Forecasting Macroeconomic Variables using Artificial Neural Network and Traditional Smoothing Techniques

Transcription

1 Journal of Applied Finance & Banking, vol. 3, no. 4, 2013, ISSN: (prin version), (online) Scienpress Ld, 2013 Forecasing Macroeconomic Variables using Arificial Neural Nework and Tradiional Smoohing Techniques Emrah Önder 1, Fɪra Bayɪr 2 and Ali Hepșen 3 Absrac For many years, economiss have been using saisical ools o esimae parameers of macroeconomic models. Forecasing plays a major role in macroeconomic planning and i is an essenial analyical ool in counries economic sraegies. In recen years, researchers are developing new echniques for esimaion. Mos of hese alernaive approaches have heir origins in he compuaional inelligence. They have he abiliy o approximae nonlinear funcions, parameers are updaed adapively. In paricular, his research focuses on he applicaion of neural neworks in modeling and esimaion of macroeconomic parameers. Neural neworks have received an increasing amoun of aenion among macroeconomic forecasers because of he abiliy o approximae any linear and nonlinear relaionship wih a reasonable degree of accuracy. Turkey is one of he European Union candidae counries such as Iceland, Monenegro, Serbia and The Former Yugoslav Republic of Macedonia. In his sudy eigh macroeconomic indicaors including gross domesic produc (volume, NGDPD), gross naional savings (NGSD_NGDP), inflaion (average consumer prices, PCPI), populaion (LP), oal invesmen (NID_NGDP), unemploymen rae (LUR), volume of expors of goods and services (TX_RPCH), volume of impors of goods and services (TM_RPCH) were used for forecasing. As analysis ools, classical ime series forecasing mehods such as moving averages, exponenial smoohing, Brown's single parameer linear exponenial smoohing, Brown s second-order exponenial smoohing, Hol's wo parameer linear exponenial smoohing and decomposiion mehods applied o macroeconomic daa. The sudy focuses mainly on he applicabiliy of arificial neural nework model for forecasing macroeconomic parameers in long erm and comparing he arificial neural nework s resuls wih he Tradiional Time Series Analysis (Smoohing & Decomposiion Techniques). To faciliae he presenaion, an empirical example is developed o forecas Turkey s eigh imporan macroeconomic parameers. Time Series saisical heory and mehods are used o selec an adequae echnique, based on residual 1Dr., Isanbul Universiy, School of Business, Deparmen of Quaniaive Mehods, Isanbul. 2 Dr., Isanbul Universiy, School of Business, Deparmen of Quaniaive Mehods, Isanbul. 3 Assoc.Prof.Dr., Isanbul Universiy, School of Business, Deparmen of Finance, Isanbul. Aricle Info: Received : May 2, Revised : May 31, Published online : July 1, 2013

2 74 Emrah Önder, Fɪra Bayɪr and Ali Hepșen analysis. Turkey will celebrae he 100h anniversary of is foundaion in Policies and implemenaions argeed for raising economic posiion. JEL classificaion numbers: C53, E00, E27, E29 Keywords: Macro Economic Parameers, Economic Growh, Arificial Neural Nework, Forecasing, Smoohing, Decomposiion, Time Series, Turkey. 1 Inroducion When a counry raises her well-being and economic condiions, his increases living sandards and social equiy in parallel. Also when srucural problems of he economy are overcome and significan improvemens are achieved in economic indicaors such as GDP curren prices, inflaion and employmen han susainable developmens can be obained. Turkey was in a deep economic crisis in Souheas Asia Crisis and 1998 Russia Crisis adversely affeced he Turkish economy, and wih he earhquakes in 1999 in Marmara region, which has an imporan share in Turkey s producion, he economy narrowed down drasically in s was a period when Turkey s economy grew less han he poenial because of he unsable growh performance, which was recorded as 3.7 percen on average annually. Turkish economy experienced a deep economic crisis a he beginning of 2000s as a resul of he srucural problems in he economy and he weaknesses in he financial secor. GDP growh rae was realized as 6.8 percen during periods. Afer he serious global financial crisis in 2009, srong growh rend has mainained again wih sound macroeconomic policies and srucural reforms and Turkish economy has been one of he fases growing economies in he world in 2010 and 2011 wih 9.2 percen and 8.5 percen growh raes, respecively. In periods, annual average increase in employmen was realized as 0.5 percen and he unemploymen rae became 10.6 percen a he end of he period. Wih he rapid growh and increase in employmen in he following period, unemploymen rae decreased o 11.9 percen in 2010 and 9.8 percen in Turkey laid he foundaions of long erm susainable developmen, especially wih he srucural ransformaion programs in he economy applied in las decades, and se up resilien condiions for he fuure generaions [1]. The main purpose of Turkish Expors Sraegy for 2023 is o reach 500 billion dollars of expors volume in 2023, he cenenary anniversary of he Turkish Republic, wih an average of 12% increase in expors annually. Becoming one of he world s 10 larges economies in 2023 and aking 1,5% share from he world s rade are also being argeed. Furhermore, i is planned o reach 80% expors/impors raio in Turkey s Expor Sraegy for 2023 aims modern and flexible expor srucure ha is based on advanced echnology and R&D (research and developmen) o respond he demands of oday s and fuure s business environmen by modernizing he srucure of our expors [2]. Turkey is one of he fases growing markes in he world wih economic growh raes, expanding by 8.5 percen in Several imporan economic arges have been menioned in Turkish governmen s 2023 economic vision repor. These are: aking place among he op 10 economies in he world by he year 2023, reaching a gross domesic produc of $1 rillion by 2014, achieving a gross domesic produc of $2 rillion by 2023, increasing annual Turkish expors o $500 billion, achieving per capia income of 25

