporan role in he naional economy of Bangladesh. Tea is he mos imporan agriculure crop which plays a grea role o earn foreign money. Moreover, a large number of people were involved in he producion and markeing of ea. Thus, i is necessary o esimae he ea producion in Bangladesh which leads us o do his research. The main purpose of his research is o idenify he Auo-Regressive Inegraed Moving Average (ARIMA) model ha could be used o forecas he ea producion in Bangladesh. The R programming language of version is used o analyze his daa se.. MATERIALS AND METHODS.1 Daa Source. This sudy considered he published secondary daa of yearly ea producion in Bangladesh which was colleced over he period 197 o 013 from he Food and Agriculural Organizaion (FAO) websie (hp://faosa3.fao.org).. ARIMA Model. Suppose ha { ζ } is a whie noise wih mean zero variance = ζ + β ζ β ζ... β ζ σ, hen { } Y is defined by q q is called a moving average process of order q and is denoed by MA ( q). If he process { } Y is given by = α α α p p + ζ is called an auo-regressive process of order p and is denoed by AR ( p). Models ha are combinaion of AR and MA models are known as ARMA models. An ( p q) ARMA, model is defined as Y = α α α ζ β ζ β ζ... β ζ p p q q, where, Y is he original series, for every, we assume ha ζ is independen of Y -1,Y -,...,Y -p. A ime series { Y } is said o follow an inegraed auoregressive moving average (ARIMA) model if he d h difference W d = is a saionary ARMA process. If { } W follows an
5 FORECASTING THE TEA PRODUCTION OF BANGLADESH ARMA ( p, q) model, we say ha { Y } is an ARIMA ( p d, q) pracical purposes, we can usually ake 1, process. Forunaely, for d = or a mos. An ARIMA ( p,1, ) q process is defined as, W = α1w α pw p + ζ + β1ζ βqζ q, where, W = 1..3 Box-Jenkins Mehod. The influenial work of Box and Jenkins [14] shifed professional aenion away from he saionary serially correlaed deviaions from deerminisic rend paradigm oward he ( p d q) ARIMA,, paradigm. I is popular because i can handle any series, saionary or no wih or wihou seasonal elemens. The basic seps in he Box-Jenkins mehodology consis of he following five seps: Preliminary Analysis: Creae condiions such ha he daa a hand can be considered as he realizaion of a saionary sochasic process. Idenificaion of a Tenaive Model: Specify he orders p,d,q of he ARIMA model so ha i is clear he number of parameers o esimae. Empirical auocorrelaion funcions play an exremely imporan role o recognize he model. Esimaion of he Model: The nex sep is he esimaion of he enaive ARIMA model idenified in sep-. By maximum likelihood mehod we esimae he parameers of he model. Diagnosic Checking: Check if he model is a good one using ess on he parameers and residuals of he model. Forecasing: If he model passes he diagnosics sep, hen i can be used o inerpre a phenomenon, forecas.
6 6 MD. MOYAZZEM HOSSAIN AND FARUQ ABDULLA.4 Jarque-Bera Tes. The normaliy assumpion is checked by using Jarque and Bera [7] es, which is a goodness of fi measure of deparure from normaliy, based on he sample kurosis ( k ) and skewness ( s ). The es saisics Jarque-Bera (JB) is defined as ( k ) n JB = s χ, ~ ( ) where n is he number of observaions and k is he sample kurosis an s is he sample skewness. The saisic JB has an asympoic chi-square disribuion wih degrees of freedom, and can be used o es he hypohesis of skewness being zero and excess kurosis being zero, since sample from a normal disribuion have expeced skewness of zero and expeced excess kurosis of zero..5 Evaluaion of Forecas Error. Before performing growh analysis i is necessary o esimae he growh model ha bes fis he ime series. There are many summary saisics available in he lieraure for evaluaing he forecas errors of any model, ime series or economeric. Here, an aemp is made o idenify he bes models for ea producion in Bangladesh using he following conemporary model selecion crieria, such as RMSPE, MPFE and TIC. Roo Mean Square Error Percenage (RMSPE): Roo Mean Square Error Percenage (RMSPE) is defined as, and as, a Y is he acual value in ime. T f a 1 Y RMSPE = a T = 1, where f is he forecas value in ime Mean Percen Forecas Error (MPFE): Mean Percen Forecas Error (MPFE) is defined T a f 1 Y MPFE = T a = 1 Y in ime., where a is he acual value in ime and f is he forecas value
