Journal for Sudies in Managemen and Planning Available a hp://inernaionaljournalofresearch.org/index.php/jsmap e-issn: 2395-463 Volume 1 Issue 2 March 215 Forecas of Adul Lieracy in Sudan Dr. Elfarazdag Mahjoub Mohammed ussein, Deparmen of Saisics-Faculy of Science-Tabuk Universiy (KSA), Sudan Absrac: The main objecive of his paper is o find ou a ime series model o monior and forecas he Adul Lieracy rae in Sudan. To achieve his objecive, a series of Adul Lieracy ranged from 199 o 29 was obained from he Sudan Cenral Bureau of saisics and Unied Naion Annual Repors, ime series analysis echnique mainly box and Jenkins were used o find he required model.analysis done by e- views package. The paper conclude ha The mos proper ime series model o forecas he Adul Lieracy rae in Sudan is he ARIMA model, The general rend of Adul Lieracy is an increasing rend wih annual increase Less han 3%. Keywords: Adul Lieracy, box and Jenkins, auo regressive moving average, Sudan. Lieracy is ypically described as he abiliy o read and wrie. I is a concep claimed and defined by a range of differen heoreical fields. The Unied Naions Educaional, Scienific and Culural Organizaion (UNESCO) provides a useful and reasonably definiion of lieracy, i is defined as he "abiliy o idenify, undersand, inerpre, creae, communicae, compue and use prined and wrien maerials associaed wih varying conexs. Lieracy involves a coninuum of learning in enabling individuals o achieve heir goals, o develop heir knowledge and poenial, and o paricipae fully in heir communiy and wider sociey." The aim of he sudy is o find ou a ime series model based on annual basis for he Adul Lieracy rae in Sudan for he period 199-29. The imporance of his sudy concenraed a he serious need of consrucing a ime series model for he fuure forecas o deec he paern of change in Adul Lieracy which helps for he fuure planning. The used Adul lieracy daa was compiled from he annual Unied Naions Developmen Program Repors saring from 199 up o 29 will be used. 2. Theoreical framework Time series analysis echniques, namely Box and Jenkins echnique was used, he series exends over he period 199-213, which is fairly long; Auoregressive Inegraed Moving Average (ARIMA) was chose for he analysis. 2.1 Time Series Componens Time series consiss of several componens, which are: (A) Trend (B) Cyclical Variaions. (C) Seasonal Variaions. (D) Irregular flucuaions. 2.2 Time Series Decomposiion Model If a ime series exhibis rend effecs and seasonal effecs, i can be useful o decompose i in order o isolae hese effecs. One model ha allows us o do his is he muliplicaive decomposiion model, i s he mos popular decomposiion model, and i s expressed as 23 Available online: hp://inernaionaljournalofresearch.org/
Journal for Sudies in Managemen and Planning Available a hp://inernaionaljournalofresearch.org/index.php/jsmap e-issn: 2395-463 Volume 1 Issue 2 March 215 follows: Y = T * S * C * Also here is decomposiion model known as he addiive model, which expressed as follows: Y = T + S + C + Where: Y: The observed value of he ime series in ime period. T: The rend componens in ime period. S: The seasonal componens in ime period. C: The cyclical componens in ime period. I: The erraic componens in ime period. 2. 3 Forecasing Mehods There are many forecasing mehods ha can be divided ino wo basic ypes which are: (A) Qualiaive Forecasing Mehods Qualiaive forecasing mehods generally use he opinion of he exper o subjecively predic fuure evens. (B) Quaniaive Forecasing Mehods Quaniaive forecasing models are grouped ino wo main models, which are: (I) Univariae Models Univariae models predic he fuure evens of ime series on he basis of he pas values of he ime series (Powerman, 1979).When a univariae model is used; hisorical daa are analyzed in an aemp o idenify a daa paern, hen assuming ha i will coninue in he fuure. Univariae forecasing models are mos useful when condiions are expeced o remain he same. (II) Causal Models The use of such models involves