3 Forecasing Macroeconomic Variables using Arificial Neural Nework 75 housand dollars and a foreign rade volume of 1 rillion dollars, increasing employmen rae and reducing unemploymen rae in Turkey o 5 percen. Forecasing echniques are imporan ools in operaional managemen for creaing realisic expecaions. In lieraure many differen echniques in he area of saisics and arificial inelligence were proposed for achieving close esimaions. [3] used radiional ime series analysis and Box Jenkins models and arificial neural nework forecasing mehod o forecas inernaional ourism arrivals o Turkey for based on daa period They found ha Winer s seasonal exponenial smoohing echnique and arificial neural neworks are wo successful esimaor mehods for regarding monhly ime series daa. [4] sudy was abou esimaing, evaluaing, and selecing among non-linear forecasing models for economic and financial ime series. They suggesed ha careful applicaion of exising echniques, and new models and ess, can resul in significan advances in undersanding. The objecive of [5] s sudy (1996) was o provide a pracical inroducory guide in he design of a neural nework for forecasing economic ime series daa. [6] conduced ime series comparisons beween he wo ypes of models on he basis of forecas performance and invesmen reurn. [7] proposed he use of recurren neural nework in order o forecas foreign exchange raes. He compared hree recurren archiecures in erms of predicion accuracy of fuure forecas for Deusche mark currency. [8] applied arificial neural nework (ANN) for forecasing governmen size in Iran. They made comparisons various archiecures, ransfer funcions and learning algorihms on he operaion of nework. Variables including ax income, oil revenue, populaion, openness, governmen expendiure, GDP and GDP per capia were used from (annually). Their bes archiecure was a nework wih wo hidden layer and welve neuron in hidden layers wih hyperbolic angen ransfer funcion. The sudy of [9] was abou demonsraed srucural change srucural change in macroeconomic ime series. They addressed he issue of how ime irreversible srucures may be generaed wihin he smooh ransiion processes. They also discussed he link beween ime irreversibiliy and loss of uniqueness in he specral represenaion of a daa generaion process. [10] compared he performance of arificial neural neworks (ANNs) wih exponenial smoohing and ARIMA models in forecasing rice expors from Thailand. Their resuls showed ha while he Hol Winers and he Box Jenkins models showed saisfacory goodness of fi, he models did no perform as well in predicing unseen daa during validaion. They also concluded ha he ANNs performed relaively well as hey were able o rack he dynamic non-linear rend and seasonaliy, and he ineracions beween hem. One of he major drawbacks of ANN is heir being black boxes, since i is impossible o solve he relaions in heir hidden layers of ANN. 2 Macroeconomic Indicaors Economiss have been using saisical ools o esimae parameers of macroeconomic models. Forecasing plays a major role in macroeconomic planning and i is an essenial analyical ool in counries economic sraegies. In his conen, he primary purpose of his research is o focus on he applicaion of neural neworks in modeling and developing o forecas Turkey s imporan macroeconomic parameers. Annual ime series daa are used for he period 1980 o The sample period is dependen on annual daa availabiliy. The daa was gahered from he Inernaional Moneary Fund world economic

4 76 Emrah Önder, Fɪra Bayɪr and Ali Hepșen oulook daa base. Our model forecass eigh variables: gross domesic produc (GDP), gross naional savings, inflaion (average consumer prices), populaion, oal invesmen, unemploymen rae, volume of expors of goods and services, volume of impors of goods and services. Gross Domesic Produc represens he economic healh of a counry. I presens a sum of a counry's producion which consiss of all purchases of goods and services produced by a counry and services used by individuals, firms, foreigners and he governing bodies. GDP consiss of consumer spending, invesmen expendiure, governmen spending and ne expors hence i porrays an all inclusive picure of an economy because of which i provides an insigh o invesors which highlighs he rend of he economy by comparing GDP levels as an index. GDP is no only used as an indicaor for mos governmens and economic decision-makers for planning and policy formulaion; bu also i helps he invesors o manage heir porfolios by providing hem wih guidance abou he sae of he economy. On he oher hand, i is good measure for an economy and wih improvemen in research and qualiy of daa, saisicians and governmens are rying o find ou measures o srenghen GDP and make i a comprehensive indicaor of naional income. Inernaional sandards regarding he compilaion of balance of paymens saisics are described in he fifh ediion of he Balance of Paymens Manual prepared by he Inernaional Moneary Fund (IMF) in order o provide guidance o member counries. In a general sense, he balance of paymens is a saisical saemen ha sysemaically records all he economic ransacions beween residens of a counry (Cenral Governmen, moneary auhoriy, banks, oher secor) and nonresidens for a specific ime period. The balance of paymens saisics are classified under wo major groups: Curren Accoun and Capial and Financial Accoun. In summary, he curren accoun covers all ransacions ha involve real sources (including volume of expors and impors of goods and services,) and curren ransfers; he capial and financial accouns show how hese ransacions are financed (by means of capial ransfer or invesmen in financial insrumens). As menioned in he European Economic series [11], curren accoun deficis and surpluses are no necessarily macroeconomic imbalances in he sense of developmens which are adversely affecing, or have he poenial o affec he proper funcioning of economies, of he moneary union, or on a wider scale. Deficis and surpluses are a naural consequence of economic ineracions beween counries. They show o which exen a counry relies on borrowing from he res of he world or how much of is resources i lends abroad. In his way, exernal borrowing and lending allows counries o rade consumpion over ime: a counry wih a curren accoun surplus ransfers consumpion from oday o omorrow by invesing abroad. In urn, a counry wih a curren accoun defici can increase is consumpion or invesmen oday bu mus ransfer fuure income abroad o redeem is exernal deb. Deficis and surpluses can hus simply be he resul of an appropriae allocaion of savings, aking ino accoun differen invesmen opporuniies across counries. Differences in economic prospecs lead o differences in saving behavior, wih brigher expecaions reducing he endency of economic agens o save and hence conribuing o he accumulaion of deficis. In paricular, counries wih a rapidly ageing populaion may find i opporune o save oday o smooh consumpion over ime. On he oher hand, curren accoun deficis and surpluses are par of he adjusmen process in a moneary union. They absorb asymmeric shocks in he absence of independen moneary policy and nominal exchange rae adjusmen.