7 FORECASTING THE TEA PRODUCTION OF BANGLADESH Theil Inequaliy Coefficien (TIC): Theil (1966) Inequaliy Coefficien (TIC) is defined as TIC = 1 T T f a ( ) = T T value in ime. T T a f ( ) + ( ) = 1 = 1, where f is he forecas value in ime and 3. RESULTS AND DISCUSSION a is he acual In order o make forecasing a ime series i is necessary o check he ime series is saionary or no firs. In his sudy Augmened-Dickey-Fuller (ADF) uni roo es, Phillips-Perron (PP) uni roo es and Kwiakowski Phillips Schmid Shin (KPSS) uni roo es are used o check wheher he daa series is saionary or no. Afer second differencing he Augmened-Dickey-Fuller (ADF) es wih Pr ( τ ) < 0.01, Phillips-Perron (PP) es wih Pr ( τ ) < 0.01 and he Kwiakowski Phillips Schmid Shin (KPSS) uni roo es wih Pr ( τ ) > 0.1 a 5% level of significance adequaely declared ha he daa series is saionary and sugges ha here is no uni roo. The graphical represenaions of he original and second differenced series are presened in Figure 1(a), (b). (a) (b)
8 64 MD. MOYAZZEM HOSSAIN AND FARUQ ABDULLA (c) (d) Figure 1. (a) Time series (original series) plo, (b) Time series ( nd differenced) plo (c) ACF and (d) PACF of nd differenced ea producion in Bangladesh. I is clear ha he yearly ea producion in Bangladesh has gradually an increasing rend wih some flucuaion over he sudy period i.e., he variance is unsable which leads he ea producion daa series is no saionary (Figure 1(a)). However, i is clear ha he second differenced ea producion daa series shows sable variance which leads he daa becomes saionary. To sabilize he variance and o make he daa saionary second difference is enough ha is difference order is and i is said ha inegraed of order (Figure 1(b)). The alernaive posiive and negaive ACF (Figure 1(c)) and exponenially decay PACF (Figure 1(d)) indicaes an auoregressive moving average process. The PACF wih significan spike a lag 3 and ACF wih significan spike a lag 1 sugges ha hird order auoregressive and firs order moving average are effecive on ea producion in Bangladesh. However, using he enaive procedure, i is clear ha ARIMA(0,,1) model wih AIC = , AICC = and BIC = is he bes seleced model for forecasing he ea producion in Bangladesh. The esimaes of he parameers of he fied ARIMA(0,,1) model are shown in Table 1. The value of he mos useful forecasing crieria of he fied ARIMA(0,,1) model are RMSPE = , MPFE = , and TIC =
9 FORECASTING THE TEA PRODUCTION OF BANGLADESH Table 1: Summary saisics and forecasing crieria of he fied ARIMA (0,,1) model Coefficiens Esimaes Sd.Error -value p-value ma Several plos of he residuals for he fied ARIMA(0,,1) model are presened in Figure, sugges ha here is no significan paern and hence here is no auocorrelaion among he residuals. Also, he lower and upper values of he runs are 15 and 8 respecively which are obained from Swed and Eisenhar [13] Tables a 5% level of significance, and here he observed number of runs is 5. So he Run es wih ( R ) Pr 15 8 = 0.95 a 5% level of significance srongly sugges ha here is no auocorrelaion among he residuals of he fied ARIMA(0,,1) model. Here Jarque-Bera es is used o check he normaliy assumpion of he residuals of he fied model. We observe ha he Jarque-Bera es wih ( ) Pr χ = a 5% level of significance moderaely suggess o accep he normaliy assumpion ha is he residuals of he fied ARIMA(0,,1) model are normally disribued. Therefore, i is clear ha our fied ARIMA(0,,1) model is he bes fied model and adequaely used o forecas he ea producion in Bangladesh. Figure. Several plos of residual.
