An Initial Study on the Forecast Model for Unemployment Rate. Mohd Nadzri Mohd Nasir, Kon Mee Hwa and Huzaifah Mohammad 1

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1 An Iniial Sudy on he Forecas Model for Unemploymen Rae Mohd Nadzri Mohd Nasir, Kon Mee Hwa and Huzaifah Mohammad 1 Absrac The purpose of he aricle is o deermine he mos suiable echnique o generae he forecas of unemploymen rae using daa from he series of Labour Force Surveys. The models undersudied are based on Univariae Modelling Techniques i.e. Naïve wih Trend Model, Average Change Model, Double Exponenial Smoohing and Hol s Mehod Model. These models are normally used o deermine he shor-erm forecass (one quarer ahead) by analyzing he paern such as quarerly unemploymen raes. The performances of he models are validaed by reaining a porion of he quarerly observaions as holdou samples. In addiion, comparisons are made o see how well he hisorical and forecased daa mached and correlaed. The selecion of he mos suiable model was indicaed by he smalles value of mean square error (MSE). Based on he analysis, Hol s Mehod Model is he mos suiable model for forecasing quarerly unemploymen raes. Keywords: Univariae Modelling Techniques; Forecas Model; Mean Square Error. Inroducion Forecasing is defined as he predicion of fuure evens based on known pas values of relevan variables (Makridakis, S., Wheelrigh, S. C. & Hyndman, R. J., 1998). Forecasing unemploymen rae accuraely is imporan because i helps economiss o have a beer idea of wha he fuure economy holds (Lewis, R., & Brown, C., 2001). Besides, i is also imporan for he governmen in erms of decision and policy making. Wih he suppor of sable economic growh, Malaysia experienced low unemploymen raes in he 1990s wih he lowes recorded in 1997 a 2.4 per cen. From 1999 onwards, he unemploymen rae has increased as a resul of he financial crisis and subsequen economic downurn. Univariae Modelling Techniques are mehods for analyzing daa on a single variable a a ime. Examples of Univariae Modelling Techniques are he Naive Models, Mehods of Average, he Exponenial Smoohing Techniques and he 1 Mohd Nadzri Mohd Nasir is currenly he Direcor of Deparmen of Saisics, Pahang, Kon Mee Hwa is Assisan Direcor of Services Saisics Division and Huzaifah Mohammad is Assisan Saisical Officer of Price, Income and Expendiure Saisics Division.

2 Mohd Nadzri Mohd Nasir, Kon Mee Hwa And Huzaifah Mohammad Box-Jenkins Mehodology. Boh Double Exponenial Smoohing and Hol s Mehod illusraed in his sudy are classified in he Exponenial Smoohing Techniques. Oher models available in his same caegory are Single Exponenial Smoohing, Adapive Response Rae Exponenial Smoohing (ARRES), Hol s Mehod and Hol-Winers Trend & Seasonaliy. This paper is divided ino several secions. Following he inroducion, he second secion describes he definiions, objecives and lieraure review of he sudy, he hird secion focuses on he mehodology and some of he aemps made o move beyond he models. In his secion, a same se of unemploymen daa were esed using four differen univariae forecasing models o obain MSE value. The fourh secion goes beyond he discussion of analysis and resuls while he fifh secion explores selecion of models. This is followed by a normaliy es, paired samples -es and a correlaion es on he chosen model. The final secion presens an evaluaion of Hol s Mehod and a brief conclusion. Definiion of unemploymen Inernaional Labour Organizaion (ILO) defines Unemployed as all individuals above a specified age who saisfies simulaneously he following crieria: a) wihou work (no in paid or self employmen); b) currenly available for paid employmen or self-employmen; and c) acively seeking work. The unemploymen rae is defined as he share of people no working, available and acively seeking for work ou of he working age populaion (ILO Geneva, 1990). Basic economic heory defines unemploymen as a siuaion where supply of labour exceeds demand. The unemploymen rae of 4 per cen or lower indicaes ha an economy is operaing in full employmen condiion. The Keynesian view saes ha unemploymen is an excess supply of labour resuling from a failure of coordinaion in he economy marke whils he classical view saes ha unemploymen is a job search for a beer mach beween producive worker and employer (Baharudin, N., 2004). Objecive of he sudy The objecive of he sudy is o choose he mos suiable model o forecas he unemploymen rae in Malaysia. The oupu of he sudy will serve as a guide in selecing a model for fuure forecasing/projecion of unemploymen rae. Forecasing on unemploymen rae is one of he areas ha should be developed in fulfilling he requiremens a naional and inernaional levels. 28