5 Forecasing Macroeconomic Variables using Arificial Neural Nework 77 This paper also aemps o analyze he difference beween rends of GDP and inflaion. I is widely believed ha here is a relaionship beween he wo. The problem is ha here are disagreemens as o wha ha relaionship is or how i operaes. As a resul, when governmens make decisions based on hese pieces of informaion, he oucome ofen canno be guaraneed. Exploraion of he relaionship beween GDP and inflaion is bes begun by developing an undersanding of each erm individually. As menioned above, GDP is an acronym for gross domesic produc, which is he value of a naion's goods and services during a specified period. This figure is generally regarded as an imporan indicaor of an economy's healh. Inflaion refers he rae a which he general level of prices for goods and services is rising, and, subsequenly, purchasing power is falling. In deermining he economic posiion of a counry is hrough a comparison of populaion, naional savings and oal invesmens o he gross domesic produc of he counry. Finally, here is a negaive relaionship beween changes in he raes of GDP growh and unemploymen. This long-run relaionship beween he wo economic variables was mos famously poined ou in he early 1960s by economis Arhur Okun (known as Okun s Law). According o he principles esablished by his law, here is a corresponding wo percen increase in employmen (decrease in unemploymen) for every esablished one percen increase in GDP. The reasoning behind his law is quie simple. I saes ha GDP levels are driven by he principles of demand and supply, and as such, an increase in demand leads o an increase in GDP. Such an increase in demand mus be accompanied by a corresponding increase in produciviy and employmen o keep up wih he demand. 3 Tradiional Time Series Techniques In his sudy wo differen radiional ime series mehods including decomposiion mehods and smoohing mehods were applied o he macro economic daa for forecasing. The mehods and regarding formulas are shown in his secion. The noaion of [12] is used o explain he ime series mehods. 3.1 Decomposiion Mehods Decomposiion mehods are using for deermining secular rend, seasonal variaion, conjuncure (cyclical variaion) and random flucuaion (irregular variaion) componens in ime series. I his sudy annual daa was used. Therefore 3 imporan rend funcion including linear, quadraic and growh were menioned in his par of his sudy Leas squares mehod for deermining rend Leas square mehod is one of he popular mehods for deermining rend. X is he ime variable (year, monh, ec.) in y f ( x) funcion. If he sum of he ime series variable (X) is idenified as zero he esimaion values of model parameers can be shown as he following formulas. The rend of y can be deermined by leas squares mehod. I is no very easy o decide which funcion we should use as a rend. By rying several funcions and finding minimum sum of squares of residuals, he suiable rend funcions can be found.

6 78 Emrah Önder, Fɪra Bayɪr and Ali Hepșen n n 2 e 2 y y min (1) Linear rend funcion The linear rend funcion is shown as below: y a bx e (2) When he leas squares mehod is applied he linear rend funcion, he equaions below are obained. n n n e y y y a bx (3) For deermining he minimum of his funcion he firs level derivaives should be done regarding o a and b parameers. y na b x (4) 2 xy a x b x (5) By solving hese equaions he parameers a and be can be found as follows: y a (6) n b xy x 2 (7) Quadraic rend funcion If he observed daa has a curved figure (in quadraic rend funcion he mean of he daa is increasing firs han sar decreasing or reverse) han quadraic rend funcion can be used. 2 y a bx cx e n n n e 2 y y y a bx cx 0 (8) Firs order derivaives of he equaion according o a, b and c parameers should be solved for wriing he quadraic rend funcion wih using leas squares mehod. The equaions below are he normal equaions. Three unknown can be found by solving hese hree equaions. y na b x c x 2 (9) 2 3 xy a x b x c x (10) x y a x b x c x (11)

7 Forecasing Macroeconomic Variables using Arificial Neural Nework 79 b xy x 2 (12) Growh rend funcion If he change of he y variable is nearly consan in ime, growh rend funcion can be used for his kind of daa. The growh rend funcion is shown below. x y ab e (13) n n n e log y log y log y log a xlog b 0 (14) log y nlog a log b x (15) 2 xlog y log a x log b x (16) log y log a (17) n xlog y log b (18) x 2 log y log a xlog b (19) 3.2 Smoohing Mehods Random or/and coincidenal flucuaions in weekly, monhly, seasonal or annual ime series daa can be removed or sofened by smoohing mehods. Six smoohing mehods including single moving averages, Brown s simple exponenial smoohing mehod, linear moving averages, Brown s linear exponenial smoohing mehods wih single parameer, Hol s linear exponenial smoohing wih wo parameers and Brown s quadraic exponenial smoohing mehods are menioned in his par of he sudy [12] Single moving averages Esimaion can be done by using arihmeic mean of number of cerain (k) prior period of daa. Single moving average mehod gives he same imporance level o he pas daa for esimaing fuure values. ( y y 1 y k 1) y 1 (20) k 1 y 1 yi k i k 1 (21) y y k y 1 y k k (22)

