Forecasting Unemployment Rate in Selected European Countries Using Smoothing Methods

Transcription

1 Ieraioal Joural of Social, Behavioral, Educaioal, Ecoomic, Busiess ad Idusrial Egieerig Vol:9, No:4, 2015 Forecasig Uemployme Rae i Seleced Europea Couries Usig Smoohig Mehods Kseija Dumičić, Aia Čeh Časi, Berislav Žmuk Ieraioal Sciece Idex, Ecoomics ad Maageme Egieerig Vol:9, No:4, 2015 wase.org/publicaio/ Absrac The aim of his paper is o selec he mos accurae forecasig mehod for predicig he fuure values of he uemployme rae i seleced Europea couries. I order o do so, several forecasig echiques adequae for forecasig ime series wih red compoe, were seleced, amely: double expoeial smoohig (also kow as Hol`s mehod) ad Hol-Wiers` mehod which accous for red ad seasoaliy. The resuls of he empirical aalysis showed ha he opimal model for forecasig uemployme rae i Greece was Hol-Wiers` addiive mehod. I he case of Spai, accordig o MAPE, he opimal model was double expoeial smoohig model. Furhermore, for Croaia ad Ialy he bes forecasig model for uemployme rae was Hol-Wiers` muliplicaive model, whereas i he case of Porugal he bes model o forecas uemployme rae was Double expoeial smoohig model. Our fidigs are i lie wih Europea Commissio uemployme rae esimaes. Keywords Europea Uio couries, expoeial smoohig mehods, forecas accuracy uemployme rae. I. INTRODUCTION RIMARY applicaio of may ecoomerics models is Pforecasig, hus his paper aims o selec he mos accurae forecasig model amog smoohig mehods for he shor-erm forecas of he uemployme rae i seleced Europea couries. The auhors foud challegig eough o explore poeial forecasig models suiable for predicig he fuure values of uemployme rae, sice rece aalysis coduced by Eurosa revealed some ieresig reds. Namely, he euro area seasoally-adjused uemployme rae i Augus 2014 reached 11.5%, which was sable whe compared o July 2014, bu also smaller he i Augus 2013 whe i was 12.0%. The EU-28 uemployme rae was 10.1% i Augus 2014, which is he lowes recorded value sice February Furhermore, uemployme rae was lower i July 2014 ad Augus 2013 whe i reached 10.2% ad 10.8%, respecively. Amog he Member Saes, he lowes uemployme raes were recorded i Ausria (4.7%) ad Germay (4.9%), while he highes recorded uemployme raes were i Greece (27.0%) ad Spai (24.4%). Followig for meioed uemployme rae reds, Dumičić, K. is wih he Faculy of Ecoomics ad Busiess, Uiversiy of Zagreb, Trg J. F. Keedyja 6, 10000, Croaia (phoe: ; e- mail: kdumicic@efzg.hr). Čeh Časi, A. is wih he Faculy of Ecoomics ad Busiess, Uiversiy of Zagreb, Trg J. F. Keedyja 6, 10000, Croaia (phoe: ; e- mail: aceh@efzg.hr). Žmuk, B. is wih he Faculy of Ecoomics ad Busiess, Uiversiy of Zagreb, Trg J. F. Keedyja 6, 10000, Croaia (phoe: ; e- mail: bzmuk@efzg.hr). i his paper quarerly daa o uemployme rae from firs quarer 2001 o fourh quarer 2013 will be aalyzed ad also, he mos suiable forecasig mehod will be seleced. Sice Eurosa already delivered daa o uemployme rae for firs wo quarers of 2014, he accuracy of esimaed forecasig models could be direcly checked. For he purpose of he empirical aalysis, we seleced five Europea couries, amely: Croaia, Greece, Ialy, Porugal ad Spai. Eve hough, subsaial differeces exis amog hem i he aalyzed period; hey all record subsaially high uemployme raes. As already meioed, he aim of his paper is o selec he mos accurae forecasig mehod for predicig he fuure values of he uemployme rae. I order o do so, several forecasig echiques adequae for forecasig ime series wih red compoe, were seleced, amely: double expoeial smoohig (also kow as Hol`s mehod) ad Hol-Wiers` mehod which accous for red ad seasoaliy. The remaider of his paper is as follows. Afer he iroducio i Secio II a brief releva lieraure review is give. Secio III preses daa ad mehods used i he empirical aalysis. Secio IV gives he resuls of he esimaed forecasig models. Fially, Secio V cocludes. II. LITERATURE