3 An Iniial Sudy on he Forecas Model For Unemploymen Rae Lieraure Review A sudy underaken by Jaafar, J. 2 (2006) showed ha Hol s Mehod wih wo parameers were suiable o forecas he five major labour force indicaors i.e. labour force, employed, unemployed, unemploymen rae and underemployed. Firs, he mehod of Ordinary Leas Squares (OLS) was used o esimae he rend line for each labour force indicaors o projec pas paern ino he fuure for forecasing purposes. Then he seasonal raios were calculaed o idenify he seasonal componens in he daa. By removing he seasonal componen from he series, he occurrence of he flucuaions refleced he rue movemens of he series. Finally, Hol s Mehod was used o forecas he major labour force indicaors while a comparison of he model s forecasing performance was deermined by Mean Squared Error (MSE). The esimaions were done wih he objecive of minimising he MSE. Floros, C. (2005) compared he ou-of-sample forecasing accuracy for he Unied Kingdom unemploymen rae using he Roo Mean Square, Mean Absolue and Mean Absolue Per cen Errors. He evaluaed he performance of he compeing models covering he period January 1971 o December The forecasing sample (January 1996 December 2002) was divided ino four subperiods. Firs, for oal forecasing sample, i was found ha Moving Average, MA (4) Auoregressive Condiional Heeroscedasiciy, ARCH (1) provided superior forecass of unemploymen rae. On he oher hand, wo forecasing samples showed ha he MA(4) model performed well, while boh MA(1) and Auoregressive, AR (4) proved o be he bes forecasing models for he oher wo forecasing periods. The empirical evidence derived from his invesigaion suggesed a close relaionship beween forecasing heory and labour marke condiions. Mongomery, A. L. e al. (1998) compared he forecasing performance for a variey of linear and nonlinear ime series models using he Unied Saes unemploymen rae. Their main emphasis was: a. on measuring forecasing performance during economic expansions and conracions by exploiing he asymmeric cyclical behaviour of unemploymen numbers; b. on building vecor models ha incorporae iniial jobless claims as a leading indicaor; and c. on uilising addiional informaion provided by he monhly rae for forecasing he quarerly rae. 2 The sudy was underaken by he Human Resource and Social Saisics Division, Deparmen of Saisics Malaysia wih he aim o esimae he five main indicaors of labour force. The resuls were presened in he Workshop in Reviewing he Labour Force/Migraion Survey in November 2006, Purajaya. 29

4 Mohd Nadzri Mohd Nasir, Kon Mee Hwa And Huzaifah Mohammad Comparisons were also made wih he consensus forecass from he Survey of Professional Forecasers. In addiion, he forecass of nonlinear models were combined wih he consensus forecass. The resuls showed ha significan improvemens in forecasing accuracy can be obained over exising mehods. Mehodology This secion described briefly abou he saisical echniques applied o analyse he daa colleced hrough he Labour Force Survey. Univariae Modelling Techniques were applied o predic fuure values of unemploymen rae based on pas observaions in a given ime series, by fiing a model o he daa. The quarerly Labour Force Survey daa from were used o deermine he suiable model. Time series forecasing analysis and forecas models were applied o predic he unemploymen rae in Malaysia. Analysis was done using four ypes of forecas models i.e. Naïve wih Trend Model, Average Change Model, Double Exponenial Smoohing and Hol s Mehod. Subsequenly, prediced unemploymen rae wih he bes model were compared wih he acual unemploymen rae obained from he Labour Force Survey o deermine he accuracy of predicion. The saisical es and daa analysis were done hrough SPSS and Microsof Excel. a. Naïve wih Trend Model This model implies ha all fuure forecas can be se o equal he acual observed value in he mos recen ime period plus he growh rae. The value Y measures he rend. If Y is greaer han Y 1 hen he rend is on he upward Y 1 and likewise if Y is less han Y 1, hen he rend is on he downward side. The one sep ahead forecas is represened as, Y F + 1 = Y where Y is he acual Y 1 value in ime, and Y 1 is he acual value in he preceding ime period. This model is highly sensiive o he changes in he acual values. A sudden drop or sharp increase in he values will severely affec he forecas. Furhermore, fiing his model ype will resul in he loss of he firs wo observaions in he series. On he oher hand, his model is only suiable o be used for shor ime series. 30