8 80 Emrah Önder, Fɪra Bayɪr and Ali Hepșen Brown s simple exponenial smoohing mehod I is a suiable mehod for ime series ha y1, y2,, yn has no significan rend or seasonal flucuaions. y is he esimaion value for he ime. y 1is he observaion daa for he ime -1. is a smoohing consan. The consan has he value beween 0 and 1. y y 1 (1 ) y 1 (23) y y 1 ( y 1 y 1) (24) y y 1 e (25) Linear moving averages When moving averages mehod is applied he daa which has a significan rend, esimaions are always remains lower han acual values. To deal wih his siuaion Linear Moving Averages mehod was developed. The main idea of his mehod is he calculaion of second moving average. y y 1 y 2 y k 1 y (26) k y y 1 y 2 y k 1 y (27) k a y ( y y ) 2y y (28) 2 b ( y y ) k 1 (29) yˆ m a b m (30) The coefficien m is he forecas period o be esimaed Brown s linear exponenial smoohing mehod wih single parameer Brown s Linear Mehod wih single parameer has some similariies wih linear moving averages mehod. Bu he difference beween firs and second smoohing values is added ino he firs smoohing value. y y 1 y 1 (31) y y 1 y 1 (32) a y y y y y (33) 2 b y y 1 (34) yˆ m a b m (35) Hol s linear exponenial smoohing mehod wih wo parameers I seems similar o previous mehod (Brown s Linear Mehod wih Single Parameer). Bu in Hol s Linear Mehod second

9 Forecasing Macroeconomic Variables using Arificial Neural Nework 81 smoohing is no used. Trend values are smoohed direcly. This adds flexibiliy ino he mehod. The parameers and have he values beween 0 and y y y b (36) b y y 1 b 1 (37) y y b m (38) ˆ m The parameers and are he smoohing consans. These parameers should be opimized for minimizing he sum of error squares Brown s quadraic exponenial smoohing mehod When he ime series are curved shape (quadraic, hird order or more) Brown s quadraic exponenial smoohing echnique is suiable for esimaion. Third parameer is added o he model. The equaions for quadraic exponenial smoohing are below: y y 1 y 1 (39) y y 1 y 1 (40) 1 1 y y y (41) a 3y 3y y (42) b y 10 8 y 4 3 y 21 2 c y y y Esimaion equaion can be shown as below: 1 2 yˆ m a b m cm (45) 2 The selecion of he α coefficien can be done as he selecion in previous mehods. (43) (44) 4 Arificial Neural Neworks for Forecasing Arificial Neural Neworks (ANN) provides a robus approach o approximaing and forecasing real, valued and vecor-value funcions. Under some condiions and for cerain ypes of problems, ANN provides beer soluions hen radiional saisical mehods. The sudy of ANNs has been inspired in par by he observaion ha biological learning sysems are buil of very complex webs of inerconneced neurons. In rough analogy, ANNs are buil ou of a densely inerconneced se of sample unis, where each uni akes a number of real-valued inpus (possibly he oupus of oher unis) and produces a single real-valued oupu, which may become inpu o oher unis [13]. The srucure of an arificial nework of mos commonly used ype is he mulilayer perceprons. I consiss of several layers of processing unis (also ermed neurons or

10 82 Emrah Önder, Fɪra Bayɪr and Ali Hepșen nodes). The inpu values (inpu daa) are fed o he neurons in he so-called inpu layer. The inpu values are processed wihin he individual neurons of he inpu layer and hen he oupu values of hese neurons are forwarded o he neurons in he hidden layers. The oupu of he sysem, ha has arge values, is lie on he oupu layer. The inpu variables are represen o he independen variables and he oupu variables are represen o he dependen variables. Each connecion (beween neurons) has an associaed parameer indicaing he srengh of his connecion, he so-called weigh. By changing he weighs in a specific manner, he nework can learn o map paerns presened a he inpu layer o arge values on he oupu layer. This descripion of he procedure, by means of which his weigh adapaion is performed, is called learning or raining algorihm [14]. There are several learning algorihms in ANN lieraures, i.e. Quick Propagaion, Conjugae Gradien Descen, Quasi-Newon, Levenberg-Marquard and Back Propagaion. In learning phase, for each daa row, he inpu values are processed in he inpu layer hen all he informaion are sen o each of he neurons on he hidden layers, hrough connecions. Bu in his ransmission, daa are muliplied by weighs of he corresponding connecions. Neurons on he hidden layer collec all he informaion from inpu layer and by using acivaion funcion, neuron produce new daa and send i o he nex layer, over he connecions by muliplying weighs. The commonly used acivaion funcions are logisic, linear, hyperbolic angen, sigmoid. In each ieraion, o mach he oupu of he sysem and oupu daa, weighs of he connecions are all adjused in accordance wih he error-correcion rule. This operaion is called learning or raining of he nework. Usually, he daa available for raining he nework is divided in wo non-overlapping pars: he so-called raining and esing ses. The commonly large raining se is used o each he nework o desire arge funcion. Then he nework is applied o daa in he es se in order o available is generalizaion abiliy, i.e. he abiliy o derive correc conclusions abou he populaion properies of he daa from he sample properies of he raining se. Someimes he validaion se can be used o validae he nework afer he raining phase bu before he es phase. As in mos oher neural neworks applicaions, daa processing -scaling and ransformingis imporan for a good predicion performance of financial ime series. The inpu and oupu variables mus be scaled beween he upper and lower bonds of he ransfer funcions (usually beween zero and one minus one and one). Two of he mos common daa ransformaions in boh radiional and neural nework forecasing are firs differencing and aking logarihm of a variable.

