Identifying the Most Effective Model for Understanding the Growth Rate of Government e-transactions: Brown's Model of Exponential Smoothing

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1 Asian Journal of Computr Scinc and Tchnology ISSN: Vol.7 No.2, 2018, pp Th Rsarch Publication, Idntifying th Most Effctiv Modl for Undrstanding th Growth Rat of Govrnmnt -Transactions: Brown's Modl of Exponntial Smoothing Indian Institut of Forign Trad, Kolkata Campus, Wst Bngal, India Abstract -Th purpos of this study is to invstigat th currnt status of -transactions tim sris growth rat in th stat of Jharkhand from January 2013 to 20th May, 2018 to undrstand th citizn adoption pattrn of various - govrnmnt srvics. Govrnmnt spnds lots of mony in dvloping and implmnting -srvics, but dspit spnding hug mony th adoption rat is low. This study will analyz th adoption rat by using tim sris modls and find th adoption pattrn to improv th futur adoption rat of - srvics. Bsids this, th papr will hlp us to undrstand whthr currnt -transaction mthods ar usr frindly or not. Thrfor, idntify th bst modl to valuat th growth rat of -transactions in th contxt of govrnmnt lctronic transactions. In this rgard, various xisting tim sris modls hav bn valuatd to obtain th rsult of this study. Th papr draws-up th mrgnt modl drivd from th analysis. Finally, a framwork is suggstd to slct Brown's Exponntial Smoothing Modl as an idal modl for valuating th growth rat of govrnmnt -transaction for th stat of Jharkhand. This will hlp govrnmnt to rcommnd and stratgiz bttr -srvics plan for th stat. This rsarch can b usd in policy making, stratgizing and finding th ky to usr accptanc of innovation in tchnology in govrnmnt lctronic transaction with th hlp of Brown's Exponntial Smoothing as it can rduc th impacts of sasonal factors. Kywords: Govrnmnt -srvics, -transaction, tim sris, xponntial smoothing, Brown's modl, Brown's doubl xponntial smoothing, growth rat, diffusion, -Govrnanc I. INTRODUCTION Jharkhand Govrnmnt has implmntd various - Govrnmnt projcts to mak th govrnmnt srvics asir, spdir and mor approachabl for popl. It can happn a littl lat or it can b said that th stat has undrstood th advantags of implmnting th nw srvic procdurs littl latr than th othr stats, howvr, Jharkhand has attaind a good rviw on th projcts of thir -Govrnanc dpartmnt. Th Govrnmnt of India has launchd th nw systm through which th govrnmnt can srv th citizns individually (Barua, 2012).Th main motto of this nw implmntation was to shift th focus to th citizns' rquirmnts as wll as to dvlop th govrnmnt portals from th point of viw of th citizns in th country. Lik othr stats Jharkhand has also implmntd ths -Govrnanc srvics in thir stat. JAP-IT is th Nodal Agncy for implmnting th - Govrnanc activitis in Jharkhand and it dlivrs mor than 100 citizn-cntric srvics in th stat. As pr th rsarch of Barua, 2012, in Jharkhand th -Govrnanc systm is dpnding on th thr pillars of SWAN, SDC, and CSC. Ths thr projcts had takn th rsponsibility to mak th stat govrnmnt srvics asir, smoothr and tim saving. In North Amrica, almost 90% of onlin rtail transactions wr mad with this paymnt typ (Ndou, 2004). Howvr, th us of crdit card or any othr smartcard nds scurity masurs to ovrcom th thrat of hacking. Th countris lik China, India has som problms to ovrcom in rgard to scurity (Ndou, 2004). Th rsarch will allow analyzing th ffctivnss of xisting tim sris modls for dfining th growth rat of govrnmnt -transactions and discuss th limitations of th xisting modls and thoris to undrstand and analyz th issus rlatd to th accptanc of govrnmnt -transaction in th Stat of Jharkhand. Thrfor, th objctivs of th