5 An Iniial Sudy on he Forecas Model For Unemploymen Rae b. Average Change Model The average change model is based on he premise ha he forecas value is equal o he acual value in he curren period plus he average of he absolue changes experienced up o ha poin in ime. The one sep ahead forecas is given as: F + l ( Y Y 1 1 Y 2 = Y + ) + ( Y 2 ) This model is useful when he hisorical daa being analysed are characerised by period-o-period changes ha are approximaely of he same size. However, his model ends o lag behind urning poins and ha all periods are weighed equally, irrespecive of heir imporance, when deriving he forecas values. c. Double Exponenial Smoohing This echnique is also known as Brown s mehod. I is useful for series ha exhibi a linear rend characerisic. The following noaions are used: Le, S be he exponenially smoohed value of Y a ime ' S be he double exponenially smoohed value of Y a ime Generally, here are four equaions involved. Equaion 1: Compues he single exponenially smoohed value S α Y + 1 α) S = ( 1 Equaion 2 : Compues he double exponenially smoohed value ' ' S α S + 1 α) S = ( 1 Equaion 3 : Compues he difference beween he exponenially smoohed values ' a = S S 2 Equaion 4 : Compues he adjusmen facor α ' b = ( S S ) 1 α Therefore, he l-sep-ahead forecas is compued by using he equaion, F = a b l where +1 + l F + is he l-sep-ahead forecas a period l made in period for l=1,2,3,... 31

6 Mohd Nadzri Mohd Nasir, Kon Mee Hwa And Huzaifah Mohammad There are several advanages ha can be obained when using double exponenial smoohing echnique: a) exponenial smoohing models mesh very easily wih compuer sysem and hence, simple spreadshee program such as Microsof Excel can be used o generae new forecass; b) daa sorage requiremens are minimal when compared o oher forecasing models; c) i embodies he advanages of a weighed moving average since curren observaions are assigned larger weighs; d) exponenial smoohing models reac more quickly o changes in daa paerns han he moving average; and e) i does no require as much daa as he Box-Jenkins mehodology or he economeric modelling echnique. The main difficuly encounered when using his mehod is he deerminaion of he size ofα. The crierion is o choose α such ha he MSE is minimum. However, wih he assisance of solver faciliy available in Microsof Excel, he enormous amoun of work is lessened when searching for he bes parameer α value. d. Hol s Mehod Hol s Mehod is a echnique ha akes ino accoun o smooh he rend and he slope direcly by using differen smoohing consans. I also provides more flexibiliy in selecing he parameer value which he rend and slopes are racked. Hol s Mehod consiss of hree basic equaions ha define he exponenial smoohed series and he rend esimae. The Hol s Mehod equaions are represened as follows: Exponenially smoohed series: S = α Y + ( 1 α)( S 1 + T 1 ) Trend esimae: T β S S ) + (1 β T = ( 1 ) 1 Therefore, he one sep ahead forecas is: F = S + T (1) + 1 where S = exponenially smoohed series Y = acual values T = rend esimae 32

7 α = smoohing consan (0<α <1) β = smoohing consan for he rend esimae (0< β <1) An Iniial Sudy on he Forecas Model For Unemploymen Rae Mean Squared Error (MSE) MSE is he sandard error measure for assessing he model s finess o a paricular daa and comparing he model s forecasing performance. For he one sep a head forecas, he MSE is wrien as: n e MSE = n for which e 2 = Y Yˆ where, Y is he acual observaion a he ime. Yˆ is he fied value in ime generaed from he origin ( = 1,2,3,..., n ) n is he number of ou-of-sample error erms generaed by he model. Esimaion and Evaluaion Procedures Basically, here are hree sages involved: i. In he firs sage, he series is divided ino wo pars. The firs par is called model esimaion par (or fied par) and he second par is he evaluaion par (or holdou par), which will be used o evaluae he model s forecasing performance; ii. iii. In he second sage, he models are esed using various forms of funcional relaionship and variable selecions; and In he hird sage, he minimum value of α and β are deermined by Solver faciliy available in Microsof Excel which derived parameer values from daa series for he relaed model. Then, all he models wih he smalles MSE value are evaluaed by comparing he MSE value of each model. Usually, a benchmark model is used as he basis of comparison agains he acual daa. 33

