Forecasting of boro rice production in Bangladesh: An ARIMA approach

Transcription

1 J. Bangladesh Agril. Univ. 8(1): , 2010 ISSN Forecasing of boro rice producion in Bangladesh: An ARIMA approach N. M. F. Rahman Deparmen of BBA, Mirpur Universiy College, Dhaka Absrac The sudy was underaken o examine he bes fied ARIMA model ha could be used o make efficien forecas boro rice producion in Bangladesh from o I appeared from he sudy ha local, modern and oal boro ime series are 1s order homogenous saionary. I is found from he sudy ha he ARIMA (0,1,0) ARIMA (0,1,3) and ARIMA (0,1,2) are he bes for local, modern and oal boro rice producion respecively. I is observed from he analysis ha shor erm forecass are more efficien for ARIMA models. The producion uncerainy of boro rice can be minimizing if producion can be forecased well and necessary seps can be aken agains losses. The governmen and producer as well use ARIMA mehods o forecas fuure producion more accuraely in he shor run. Keywords: Producion, ARIMA model, Forecasing. Inroducion Agro-based developing counry like Bangladesh is sriving hard for rapid developmen of is economy. The economic developmen of he counry is mainly based on agriculure. The conribuion of agriculure secor in GDP is percen (BER, 2008). In he agriculure secor, he crop sub-secor dominaes wih percen in GDP of which rice alone conribues abou 53 percen. In Bangladesh alhough 63 percen of he labour force is direcly engaged in agriculure and 78 percen of oal crop is devoed o rice producion, he counry has sill a chronic shorage of food-grain (BBS.2003). Boro - a Bengali erm originaed from he Sanskri word 'BOROB'. I refers o a special culivaion of rice in low land pockes during November-May; aking advanage of he residual waer in he field afer harves of Kharif crop, longer moisure reeniviy of he soil and surface waer sored in he near by diches (Singh e al 2003a). Thakur e al. (2003) repored boro in Shivapuran as one of he offerings o he God. In Bangladesh rice is grown in hree disinc seasons; boro (January o June), aus (April o Augus), and amon (Augus o December). Modern rice varieies were inroduced for he boro and aus seasons in 1967 and for he amon seasons in 1970 (Hossain e al. 1994). In Bangladesh boro rice occupied nearly 35% of he million ha of rice harvesed area, and conribued 50% of he 38.7 million ons of rice produced in 2001/2002. The yield in 2001/2002 was 4.9 on/ha (Singh e al 2003b). For fuure planning i is necessary o evaluae he growh paern of boro rice producion ha is achieved a he ime in he counry as a whole and also in he differen varieies of he counry. To reveal he growh paern and o make he bes forecas of boro producion in Bangladesh appropriae ime series model ha can be able o describe he observed daa successfully are necessary. For predicion purpose one or boh of wo ypes of models, usually known as srucural regression models and ime series models are ofen used in pracice. The use of srucural regression models requires informaion abou he facors affecing he ime series. On he oher hand, ime series analysis, especially Box-Jenkin ype ARIMA models, le he daa speak for hemselves i.e. he fuure movemens of a ime series are deermined using is own presen and pas values (Box and Jenkins, 1978). Among he sochasic ime series models ARIMA ypes are very powerful and popular as hey can successfully describe he observed daa and can make forecas wih minimum forecas error. These ypes of models are very difficul o idenify and esimae. They are also expensive, ime consuming and possesses a complex model building mechanism. So far we know few works have been underaken for forecasing boro rice producion in Bangladesh using ARIMA models. The objecive of he sudy is o develop appropriae ARIMA models for he ime series of local, modern and oal boro rice producion in Bangladesh and o make five year forecass for all he ime series wih appropriae predicion inerval.