REVIEW I heir research [7] aalyzed accuracy, bias ad forecass efficiecy for he followig macroecoomic variables: gross domesic produc, iflaio, idusrial producio ad privae cosumpio i G7 couries. Sice mos ieraioal isiuios provide heir ow macroecoomic forecass, large discrepacies i he resuls are o prese oly bewee couries, bu also wihi idividual coury [9]. The accuracy of forecass is especially releva i he case of ecoomic crisis. Uemployme rae forecass are compared i he USA coduced by differe isiuios, accordig o [11]. I he process of forecas accuracy evaluaig, muli-crieria rakig were used ad he followig idicaors, amely: roo mea squared error (RMSE), mea error (ME), mea absolue error (MAE) ad U Theil s saisics were ake io accou. I order o evaluae forecas accuracy of uemployme rae i Romaia accordig o [8] i muli-crieria rakig, he followig measures of accuracy were used: RMSE, ME, MAE, U1 ad U2 Theil s saisics. Excep he muli-crieria rakig he mehod of relaive disace was used, leadig o he same coclusios. Furhermore, [13] emphasized sigifica icrease of he Ieraioal Scholarly ad Scieific Research & Iovaio 9(4) scholar.wase.org/ /

2 Ieraioal Joural of Social, Behavioral, Educaioal, Ecoomic, Busiess ad Idusrial Egieerig Vol:9, No:4, 2015 Ieraioal Sciece Idex, Ecoomics ad Maageme Egieerig Vol:9, No:4, 2015 wase.org/publicaio/ eed for high-qualiy saisics i labor policy. I order o forecas mohly uemployme rae i Romaia, hey used double expoeial smoohig or Hol's liear expoeial smoohig model. Accordigly, he expoeial smoohig models reac more quickly o chages i daa paers ha he movig average models. O he oher had, he mai problem, whe usig expoeial smoohig models, is deermiig he size of smoohig coefficies [13]. I he case of he iflaio rae, he uemployme rae ad he ieres rae i he Czech Republic, [10] has show ha expoeial smoohig echiques geerae beer shor ru predicios ha simple ecoomeric models. The research of [4] led o similar coclusio. They used ARIMA ad expoeial smoohig modellig o forecas ouris arrivals i Greece. I heir aalysis, hey icluded uemployme, ouriss cos of livig ad he cosumer cofidece idicaor. The aalysis has show ha he ARIMA (1,1,1) model has beer saisical properies ha oher expoeial smoohig models kow as direc forecasig ools. Furhermore, i was show ha expoeial smoohig models were more accurae whe compared o ARIMA models. I order o forecas mai macroecoomic variables i Turkey, which is a EU cadidae, [5] used variey of differe forecasig mehods. Accordig o heir research he Hol s liear expoeial smoohig mehod was he mos appropriae for uemployme rae forecasig. Afer he period of icreasig uemployme rae, [6] forecased declie of he uemployme rae for he EU ad euro area i forhcomig years. However, he uemployme rae forecas for Croaia is se a 18% i 2014 ad Cosequely, Croaia afer Greece (forecas for 2014 ad 2015 is 26% ad 24%, respecively), Spai (forecas for 2014 ad 2015 is 25.5% ad 24%, respecively) ad Cyprus (forecas for 2014 ad 2015 is 19.2% ad 18.4%, respecively), has he highes forecased uemployme rae i Europea Uio. Accordigly, here is a eed for a closer aalysis of a uemployme rae i Europea couries. Our paper coribues o he exisig lieraure by givig isighs o he mos appropriae forecasig mehods amog smoohig mehods for predicig uemployme rae. Our fidigs are i lie wih Europea Commissio uemployme rae esimaes. III. DATA AND METHODS I he empirical aalysis of his paper, he quarerly daa o uemployme rae i he period from firs quarer of 2001 o fourh quarer of 2013 is used. Sice he global fiacial crisis sared i he hird quarer of 2008, i our aalysis, we will be able o capure he impac of ha crisis o he uemployme rae. The daa was ake from Eurosa daabase (Europea Uio labour force survey, EU-LFS) for he followig 5 Europea couries: Croaia, Greece, Ialy, Porugal ad Spai. Based o Ieraioal Labour Office (ILO) defiiio, he uemployme rae represes uemployed persos as a perceage of he labour force. The