11 Forecasing Macroeconomic Variables using Arificial Neural Nework 83 5 Forecasing Resuls 5.1 Resuls of Smoohing Mehods Forecasing resuls of indicaor 1 (Gross Domesic Produc, Curren Prices) Table 1: Selecion of Mehod for Forecasing Gross Domesic Produc, Curren Prices Coefficiens Average(e 2 ) Selecion 1) Linear Trend Funcion Decomposiion Mehods (Trend Funcions) 2. Exponenial Smoohing Mehods 2) Quadraic Trend Funcion ) Growh Trend Funcion ) Single Moving Averages 5) Brown s Simple Mehod 6) Linear Moving Averages 7) Brown s Linear Mehod 8) Hol s Linear Mehod 9) Brown s Quadraic Technique 5996 α = α = α = Υ= Seleced α = Figure 1: Esimaion of Gross Domesic Produc, Curren Prices Daa Using Hol s Linear Mehod

12 84 Emrah Önder, Fɪra Bayɪr and Ali Hepșen Forecasing resuls of indicaor 2 (Toal Invesmen) Table 2: Selecion of Mehod for Forecasing Toal Invesmen Coefficiens Average(e 2 ) Selecion 1) Linear Trend Decomposiion Funcion 2) Quadraic Trend Mehods 6.03 Seleced Funcion (Trend Funcions) 3) Growh Trend 6.07 Funcion 4) Single Moving 6.84 Averages 5) Brown s Simple α = Mehod 6) Linear Moving Averages 2. Exponenial Smoohing 7) Brown s Linear Mehods α = Mehod 8) Hol s Linear α = Υ= Mehod 9) Brown s Quadraic α = Technique 2 Trend Funcion of Toal Invesmen : y x x e Figure 2: Esimaion of Toal Invesmen Daa Using Decomposiion (Quadraic Trend) Mehod

13 Forecasing Macroeconomic Variables using Arificial Neural Nework Forecasing resuls of indicaor 3 (Gross Naional Savings) Table 3: Selecion of Mehod for Forecasing Gross Naional Savings Coefficiens Average(e 2 ) Selecion 1) Linear Trend Decomposiion Funcion Mehods 2) Quadraic Trend 3.91 (Trend Funcion Funcions) 3) Growh Trend 6.45 Funcion 4) Single Moving 5.41 Averages 5) Brown s Simple 3.48 Mehod α = Exponenial 6) Linear Moving Smoohing 7.28 Averages Exponenial α = Υ= Seleced 5.52 Mehods Smoohing 9) Brown s Quadraic Mehod 7) Brown s Linear α = Mehod 8) Hol s Linear Technique α = Figure 3: Esimaion of Gross Naional Savings Daa Using Hol s Linear Exponenial Smoohing Mehod

14 86 Emrah Önder, Fɪra Bayɪr and Ali Hepșen Forecasing resuls of indicaor 4 (Inflaion, Average Consumer Prices) Table 4: Selecion of Mehod for Forecasing Inflaion, Average Consumer Prices Coefficiens Average(e 2 ) Selecion 1. Decomposiion Mehods (Trend Funcions) 1) Linear Trend Funcion ) Quadraic Trend Funcion 3) Growh Trend Funcion ) Single Moving Averages Exponenial Smoohing Mehods 5) Brown s Simple Mehod α = ) Linear Moving Averages 7) Brown s Linear α = Mehod 8) Hol s Linear α = Υ= Mehod 9) Brown s Quadraic α = Technique Seleced Figure 4: Esimaion of Inflaion, Average Consumer Prices Daa Using Brown s Linear Mehod

15 Forecasing Macroeconomic Variables using Arificial Neural Nework Forecasing resuls of indicaor 5 (Volume of Impors of Goods and Services) Table 5: Selecion of Mehod for Forecasing Volume of Impors of Goods and Services Coefficiens Average(e 2 ) Selecion 1. Decomposiion Mehods (Trend Funcions) 2. Exponenial Smoohing Mehods 1) Linear Trend Funcion ) Quadraic Trend Funcion Seleced 3) Growh Trend Funcion - 4) Single Moving Averages ) Brown s Simple Exponenial Smoohing Mehod α ) Linear Moving Averages ) Brown s Linear Exponenial Smoohing Mehod α ) Hol s Linear Exponenial Smoohing Mehod α Υ , ) Brown s Quadraic Exponenial α Smoohing Technique Trend Funcion of Volume of Impors of Goods and Services y x x e Figure 5: Esimaion of Volume of Impors of Goods and Services Daa Using Decomposiion (Quadraic Trend) Mehod

16 88 Emrah Önder, Fɪra Bayɪr and Ali Hepșen Forecasing resuls of indicaor 6 (Volume of Expors of Goods and Services) Table 6: Selecion of Mehod for Forecasing Volume of Expors of Goods and Services Coefficiens Average(e 2 ) Selecion 1) Linear Trend Decomposiion Funcion Mehods 2) Quadraic Trend 216 (Trend Funcion Funcions) 3) Growh Trend - Funcion 4) Single Moving Averages 249 5) Brown s Simple α = Mehod Averages 6) Linear Moving Exponenial Smoohing Mehods 7) Brown s Linear Exponenial Smoohing Mehod α = ) Hol s Linear Mehod α = Υ= ) Brown s Quadraic Technique α = Seleced Figure 6: Esimaion of Volume of expors of goods and services daa using Brown s Linear Mehod