2 104 Forecasing of boro rice producion in Bangladesh Maerial and Mehods To achieve he sipulaed objecives, he presen sudy has been carried ou on he basis of local, modern and oal boro rice producion daa peraining he period o , which were colleced from secondary (BBS various issues) source. The ime series daa of local, modern and oal boro rice producion were modeled by Box-Jenkins ype sochasic auoregressive inegraed moving average (ARIMA) process. The Box-Jenkins ype ARIMA process (Box and Jenkins, 1978) can be d defined as φ ( B)( y µ ) = θ ( B) ε, Here, y denoes local, modern and oal boro rice producion million meric ons, µ is he mean of, (B) d Y p φ = φ B L φ B q 1 p, θ (B) = 1 θ B L θ B q, θi denoes he ih moving average parameer, φ i denoes he ih auoregressive parameer, p, q and d denoe he auoregressive, moving average and difference order of he process respecively, and B denoe he difference and back-shif operaors respecively. The esimaion mehodology of he above model consiss of hree seps, namely, idenificaion, esimaion of parameers and diagnosic checking. The idenificaion sep involves he use of he echniques for deermining he value of p, d and q. Here, hese values are deermined by using auocorrelaion and parial auocorrelaion funcions () and Augmened Dickey-Fuller (ADF) es. The model used for ADF is y y 1 = α + β + ( ρ 1) y 1+ λ y (Pindyck and Rubinfeld, 1991, p.461).the 1 second sep is o esimae he parameers of he model. Here, he mehod of maximum likelihood is used for his purpose. The hird sep is o check wheher he chosen model fis he daa reasonably well. For his reason he residuals are examined o find ou if hey are whie noise. To es if he residuals are whie noise he ACF of residuals and he Ljung and Box (1978) saisic are used. In case of wo or more compeing models passing he diagnosic checks he bes fied model is seleced using he following crieria muliple R 2 2, Adjused R, Roo mean squared error (RMSE), Akaike Informaion Crierion (AIC), Bayesian Informaion (BIC), Mean absolue error (MAE) and Mean absolue proporion percen error (MAPPE). Resuls and Discussion Saionariy checking using ACF Auo correlaion funcion is a very consrucive ool o find ou wheher a ime series is saionary or no. Boh are used o deermine auo-regression and moving average orders of he models. of our hree ime series of local, modern and oal Boro rice producion are consruced. All he graphs represen ha auocorrelaions aper of very slowly indicaing ha all he series are nonsaionary (Fig. 1, Fig. 3 and Fig. 5. Now i is needed o ake 1s-difference of all he ime series and consruc auocorrelaion funcions o see if hey are saionary or no. The auocorrelaion funcions of 1s differenced ime series of local, modern and oal boro rice producion are presened in Fig. 2, Fig. 4 and Fig. 6 respecively. The 1s differenced ime series shows saionariy, as he auocorrelaion declines faser han he auo correlaion of undifferenced series. Now i is clear ha ACFs of all he 1 s -differenced series decline rapidly. So, i is revealed ha local, modern and oal Boro ime series are saionary of order one. Before aking decision abou saionariy of he series, he sudy need o carry ou he formal ADF es of saionariy. Saionariy Checking using ADF A par from he graphical mehods of using ACF for deermining saionariy of a ime series, a very popular formal mehod of deermining saionariy is he Augmened Dickey-Fuller es. Here, hese ess done for all he ime series. The esimaes of necessary parameers and relaed saisics for he ime series of local, modern and oal Boro rice producion are presened in Table