labour force is he oal umber of people employed ad uemployed. Uemployed persos comprise persos aged 15 o 74 who: are wihou work durig he referece week; are available o sar work wihi he ex wo weeks; ad have bee acively seekig work i he pas four weeks or had already foud a job o sar wihi he ex hree mohs. I his paper, accordig o Eurosa defiiio, he variable of ieres is oal uemployme rae by sex ad age groups give as quarerly average, expressed i perceages (Eurosa variable code: ue_r_q). Variey of forecasig mehods exiss, bu a pragmaic quesio sill remais: how ca a forecaser choose a righ model for a daa se? A mai objecive is o decide o he aure of red ad seasoaliy ad a usual way o do so is o cosruc a ime plo of he raw daa. Accordigly, i Fig. 1, a ime plo of uemployme rae i seleced Europea couries for he aalyzed period is give Q1 2000Q4 2001Q3 2002Q2 2003Q1 2003Q4 2004Q3 2005Q2 2006Q1 2006Q4 2007Q3 2008Q2 2009Q1 2009Q4 2010Q3 2011Q2 2012Q1 2012Q4 2013Q3 2014Q2 Greece Spai Croaia Ialy Porugal Fig. 1 Quarerly uemployme rae i seleced Europea couries As i ca be see from he graph, wo differe reds i uemployme rae i all aalyzed couries may be observed. Namely, i all couries bu Porugal, here is a dowward red i uemployme rae from firs quarer of 2001 o hird quarer of 2008 whe he global fiacial crisis bega. From he o, i all aalyzed couries, a growh i uemployme rae ca be observed. Ieresigly, i Porugal, for he whole aalyzed period, a growh i uemployme rae is evide. Exremely ufavorable period for he uemployme rae i Croaia bega i The developme of such siuaio is due o fore meioed global ecoomic crisis, which reached is peak i he hird quarer of The impac of ha crisis o he labour marke ca easily be explaied o he example of Greece, where i all bega by a credi crisis developme. Cosequely, i led o he ecoomic crisis ha adversely affeced he fiacial codiio of Greece. The repored declie i GDPs also led o a drop i budge reveues. A he same ime, a declie i budge reveues has led o he growh of corrupio ad he gray ecoomy. The labor marke was o lef behid. Risig uemployme caused a icrease i public expediure due o risig coss of uemployme beefis. Furhermore, expeses exceeded reveues which led o a budge defici. For is coverage, Greece used foreig loas ha resuled i over-idebedess ad deepeig credi crisis. However, he crisis did o skip Spai, Ialy ad Porugal, bu Ieraioal Scholarly ad Scieific Research & Iovaio 9(4) scholar.wase.org/ /

3 Ieraioal Joural of Social, Behavioral, Educaioal, Ecoomic, Busiess ad Idusrial Egieerig Vol:9, No:4, 2015 Ieraioal Sciece Idex, Ecoomics ad Maageme Egieerig Vol:9, No:4, 2015 wase.org/publicaio/ i had less impac o hose couries whe compared o Greece. Sill, hese couries recorded a egaive edecy of he uemployme rae. As far as he mehods for he empirical aalysis i his paper are cocered, as meioed before, expoeial smoohig mehods will be used, sice hey reac more quickly o he chages i daa paer. Moreover, expoeial smoohig was firs suggesed by [2] i he 1957 ad was ieded o be used for ime series wihou red. Bu i 1958, Hol offered a mehod ha also hadles red i daa, which is ow kow as Hol`s liear mehod. Furhermore, i 1965 Wiers geeralized ha mehod o iclude seasoaliy, which is called Hol-Wiers Mehod. Accordig o Fig. 1, here is proouced red ad seasoal compoe i uemployme rae, wih he seasoal compoe beig mos proouced i he case of Croaia ad Ialy. Thus, i he empirical aalysis Hol double expoeial smoohig ad Hol Wiers mehod will be used i forecasig fuure uemployme rae. The Hol's forecasig model cosiss of boh a expoeially smoohed permae compoe deoed by L ad a smoohed red compoe b. Cosequely, he echique is someimes called woparameer double expoeial smoohig [1]. The red compoe is used i he calculaio of he expoeially smoohed value. The followig equaios show ha boh L ad b are weighed averages [12]: L b Y L b (1) L L b I should be oed ha he equaios require wo subjecively chose smoohig cosas, α