rsarch ar: 1. To undrstand th adaption pattrn of -Govrnanc srvics in th Stat of Jharkhand in India 2. To propos a modl for analyzing th growth pattrn of govrnmnt -transactions in th stat of Jharkhand 3. To valuat th futur potntiality of ths govrnmnt - Transactions in th Stat of Jharkhand in India II. LITERATURE REVIEW Usually, th litratur rviw sction is rlatd to analysis various prvious thoris and modls for giving vidnc of th rsarch topic. Although thr ar a numbr of rsarchs on -commrc or banking, howvr, thr ar no such rsarchs on govrnmnts, -Transactions. Thrfor, Tim Sris, Brown's Exponntial Smoothing Modls and many xisting applications rgarding this has bn valuatd and thn a modl is suggstd in ordr to suggst th bst modl suitd for undrstanding th growth rat of Jharkhand's -transactions. As th numbr of rsarchs on govrnmnt's -transaction is vry low, thrfor, th study has valuatd th data gaind from a fw pics of rsarch on dvloping countris -Govrnanc policis. In th dvloping countris lik China, India, -Govrnanc has not yt rachd th masss (Ndou, 2004).According to "Computr- Basd Forcasting In Managing Risks Associatd With 81 AJCST Vol.7 No.2 July-Sptmbr 2018

2 Elctronic Banking In Nigria" papr, th rsults showd an asir and bttr way of analyzing and managing lctronic banking risks in Nigria rducing th risk factors of lctronic banking. According to th study of " Evaluating Th Dvlopmntal Impact of -Govrnanc Initiativs: An Exploratory Framwork", th impact of two nw implmntations of FRIENDS and AKSHAYA - govrnanc projcts in th southrn stat of Krala has bn valuatd. Lik many othr dvloping countris, India has takn grat stps in implmnting -govrnanc applications in rcnt yars. In th papr namd, "Citizn-cntric -govrnmnt prformanc: satisfaction with -information", th citizncntric govrnmnt systms of China has bn discussd to valuat th raction of popl of that country. It shows that th popl of th country wr vry happy and hlpful to us th -information and -Govrnanc srvics (Chn and Zhang, 2012). Th papr " Rsponding to information nds of th citizns through -govrnmnt portals and onlin srvics in India " has focusd on National Portal of India, which provids singl window accss to 601 -govrnmnt portals and wbsits in India and valuatd digitization of documnts, acts, ruls and schms of cntral and stat govrnmnt dpartmnts and thir availability and accssibility through govrnmnt portals. In Nigria, th risks and challngs facd in th lctronic banking systm hav bn discussd in " Computr-Basd Forcasting In Managing Risks Associatd With Elctronic Banking In Nigria " by Onu, (2017). Hirwad, (2010) has rsarchd about th xisting govrnmnt portals in India and valuatd th advantags as wll as disadvantags of ths. Th study has rvald that th dlivry of onlin srvics through govrnmnt portals is an volutionary phnomnon, and rquirs a chang in th mindst of on and all citizns, xcutivs and th govrnmnt in a dvloping country lik India. With th support of th Intrnt, govrnmnt procsss can b mad fficint, ffctiv, and citiznfrindly. A. Thoris 1. Tim Sris A tim sris is a grouping of obsrvations which ar rqustd in tim. A modl of th arrangmnt that clarifid th past qualitis may likwis anticipat whthr and how much th nxt coupl of qualitis will incrmnt or dclin and this is th formost purpos of this Tim Sris as it xamins and analyss th futur figur stimations of th arrangmnt. Tim sris analysis can b prformd ovr both columns basd and multidimnsional data. 2. Exponntial Smoothing In 1950's th dfinition of xponntial smoothing forcasting tchniqus has bcom known from th first work of Brown (1959, 1962) and Holt (1960) who wr working on constructing dtrministic modls for stock control framworks. Evry sampl of data collctd ovr tim xprincs from on or th othr kind of random variation. Thr ar diffrnt masurs which ar usd for wiping out th impact of random variation in data. Random variation maks it difficult to prdict th modl fitting th data and also gnrats inconsistncy during forcasting and prdictiv modling. Smoothing is primarily utilizd to hlp forcast trnds. Two most popular smoothing tchniqus usd ar Moving Avrags and Exponntial Smoothing. 