3 Rahman 105 Table 1. ADF es of saionariy of local, modern and oal Boro rice producion in Bangladesh Area Model α β (ρ-1) λ RSS DF DW F F 05, 41 Local Modern Toal Unresriced S. Error Resriced S. Error Unresriced S. Error Resriced S. Error Unresriced S. Error Resriced S. Error The analysis exposed ha he hypohesis of random walk ha underlying process of generaing he ime series is non-saionary can no be rejeced, as he relaed F saisics is insignifican a 5% level. So, all he undifferenced ime series are non saionary and hey mus be 1 s -differenced o see if 1 s -differenced are nonsaionary. To perform he ADF es for he 1 s -differenced ime series of local, modern and oal Boro rice producion essenial analysis are presened in Table 2. A furher, he analysis shows ha local, modern and oal Boro rice producion, he 1 s -differenced ime series are saionary as he F saisics are significance a 5% level. From he ACFs and ADF es, we can ake decision ha local, modern and oal boro imes series are saionary of order one. Table 2. ADF es of saionariy of local, modern and oal Boro rice 1 s differen producion Area Model α β Local Modern Toal (ρ-1) λ RSS DF DW F F 05, 40 Unresriced S.Error Resriced S.Error Unresriced S.Error Resriced S.Error Unresriced S.Error Resriced S.Error Modeling ime series of local boro rice producion For selecing ARIMA model for local boro rice producion series a rouine es of idenificaion applied before using Box-Jenkins mehodology. Figure 1 represens he plos of local boro rice producion series a heir level up o 16 lags. From his figure, he facs sand ou ha a he beginning ACF has five significan spikes and PACF has only one significan spike.on he oher hand, he ACF plos and PACF plos in he Fig. 2 is showing a differen configuraion. In his figure, he ACF shows no significan auo-correlaion a any lag. I is also eviden from he Box-Ljung saisic presened on he op of ACF ha all he differenced values are wihin he 95% confidence limi. This implies ha he series is non-saionary a heir level and saionary a firs difference. Moreover, he residuals are uncorrelaed. Augmened Dickey-Fuller uni roo ess are showing he saionariy posiion of his series a same order of difference

4 106 Forecasing of boro rice producion in Bangladesh ACF PACF Fig. 1. Figure Undifferenced 1: Undifferenced local boro local rice boro producion rice producion in Bangladesh in ACF PACF Fig. Figure 2. 1s-differenced 2: local local boro boro rice rice producion in Bangladesh in 1 ACF PACF Fig. 3. Figure Undifferenced 3: Undifferenced modern modern boro boro rice producion rice producion in Bangladesh in

5 Rahman ACF PACF Fig. 4. Figure 1s-differenced 4: 1s-differenced modern modern boro boro rice producion rice producion in Bangladesh in ACF PACF Fig. 5. Figure Undifferenced 5: Undifferenced oal boro oal rice boro producion rice producion in Bangladesh in Bangladesh 0.1 ACF PACF Fig. 6. Figure 1s-differenced 6: 1s-differenced oal boro oal rice boro producion rice producion in Bangladesh in Bangladesh