8 Mohd Nadzri Mohd Nasir, Kon Mee Hwa And Huzaifah Mohammad The model ha mees all he crieria is hus seleced as he mos suiable model. The selecion crierion is based on he resuls of comparing heir respecive error measures. Analysis and Resuls Univariae forecasing model was used o predic unemploymen rae for he firs quarer of year 2008 in Malaysia. The esimaions were done using daa from firs quarer of 1998 o he fourh quarer of 2003 while he remaining observaions from firs quarer of 2004 o he fourh quarer of 2007 were used o evaluae he model s forecasing performance. Unemploymen rae (%) for he period of sudy from he firs quarer 1998 o fourh quarer 2007 is as shown in Table 1. Table 1: Quarerly Unemploymen Raes, Malaysia, 1998 o 2007 Year Quarer Unemploymen rae, (%),Y 1998 I 2.9 II 3.3 III 3.3 IV I 4.5 II 3.3 III 2.9 IV I 3.0 II 3.3 III 3.1 IV I 4.0 II 3.7 III 3.3 IV I 3.7 II 3.8 III 3.2 IV I 3.8 II 4.1 III 3.4 IV

9 An Iniial Sudy on he Forecas Model For Unemploymen Rae Year Quarer Unemploymen rae, (%),Y 2004 I 3.7 II 3.7 III 3.4 IV I 3.5 II 3.1 III 3.8 IV I 3.8 II 3.4 III 3.1 IV I 3.4 II 3.4 III 3.1 IV 3.0 Source: Labour Force Survey Repor, Deparmen of Saisics Malaysia Figure 1 shows he graph and he rend line of he unemploymen raes from firs quarer of 1998 o fourh quarer of Values indicae ha maximum raes are reached during he firs and second quarer, while minimum raes are reached during he hird and fourh quarer. The overall rend line equaion for quarerly daa is given by y = x The rend line indicaes ha he underlying paern of he daa follows a relaively sable upward rend. Figure 1: Quarerly Unemploymen Rae, Malaysia, Unemploymen Rae (%) y = x I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV Unemploymen rae (%), Y Year Linear (Unemploymen rae (%), Y) 35

10 Mohd Nadzri Mohd Nasir, Kon Mee Hwa And Huzaifah Mohammad Univariae Modelling Techniques The esimaions were done wih he objecive of minimising Mean Squared Error (MSE). Resuls of he corresponding MSE value for each model are shown below. Naïve wih Trend Figure 2: Fied Naïve Wih Trend Model, Malaysia, Unemploymen Rae (%) I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV Year Unemploymen rae (%), Y Fied, F Fied Period ( ): MSE = Evaluaion Period ( ): MSE = Average Change Model Figure 3: Fied Average Change Model, Malaysia, Unemploymen Rae (%) I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV Year Unemploymen rae (%), Y Fied, F Fied Period ( ): MSE = Evaluaion Period ( ): MSE =

11 An Iniial Sudy on he Forecas Model For Unemploymen Rae The deerminan for he bes forecasing model is proven by a smaller MSE value. For example in he above cases, Naïve wih Trend Model (MSE = ) generaed a beer forecas daa if compared wih Average Change Model (MSE = ) which has higher MSE values. Therefore, MSE is he bes sandard error measure for assessing he finess and he forecasing performance by comparing he MSE value of each model. Double Exponenial Smoohing Compuaion of he minimum value of α was deermined by solver faciliy available in Microsof Excel. Based on he solver resul, he bes α o use is since i minimises he error measure (Figure 4). Figure 4: Fied Double Exponenial Smoohing Model, Malaysia, Unemploymen Rae (%) I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV Year Unemploymen rae (%), Y Fied, F Fied Period ( ): MSE = Evaluaion Period ( ): MSE = Hol s Mehod Compuaion of he minimum value of α and β were done using solver faciliy available in Microsof Excel. Based on he solver resul, he bes parameer o use is α = 0.03 and β = 1.0, since i minimises he error measure (Figure 5). 37

12 Mohd Nadzri Mohd Nasir, Kon Mee Hwa And Huzaifah Mohammad Unemploymen Rae (%) Selecion of Model Figure 5: Fied Hol s Mehod, Malaysia, I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV I II III IV Year Unemploymen rae (%), Y Fied, F Fied Period ( ): MSE = Evaluaion Period ( ): MSE = Table 2 presens he summaries and comparison on MSE figures for Naïve wih Trend Model, Average Change Model, Double Exponenial Smoohing and Hol s Mehod. On he basis of he size of MSE calculaed over he evaluaion period, i can be concluded ha he mos suiable model o forecas he unemploymen rae is Hol s Mehod wih α = 0.03 and β = 1.0 since i has he smalles value of MSE compared o oher forecasing echniques. Period Fied Period: ( ) Evaluaion Period: ( ) Table 2: MSE values by ype of model Naïve wih Trend Average Change Model Type of model Double Exponenial Smoohing, α = Hol s Mehod α =0.03, β = As menioned earlier, 16 daa poins (firs quarer of 2004 o fourh quarer 2007) are used as holdous or evaluaion period for he purpose of model validaion. Figure 6 shows how he Hol s Mehod wih α = 0.03 and β = 1.0 forecass compared wih hose acual values for he holdou sample. The resuls indicaed ha ou-of-sample forecass rack closely he acual daa. 38