3. Brown s Modl for Exponntial Smoothing Th brown's modl is appropriat for sris in which thr ar a linar trnd and no sasonality (Brown and Myr, 1961). Brown's modl is, thrfor, a spcial cas of Holt's modl. Brown's xponntial smoothing is most similar to an ARIMA (Autorgrssiv Intgratd Moving Avrags) modl with zro ordrs of auto rgrssion, two ordrs of diffrncing, and two ordrs of moving avrag, with th cofficint for th scond ordr of moving avrag qual to th squar of on-half of th cofficint for th first ordr, which uss two diffrnt smoothd sris that ar cntrd at diffrnt points in tim. Th Brown's modl for xponntial smoothing is also known as Doubl Exponntial Smoothing mthod. Th forcasting formula is basd on an xtrapolation of a lin through th two cntrs. Brown's forcasting mthod is similar to Simpl Exponntial Smoothing, xcpt that th smoothing constant in Doubl Exponntial Smoothing is drivd by "r-smoothing" th singl smoothd constant from Singl Exponntial Smoothing modl. Exponntial smoothing must b updatd ach priod - lvl and trnd. B. Charactristics of Brown s modl Brown modl should b usd whn th tim sris data has a trnd but no sasonality. Th lattr occurs whn th data xhibits ris and fall that ar not for a fixd priod. Ths fluctuations ar usually du to conomic conditions and ar oftn rlatd to th "businss cycl." Th priod of tim gnrally xtnds byond a singl yar and th fluctuations ar usually of at last two yars. For dtcting sasonality in absolut trms, that is whthr sasonality is prsnt or absnt, vn a dtaild data obsrvation can giv rsults. Th prsnc of sasonality can b confirmd by th prsnc of continuous spiks in various sris plots lik run squnc plot, sasonal subsris plot, multipl box plots and autocorrlation plot. Sinc th brown modl is mor suitd for non-sasonal data, th fitting paramtrs ar rstrictd to lvl and trnd. Howvr, th indics ar dfind for all th thr paramtrs. At any givn tim, th lvl indx givs an stimat of th local man, or "lvl" of th data-gnrating procss (DGP), at this tim. Th trnd indx givs an stimat of th trnd at this tim, and th sasonality indx calculats approximatly th digrssion from th local man du to sasonality. Brown modl mak us of a lvl componnt and a trnd componnt at vry priod. It uss two wights or smoothing paramtrs, to updat th componnts at ach priod. AJCST Vol.7 No.2 July-Sptmbr

3 Idntifying th Most Effctiv Modl for Undrstanding th Growth Rat of Govrnmnt -Transactions: Brown's Modl of Exponntial Smoothing In his original papr in 1961(Brown & Myr, 1961), R.G brown assrtd that givn a tim sris {Xt} with obsrvations at qually spacd intrvals, th first N+1 dgrs of xponntial smoothing can b combind, using th binomial cofficints, to giv an stimat of th valus of th cofficints of an Nth dgr polynomial modl of th obsrvations to dat, valuatd at th tim of th most rcnt obsrvation. Brown also stats that if th sampl intrval is short, thr will b a larg annual cost of doing th computations. Also if th sampling intrval is too larg, thn a chang in th data pattrn will not b rflctd quickly in th computations. Hnc a mdium-sizd sampl is most suitd for Brown's modl. Brown's slction of th sampl intrval also taks into considration a) th cost of th data procssing b) th cost of bing lat in