ad γ, each of which is bewee zero ad oe. If wo cosas are equal he model is called Brow s double expoeial smoohig. The cosa α corols he smoohess of L. The closer he cosa α is o zero, he more emphasis is give o he pas values of he ime series, while a value of α ear oe gives more weigh o he curre values of he series, miimizig he ifluece of hisorical values. The red compoe of he series is esimaed adapively, usig a weighed average of he mos rece chage i he level ( L L ), ad he red esimae (b -1 ) from he previous period. Furhermore, a choice of he weigh γ ear zero places more emphasis o he pas esimaes of red, while a choice of γ ear oe gives more weigh o he curre value of a chage i level. I he empirical applicaios of models o macroecoomics ime series, i our case uemployme rae, Hol-Wiers` muliplicaive mehod is ofe used, whereas he basic equaios are give by: y L (1 )( L b ) S s b ( L L ) (1 ) b y S 1 S s L (2) Namely, s is he legh of seasoaliy (i our case umber of quarers i a year), L represes he level of he series, b deoes he red ad S seasoal compoe [12]. Cosas ha eed o be chose for his model are: α (level smoohig cosa), γ (red smoohig cosa) ad (seasoal smoohig cosa). As i Hol double expoeial model smoohig cosa ake o he values bewee 0 ad 1. Whe he seasoal compoe of he aalyzed ime series has saisically cosa ampliude, addiive Hol-Wiers` mehod is usually used, wih he followig basic equaios: L y S s L b b L L b S y L S s Iiial values for L S ad b S are ideical as i he case of he muliplicaive Hol-Wier`s mehod. Usually, for he seasoal idices iiial values, he followig expressios are used: S (3) y LS, S y LS,..., SS ys L (4) S There is o uiversally acceped way of choosig he mos appropriae smoohig cosas. Some praciioers recommed always usig a value aroud 0.1 or 0.2. Ohers recommed experimeig wih differe values of smoohig cosas uil a measure such as he mea absolue perceage error (MAPE) is miimized. Fially, [14] suggesed usig a opimizaio opio o selec he bes smoohig cosas. I he empirical aalysis of his paper a opimizaio opio of selecig smoohig cosas i he case of Hols double expoeial smoohig models are used, whereas i he case of addiive ad muliplicaive Hol- Wiers` models, smoohig cosas are chose by experimeig wih differe values of smoohig cosas uil Mea absolue perceage error (MAPE) is miimized. I he ex secio, oly models wih opimal smoohig cosas are show ad ierpreed. I order o check he accuracy of he esimaed progosic models, he followig accuracy measures were employed: MSD (Mea Square Deviaio), also called MSE (Mea Square Error), which is a measure of he variabiliy i he forecas error, calculaed usig he expressio: MSD Y F 2 (5) MAD (Mea Absolue Deviaio), which measures he average magiude of he forecas error, give by: MAD Y F ad MAPE (Mea Absolue Perceage Error), which idicaes ha o average, he chose expoeial smoohig model produced a forecas ha differs from he acual value by calculaed perceage. MAPE is give by: (6) Ieraioal Scholarly ad Scieific Research & Iovaio 9(4) scholar.wase.org/ /

4 Ieraioal Joural of Social, Behavioral, Educaioal, Ecoomic, Busiess ad Idusrial Egieerig Vol:9, No:4, 2015 Ieraioal Sciece Idex, Ecoomics ad Maageme Egieerig Vol:9, No:4, 2015 wase.org/publicaio/ MAPE Y F Y 00 I he ex secio, oly models wih opimal smoohig cosas, seleced by he opimizaio algorihm or wih he smalles values of MAPE are show ad ierpreed. IV. RESULTS OF THE EMPIRICAL ANALYSIS Forecasig fuure reds of uemployme rae based o is hisorical behaviour, wihou cosiderig causal relaioship wih oher variables, is a simple bu direc way of forecasig. Empirical sudies have show ha he forecass obaied by uivariae mehods of modelig ime series are sesiive, bu also ime-ad cos-effecive, sice hey use hisorical daa of he variable of ieres, whose behavior wih he respec o oher associaed variables is ukow ad/ or difficul o explai. I his secio, he series of oal uemployme rae by sex ad age groups give