he idenificaion of oher variables ha are relaed I I o he variable o be prediced, once hese relaed variables have been idenified, a saisical model ha describes he relaionships beween hese variables and he variable o be forecased is developed. The saisical relaionship derived is hen used for forecasing he variable of ineres. Generally we can say ha quaniaive forecasing mehods are used when hisorical daa are available univariae models predic fuure values of he variable of ineres on he basis of hisorical paern of ha variable, assuming he hisorical paern will coninue; causal models predic fuure values of he variable of ineres based on he relaion beween ha variable and oher variables. Qualiaive forecasing echniques are used when hisorical daa are scarce or no available a all and depend on he opinions of expers 2.4 Choosing he Forecas Technique In choosing he forecasing echnique he forecaser mus consider he following facors 1. The naure of he sudy variable. 2. The ime frame. 3. The paern of daa. 4. The cos of forecasing. 5. The accuracy desired. 6. The availabiliy of daa. 7. The ease of operaion and undersanding. The firs facor o be considered in choosing a forecasing mehod is he form in which he forecas is desired i.e. deermine wheher he forecaser will use poin or inerval forecas. The second facor ha can influence he choice of forecasing mehod is he ime frame of he forecasing siuaion. Forecas are generaed for poin in ime may be a number of days, weeks, monhs, quarers or years in he fuure. This 231 Available online: hp://inernaionaljournalofresearch.org/
Journal for Sudies in Managemen and Planning Available a hp://inernaionaljournalofresearch.org/index.php/jsmap e-issn: 2395-463 Volume 1 Issue 2 March 215 lengh of ime is called he ime frame; he lengh of he ime frame is usually caegorized as follows: 1. Immediae less han monh. 2. Shor erm more han hree monhs o less han wo years. 3. Long erm wo years or more. The lengh of he ime frame influence he choice of forecasing echnique, ypically a longer ime frame makes accurae forecasing more difficul. The paern of daa mus also be considered when choosing forecasing model. Thus, i is imporan o idenify he exising daa paern. One of he mos imporan facor ha affec he choice of forecasing echnique is he desired accuracy of he forecas, he availabiliy of informaion and las he ease wih which he forecasing mehod is operaed and undersood is imporan. 2.5 The Box-Jenkins Mehodology This mehodology developed by G. E. P. Box and G. M. Jenkins, consiss of four basic seps. The firs sep, called enaive idenificaion sep, involves enaively idenifying a model. Once a model has been idenified, we esimae he model parameers in he second sep ha called he esimaion sep. The hird sep is called he diagnosic checking sep, here we check he adequacy of he model, if he model proves o be inadequae, i mus be modified. When a final model is deermined, we use he model o forecas fuure ime series values; his fourh sep is called he forecasing sep. There are many Box-Jenkins models; hese models can be grouped ino he following hree basic classes: (A) Auoregressive models. (B) Moving average models. (C) Mixed auoregressive- moving average models. Box-Jenkins models are ofen called ARIMA models [Auoregressive Inegraed Moving Average]. The Univariae Box Jenkins models have proven o provide accurae forecas in shor erm forecasing applicaions. 2.6 Saionary and Non-Saionary Time Series The classical Box Jenkins models describe saionary ime series, hus in order o enaively idenify a Box Jenkins models, we mus firs deermine wheher or no a ime series under invesigaion is saionary, if i is no, we mus ransform i ino a series of saionary ime series values eiher by using he log or he reciprocal. A ime series is said o be saionary if he saisical properies such as mean and variance of ime series are consan hrough ime, if we have observed n values y 1, y 2, y 3,., y n, of a ime series, we can use a plo of hese values agains ime o help us o deermine wheher he ime series is saionary or no. If he n values seem o flucuae wih consan variaion around a consan mean, hen i is reasonable o believe ha he ime series is saionary, if he n values do no flucuae wih consan variaion, hen i is reasonable o believe ha he ime series is no saionary. If we decided ha he ime series is no saionary we can ransform i from nonsaionary o saionary by aking he firs differences of he non-saionary ime series. 2.7Uni Roo Tes -Augmened Dickey- Fuller (DF) Tes 1 : ρ = : ρ 232 Available online: hp://inernaionaljournalofresearch.org/
