Global Journal of Managemen and Business Research Finance Volume 3 Issue 3 Version.0 Year 03 Type: Double Blind Peer Reviewed Inernaional Research Journal Publisher: Global Journals Inc. (USA) Online ISSN: 49-4588 & Prin ISSN: 0975-5853 Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. By Dr. Jiban Chandra Paul, Md. Shahidul Hoque & Mohammad Morshedur Rahman Universiy of Chiagong, Bangladesh Absrac - This work is an aemp o examine empirically he bes ARIMA model for forecasing. Average daily share price indices of he daa series of Square Pharmaceuicals Limied (SPL) have been used for his purpose. A firs he saionariy condiion of he daa series are observed by ACF and PACF plos, hen checked using he Saisics such as Ljung-Box-Pierce Q-saisic and Dickey-Fuller es saisic. I has been found ha he average daily share price indices of he daa series of Square Pharmaceuicals Limied (SPL) are non-saionary. The average daily share price indices of SPL daa series are nonsaionary even afer log-ransformaion. Bu afer aking firs difference of logarihmic values of SPL daa series, he same ypes of plos and he same ypes of saisics show ha he daa is saionary. The bes ARIMA model have been seleced by using he crieria such as AIC, AIC c, SIC, AME, RMSE and MAPE ec. To selec he bes ARIMA model he daa spli ino wo periods, viz. esimaion period and validaion period. The model for which he values of crieria are smalles is considered as he bes model. Hence, ARIMA (,, and ) is found as he bes model for forecasing he SPL daa series. GJMBR-C Classificaion : JEL Code: F37 Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh A Case Sudy on Square Pharmaceuical Ld. Sricly as per he compliance and regulaions of: 03. Dr. Jiban Chandra Paul, Md. Shahidul Hoque & Mohammad Morshedur Rahman. This is a research/review paper, disribued under he erms of he Creaive Commons Aribuion-Noncommercial 3.0 Unpored License hp://creaivecommons.org/licenses/by-nc/3.0/), permiing all non-commercial use, disribuion, and reproducion in any medium, provided he original work is properly cied.
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. Dr. Jiban Chandra Paul α, Md. Shahidul Hoque σ & Mohammad Morshedur Rahman ρ Absrac - This work is an aemp o examine empirically he bes ARIMA model for forecasing. Average daily share price indices of he daa series of Square Pharmaceuicals Limied (SPL) have been used for his purpose. A firs he saionariy condiion of he daa series are observed by ACF and PACF plos, hen checked using he Saisics such as Ljung-Box- Pierce Q-saisic and Dickey-Fuller es saisic. I has been found ha he average daily share price indices of he daa series of Square Pharmaceuicals Limied (SPL) are nonsaionary. The average daily share price indices of SPL daa series are non-saionary even afer log-ransformaion. Bu afer aking firs difference of logarihmic values of SPL daa series, he same ypes of plos and he same ypes of saisics show ha he daa is saionary. The bes ARIMA model have been seleced by using he crieria such as AIC, AIC c, SIC, AME, RMSE and MAPE ec. To selec he bes ARIMA model he daa spli ino wo periods, viz. esimaion period and validaion period. The model for which he values of crieria are smalles is considered as he bes model. Hence, ARIMA (,, ) is found as he bes model for forecasing he SPL daa series. Then, forecass of he daa have been made using seleced ype of ARIMA model. Finally, he values of ADSPI of SPL up o February 0 are prediced and repored in he sudy. I. Inroducion S ock exchange plays a vial role in he naional economy of Bangladesh. Sock marke is an essenial par of he capial marke. The economy of a counry largely depends on capial marke. In he capial marke he invesors inves he money o ge he profi. The invesors buy he securiy bond of differen company on he prioriy basis. They choose he securiy bond of differen company on he basis of he differen facors. Some of he significan facors are Company s informaion analysis & predicion, dividend declaraion, ec. A large amoun of