13 Unemploymen Rae (%) Figure 6: Resuls from he Hol s Mehod Model An Iniial Sudy on he Forecas Model For Unemploymen Rae I II III IV I II III IV I II III IV I II III IV Acual Year Forecas The forecass and he acual unemploymen rae of Hol s Mehod Model showed he same rend. Several ess were performed o ascerain he normaliy, level of significance and correlaion beween he acual and forecas values obained from he recommended model. Before any saisical echnique is used o compare means, i is imporan ha he normaliy assumpions are me. Therefore, normaliy es on he acual and forecas daa was done. Based on he Kolmogorov-Smirnov Tes (significance value greaer han 0.05), he disribuion of he acual and forecas values are normal (Table 3). Table 3: One Sample Kolmogorov-Smirnov Tes for acual and forecas values of unemploymen rae N Normal Parameers a,b Mean Sandard Deviaion Mos Exreme Absolue Differences Posiive Negaive Kolmogorov-Smirnov Z Asympoic Significance (2-ailed) a. Tes disribuion is Normal. b. Calculaed from daa. Acual Forecas

14 Mohd Nadzri Mohd Nasir, Kon Mee Hwa And Huzaifah Mohammad Paired samples -es The paired samples -es is used o compare he means of acual and forecas values of unemploymen raes. Table 4: Resuls of paired samples -es for acual and forecas Pair 1 ACTUAL FORECAST Sandard Sandard Mean N Deviaion Error Mean Pair 1 Acual - Forecas Paired Differences 95% Confidence Sandard Inerval of he Sandard Error Difference Significance Mean Deviaion Mean Lower Upper df (2-ailed) Table 4 presens he resuls of paired samples -es using SPSS. The resuls showed here is no significan difference in he mean of acual and forecas unemploymen raes. The mean absolue percenage error for he wo values is per cen. Therefore, i can be concluded ha he Hol s Mehod is more appropriae in forecasing unemploymen rae. Coefficien of Correlaion The coefficien of correlaion measures he degree of linear and direcion of he relaionship of variables. Acual Table 5 : Resuls of Pearson Correlaion Forecas Pearson Correlaion Significance (1-ailed) N Pearson Correlaion Significance (1-ailed) N Acual Forecas * * *. Correlaion is significan a he 0.05 level (1-ailed). 40

15 An Iniial Sudy on he Forecas Model For Unemploymen Rae Table 5 exhibis he resuls of Pearson correlaion using SPSS which concluded ha here is significan correlaion of p-value equals and posiive moderae correlaion of (r 0. 5 ) beween he acual and forecas values. This suggess ha he Hol s Mehod wih α=0.03 and β=1.0 is suiable in forecasing he unemploymen rae. An Evaluaion of Hol s Mehod The forecasing of unemploymen rae has become one of he major fields of research in recen years. I serves as an imporan indicaor in human resource developmen planning and policy formulaion. MSE and correlaion were used o deermine he suiable forecas model. From he resuls of he analysis, Hol s Mehod wih α=0.03 and β=1.0 and he resuling correlaion of and MSE of seems o be he mos reliable model in generaing he forecas value of unemploymen rae. The model forecased 3.1 per cen for he firs quarer of 2008 as compared o he acual rae of 3.6 per cen. The advanage of using he Hol s Mehod Model is ha recen observaions are given relaively more weigh in forecasing han he older observaions. The onesep-ahead forecas is made in he fi region (in sample) and he muli-sepahead forecass are made in he holdou sample region (ou of sample). However, in forecasing for longer erm, i is less saisically fi han he one-sepahead forecas because he more recen daa may depar from he previous underlying process. Conclusion Based on he one sep ahead forecas analysis, Hol s Mehod Model is he mos suiable model for forecasing quarerly unemploymen rae. Each model ype has unique characerisic which fis o a paricular daa series. More forecasing echniques should be explored o ensure finess o longer series of unemploymen rae. Univariae Modelling Techniques are basically single variable models ha use heir pas informaion as he basis o generae he forecas values. This is made on he assumpion ha he forecas values are dependen solely on he pas paern of he daa series. 41

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