Journal for Sudies in Managemen and Planning Available a hp://inernaionaljournalofresearch.org/index.php/jsmap e-issn: 2395-463 Volume 1 Issue 2 March 215 Uni roo es is designed o es wheher he ime series daa are saionary or no. Saionary ime series daa have he following characerisics: 1. Consan mean. 2. Finie variance. 3. The Correlogram diminishes as lag lengh increases. The DF uni roo es is based on he following regression forms: 1. Wihou Consan and Trend Y = δ Y + 1 2. Wih Consan µ Y = α + δ Y + 1 µ 3. Wih Consan and Trend Y = α + βt + δ Y + 1 µ Where:α is consan, β and δ are he coefficiens of he model. 2.8 DF Uni Roo Tes ypohesis 2.9. Decision Rule 1 : δ = : δ If * > ADF criical value, accep he null hypohesis. (Uni roo exis). If * > ADF criical value, rejec he null hypohesis. (Uni roo no exis). 2.1 Tes of Serial Correlaion The Correlogram es he serial auocorrelaion under he following ypohesis: If Prob. >.5 we accep, which means serial correlaion does no exis. If Prob. <.5 we rejec, which means serial correlaion exis. 3. Empirical Analysis 3.1. Calculaion Adul Lieracy Rae The saring poin for calculaing Adul Lieracy Rae is he number of lierae people in age 15 year and above in addiion o he oal number of populaion in he same age group. AL Rae = (Number of lierae populaion (15+ yrs))* 1 7 6 5 4 3 (Toal number of (15+ yrs) populaion) Figure 1: Adul Lieracy 2 9 95 5 1 15 2 Figure (1) shows ha he Adul Lieracy series is no saionary, here is an increasing rend. Table 1: Augmened Dickey-Fuller Tes ADF -6.888311 1% Criical Value* -2.7158 Tes Saisic 5% Criical Value -1.9627 1% Criical Value -1.6262 Augmened Dickey-Fuller Tes Equaion Dependen Variable: D(AL,3) Mehod: Leas Squares Sample(adjused): 1993 29 Included observaions: 17 afer adjusing endpoins Variable Coefficien Sd. Error -Saisic Prob. D(AL(-1),2) -1.49477.2169-6.888311. R-squared Adjused R- squared S.E. of regression Sum squared resid Log likelihood Adul Lieracy in Sudan.747813 Mean dependen var -.76471.747813 S.D. dependen var 9.996439 5.238 Akaike info crierion 6.121774 43.2125 Schwarz crierion 6.17787-51.358 Durbin-Wason sa 2.398132 Table (1): Shows ha he compued ADF essaisics -6.888311 is less han he criical values of au ( -2.7158, -1.9627, -1.6262) a 1%, 5% and 1% significan level respecively, he Durbin-Wason es is 233 2.398132 which is around 2, lead o rejec Available online: hp://inernaionaljournalofresearch.org/
Journal for Sudies in Managemen and Planning Available a hp://inernaionaljournalofresearch.org/index.php/jsmap e-issn: 2395-463 Volume 1 Issue 2 March 215 and accep 1 which mean ha Lieracy difference. he Adul Series is saionary a he second Table 2: Second Difference Correlogram Sample: 199 29 Included observaions: 18 Lag AC PAC Q-Sa Prob 1 -.495 -.495 5.18.23 2 -.77 -.426 5.3145.7 3 -.42 -.497 5.3568.147 4.242 -.22 6.8653.143 5 -.55 -.19 6.9484.225 6 -.175 -.129 7.8699.248 7.154.55 8.6471.279 8 -.52 -.35 8.7457.364 9.112.147 9.2511.414 1 -.315 -.247 13.77.187 11.33 -.97 18.428.72 12 -.73 -.12 18.747.95 Table (2): shows ha he probabiliy increases as he lag increase, which is a good indicaor for he absence of serial auocorrelaion a he second difference. 