rcognizing a chang c) th probability distribution of changs, by magnitud and tim. Garcia (García t al., 2016) compars thr diffrnt mthods for multi-stp forcasting of chlorin dcay including th Brown's mthod, in an attmpt to diagnos th quality snsors in th Barclona drinking watr ntwork. In this study, th brown modl is found to b prforming rlativly bttr in stimating th PH of th watr, which is an important dtrminant of rmaining usful lif (RUL) of a watr body. Th absnc of sasonality in th data for watr bodis is an important rason why Brown modl prforms significantly bttr than th othr modls. Hansun (Hansun and Subanar, 2016) introducs a nw approach to Brown's Doubl Exponntial Smoothing in tim sris analysis. Th nw approach combins th calculation of wighting factor in Wightd Moving Avrag and implmnts th rsults with Brown's Doubl Exponntial Smoothing mthod. Th proposd mthod is tstd on Jakarta Stock Exchang (JKSE) composit indx, for which th data has a trnd but is dvoid of sasonality. Kumari (Kumari t al., 2014) compars th forcasting ability of diffrnt statistical modls for th productivity of ric in India. Brown's mthod uss only on smoothing constant and that th stimatd trnd valus ar vry snsitiv to random influncs. Saputra (Saputra, 2016) uss Brown's and Holt's Doubl Exponntial Smoothing for prdicting Indonsian Crud Oil Pric (ICP). Asadi (Al-Asadi t al., 2017) attmpts th forcasting of th numbr of brick production using th xponntial smoothing holt-wintr mthod which is similar to th Brown modl xcpt for th fact that th Man Squard Error (MSE) is rlativly smallr compard to th Brown modl. Fomby (Fomby, 2008) stats that xponntial smoothing mthods suffr from not having an objctiv statistical idntification and diagnostic systm for valuating th goodnss of compting xponntial smoothing modls. C. Importanc of Sasonality Prdiction In tim sris data, Sasonality is th prsnc of variations that occur at spcific rgular intrvals lss than a yar, such as wkly, monthly, or quartrly. Sasonality may b causd by various factors, such as wathr, vacation, and holidays and consists of priodic, rptitiv, and gnrally rgular and prdictabl pattrns in th lvls of a tim sris (Nazim and Afthanorhan, 2014). Thrfor, it is a vry important factor that can impact th -transaction applications. In ordr to gt this sasonality ffct proprly Brown's Modl for Exponntial Smoothing is accptd in this cas as th only modl that can idntify th sasonality prdiction. III. METHODOLOGY In ordr to conduct this rsarch, th complt viw of what ar th factors rlatd to -transactions, a litratur rviw of slctd paprs has discussd. Brown's modl, Brown s doubl xponntial smoothing. Th litratur rviw usd a mta-analysis approach so as to undrstand th ways of valuating th rat of -transaction in th systms of onlin paymnt or transactions. Th prvious studis hav hlpd in this analysis procss to idntify th appropriat modl that can giv a smooth and fast way to calculat th - transaction rat. Th articls publishd in th journals wr codd for capturing th publication yar, kywords, topics, concpts, variabls, thoris and modls and mthodologis usd. Th kywords wr takn as is givn by th authors and also capturd from th main txt of th articls sinc th dtails of th concpts, variabls, framworks; thoris xplain th rsarch in totality. This way valuabl dtail of ach papr was capturd. Thos that wr not found suitabl for th contxt of this study wr rjctd. For survys, thy hav usd onlin qustionnairs, postal qustionnairs and tlphonic survys. Th data has bn acquird from th portal -Taal, which is a portal dvlopd by India's National Informatics Cntr to masur th impact of various -govrnanc initiativs at national and stat lvls. -Taal