17 Forecasing Macroeconomic Variables using Arificial Neural Nework Forecasing resuls of indicaor 7 (Unemploymen Rae) 1. Decomposiion Mehods (Trend Funcions) Table 7: Selecion of Mehod for Forecasing Unemploymen Rae Coefficiens Average(e 2 ) Selecion 1) Linear Trend Funcion ) Quadraic Trend Funcion ) Growh Trend Funcion ) Single Moving Averages ) Brown s Simple Mehod α Exponenial Smoohing Mehods 6) Linear Moving Averages ) Brown s Linear Mehod α ) Hol s Linear Mehod α Υ ) Brown s Quadraic α Technique Seleced Figure 7: Esimaion of Unemploymen Rae Daa Using Hol s Linear Exponenial Smoohing Mehod

18 90 Emrah Önder, Fɪra Bayɪr and Ali Hepșen Forecasing resuls of indicaor 8 (Populaion) 1. Decomposiion Mehods (Trend Funcions) Table 8: Selecion of Mehod for Forecasing Populaion Coefficiens Average(e 2 ) Selecion 1) Linear Trend Funcion ) Quadraic Trend Funcion 3) Growh Trend Funcion Exponenial Smoohing Mehods 4) Single Moving Averages 5) Brown s Simple Mehod α = ) Linear Moving Averages 7) Brown s Linear Mehod α = ) Hol s Linear Mehod α = Υ= ) Brown s Quadraic Technique α = Seleced Figure 8: Esimaion of Populaion Daa Using Hol s Linear Mehod

19 Forecasing Macroeconomic Variables using Arificial Neural Nework 91 Table 9: Esimaed Values of Macro Economic Indicaors Hol's Quadraic Hol's Brown' s Quadrai c Brown's Hol' s Hol' s Year NGPD NID_NGP NGSD_NGD PCPI TM_RPC TX_RPC LUR LP s D P H H ,37 19, ,12 222,99 6,34 11,72 9,44 75, ,02 19, ,91 239,46 5,98 11,72 9,46 76, ,68 19, ,71 255,93 5,61 11,72 9,47 77, ,34 19, ,50 272,40 5,24 11,72 9,49 78, ,00 19, ,30 288,87 4,86 11,73 9,51 79, ,65 19, ,09 305,34 4,48 11,73 9,53 80, ,3 1045, , , , , ,89 321,81 4,09 11,73 9,54 81,67 19, ,68 338,28 3,70 11,74 9,56 82,63 19, ,48 354,75 3,30 11,74 9,58 83,60 19, ,27 371,22 2,90 11,74 9,60 84,57 19, ,07 387,69 2,49 11,74 9,62 85, Resuls of Arificial Neural Nework To perform an ANN analysis, we use Alyuda Nero-inelligence 2.2 (Build 577) sofware. The process of performing a neural nework successfully predicing a financial ime series has some seps, i.e. daa preparaion, designing, raining, esing and forecasing Daa preparaion In his paper, all he variables are linearly scaled ino he inerval [-1,1] by using corresponding scaling facor for each variable. Each variable are reaed as a ime series and lagged series used for predicion. We used 3 or 4 lagged series, i.e. for 3 lagged series; firs, second and hird period lags are used o predic he original variable. By his way, each lag of he series become an esimaor and represen as an inpu neuron in ANN. Common pracice is o divide he ime series ino hree disinc ses called he raining, esing and validaion ses. The raining se is he larges se and is used by neural nework o learn he paerns presen in daa. The esing se, ranging in size from 10% o 30% of he raining se, is used o evaluae he generalizaion abiliy of a supposedly rained nework. A final check on he validaion se chosen mus srike a balance beween obaining a sufficien sample size o evaluae a rained nework and having enough remaining observaions for boh raining and esing. The validaion se should consis of he mos recen coniguous observaions. In his work he approach in evaluaion neural neworks used as fallows; raining (68%), validaion (16%), es ses (16%) Design of neworks For mulilayer perceprons, here are an infinie number of ways o se up a nework. The number of inpu neurons is rivial bu he asks of selecion of he number of hidden layers, he number of he neurons in he hidden layers, he number of inpu neurons as well as he ransfer funcions are much more difficul. In his paper, some series have

20 92 Emrah Önder, Fɪra Bayɪr and Ali Hepșen hree inpu neurons (hree lagged series) some of hem have four. All series has one hidden layer wih differen number of neurons. The acivaion mehods and he ANN models are lised below. Table 10: Design of Neworks Model Acivaion Funcion NGPD (Gross domesic produc, curren prices) Linear NID_NGPD (Toal invesmen) Hyperbolic Tangen NGSD_NGDP (Gross naional savings) Linear PCPI (Inflaion, average consumer prices) Linear TM_RPCH (Volume of impors of goods and services) Hyperbolic Tangen TX_RPCH (Volume of expors of goods and services) Hyperbolic Tangen LUR (Unemploymen rae) Hyperbolic Tangen LP (Populaion) Logisic Training of neworks Training a neural nework o learn paerns in he daa involves ieraively presening i wih examples o he correc known answers. The objecive of raining is o find he se of weighs beween he neurons ha deermine he global minimum of he error funcion. In his paper, all he neworks are rained by using Levenberg-Marquard raining algorihm which uses Levenberg-Marquard Opimizaion mehod. The Levenberg-Marquard (LM) algorihm is an ieraive echnique ha locaes he minimum of a mulivariae funcion ha is expressed as he sum of squares of non-linear real-valued funcions. I has become a sandard echnique for non-linear leas-squares problems, widely adoped in a broad specrum of disciplines. LM can be hough of as a combinaion of seepes descen and he Gauss-Newon mehod. When he curren soluion is far from he correc one, he algorihm behaves like a seepes descen mehod: slow, bu guaraneed o converge. When he curren soluion is close o he correc soluion, i becomes a Gauss-Newon mehod. Nex, a shor descripion of he LM algorihm based on he maerial in is supplied [15]. The erminaion crieria were se o ieraion number of 500 and by error improvemen. In all he neworks raining phases, raining sop reasons were no error improvemen. Number of ieraions, ieraion speeds and error improvemens wih absolue error of he neworks for boh raining and validaion phases are shown below.