invesors has no knowledge abou he marke analysis and proper predicion of he fuure prices of differen ypes of shares available in he marke. So, mos of he ime hey spend he money o Auhor α : Professor, Deparmen of Saisics, Universiy of Chiagong. Auhor σ : Lecurer, Deparmen of Saisics, Universiy of Chiagong. Auhor ρ : Assisan Professor, Deparmen of Accouning and Informaion Sysem, Universiy of Chiagong, Bangladesh. E-mail : mmrseu@yahoo.com buy securiy bond of differen companies on he basis of wrong and humb idea, wihou any idea abou daa analysis and predicion. For his reason here are exreme ups and downs in he daily share price indices, someimes rise very quickly and fall sharply. In his siuaion, he marke condiion becomes unpredicable. Hence, a large amoun of invesors loss heir capial in his unsable capial marke. As a resul he general invesors do no find ineres o inves he money in he capial marke. Then here arises a crisis in he capial marke which creaes problem and hampers he naional economic growh. Therefore, if i is possible o provide a beer model for he share marke which can enable he invesors o predic he prices in advance, i would help he invesors as well as keep sabiliy of he naional economy. This sudy is an effor owards ha direcion. II. Lieraure Review Conreras e al. (003) used ARIMA models o predic nex day elecriciy prices; hey have found wo ARIMA models o predic hourly prices in he elecriciy markes of Spain & California. The Spanish model needs 5 hours o predic fuure prices as opposed o he hours needed by he Californian model. Kumar e al. (004) used ARIMA model o forecas daily maximum surface ozone concenraions in Brunei Darussalam. They have found ha ARIMA (, 0, ) was suiable for he surface O 3 daa colleced a he airpor in Brunei Darussalam. Tsisika e al. (007) used ARIMA model o forecas pelagic fish producion. The final model seleced were of he form ARIMA (, 0, ) & ARIMA (0,, ). Azad e al. (0) used ARIMA model in forecasing Exchange Raes of Bangladesh. By using Box Jenkins mehodology hey ried o find ou bes model for forecasing. They have found ha ERNN (exchange rae neural nework) model shows beer performance han ARIMA. Merh (0) used ANN & ARIMA models in nex day sock marke forecasing. They used ANN (4-4-) and ARIMA (,, and ) for forecasing he fuure index value of sensex (BSE 30). Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 5
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 6 The forecasing accuracy obained for ARIMA (,,) is beer han ANN(4-4-). Liv e al. (0) used ARIMA model in forecasing incidence of hemorrhagic fever wih renal syndrome in China. The goodness of fi es of he opimum ARIMA (0, 3, and ) model showed nonsignifican auocorrelaion in he residuals of he model. Daa (0) used ARIMA model in forecasing inflaion in he Bangladesh Economy. He showed ha ARIMA (, 0, ) model fis he inflaion daa of Bangladesh saisfacorily. Al-Zeaud (0) used ARIMA model in modeling &forecasing volailiy. The resul shows ha bes ARIMA models a 95% confidence inerval for banks secor is ARIMA (, 0, and ) model. Uko e al. (0) examined he relaive predicive power of ARIMA, VAR & ECM models in forecasing inflaion in Nigeria. The resul shows ha ARIMA is a good predicor of inflaion in Nigeria & serves as a benchmark model in inflaion forecasing. From he above menioned sudies i is clear ha ARIMA can be used o forecas. In very few of hem he auhors ried o find ou bes ARIMA model, bu in mos of he aricles he auhors used ARIMA o forecas. The presen sudy is designed o selec he bes ARIMA model o forecas average daily price index of lised companies in Dhaka Sock Exchange. III. Objecives of he Sudy Share price index is a ime series daa. One of he imporan objecives of he ime series analysis is o sudy he pas behavior of he available daa and hen forecas wih fiing a suiable model wih he help of economeric or saisical echniques. Thus, he specific objecives of his sudy are as follows:. To check wheher he seleced ime series daa is saionary or no. If no, he daa are o be ransformed ino saionary using suiable ransformaion.. To selec he bes ARIMA model using some selecion crieria. Then ARIMA echniques are applied o fi and forecas he average daily share price indices of DSE daa for he Square Pharmaceuicals Limied (SPL) Company. 