provids a ral-tim viw of -transactions taking plac undr various -Govrnanc applications implmntd by Govrnmnt, on th basis of transaction count shard by thm in an automatd mannr using Wb Srvics tchnology. Ral tim utilization status and consolidatd -Transaction statistics of -Govrnanc Projcts across India can b viwd on -Taal. - transactions data for th stat of Jharkhand has bn downloadd from -Taal for this study. IV. FINDING AND ANALYSIS A. Data dscription and rsults Th -transaction data for th Stat of Jharkhand downloadd from -Taal from 1st January 2013 to 20th May Th downloadd data was alignd and dfind as tim sris daily data in SPSS. This data is daily and consists of 1977 data points from 1/01/2013 to 20/05/2018 B. SPSS Tim Sris Modl dtails Normalizd BIC - Normalizd Baysian Information Critrion. A gnral masur of th ovrall fit of a modl that attmpts to account for modl complxity. 83 AJCST Vol.7 No.2 July-Sptmbr 2018

4 TABLE I MODEL SUMMARY RESULT OF SPSS Fit Statistic Man SE Minimum Maximum Prcntil Stationary RMSE MAPE E MAE MaxAE Normalizd BIC : It is th proportion of variation in th dpndnt variabl xplaind by th rgrssion modl. It rangs in valu from 0 to 1. Stationary : A masur that compars th stationary part of th modl to a simpl man modl. Positiv valus man that th modl undr considration is bttr than th baslin modl. RMSE: Root Man Squard Error masurs th avrag magnitud of rrors in a quadratic scoring rul. MAE - This is on of th masurmnt procsss for forcasting tim sris, whr th avrag magnitud of th rrors in a st of prdictions, without considring thir dirction. MAPE - Man Absolut Prcntag Error is usd to masur prdiction accuracy of forcasting mthod in statistics. It uss prcntag as th mdium of xprssing accuracy. MaxA - Maximum Absolut Error. Th largst forcastd rror xprssd in th sam units as th dpndnt sris. TABLE II MODEL STATISTICS Modl Statistics Modl Fit statistics Ljung-Box Q(18) Modl Numbr of Prdictors Stationary Statistics DF Sig. Jharkhand-Modl_ Nxt, w hav a look at th modl statistics obtaind from SPSS. Looking at th Ljung-Box Q tst, w find that th valu of Q statistic for th tst coms out to b corrsponding to 17 dgrs of frdom. Howvr, th tst is found to b significant only at lvl which lads to th conclusion that th data is not indpndntly distributd and it xhibits srial corrlation. C. Slction of Bst Tim Sris modl on th basis of MAPE and BIC valus W can also hav a look at th Man Absolut Prcntag Error and Baysian Information Critrion statistics to dtrmin th bst fitting modl for our data and for stimation purposs. Sinc th man absolut prcntag rror is a masur of dviation, it is prfct as a masur of prdiction accuracy of a forcasting mthod in statistics, for xampl in trnd stimation. On th othr hand, Baysian Information Critrion (BIC) is a modl slction tool. If a modl is stimatd on a particular data st (training st), BIC scor givs an stimat of th modl prformanc on a nw, frsh data st (tsting st). BIC is givn by th formula: BIC = -2 * log liklihood + d * log(n), whr N is th sampl siz of th training st and d is th total numbr of paramtrs. Th lowr BIC scor signals a bttr modl. BIC attmpts to mitigat th risk of ovrfitting by introducing th pnalty trm d * log(n), which grows with th numbr of paramtrs. This prmits filtring out of pointlssly complx modls, which hav too many paramtrs to b anticipatd accuratly on a givn data st of siz N. W can us th combination of ths 2 paramtrs for slcting th bst modl for our data. Th statistical softwar that w us for calculating ths 2 valus for diffrnt pr-dfind modls is IBM SPSS. IBM SPSS includs Simpl, Simpl Sasonal, Holt's Linar Trnd, Brown's Linar Trnd, Dampd Trnd, Wintrs' Additiv, and