6 108 Forecasing of boro rice producion in Bangladesh Observing he naure of plos of he series and heir heoreical properies, he order of auo-regression and moving average process of local boro rice producion series are seleced by esimaing he ARIMA models a p=0,l and q==0,1,2,3,4,5 using he SPSS 11.5 sofware packages. Twelve ARIMA models a differen values of p, d, and q are esimaed using he same packages as menioned in he previous secion. The enaively seleced models are ARIMA (0,1,0), ARIMA (0,1,1), ARIMA (0,1,2), ARIMA (0,1,3), ARIMA (0,1,4), ARIMA (0,1,5), ARIMA (1,1,0), ARIMA (1,1,1), ARIMA (1,1,2), ARIMA (1,1,3), ARIMA (1,1,4) and ARIMA (1,1,5). Ou of hese welve models hree models are seleced comparing he minimum values of he crieria A1C and B1C. The seleced models are ARIMA (0,1,0), ARIMA (0,1,1) and ARIMA (1,1,0). These hree models are again compared according o he minimum values of RMSE, MAE, MSE and MAPPE and maximum value of R 2 2 and R which are given in Table 3. Hence, i can be concluded ha ARIMA (0,1,0) is he bes fied model for forecasing he local boro rice producion in Bangladesh. This jusified ha he selecion of ARIMA (0,1,0) is he bes model o represen he daa generaing process very precisely. From he above able 3 i is observed ha he model ARIMA (0,1,0) is beer han he oher models because his model saisfied he all crierion excep 2 MSE and R. So he selec ARIMA (0,1,0) is he bes model. Table 3. Diagnosic ools and model selecion crieria for local boro rice producion of bes fied models Values of selecion crieria Model MAE MSE RMSE AIC BIC MAPPE R 2 2 R ARIMA(0,1,0) ARIMA(0,1,1) ARIMA(1,1,0) Noe: The value of he crierion for a model wih bold numerals ha he model is beer han oher models wih respec o ha crierion Modeling ime series of modern boro rice producion For selecing ARIMA model of modern boro producion series a rouine es of idenificaion applied before using Box-Jenkins mehodology. Fig. 3 represens he plos of modern boro rice producion series a heir level up o 16 lags. From his figure, he facs sand ou ha a he beginning ACF has nine significan spikes and PACF has only one significan spike.on he oher hand, he ACF plos and PACF plos in he Fig. 4 is showing a differen configuraion. In his figure, he ACF shows no significan auo-correlaion a any lag. I is also eviden from he Box-Ljung saisic presened on he op of ACF ha all he differenced values are wihin he 95% confidence limi. This implies ha he series is non-saionary a heir level and saionary a firs difference. Moreover, he residuals are uncorrelaed. Augmened Dickey-Fuller uni roo ess are showing he saionariy posiion of his series a same order of difference. Observing he naure of plos of he series and heir heoreical properies, he order of auo-regression and moving average process of modern boro rice producion series are seleced by esimaing he ARIMA models a p=0,l and q==0,1,2,3,4,5,6,7,8,9 using he same sofware packages. Tweny ARIMA models a differen values of p, d, and q are esimaed using he same packages as menioned in he previous secion. The enaively seleced models are ARIMA (0,1,0), ARIMA (0,1,1), ARIMA (0,1,2), ARIMA (0,1,3), ARIMA (0,1,4), ARIMA (0,1,5), ARIMA (0,1,6), ARIMA (0,1,7), ARIMA (0,1,8), ARIMA (0,1,9), ARIMA (1,1,0), ARIMA (1,1,1), ARIMA (1,1,2), ARIMA (1,1,3), ARIMA (1,1,4), ARIMA (1,1,5), ARIMA (1,1,6), ARIMA (1,1,7), ARIMA (1,1,8) and ARIMA (1,1,9). Ou of hese weny models hree models are seleced comparing he minimum values of he crieria A1C and B1C. The seleced models are ARIMA (0,1,0), ARIMA (0,1,3) and ARIMA (1,1,0). These hree models are again compared according o he minimum values of RMSE, MAE, MSE and MAPPE and maximum value of R 2 2 and R which are given in Table 4. Hence, i can be concluded ha ARIMA (0,1,3) is he bes fied model for forecasing he modern boro rice producion in Bangladesh. This jusified ha he selecion of ARIMA (0,1,3) is he bes model o represen he daa generaing process very precisely.

7 Rahman 109 Table 4. Diagnosic ools and model selecion crieria for modern boro rice producion of bes fied models Values of selecion crieria Model MAE MSE RMSE AIC BIC MAPPE R 2 2 R ARIMA(0,1,0) ARIMA(0,1,3) ARIMA(1,1,0) Noe: The value of he crierion for a model wih bold numerals ha he model is beer han oher models wih respec o ha crierion From he above Table 4 i is observed ha he model ARIMA (0,1,3) is beer han he oher models because his model saisfied he maximum crierion excep MAE and MAPPE. So he selec ARIMA (0,1,3) is he bes model. Modeling ime series of oal boro rice producion For selecing ARIMA model of oal boro producion series a rouine es of idenificaion applied before using Box-Jenkins mehodology. Fig. 5 represens he plos of oal boro rice producion series a heir level up o 16 lags. From his figure, he facs sand ou ha a he beginning ACF has nine significan spikes and PACF has only one significan spike.on he oher hand, he ACF plos and PACF plos in he Fig. 6 is showing a differen configuraion. In his figure, he ACF shows no significan auocorrelaion a any lag. I is also eviden from he Box-Ljung saisic presened on he op of ACF ha all he differenced values are wihin he 95% confidence limi. This implies ha he series is non-saionary a heir level and saionary a firs difference. Moreover, he residuals are uncorrelaed. Augmened Dickey- Fuller uni roo ess are showing he saionariy posiion of his series a same order of difference. Observing he naure of plos of he series and heir heoreical properies, he order of auo-regression and moving average process of oal boro rice producion series are seleced by esimaing he ARIMA models a p=0,l and q==0,1,2,3,4,5,6,7,8,9 using he SPSS same sofware packages. Tweny ARIMA models a differen values of p, d, and q are esimaed using he same packages as menioned in he previous secion. The enaively seleced models are ARIMA (0,1,0), ARIMA (0,1,1), ARIMA (0,1,2), ARIMA (0,1,3), ARIMA (0,1,4), ARIMA (0,1,5), ARIMA (0,1,6), ARIMA (0,1,7), ARIMA (0,1,8), ARIMA (0,1,9), ARIMA (1,1,0), ARIMA (1,1,1), ARIMA (1,1,2), ARIMA (1,1,3), ARIMA (1,1,4), ARIMA (1,1,5), ARIMA (1,1,6), ARIMA (1,1,7), ARIMA (1,1,8) and ARIMA (1,1,9). Ou of hese weny models hree models are seleced comparing he minimum values of he crieria A1C and B1C. The seleced models are ARIMA (0,1,0), ARIMA (0,1,2), and ARIMA (1,1,0). These hree models are again compared according o he minimum values of RMSE, MAE, MSE and MAPPE and maximum value of R 2 2 and R which are given in Table 5. Hence, i can be concluded ha ARIMA (0,1,2) is he bes fied model for forecasing he oal boro rice producion in Bangladesh. This jusified ha he selecion of ARIMA (0,1,2) is he bes model o represen he daa generaing process very precisely. Table 5. Diagnosic ools and model selecion crieria for oal boro rice producion of bes fied models Values of selecion crieria Model MAE MSE RMSE AIC BIC MAPPE R 2 2 R ARIMA(0,1,0) ARIMA(0,1,2) ARIMA(1,1,0) Noe: The value of he crierion for a model wih bold numerals ha he model is beer han oher models wih respec o ha crierion