3. Finally, o draw a conclusion for forecasing he average daily share price indices of he seleced company efficienly. IV. Daa and Mehodology The ADSPI daa recorded agains SPL have been colleced from Dhaka Sock Exchange (DSE) for he year 0. Thus we obained a oal of 36 observaions agains all working days from Square Pharmaceuicals limied. The sepwise mehodology used in his sudy is oulined below: Firsly, he daa is presened graphically o check wheher he daa series is saionary or no. For his purpose, he saisics like Ljung-Box-Pierce Q- saisic (978) based on auo correlaion; Dickey-Fuller es (DF) (979), Augmened Dickey-Fuller (ADF) es (98) based on uni roo process have been applied. To selec he bes ARIMA (p, d, q) ype of models fied for he company, heir goodness of fi have been compared using following crieria; a) The Akaike Informaion Crieria (AIC) b) The Correced Akaike Informaion Crieria (AICc) c) Schwarz Informaion Crieria (SIC) d) Mean Absolue Percen Error (MAPE) e) Roo Mean Square Error (RMSE) and f) Absolue Mean Error (AME) A brief descripion abou he crieria for he selecion of bes ARIMA model is given below: a) Akaike Informaion Crierion (AIC) AIC is an imporan and leading saisics by which we can deermine he order of an auoregressive model Mr. Akaike developed his saisics. According o his name his saisics is known as Akaike Informaion Crierion (AIC). The AIC akes ino accoun boh how well he model fis he observed series and he number of parameers o be used in he fi. AIC due o Akaike (969) is defined as AIC = N Inδ + + ( p + ) Where he parameer bears he usual meaning. Akaike also menion ha he minimum AIC crierion produced a seleced model, which is hopefully closer o he bes possible choice. b) Correced Akaike Informaion Crierion Someimes he AIC does no provide he efficien order of model selecion, which asympoic efficiency is more desirable crierion. Shibaa in 976 shown ha AIC crierion is no consisen oo. Thus Hurvich and Tsai (989) provide a crierion of AIC for bias. The correlaion is of paricular use when he sample size is small or when he number of fied parameer is a moderae o a large fracion of sample size. The crierion is defined as i.e, P + AIC N N c = lnδ + P + N P + AIC = + N c AIC = P + N ( Ρ + )( Ρ + ) ( Ν Ρ + )
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. Thus AIC c is he sum of AIC and an addiional non-sochasic penaly erm (p+) (p+) / (N-p+), where he parameer bears he usual meaning. c) Schwaez Informaion Crieria In 978 Schwaez discussed a crierion denoed by SIC which help in deciding he order of auo regression. Iniially he developed his crierion for aking decisions abou he regress subse. Laer Engel e. al, in 99 use his crierion as a ool for deermining he order of auo regression and hey defined his crierion as below p SIC = δ N N Where, he parameers bear he usual meaning. Schwarz also shows ha his crierion is beer han AIC. The model wih minimum SIC assumes o describe he daa series adequaely. The minimum value of his crierion is desirable for he adequacy of a model. Crieria used for esing he validiy of model The crieria menioned above are compared for correc deerminaion of he order of auo regression and he degree of differencing and his crierion is compued only for esimaion period. Bu for he selecion of an ARIMA model, which adequaely describes he daa series, he values of he following crieria are compared for hree periods viz, esimaion period, validaion period and oal period. The crieria used in his sudy are as follows: a) Absolue Mean Error (AME) b) Roo Mean Square Error (RMSE) c) Mean Absolue Percen Error (MAPE) d) Absolue Mean Error (AME) The mean of he absolue deviaion of prediced and observed values is called absolue mean error and is defined as T Ζ obs Ζ pred AME = I= Τ This crierion is