as quarerly average, expressed i perceages, for five seleced Europea couries from hird quarer of 2008 o fourh quarer of 2013 is forecased usig saisical sofware MINITAB 14. I is impora o sress, ha he period from 2001Q1 o 2008Q2 is o icluded i he aalysis, sice his was he period before he global fiacial crisis whe all couries of ieres recorded dowward Mehod/ Coury (7) TABLE I FORECASTING MODELS AND ACCURACY MEASURES uemployme rae red. The break i ha red was he begiig of global fiacial crisis which sared i hird quarer of Namely, from he o, i all aalyzed couries, a upward red i oal uemployme rae is oiced ad aalyzed here i more deail. I his secio, he aim is o defie a adequae model wihi he group of expoeial smoohig models, described i Secio III, ha will provide mos accurae shor-erm forecass. Furhermore, based o he chose model, he fuure value of oal uemployme rae will be he esimaed for Fore meioed forecas are shor-erm forecass ad akig io accou ha a large umber of facors are affecig uemployme rae, i is fairly realisic, ha forecas are possible oly i a very shor period of ime. Sice we use quarerly daa o oal uemployme rae, forecasig horizo τ = 4 is sill cosidered reliable because of "seasoal" erms, amely accordig o [3], i is acually a forecas for oly oe period ahead (oe-sep-ahead forecas). Accordig o seleced crieria described i Secio III, amely: MSD, MAD ad MAPE, he mos accurae forecasig model for he variable of ieres i aalyzed five Europea couries will be seleced. The accuracy measures for aalyzed forecasig mehods ad couries are give i Table I. Greece Spai Croaia Ialy Porugal MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD Model 1: Double expoeial smoohig Seleced smoohig cosas(algorihm: opimal ARIMA) α(level)= γ(red)= Model 2: Hol-Wiers` muliplicaive mehod Seleced smoohig cosas: α(level)= γ(red)= δ(seasoal)= Model 3: Hol-Wiers` addiive mehod Seleced smoohig cosas: α(level)= γ(red)= δ(seasoal)= Accordig o he resuls give i Table I ad measure of forecas accuracy Mea Absolue Perceage Error (MAPE), he opimal model for forecasig uemployme rae i Greece is Model 3, amely Hol-Wiers` addiive mehod. I he case of Spai, accordig o MAPE, he opimal model is Model 1 (double expoeial smoohig). Furhermore, for Croaia ad Ialy he bes forecasig model for uemployme rae is Model 2 (Hol-Wiers` muliplicaive mehod). This is a ieresig ad logical foudig, sice he uemployme rae for he aalyzed period i hese wo couries had proouced seasoal compoe, as show i Figs. 2 (a) ad (b), respecively. Fially, he bes model o forecas uemployme rae i Porugal is Model 1 or Double expoeial smoohig model. Furhermore, if we look a he acual daa published by Eurosa for he uemployme rae for firs quarer of 2014, we come o a bi differe coclusios. Namely, i Table II, he acual ad forecased uemployme rae daa for firs quarer of 2014 usig aalyzed forecasig mehods are give. Accordigly, we ca coclude ha i all aalyzed couries, bu Ialy, Model 1, or double expoeial smoohig mehod, show o be he mos accurae. I he case of Ialy, Model 3 or Ieraioal Scholarly ad Scieific Research & Iovaio 9(4) scholar.wase.org/ /

5 Ieraioal Joural of Social, Behavioral, Educaioal, Ecoomic, Busiess ad Idusrial Egieerig Vol:9, No:4, 2015 Ieraioal Sciece Idex, Ecoomics ad Maageme Egieerig Vol:9, No:4, 2015 wase.org/publicaio/ Hol-Wiers` addiive mehod, gave he mos accurae forecass. Fig. 2 (a) Quarerly uemployme rae from 2008Q4-2014Q4 for Croaia Fig. 2 (b) Quarerly uemployme rae from 2008Q4-2014Q4 for Ialy TABLE II ACTUAL AND FORECASTED UNEMPLOYMENT RATE FOR SELECTED EUROPEAN COUNTRIES Coury Acual daa Model 1 Model 2 Model 3 Greece Spai Croaia Ialy Porugal V. CONCLUSION The auhors foud challegig eough o explore poeial forecasig models suiable for predicig he fuure values of uemployme rae, sice rece aalysis coduced by Eurosa revealed some ieresig reds. For he purpose of he empirical aalysis, five Europea couries, amely: Croaia, Greece, Ialy, Porugal