8 110 Forecasing of boro rice producion in Bangladesh From he above Table 5 i is observed ha he model ARIMA (0,1,2) is beer han he oher models because his model saisfied he maximum crierion excep MAE and MAPPE. So he selec ARIMA (0,1,2) is he bes model. The above discussion abou he finess of various models o he ime series of boro rice producion in Bangladesh reveals ha ARIMA(0,1,0), ARIMA (0,1,3) and ARIMA (0,1,2) models are appropriae for local, modern and oal boro rice producion respecively. I also reveals ha he selecion of he bes model for a paricular caegory can someimes be very confusing. However he discussion recommends a bes model for a paricular caegory as given in Table 6. Table 6. Bes esimaed models for boro rice producion in Bangladesh Variey Local boro Modern boro Toal boro The name of he bes model ARIMA(0,1,0) ARIMA(0,1,3) ARIMA(0,1,2) The funcional form of he model ( Y ) = ε ( Y ) = ( B B ( Y ) = ( B B 0.976B 2 ) ε 3 ) ε Diagnosic checking For diagnosic checking ACF of residuals and Ljung and Box chi square saisic are widely used in pracice. In Table 7 he chi square saisics are given for all he bes-seleced sochasic models wih P- values. All he chi square values are insignifican. I implies ha he residuals of he respecive ime series are whie noise implying ha he model finess is accepable. Table 7. Diagnosic ools and model selecion crieria for he bes fied models Area Model MAE RMSE AIC BIC MAPPE R 2 2 R Local Modern Toal Forecasing ARIMA (0,1,0) ARIMA (0,1,3) ARIMA (0,1,2) No saisfied No saisfied No saisfied No saisfied No saisfied χ 2 (BL a 16 lag) P-value Five years forecass of local, modern and oal boro producion are esimaed using he bes seleced models and are presened in Table 8. Predicion inervals of forecas are also presened. Table 08 reveals ha he forecased oal local boro rice producion in he year of was meric ons wih a 95% confidence inerval of ( , ) meric ons whereas for modern and oal boro rice producion hese values are meric ons and meric ons wih a 95% confidence inerval of ( , ) meric ons and ( , ) meric ons respecively. The analysis found ha if he presen growh raes coninue hen he local boro rice producion, modern boro rice producion and oal boro rice producion in Bangladesh in he year of will be meric ons, meric ons and meric ons wih a 95% confidence inerval of ( , ) meric ons, ( , ) meric ons and ( , ) meric ons respecively.