10 66 MD. MOYAZZEM HOSSAIN AND FARUQ ABDULLA By using he bes fied model ARIMA(0,,1), he forecased ea producion and 95% confidence level for welve years are shown in Table. Table : Forecased ea producion (onnes) in Bangladesh Year Forecased LCL UCL Noe: LCL= Lower Confidence Limi and UCL=Upper Confidence Limi The graphical comparison of he original series and he forecas series is shown in Figure 3. I is observed ha he forecas series (blue-color) flucuaed from he original series (dark-green-color) wih a very small amoun ha is i shows he producion in same manner of he original series (Figure 3). Therefore, he forecased series is really beer represenaion of he original ea producion series in Bangladesh.
11 FORECASTING THE TEA PRODUCTION OF BANGLADESH Figure 3: Comparison beween he original and forecased ea producion in Bangladesh. 4. Conclusion The bes seleced Box-Jenkins ARIMA model for forecasing he ea producions in Bangladesh is ARIMA (0,,1). The comparison beween he original series and forecased series shows he same manner indicaing he fied model behaved saisically well and suiable o forecas he Tea producions in Bangladesh i.e., he models forecas well during and beyond he esimaion period. Thus, his model can be used for policy purposes as far as forecass he ea producion in Bangladesh.
12 68 MD. MOYAZZEM HOSSAIN AND FARUQ ABDULLA REFERENCES [1]. Consul, P.C., A simple urn model dependen on predeermined sraegy, Sankhya, Ser. B, 36(3) (1974) []. A. B. Kamah, L. Wang, H. Das, L. Li, V. N. Reinhold, and J. F. Bukowski, Anigens in eabeverage prime human Vgamma Vdela T cells in viro and in vivo for memory and nonmemory anibacerial cyokine responses, Proc Nal Acad Sci USA 100(003), [3]. American Diabees Associaion (ADA), Diagnosis and Classifiaion of Diabees Mellius, Diabees Care 35(01), S64 S71. [4]. B. S. Dhekale, P. K. Sahu, K. P. Vishwajih, P. Mishra and M. Noman, Modeling and forecasing of ea producion in Wes Bengal, Journal of Crop and Weed 10(014), [5]. BTD (Bangladesh Tea Board) (01). hp://www. Teaboard.gov.bd/ [6]. BTRI (Bangladesh Tea Research Insiue), Brief noe on ea culure for he BTRI, Annual Repor, Shromongal, Bangladesh, (01). [7]. C. M. Jarque and A. K. Bera, A es for normaliy of observaions and regression residuals, Inernaional Saisical Review 55(1987), JSTOR [8]. C. S. Yang, J. Y. Chung, G. Yang, S. K. Chhabra and M. J. Lee, Tea and ea polyphenols in cancer prevenion, The Journal of Nuriion 130(000), 47S 478S. [9]. C. S. Yang, P. Maliakal and X. Meng, Inhibiion of carcinogenesis by ea, Annual Review of Pharmacology and Toxicology 4(00), [10]. D. L. McKay and J. B. Blumberg, The role of ea in human healh: an updae, Journal of he American College of Nuriion 1(00), [11]. E. V. Gijo, Demand forecasing of ea by seasonal ARIMA model, In. J. of Business Excellence 4(011), [1]. F. S. Hamid, Yield and Qualiy of Tea under Varying Condiions of Soils and Nirogen Availabiliy, Pakisan Research Reposiory, Higher Educaion Commision Pakisan (006). hp:// eprins.hec.gov.pk/ 348/1/03.hm. [13]. F. S. Swed and C. Eisenhar, Tables for Tesing Randomness of Grouping in a Sequence of Alernaives, The Annals of Mahemaical Saisics 14(1943), [14]. G. Box and G. Jenkins, Time Series Analysis: Forecasing and Conrol, San Francisco: Holden- Day, (1970). [15]. H. A. Linke and R. Z. LeGeros, Black ea exrac and denal caries formaion in hamsers, In. J. Food Sci. Nur. 54(003),