Wintrs' Multiplicativ in th Tim-Sris modling procdur within its Statistics and Modlr statistical packags. Th xprt modlr function of IBM SPSS works in a similar mannr, that is, it compars th MAPE and BIC valus for dtrmining th bst modl for a datast. W will now hav a look at th diffrnt modls and th MAPE and BIC valus for ach of thm for slction of th bst modl through comparativ analysis. Brown's linar trnd- This modl is appropriat for sris in which thr is a linar trnd and no sasonality. Its smoothing paramtrs ar lvl and trnd, which ar assumd to b qual. Brown's modl is thrfor a spcial cas of Holt's modl. A mathmatically quivalnt form of Brown's linar xponntial smoothing modl, which mphasizs its non-stationary charactr, is th following: Y(hat) t Y t-1 = Y t-1 Y t-2 2(1- ) t-1 + ((1- )^2) t-2 AJCST Vol.7 No.2 July-Sptmbr

5 Idntifying th Most Effctiv Modl for Undrstanding th Growth Rat of Govrnmnt -Transactions: Brown's Modl of Exponntial Smoothing TABLE III MODEL DESCRIPTIONS Modl Nam Simpl Exponntial Smoothing Holt's Linar Trnd Brown's Linar Trnd Dampd Trnd Fit Statistic S. Sq MAE MaxA N. BIC S. Sq MAE MaxA N. BIC S. Sq MAE MaxA N. BIC S. Sq MAE MaxA N. BIC Man Minimum Maximu m TABLE IV COMPARISON RESULT OF DIFFERENT MODELS Stationary Man Absolut Modl Nam MAPE BIC R Squard R Squard RMSE Error Simpl Exponntial Smoothing Holt's Linar Brown's Linar Dampd Trnd Hnc Brown Modl is a good rprsntation of th data st of th stat of Jharkhand and is th bst fitting modl for forcasting through our data. Bsids this, th valu of MEA is also lowst for Brown modl according to th analysis. Thrfor, Brown modl stands out to b th suitabl forcasting modl for Jharkhand. D. Limitation of this Study Th study has bn conductd with th data downloadd from th -TAAL, which provids a ral-tim viw of - transactions taking plac undr various -Govrnanc applications implmntd by Govrnmnt, on th basis of transaction count shard by thm in an automatd mannr using Wb Srvics tchnology. As such -transaction data of only applications connctd to th -Taal portal has bn capturd & analyzd in th study. Any -Govrnanc application/s of Jharkhand Govrnmnt, not intgratd to th -Taal portal has not bn capturd and analyzd in this study, du to non-availability of th -transactions data of such projcts at a cntral lvl V.CONCLUSION To solidify th rsult obtaind through thortical analysis, w apply Tim Sris Modlr to th data sampl in SPSS. Onc again, th bst fitting modl is found to b Brown s modl, hnc raffirming th rsult of our analysis. This study provs that any data with th prsnc of trnd and th absnc of sasonality can b analyzd through Brown s xponntial smoothing sinc Brown modl is usually th bst fitting modl and can b usd to obtain rlativly mor accurat forcast rsults for th givn data. Th diagram blow shows th forcast rsult for transactions data in Jharkhand, using Brown s modl. As w can s in th diagram, th stimat obtaind is linar, and indicats that th stimatd numbr of transactions would ris as th tim priod incrass to Fig. 1 forcast rsult for transactions data in Jharkhand, using Brown s modl Th futur implications of this prdiction ar that th transactions, in thir prsnt format, will continu to incras linarly. Howvr, if w can com up with bttr idas, dsigns and implmntations for such srvics in futur, w can xpct an xponntial incras in th stimats for th sam. Also if w ar abl to obtain th data for usr bas xpctations and fdback rgarding prvious srvics, w would b abl to fostr bttr dvlopmnt stratgis and combin th data for usr bas with srvics analysis to com up with bttr quality of srvics. 85 AJCST Vol.7 No.2 July-Sptmbr 2018

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