9 Rahman 111 Table 8. Forecas of boro rice producion in Bangladesh for he period of o a 95% level Variey Local boro rice producion ARIMA (0,1,0) Modern boro rice producion ARIMA (0,1,3) Toal boro rice producion ARIMA (0,1,2) Descripion Forecas year LPL Forecas UPL LPL Forecas UPL LPL Forecas UPL Conclusion A ime series model accouns for paerns in he pas movemen of a variable and uses ha informaion o predic is fuure movemens. In a sense a ime series model is jus a sophisicaed model of exrapolaion. Time series daa have become very popular o be inensively used in empirical research and economericians have recenly begun o pay very careful aenion o such daa. To selec he bes model for a paricular ime series he laes available model selecion crieria are used. The sudy revealed ha ARIMA (0,1,0), ARIMA (0,1,3) and ARIMA (0,1,2) models are appropriae for local, modern and oal boro rice producion in Bangladesh respecively and i is o be noed ha he shor-erm forecas is beer as he error of forecas increases wih he increase of he period of forecas. References Alam, S The Effecs of Price and Non-Prices Facors on he Producion of Major Crops in Bangladesh. A Thesis Submied o he Universiy of New Casle Upon Tyne for he Degree of Docor of Philosophy in he Deparmen of Agriculural Economics and Food markeing. Bangladesh Bureau of Saisics Saisical Yearbook of Bangladesh, Minisry of Planning, Governmen of he People s Republic of Bangladesh, Dhaka. Bangladesh Bureau of Saisics. various issue (1976 o 2005). Yearbook of Agriculural Saisics of Bangladesh, Minisry of Planning, Governmen of he People s Republic of Bangladesh, Dhaka. Bangladesh Bureau of Saisics Bangladesh Economic Review. Minisry of Planning, Governmen of he People s Republic of Bangladesh, Dhaka. Gujarai, D. N. (2003): Basic Economerics. 4h ediion, McGraw-Hill, Inc. New York. Haque, M. E., Hossain, M. I. and Rahman, K. M. M Forecasing fish producion in Bangladesh using ARIMA model, J. Bangladesh Agril. Univ.3(2): Haque, M.E., Imam, M.F. and Awal, M.A Forecasing shrimp, frozen food expor earning of Bangladesh using ARIMA model. Pakisan Journal of Biological Sciences.9(12): Hossain M Developmen of boro rice culivaion in Bangladesh: Trends and policies. In: Boro rice (Singh, R.K., Hossain, M. and Thakur, R. eds). IRRI-India Office. Pp Johnson, J Economeric Mehods, Third Ediion, MoGraw-Hill Inc, New York. Kousoyiannis, A Theory of Economerics. Second Ediion (Low-Priced Ediion), English Language Book Sociey, Macmillan Educaion Ld, London. Maddala, G.S Inroducion o Economerics. Macmillan Publishing Company, New York,

10 112 Forecasing of boro rice producion in Bangladesh Pindyck, R.S. and Rubinfeld, D.L Economeric Models and Economeric Forecass. 4h ed. McGraw-Hill, Boson, Massachuses Burr Ridge, Illinois Dubuque, Iowa Madison, Wisconsin New York, New York San Francisco, California S. Louis, Missouri. Razzaque, M.A Annual Repor Lenil, Blackgram, Mungbean Developmen Pilo Projec, Bangladesh Agriculural research Insiue. Joydebpur, Gazipur, Bangladesh. Singh, P.K., Hossain, M. and Thakur, R. 2003a. In: Boro rice (RK Singh, M Hossain and R Thakur, eds). IRRI-India Office. Singh, R.K., Thakur, R. and S.D. Chaarjee. 2003b. Harnessing boro rice poenial for increasing rice producion in deepwaer areas of Easern India, An overview. In: Boro rice (RK Singh, M Hossain and R Thakur, eds). IRRI-India Office. Pp Thakur R, Singh, N.K. and Chaudhary, V.K Recen advances in boro rice research in Bihar. In: Boro rice (RK Singh, M Hossain and R Thakur, eds). IRRI-India Office. Pp