used for he comparison of he models in hree periods. e) Roo Mean Square Error (RMSE) The square roo of he sum of square of he deviaion of he prediced values from he observed value dividing by heir number of observaion is known as he roo mean square error. The roo mean square error is defined as RMSE = T Τ I= p N ( ) Ζ Ζ obs pred Where, T is he number of periods. This crierion is used for he comparison of he models in hree periods. f) Mean Absolue Percen Error (MAPE) The mean of he sum of absolue deviaion of prediced and observed value dividing by he observed value is called mean absolue error. For comparison we have muliplied by 00, which is called mean absolue percen error and which is defined as T Ζ MAPE = Τ = obs Ζ Ζ obs pred 00 Where, he parameers bear he usual meaning. From he above discussion i is clear ha he smaller error beer he forecasing performance of he observed variables and if he model variable perform well, so will he model as a whole do oo. For he daa series a separae ARIMA model has been used. For ha purpose, a general concep of ARIMA (p, d, and q) model is discussed below: ARIMA models are, in heory, he mos general class of models for forecasing a ime series ha can be saioneries by ransformaions such as differencing and logging. If we have o difference a ime series d imes o make i saionary and hen apply he ARMA (p, q) model o i, we can say ha he original ime series is ARIMA (p, d, q), ha is i is an auoregressive inegraed moving average ime series, where p denoes he number of auoregressive erms, d denoes he ime series have o be differenced before i becomes saionary and q denoes he number of moving average erms. Thus an ARIMA (,,) ime series has o be differenced once (d=) before i becomes saionary and he saionary ime series can be modeled as an ARMA (,) process ha is i has wo AR and wo MA erms. Of course if d=0 hen ARIMA (p, d=0,q) = ARMA (p, q). A mos general ARIMA model consiues hree ypes of process named as auoregressive (AR) process, differencing o srip of he inegraion (I) and moving average (MA) process. The goodness of fi wih respec o every crierion are examined and he model which saisfies mos of he crierion, is considered as he bes one. Auo Regressive (AR) Process In an auoregressive process each value in a series is linear funcion of he preceding value. Thus in he firs order auoregressive process only he single preceding value is used as a funcion of curren value. In he second order auoregressive process wo preceding values are used as a funcion of he curren value and so on. The firs order auoregressive is denoed by AR (), he second order auoregressive is denoed by AR () and up o he p h order auoregressive is denoed by AR (p). Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 7
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 8 Le us suppose ha he variable is a linear funcion of he preceding variable. Therefore he model can be wrien as Where u IN( 0, σ ) ~ u The model () is known as AR () model. Bu if we consider he model = θ + φ Where u IN( 0, σ ) ~ u + ϕ The model () is known as AR () model. In general we can wrie = θ + φ + u = θ + φ + ϕ +... + φ + u + u () () p p (3) Where φ is known as he firs order auoregressive coefficien, φ is known as he second order auoregressive coefficien and so on The model (3) is known as AR (p) model. Differencing Differencing is a comparaively simple operaion ha involves calculaing consecuive changes in he values of he daa series. Differencing is used when he mean of a series is changing over ime o ime. A consciousness ha is homogeneously non-saionary can be ransform ino saionary by differencing. Differencing is no dealing wih non-saionary variance. To difference a series once (d=) we have o calculae he period o period change, o difference a series wice (d=) we have o calculae he period o period changes in he firs difference series and so on for furher differences. Moving Average In Saisics, a moving average or rolling average is one of a family of similar echniques used o analyze ime