ad Spai were seleced, eve hough, subsaial differeces exis amog hem, i he aalyzed period; hey all recorded subsaially high uemployme raes. The aim of his paper was o selec he mos accurae forecasig mehod for predicig he fuure values of he uemployme rae ad several forecasig echiques adequae for forecasig ime series wih red compoe, were explored. The resuls of he empirical aalysis showed ha he opimal model for forecasig uemployme rae i Greece was Hol-Wiers` addiive mehod. I he case of Spai, accordig o MAPE, he opimal model is double expoeial smoohig model. Furhermore, for Croaia ad Ialy he bes forecasig model for uemployme rae is Hol-Wiers` muliplicaive model. Fially, he bes model o forecas uemployme rae i Porugal is Double expoeial smoohig model. Furhermore, whe we explored he acual daa published by Eurosa for he uemployme rae for firs quarer of 2014 ad he forecased daa, we came o differe coclusios. Accordigly, we cocluded ha i all aalyzed couries, bu Ialy, Model 1, or double expoeial smoohig mehod, show o be he mos accurae, whereas, i he case of Ialy, Model 3 or Hol-Wiers` addiive mehod, gave he mos accurae forecass. This paper coribues o he exisig lieraure by givig isighs o he mos appropriae forecasig mehods amog smoohig mehods for predicig uemployme rae. The fidigs are i lie wih Europea Commissio uemployme rae esimaes. REFERENCES [1] B. L. Bowerma, ad R. T. O'Coell, Forecasig ad Time Series. 3rd ed., Belmo, CA: Duxbury Press, [2] C. C. Hol, Forecasig seasoal ad reds by expoeially weighed movig averages. Office of Naval Research, Research Memoradum o. 52, [3] D. C. Mogomery, C. L. Jeigs, ad M. Kulahci, Iroducio o Time Series Aalysis ad Forecasig. New Jersey: Joh Wiley & Sos, [4] D. Gouopoulos, D. Pemezas, ad D. Saamaria, Forecasig Touris Arrivals i Greece ad he Impac of Macroecoomic Shocks from he Couries of Touriss Origi, Aals of Tourism Research, vol. 39, o. 2, pp , [5] E. Öder, F. Bayır, ad A. Hepse, Forecasig Macroecoomic Variables Usig Arificial Neural Nework ad Tradiioal Smoohig Techiques, Joural of Applied Fiace ad Bakig, vol. 3, o. 4, pp , [6] Europea Commisio, (2014), Europea Ecoomic Forecas: Sprig 2014, available a: hp://ec.europa.eu/ecoomy_fiace/publicaios/ europea_ecoomy/2014/pdf/ee3_e.pdf (15 Ocober 2014). [7] J. Dover, ad J. Weisser, Accuracy, ubiasedess ad efficiecy of professioal macroecoomic forecass: A empirical compariso for he G7, Ieraioal Joural of Forecasig, vol. 27, o. 2, pp , [8] M. Simioescu, The Performace of Uemployme Rae Predicios i Romaia: Sraegies o Improve he Forecass Accuracy, Review of Ecoomics Perspecives, vol. 13, o. 4, pp , [9] S. M. Brau, Forecass for Iflaio ad Uemployme Rae Based o Models Usig Resample Techiques, Ieraioal Joural of Ecoomic Pracices ad Theories, vol. 3, o. 2, pp , [10] S. M. Brau, Predicig Macroecoomic Idicaors i he Czech Republic Usig Ecoomeric Models ad Expoeial Smoohig Techiques, Souh Eas Europea Joural of Ecoomics ad Busiess, vol. 7, o. 2, pp , 2012a. [11] S. M. Brau, The Accuracy ad Bias Evaluaio of he Uemployme Rae Forecass: Mehods o Improve he Forecass Accuracy, Aals of he Uiversiy of Perosai Ecoomics, vol. 12, o. 4, pp , 2012b. [12] S. Makridakis, S. C. Wheelwrigh, ad R. J. Hydma, Forecasig, Mehods ad Applicaios. 3rd ed., New York: Wiley, [13] V. Voieagu, S. Pisica, ad N. Caragea, Forecasig Mohly Uemployme by Ecoomeric Smoohig Techiques, Joural of Ieraioal Scholarly ad Scieific Research & Iovaio 9(4) scholar.wase.org/ /

6 Ieraioal Joural of Social, Behavioral, Educaioal, Ecoomic, Busiess ad Idusrial Egieerig Vol:9, No:4, 2015 Ecoomic Compuaio ad Ecoomic Cybereics Sudies ad Research, vol. 46, o. 3, pp , [14] W. L. Wiso, S. C. Albrigh, ad M. Broadie, Pracical Maageme Sciece. 2d ed., Duxbury, Pacific Grove: Thomso Learig Ieraioal Sciece Idex, Ecoomics ad Maageme Egieerig Vol:9, No:4, 2015 wase.org/publicaio/ Ieraioal Scholarly ad Scieific Research & Iovaio 9(4) scholar.wase.org/ /