21 Forecasing Macroeconomic Variables using Arificial Neural Nework 93 Table 11: Residual and Ieraion Saisics Absolue Error Error Ieraion Speed Training Validaion Improvemen Ieraion (ie/sec) NGPD 147, ,567 1, NID_NGPD 2,401 1,432 6, NGSD_NGDP 3,542 3,250 1, PCPI 2,306 2, TM_RPCH 15,046 13,676 1, ,5 TX_RPCH 16,792 13,871 1, LUR 2,007 1,518 5, ,5 LP 0,044 0,540 1, Tes of neworks Mean absolue error of es daa, correlaion and R-Square as follows: Table 12: Tes Saisics Absolue Error Mean Sd. Dev. Correlaion R-Square NGPD 44,991 44,399 0,963 0,928 NID_NGPD 1,712 1,750 0,552 0,305 NGSD_NGDP 1,176 0,889 0,925 0,856 PCPI 2,790 2,509 0,999 0,997 TM_RPCH 10,491 7,504 0,643 0,413 TX_RPCH 7,653 5,389 0,723 0,522 LUR 0,656 0,567 0,873 0,762 LP 0,386 0,368 0,998 0,996 The finess graphics of arge and oupu of neworks are shown as follows: Figure 9: Finess of Acual Gross Domesic Produc, Curren Prices, NGPD vs. Oupu

22 94 Emrah Önder, Fɪra Bayɪr and Ali Hepșen Figure 10: Finess of Acual Toal Invesmen, NID_NGPD vs. Oupu Figure 11: Finess of Acual Gross Naional Savings, NGSD_NGDP vs. Oupu Figure 12: Finess of Acual Inflaion, Average Consumer Prices, PCPI vs. Oupu

23 Forecasing Macroeconomic Variables using Arificial Neural Nework 95 Figure 13: Finess of Acual Volume of Impors of Goods and Services, TM_RPCH vs. Oupu Figure 14: Finess of Acual Volume of Expors of Goods and Services, TX_RPCH vs. Oupu Figure 15: Finess of Acual Unemploymen Rae, LUR vs. Oupu

24 96 Emrah Önder, Fɪra Bayɪr and Ali Hepșen Forecasing Figure 16: Finess of Acual Populaion, LP vs. Oupu Afer he learning session, for all of he variables, series of esimaions from end of he year 2013 o 2023 were performed as follows: Table 13: Esimaion of Variables Yea NGP NID_NGP NGSD_NG PCP TM_RPC TX_RPC LU LP ,0 20,96 11,85 211, 28,772 34,389 10,4 76, ,0 21,72 11,36 220, 9-8,715 30,030 11,5 4 78, ,9 22,05 10,84 231, 2 5,117 5,279 12,4 4 79, , 17,55 10,37 245, 9 37,094 7,512 12,7 4 81, , 8 17,89 9,90 260, 4 2,687 0,299 13,0 5 84, , 0 15,27 9,43 276, 6-0,052-0,075 13,4 8 86, , 8 21,31 8,96 294, 9 37,077 27,879 13,5 0 88, , 1 22,14 8,49 312, 1-5,192 26,972 13,6 9 90, , 5 22,15 8,02 331, 1 2,636 17,349 13,6 4 93, , 1 17,79 7,55 350, 0 37,426 0,443 13,6 7 95, , ,04 7,08 371, 6 0 0,762 5,188 13, ,4 6 3 Figure 17: Esimaion of Gross Domesic Produc, Curren Prices, NGPD

25 Forecasing Macroeconomic Variables using Arificial Neural Nework 97 Figure 18: Esimaion of Toal Invesmen, NID_NGPD Figure 19: Esimaion of Gross Naional Savings, NGSD_NGDP Figure 20: Esimaion of Inflaion, Average Consumer Prices, PCPI

26 98 Emrah Önder, Fɪra Bayɪr and Ali Hepșen Figure 21: Esimaion of Volume of Impors of Goods and Services, TM_RPCH Figure 22: Esimaion of Volume of Expors of Goods and Services, TX_RPCH Figure 23: Esimaion of Unemploymen Rae, LUR