series daa. I is applied in finance and especially in echnical analysis. I can also be used as a generic smoohing operaion, in which case he raw daa need no be a ime series. A moving average series can be calculaed for any ime series. In finance i is mos ofen applied o sock prices, reurns or rading volumes. Moving averages are used o smooh ou shor-erm flucuaions, hus highlighing longer-erm rends or cycles. The hreshold beween shor-erm and long-erm depends on he applicaion, and he parameers of he moving average will be se accordingly. Mahemaically, each of hese moving averages is an example of a convoluion. These averages are also similar o he low-pass filers used in signal processing. In moving average process, each value is deermined by he average of he curren disurbance and one or more previous disurbances. Suppose he model Y as follows: = θ + u + β u (4) Where θ is consan and u is he whie noise error erm i.e., u~n ( 0, σ ). Here Y a ime is equal o a consan plus a moving average of he curren and pas error erms. In his case, we say ha Y follows a firs order moving average or MA () process. Bu if Y follows he expression = θ + u + β u + β u (5) Then we say ha Y follows a second order moving average or MA () process. In general, = θ + u + β u + β u +... + β q u q Then we say ha Y follows a q h order moving average or MA (q) process. In shor, a moving average process is simply a linear combinaion of whie noise error erms. Characerisics of a good ARIMA model Our main moivaion is o build up a good ARIMA model in his sudy. The Characerisics of a good ARIMA model are as follows:. A good model is saionary, ha is, i has an AR coefficien ha saisfies some mahemaical inequaliies.. A good model is inverible, ha is, i has MA coefficien, which saisfies some mahemaical inequaliies. 3. A good model is parsimonious i.e., uses he small number of coefficiens needed o explain he available daa. 4. A good model has saisically independen residuals. 5. A good model has high-equaliy esimaed coefficien a he esimaion sage. 6. A good model fis he available daa sufficienly well a he esimaion sage. 7. Roo-Mean Squared Error (RMSE) is accepable. 8. Mean-Absolue percen error (MAPE) is accepable. 9. A good model has sufficienly small forecas errors i.e., i forecass he fuure saisfacory. Selecion of ARIMA models for ADSPI of SPL daa series In order o idenify he enaive ARIMA model for he ADSPI of SPL, he seps described by Box and Jenkins have been followed. For his purpose he daa (6)
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. are pariioned ino wo sages. The firs sage is known as he esimaion sage and second is known as he validaion sage. The sample of observaions o 6 has been used in esimaion sage and he res has been used for esing he validiy of model. Ten ARIMA models wih enaively seleced various values of p, d and q are esimaed by using compuer sofware SHAZAM versions 8.0 for windows. The en enaively seleced models are ARIMA (,,), ARIMA (,,), ARIMA (,,), ARIMA (,,), ARIMA (,,3), ARIMA (,,3), ARIMA (3,,), ARIMA (3,,), ARIMA (3,,3) and ARIMA (,,4). Among he models only five comparaively well performed models are displayed in he able -c. Table- c discloses ha ARIMA wih p=, d = and q= process has maximum number of lowes values of all he seleced crieria AIC, AICc, SIC, and AME, RMSE, MAPE in he hree periods i.e., esimaion period, validaion period and oal period Hence, ARIMA (,,) model has been seleced for forecasing he ADSPI of SPL daa series. The fied ARIMA (,, and ) model seleced for SPL daa series is given by (-0.6636*B-0.6003*B ) SPL - = 0.00405+ (-0.449*B-0.489*B ) a (0.95) (0.737) (0.3036) (0.97) (Values in he parenhesis are corresponding -values and * means saisical significance p<0.0) v. Resuls and Discussion The major findings of he sudy are as follows:. The upward rends of plos of he daa series are visualized alhough he overall rends are no smooh.. The ACF and PACF plos of original daa series show ha he Average Daily Share Price Indices (ADSPI) of Square Pharmaceuicals