2 1-1 -2 Figure 2:Second difference Adul Lieracy -3 9 92 94 96 98 2 4 6 8 Second Difference AL Figure (2): shows ha he Adul Lieracy Series is saionary a he second difference. Esimaion Command: ===================== LS @LOG (AL) C @TREND AR (1) MA(5) Esimaion Equaion: ===================== @LOG(AL) = C(1) + C(2)*(@TREND) + [AR(1)=C(3),MA(5)=C(4),BACKCAST=1991] Subsiued Coefficiens: ===================== @ LOG (AL) = 3.695116792 +.2592858574*(@TREND) + [AR(1)=.565445982,MA(5)=-.957238173,BACKCAST=1991] Table3: Model Esimaion Dependen Variable: @LOG(AL) Mehod: Leas Squares Included observaions: 19 afer adjusing endpoins Convergence achieved afer 58 ieraions Backcas: 1986 199 Variable Coefficien Sd. Error -Saisic Prob. C 3.695117.96515 38.28529. @TREND.25929.6733 3.85917.16 AR(1).565446.82294 6.8715. MA(5) -.95724 8.62E-5-1125.8. R-squared.986777 Mean dependen var 3.843747 Adjused R- squared.984133 S.D. dependen var.32424 S.E. of regression.4362 Akaike info crierion -3.397171 Sum squared resid Log likelihood Durbin- Wason sa Table (3): shows ha he esimaed coefficiens are saisically significan under a 5% level of significance. The overall regression fi, as measured by he R2 saisics (R2=.986777), indicae a good fi. Since he Durbin Wason value is (2.43667) which is around (2) indicaes ha here is no serial auocorrelaion. The Akaike, Schwarz crieria (-3.397171, -3.198341) indicae ha he C @rend AR (1), MA (5) model should be preferred because hey have he leas values among he differen models which can be fied. The Prob. (F-saisics=.) indicae ha he whole model is saisically significan under 5% level of significance. Figure 3: Fied, Acual and Residual Adul 4 2-2 -4.24437 Schwarz crierion -3.198341 36.27312 F-saisic 373.1353 2.43667 Prob(F-saisic). Lieracy 92 94 96 98 2 4 6 8 7 6 5 4 3 2 Residual Acual Fied 234 Available online: hp://inernaionaljournalofresearch.org/
Journal for Sudies in Managemen and Planning Available a hp://inernaionaljournalofresearch.org/index.php/jsmap e-issn: 2395-463 Volume 1 Issue 2 March 215 Figure (3) shows ha he fied values have no significan difference from he acual one. Year Table 4: Forecased Adul Lieracy Forecased AL Annual Change of AL Rae % of Annual change of AL 21 67.652 ***** ***** 211 69.3814.26271 2.62753 212 71.2362.26269 2.626914 213 73.744.26269 2.626861 214 74.99356.26268 2.626815 215 76.96348.26268 2.626786 216 78.98515.26268 2.626791 217 81.5991.26268 2.626772 218 83.18917.26268 2.626773 219 85.37435.26268 2.62676 Tables (4): shows he forecased Adul Lieracy in Sudan up o 219. 4. Conclusion 4.1 Resuls 1. The mos proper ime series model o forecas he Adul Lieracy Rae in Sudan is he ARIMA model. 2. The general rend of Adul Lieracy in Sudan is an increasing rend. 3. The annual increase of Adul Lieracy in Sudan is less han 3%. 4.2 Recommendaions 1. Formal educaion is a very imporan facor in building human capial; herefore new schools is recommended o be consruced especially in he rural areas, moivaion of young poor people for he basic educaion also needed. 2. Ensuring ha he poor are no excluded on accoun of povery. In some cases his means going beyond free educaion. For he exremely poor some form of acion based on scholarships may be needed. 3. Qualiy of educaion, including relevance o conex-specific life skills and labour marke requiremens, should be coninuously improved in all sages. 4. Training and recruiing more eachers and sriving o reain hem for long period. Bibliography Auocorrelaion in Auoregressiveinegraed moving Average Time Series Models", JASA, VOL.65, P. (152-1526). (197), Box, G.E.P and Jenkins, G.M., "Time Series Analysis Forecasing and conrol", olden day, London. (1976) Box, G.E.P. & Pierce, D.A., "Disribuion of he Residual hp//www.developmengoals.org. Kaiser, R. and Maravall, A. Noes on Time Series Analysis ARIMA Models and Signal Exracion, Benco de Espona servicio E sudios(21), Nuno Crao, Some Resuls on he Specral Analysis of saionary Time Series Porugal Mahemaic Vol. 53. Fasc. 2-1996. Sen, A, 1999. A decade of uman Developmen. Key noe speech. uman Developmen Repor Office. UNDP. Sree, B, 1984. Lieracy in heory and pracice. Cambridge: Cambridge Universiy Press.p.2. ISBN 97852128961. 235 Available online: hp://inernaionaljournalofresearch.org/