13 FORECASTING THE TEA PRODUCTION OF BANGLADESH [16]. H. Huang and X. Xu, Anicancer aciviy of ea: evidence from recen animal experimens and human sudies, Journal of Tea Science 4(004), [17]. H. Theil, Applied Economic Forecasing. Norh-Holland Publishing Company, Amserdam (1966). [18]. J. Blumberg, Inroducion o he proceedings of he hird Inernaional scienific symposium on ea and human healh: role of flavonoids in he die, The Journal of Nuriion 133(003), 344s 346s. [19]. J. Hazarika, Developmen of ARIMA Model for Tea Producion of Assam, India: A Case Sudy, In. J. Agricul. Sa. Sci. 6(010), [0]. J. H. Weisburger, Tea and healh: a hisorical perspecive, Cancer Leers 114(1997), [1]. J. H. Weisburger, Tea and healh: he underlying mechanisms, Proceedings of he Sociey for Experimenal Biology and Medicine 0(1999), []. K. M. Ahammed, Invesmen for Susainable Developmen of Bangladesh Tea Indusry An Empirical Sudy, BEA XVIIl Biennial Conference Papers 01, 1-0. [3]. K. P. Borodoloi, Global ea producion and expor rend wih special reference o India, Two and a Bud 59(013), [4]. K. S. Soe, and D. J. Baer, Tea consumpion may improve biomarkers of insulin sensiiviy and risk facors for diabees, J. Nur. 138(008), 1584S 1588S. [5]. M. L. Rahman, Impac of Price and Oher Facors on Tea in Bangladesh: Sources of Variaion and Dispariy over Division, BRAC Universiy Journal 4(007), [6]. M. R. Dissanayake, Time Flucuaion Models o Forecas Tea Producion and Prices in Sri Lanka, 10h Inernaional Conference on Sri Lankan Sudies., December 005. [7]. M. Redowan and A. H. Kanan, A Sudy on Maximizaion of Land Use wih Associaed Crops Oher han Tea and Managemen, In. J. of Ecol. and Dev. 5(013), [8]. M. Y. Bekhi, Levels of Essenial and Non- Essenial Meals in Leaves of he Tea Plan (Camellia sinensis L.) and Soils of Wushwush Farms, Ehiopia, (006). hp://ed.aau.edu.e/dspace/bisream/ /307/1/michael%0yemane.pdf. [9]. P. Khisa and M. Iqbal, Tea Manufacuring in Bangladesh: Problems and Prospecs, 4h Inernaional Conference on Mechanical Engineering, December 6-8, Dhaka, Bangladesh, 6(001), [30]. R. A. Anderson and M. M. Polansky, Tea enhances insulin aciviy, J. Agric. Food Chem. 50(00),
14 70 MD. MOYAZZEM HOSSAIN AND FARUQ ABDULLA [31]. R. Dua, T. A. Sein, M. A. Smaling, R. M. Bhaga and M. Hazarika, Modelling and quanifying ea produciviy in Norheas India, Two and a Bud 59(01), [3]. T. K. Mondal, A. Bhaacharya, M. Laxmikumaran and P. S. Ahuja, Recen advances of ea (Camellia sinensis) bioechnology, Plan Cell, Tissue and Organ Culure 76(004), [33]. T. Nasir and M. Shamsuddhoa, Tea producion, Consumpion and Expors: Bangladesh Perspecive, Inernaional Journal of Educaion Research and Technology (011), [34]. X. X. Zheng, Y. L.Xu, S. H. Li, R. Hui, Y. J. Wu, and X. H. Huang, Effecs of green ea caechins wih or wihou caffeine on glycemic conrol in aduls: a mea-analysis of randomized conrolled rials, Am. J. Clin. Nur. 97(013), [35]. Y. Kamal and N. U. Bhuiyan, The Tea Indusry of Bangladesh A Synopsis of is Problems, Prospecs and Expor Poenialiies, IBS Business Review (004), [36]. Yong-xing Zhu, Herve Huang and You-ying Tu, A review of recen sudies in China on he possible beneficial healh effecs of ea, Inernaional Journal of Food Science and Technology 41(006), [37]. Z. Chen, Major progress in he invesigaion on ea and human healh in 0h cenury, China Tea 4(001), [38]. Z. Chen, Biochemical and molecular biological basis of he anicarcinogenic aciviy of ea polyphenolic compounds, Journal of Tea Science 3(003), (1) Deparmen of Saisics, Jahangirnagar Universiy, Savar, Dhaka-134, Bangladesh. address: mmhmm.jusa@gmail.com () Deparmen of Saisics, Islamic Universiy, Kushia-7003, Bangladesh. address: faruqiusa09mnil@gmail.com
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