Limied (SPL) are non-saionary, ha is, mos of he ACF and PACF plos are beyond he confidence limis shown in Figure- a. 3. From ACF and PACF plos of logarihmic ransformaion daa series has been found ha he ADSPI of SPL daa series is sill non-saionary, ha is, all he ACF & PACF plos are ou of he confidence limis.shown in figure-b. Bu afer aking firs difference of logarihmic values of SPL daa series, he same plos shows ha he daa is saionary shown in Figure- c. 4. The Dickey-Fuller uni roo es saisic and he Ljung-Box-pierce Q-Saisic also indicae ha he Average Daily Share Price Indices (ADSPI) of SPL daa series is non-saionary. The compued absolue values of he τ-saisic for SPL is found as τ =.733, none of which exceeds he DF or Mackinnon DF absolue criical τ values (o be noed ha %, 5% and 0% level of significance he absolue DF values are 4.047, 3.46 & 3.3 respecively) shown in Table- a. 5. Afer aking firs difference of logarihmic values of SPL daa series, he same es saisic shows ha he daa is saionary, because hence he compued absolue value of he τ-saisic is τ = 4.65 which exceeds he DF or Mackinnon DF absolue criical τ values shown in Table- b. 6. For SPL daa series en ypes of enaively ARIMA models wih varied values of p, d & q are seleced of which five-performed model for he daa series are esimaed and he validiy of he model is esed by using AME, RMSE & MAPE for hree differen period shown in Tabil -c. 7. I is found ha ARIMA (,, ) is he bes model for forecasing he SPL daa series. 8. Finally, he Average Daily Share Price Indices (ADSPI) for Square Pharmaceuicals Limied (SPL) daa series have been forecased by using he seleced model and repored in able- d. Table (a) : The values of he various saionary ess of he company for average daily share price indices of DSE daa series Tes Saisic Ljung-Box-Pierce Q- saisic SPL Time lag-0 947.0 Time lag-0 999.7 Dickey-Fuller es -.733 A %, 5% and 0% level of significance he DF values are 4.047, -3.46 and 3.3 respecively. Table (b) : Values of Dickey-Fuller es saisic for differen values of differencing of Logarihmic Transformaion SPL daa series Difference SPL 0 -.6605-4.65-0.07 Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 9
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 0 VI. Conclusion This sudy made he bes endeavor o develop he bes ARIMA model o efficienly forecasing he Average Daily Share Price Indices (ADSPI) of he Square Pharmaceuicals Limied (SPL), because if i is possible o provide a beer model for he share marke which can enable he invesors o predic he prices in advance, i would help he invesors as well as sabiliy of he naional economy. The empirical analysis indicaed ha he ARIMA (,,) model is bes for forecasing he Average Daily Share Price Indices (ADSPI) of he Square Pharmaceuicals Limied (SPL) daa series so far he diagnosic crieria are concerned. Finally, he Average Daily Share Price Indies (ADSPI) for Square Pharmaceuicals Limied (SPL) daa series is forecased up o February, 0 by using he seleced model. References Références Referencias. Al-Zeaud, H.A. (0) Modeling &Forecasing Volailiy using ARIMA model, European Journal of Economics, Finance & Adminisraive Science, Issue 35, pp. 09-5.. Azad, A.K. & Mahsin, M. (0) Forecasing Exchange Raes of Bangladesh using ANN & ARIMA models: A comparaive sudy, Inernaional Journal of Advanced Engineering Science & Technologies, Vol. No. 0, Issue No., pp. 03-036. 3. Conreras, J., Espinola, R., Nogales, F.J. and Conejo, A.J. (003) ARIMA models o predic Nex Day Elecriciy Prices, IFEE Transacions on power sysem, Vol. 8, No. 3, pp 04-00. 4. Daa, K. (0) ARIMA Forecasing of Inflaion in he Bangladesh Economy, The IUP Journal of Bank Managemen, Vol. X, No. 4, pp. 7-5. 5. Kumar, K.; Yadav, A.K.; Singh, M.P.; Hassan, H. and Jain, V.K. (004) Forecasing Daily Maximum Surface Ozone." 6. Concenraions in Brunei Darussalam- An ARIMA Modeling Approach, Journal of Air & Wase Managemen and Associaion, Volume 54, pp 809-84. 