27 Forecasing Macroeconomic Variables using Arificial Neural Nework 99 Figure 24: Esimaion of Populaion, LP 5.3 Comparison of Tradiional Time Series Mehods and Arificial Neural Neworks Resuls Smoohing mehods have good shor-erm accuracy. Also heir simpliciy is one of he oher advanages. Large amoun of hisorical daa are no required. However in smoohing mehods choosing smoohing coefficien (α and/or γ) properly is very imporan. I affecs he qualiy of forecasing. Neural neworks are universal funcions approximaion and hey can model any coninuous and nonlinear funcion o and desired accuracy, and do no have any assumpion abou inpu or residual probabiliy disribuion as regression analyze. Theoreically, here can be an infinie number of ways o se up a nework. The asks of selecion of he number of hidden layers, he number of he neurons in he hidden layers, he number of inpu neurons as well as he ransfer funcions are effec he oucome of neworks. Parameers are influenial on performance of nework. Choosing parameers of ANN is depends on some crieria, i.e. number of inpu and arge variables, complexiy and srucure of daa, heoreical knowledge and facs abou sudy area and previous experiences on ANN. Number of cases and iniial values of weighs are oher imporan crieria ha effec he performance of neworks. In his paper, he numbers of cases are less o se up an accurae nework. Every combinaion of parameers gave disinc ype of approximaions. Hence, choosing he righ nework was so confusing and needed some heoreical knowledge on macro economy. In forecasing phase, here were slighly differences beween classic ime series analysis and neural neworks. These differences shown on he graphics below:

28 100 Emrah Önder, Fɪra Bayɪr and Ali Hepșen Figure 25: Comparison of Gross Domesic Produc (Volume, NGDPD) Esimaions Figure 26: Comparison of Toal Invesmen (NID_NGDP) Esimaions Figure 27: Comparison of Gross Naional Savings (NGSD_NGDP) Esimaions

29 Forecasing Macroeconomic Variables using Arificial Neural Nework 101 Figure 28: Comparison of Inflaion (Average Consumer Prices, PCPI) Esimaions Figure 29: Comparison of Volume of Expors of Goods and Services (TX_RPCH) Esimaions Figure 30: Comparison of Volume of Impors of Goods and Services (TM_RPCH) Esimaions

30 102 Emrah Önder, Fɪra Bayɪr and Ali Hepșen Figure 31: Comparison of Unemploymen Rae (LUR) Esimaions Figure 32: Comparison of Populaion (LP) Esimaions 6 Conclusion and Suggesions Global economic power is shifing and Turkey has he poenial o be one of he bigges beneficiaries of his change. The counry has he opporuniy o capialize on a growing skilled labor force and favorable climae, as well as geographical locaion a he crossroads of a number of wealhy regions, all of which could be used o susain longerm economic growh and developmen. On he oher hand, he Turkish economy has shown remarkable performance wih is seady growh over las years. A sound macroeconomic sraegy in combinaion wih pruden fiscal policies and major srucural reforms in effec has inegraed he Turkish economy ino he globalized world, while ransforming he counry ino one of he major recipiens of foreign direc invesmen in is region. The srucural reforms, hasened by Turkey s European Union accession process, have paved he way for comprehensive changes in a number of areas. The main objecives of hese effors were o increase he role of he privae secor in he Turkish

31 Forecasing Macroeconomic Variables using Arificial Neural Nework 103 economy, o enhance he efficiency and resiliency of he financial secor, and o place he social securiy sysem on a more solid foundaion. To undersand he fuure poenial of he Turkish economy, he auhors have used wo differen ypes of long-run economic growh model o forecas Turkish GDP in 2023, he cenenary anniversary of he Turkish Republic. By using Hol s analysis, i is forecased ha Turkish GDP level is more han 1.14 rillion dollars and Turkey s GDP per capia (esimaed value of populaion in 2023 is 85,530,000) is expeced o more han US$13,300. Whereas by using Arificial Neural Nework (ANN) analysis, GDP is esimaed 2.30 rillion dollars and GDP per capia (forecased value of populaion in 2023 is 98,430,000) is expeced o more han US$23,400 in Our resuls displays ha Turkey reaches 500 billion dollars of expors volume in 2023, wih an average of 11.7% increase in expors annually; on he oher hand volume of impors of goods and services are esimaed o increase wih an average of 4.5% annually. Furhermore, i is planned o reach 80% expors/impors raio in Gross naional savings as a percen of GDP expressed as a raio of gross naional savings and GDP. Gross naional saving is gross disposable income less final consumpion expendiure afer aking accoun of an adjusmen for pension funds. In addiion o his, oal invesmens as a percen of GDP expressed as a raio of oal invesmen and GDP. Invesmen or gross capial formaion is measured by he oal value of he gross fixed capial formaion and changes in invenories and acquisiions less disposals of valuables for a uni or secor. The auhors of his paper esimae he gross naional savings and oal invesmen as a percen of GDP 10.07% and 19.2% respecively in Finally his paper forecass ha annual inflaion rae will be around 5.7%; annual unemploymen rae will be around 9.6% (by using Hol s analysis) and will be around 13.7% (by using ANN analysis) in he cenenary anniversary of he Turkish Republic. The findings of his paper would help Turkish governmen and invesors for creaing more effecive macroeconomic sraegies. For he governmen side, fuure rises, falls, and urning poins of he macro indicaors pus ino perspecive he effecs of governmen policy creaed o deal wih hem. For he invesors side, fuure values migh increase he possibiliy of diligen invesor in he financial marke. References [1] Republic of Turkey Minisry of Developmen, Turkey s susainable developmen repor: Claiming he fuure, Ankara, June [2] Republic of Turkey Minisry of Economy, Turkey s Expor Sraegy for 2023, [Online] Available from: hp:// [3] E. Onder and O. Hasgul, Time series analysis wih using Box Jenkins models and arificial neural nework for forecasing number of foreign visiors, Journal of Insiue of Business Adminisraion, 20(62), (2009), [4] M.P. Clemens, P.H. Franses and N.R. Swanson, Forecasing economic and financial ime-series wih non-linear models, Inernaional Journal of Forecasing, 20, (2004), [5] I. Kaasra and M. Boyd, Designing a neural nework for forecasing financial and economics ime series, Neurocompuing, 10, (1996),

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