7. Liv, Q.; Liu, X.; Jiang, B. & Yang, W. (0) Forecasing incidence of hemorrhagic fever wih renal syndrome in China using ARIMA model, Biomed Cenral, pp. -7. 8. Merh, N.; Saxena, V.P. & Pardasani, K.R. (0) Nex Day Sock marke Forecasing: An Applicaion of ANN & ARIMA, The IUP Journal of Applied Science, Vol. 7 No., pp. 70-84. 9. Tsisika, E.V.; Maravelias, C.D & Haralaous, J. (007) Modeling & forecasing pelagic fish producion using univariae and mulivariae ARIMA models, Fisheries Science, Volume 73 pp 979-988. 0. Uko, A.K; Nkoro, E. (0) Inflaion Forecass wih ARIMA, Vecor Auoregressive & Error Correcion Models in Nigeria, European Journal of Economics, Finance & Adminisraive Science, Issue 50, pp. 7-87.
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. Appendix Figure (a) : The ACF and PACF plos of original daa for average daily share price indices of SPL daa series AUTOCORRELATION FUNCTION OF THE SERIES 0 0 0 (-B) (-B) AVG 0.98. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 0.96. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 3 0.95. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 4 0.93. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 5 0.9. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 6 0.89. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 7 0.87. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 8 0.84. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 9 0.8. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 0 0.78. + RRRRRRRRRRRRRRRRRRRRRRRRRRRR. 0.75. + RRRRRRRRRRRRRRRRRRRRRRRRRRR. 0.73. + RRRRRRRRRRRRRRRRRRRRRRRRRR. 3 0.70. + RRRRRRRRRRRRRRRRRRRRRRRRR. 4 0.67. + RRRRRRRRRRRRRRRRRRRRRRRR. 5 0.65. + RRRRRRRRRRRRRRRRRRRRRRR. 6 0.6. + RRRRRRRRRRRRRRRRRRRRRR. 7 0.60. + RRRRRRRRRRRRRRRRRRRRR+. 8 0.58. + RRRRRRRRRRRRRRRRRRRRR+. 9 0.56. + RRRRRRRRRRRRRRRRRRRR +. 0 0.54. + RRRRRRRRRRRRRRRRRRR +. 0.5. + RRRRRRRRRRRRRRRRRRR +. 0.50. + RRRRRRRRRRRRRRRRRR +. 3 0.49. + RRRRRRRRRRRRRRRRRR +. 4 0.48. + RRRRRRRRRRRRRRRRR +. PARTIAL AUTOCORRELATION FUNCTION OF THE SERIES 0 0 0 (-B)(-B) AVG 0.98. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 0.3. + RRRRRR. 3 0.0. + RR +. 4 -.3. RRRRR +. 5 -.0. + RR +. 6 -.06. + RRR +. 7 -.. RRRRR +. 8 -.3. RRRRR +. 9 -.0. + R +. 0 -.0. RRRRR +. 0.08. + RRRR+. 0.09. + RRRR+. Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. Figure (b) : The ACF and PACF plos of Logarihmic Transformaion daa for average daily share price indices of SPL daa series AUTOCORRELATION FUNCTION OF THE SERIES 0 0 0 (-B) (-B) X Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 0.98. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 0.97. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 3 0.96. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 4 0.94. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 5 0.9. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 6 0.9. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 7 0.89. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 8 0.86. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 9 0.84. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 0 0.8. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 0.80. + RRRRRRRRRRRRRRRRRRRRRRRRRRRR. 0.78. + RRRRRRRRRRRRRRRRRRRRRRRRRRR. 3 0.76. + RRRRRRRRRRRRRRRRRRRRRRRRRRR. 4 0.74. + RRRRRRRRRRRRRRRRRRRRRRRRRR. 5 0.7. + RRRRRRRRRRRRRRRRRRRRRRRRR. 6 0.70. + RRRRRRRRRRRRRRRRRRRRRRRRR. 7 0.68. + RRRRRRRRRRRRRRRRRRRRRRRR. 8 0.66. + RRRRRRRRRRRRRRRRRRRRRRR. 9 0.64. + RRRRRRRRRRRRRRRRRRRRRRR+. 0 0.6. + RRRRRRRRRRRRRRRRRRRRRR +. 0.6. + RRRRRRRRRRRRRRRRRRRRRR +. 0.59. + RRRRRRRRRRRRRRRRRRRRR +. 3 0.57. + RRRRRRRRRRRRRRRRRRRRR +. 4 0.56. + RRRRRRRRRRRRRRRRRRRR +. PARTIAL AUTOCORRELATION FUNCTION OF THE SERIES 0 0 0 (-B) (-B) X 0.98. + RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR. 0.5. + RRRRRR. 3 0.03. + RR +. 4 -.. RRRRR +. 5 -.0. + R +. 6 -.05. + RRR +. 7 -.09. +RRRR +. 8 -.09. +RRRR +. 9 0.0. + R +. 0 -.. RRRRR +. 0.04. + RR +. 0.08. + RRRR+.
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. Figure (c) : The ACF and PACF plos of Logarihmic Transformaion daa for average daily share price indices of SPL daa series wih difference one AUTOCORRELATION FUNCTION OF THE SERIES 0 0 (-B) (-B) X -.3. RRRRRRRRR +. 0.00. + R +. 3 0.3. + RRRRR+. 4 -.03. + RR +. 5 0.06. + RRR +. 6 0.09. + RRRR +. 7 0.09. + RRRR +. 8 -.05. + RRR +. 9 0.4. + RRRRRR +. 0 -.08. + RRRR +. -.03. + RR +. 0.04. + RR +. 3 0.06. + RRR +. 4 -.03. + RR +. 5 -.. +RRRRR +. 6 0.. + RRRRR+. 7 -.0. + RRRR +. 8 -.03. + RR +. 9 -.0. + RR +. 0 -.04. + RR +. 0.0. + RRRR +. -.9. RRRRRRR +. 3 -.05. + RRR +. 4 0.09. + RRRR +. PARTIAL AUTOCORRELATION FUNCTION OF THE SERIES Table (c) : The values of diagnosic crieria for ARIMA model for logarihmic ransformaion difference series of average daily share price indices of DSE daa of Square Pharmaceuicals limied Transformaion Difference= 0 0 (-B) (-B) X -.3. RRRRRRRRR +. -.05. + RRR +. 3 0.. + RRRRR +. 4 0.03. + RR +. 5 0.07. + RRRR+. 6 0.. + RRRRR. 7 0.5. + RRRRRR+. 8 -.0. + R +. 9 0.. + RRRRR. 0 -.06. + RRR +. -.08. +RRRR +. -.06. + RRR +. Validaion of diagnosic crieria for he model Crieria Period ARIMA (,,) ARIMA (,,) ARIMA (,,3) ARIMA (,,) ARIMA (,,) AIC Esimaion -6.478-6.50* -6.479-6.4797-6.4679 AICc Esimaion -6.475-6.4506* -6.43-6.3780-6.366 SIC Esimaion -6.4339-6.443* -6.3993-6.408-6.3943 Esimaion 0.00098364 0.000903 0.0009609 0.0009369 0.0008849* AME Validaion 0.000963* 0.009 0.00044 0.0047 0.00409 Toal 0.0006053 0.0006709 0.0005933 0.00057657 0.0005446* Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 3
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 4 Esimaion 0.0039346 0.004364 0.003933* 0.0037477 0.0035398 RMSE Validaion 0.0030400* 0.0035393 0.0038436 0.0046554 0.0076556 Toal 0.0030865 0.00343 0.00305 0.009399 0.007768* Esimaion 0.00008956 0.0000309 0.0000887 0.0000758 0.000060* MAPE Validaion 0.000098* 0.00003470 0.0000393 0.00004565 0.000075 Toal 0.0000789 0.0000995 0.00007407 0.0000697 0.000060* No. Of lowes values 03 03 0 0 05 Noe: A * (sarle) indicae he lowes value in each row. Table (d) : The observed and forecased values wih is lowes and highes values obained by ARIMA (,,) model for ADSPI of SPL daa series Fuure Dae Lower Forecas Upper Acual Error 0 8.0453 8.908 8.9303 8.73-0.76589E-0 8.0366 8.080 8.0894 8.0848-0.39335E-0 8.060 8.78 8.396 8.066-0.565736E-0 3 8.007 8.475 8.374 8.0848-0.437E-0 4 8.0036 8.67 8.498 8.093-0.35393E-0 5 7.99597 8.868 8.639 8.07683-0.5857E-0 6 7.98898 8.3064 8.73 8.6990 0.39577E-0 7 7.985 8.36 8.87 8.07869-0.5399E-0 8 7.97650 8.3458 8.965 8.08487-0.497067E-0 9 7.97088 8.3654 8.30 8.08364-0.59064E-0 30 7.96558 8.385 8.344 8.09040-0.48075E-0 3 7.96058 8.4048 8.3037 8.0765-0.639606E-0 3 7.95584 8.444 8.3904 8.0774-0.653055E-0 33 7.9533 8.444 8.33749 8.5306 0.865358E-0 34 7.94703 8.4637 8.3457 8.0845-0.605E-0 35 7.949 8.4834 8.35376 8.9395 0.456E-0 36 7.93899 8.503 8.366 8.356-0.6749E-0 37 7.935 8.57 8.36933 38 7.9359 8.544 8.37688 39 7.98 8.56 8.38430 40 7.9475 8.587 8.3960 4 7.950 8.604 8.39877 4 7.9837 8.60 8.40583 43 7.9535 8.6407 8.479 44 7.94 8.6604 8.4965 45 7.90959 8.6800 8.464 46 7.90684 8.6997 8.4330 47 7.9047 8.794 8.43970 48 7.9059 8.7390 8.446 49 7.89908 8.7587 8.4566 50 7.89664 8.7783 8.45903 5 7.8947 8.7980 8.46533 5 7.8996 8.877 8.4757 53 7.8897 8.8373 8.47775 54 7.88753 8.8570 8.48387 55 7.88540 8.8766 8.48993 56 7.88333 8.8963 8.49593 57 7.883 8.960 8.5089 58 7.87934 8.9356 8.50779 59 7.8774 8.9553 8.5364 60 7.87554 8.9750 8.5945 6 7.8737 8.9946 8.55 6 7.8793 8.043 8.53093 63 7.8708 8.0339 8.5366 64 7.86848 8.0536 8.544 65 7.8668 8.0733 8.54784 66 7.8659 8.099 8.55339
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. 67 7.86360 8.6 8.5589 68 7.8605 8.33 8.56440 69 7.86054 8.59 8.56985 Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 5
Selecion of Bes ARIMA Model for Forecasing Average Daily Share Price Index of Pharmaceuical Companies in Bangladesh: A Case Sudy on Square Pharmaceuical Ld. Global Journal of Managemen and Business Research ( C ) Volume XIII Issue III Version I Y ear 03 6 This page is inenionally lef blank