A Methodology for Identifying Time-Trend Patterns: An Application to the Advertising Expenditure of 28 European Countries in the Period

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1 Meoološi zvezi, Vol. 5, No., 008, 6-7 A Mehoology for Ienifying ime-ren Paerns: An Applicaion o he Averising Expeniure of 8 European Counries in he Perio Kaarina Košmelj an Vesna Žabar Absrac he aim of our suy is o reveal ifferen ime-ren paerns in he raio of averising expeniure o gross omesic prouc for 8 European counries in he perio. o fulfil he objecive, we applie wo muliimensional saisical approaches: cluser analysis an muliimensional scaling for ime-varying aa, followe by linear regression analysis of he ime-series wihin he clusers. A proximiy marix was calculae using he issimilariy beween wo ime series, which aes ino accoun he orer of ime poins, he informaion on he fixe ime poins, an he weighs. We ienifie four clusers of counries wih similar ren paerns in he perio: awaening counries, sable counries, caching-up counries, an he leaing cluser. Inroucion he averising inusry is an imporan componen of he economic aciviies of a cerain counry. Averising expeniure a he counry level inclues he aggregae value of averising expeniure in he press (newspapers an magazines), elevision, raio, ouoor an cinema. he aa for averising expeniure are presene in he local currency an in curren prices an are no irecly comparable over ime an beween counries. We herefore consiere averising expeniure on a relaive scale, as he raio of averising expeniure o gross omesic prouc, which is an inernaionally recognise sanar for measuring naional economic aciviy. hus, he variable uner suy is he raio of averising expeniure o gross omesic prouc for 8 European counries for he perio. Our main research quesions are he following: Bioehnical Faculy, Universiy of Ljubljana, Slovenia; aarina.osmelj@bf.uni-lj.si Faculy of Economics, Universiy of Ljubljana, Slovenia; vesna.zabar@ef.uni-lj.si

2 6 Kaarina Košmelj an Vesna Žabar Are here ifferen ime-ren paerns for he variable uner suy? Which European counries have similar paerns over ime? Mehoology an analysis. Daa We consiere he aa for averising expeniure (AD) an gross omesic prouc (GDP). he erive variable, AD/GDP %, represens he percenage of AD in GDP. Is values range from 0.059% (Russia in 994) o.4% (Cyprus in 004), whereas he meian is 0.759%. he number of counries (8) an he - year perio correspon o he larges aa marix for which he aa were available (Euromonior, 006). Hence, 8 ime-series of lengh were he inpu for he saisical analysis (see Appenix ).. Dissimilariy o mee our research objecives, we applie wo mulivariae saisical mehoologies: cluser analysis an mulivariae scaling for ime-varying aa. he firs sep for boh approaches is he calculaion of a proximiy marix, in our case a issimilariy marix beween counries, wih each being represene by one ime series. Sanar issimilariy measures are no appropriae for ime series an shoul be replace by a measure ha aes he ime imension an is orering propery ino accoun. In Appenix we presen he raionale for he erivaion of issimilariy D beween wo ime series (Košmelj an Baagelj, 990). I aes ino accoun he issimilariies a successive ime poins,,,, where is a sanar issimilariy measure, an he corresponing weighs, which assess he impac of an imporan exernal characerisic a ime poins. he weighs express he relaive imporance of he issimilariies in he calculaion of D an incorporae a srong ime-orering coniion. We use a square Eucliean isance o measure he issimilariy beween ime series x an y a ime poin, ( ) w x y. In he efiniion of he weighs w, we oo ino accoun informaion on he aggregae averising expeniure for enire Europe, ADE. We efine as he raio of wo successive values for ADE an expresse i in erms of is growh rae r :

3 A Mehoology for Ienifying ime-ren Paerns 63 ADE ADE r 00 he weighs w were calculae from he values using he formula given in Appenix..3 Clusering an orinal scaling Several clusering mehos an orinal muliimensional scaling were use o ienify ifferen ime paerns in AD/GDP % for he 8 counries uner suy. he analysis was one using he R.4 an SPSS 4.0 programmes. 3 Resuls he growh raes for aggregae averising expeniure for enire Europe (ADE) an he weighs w are presene in Figure. he figure reveals he highes growh raes for ADE in 997, 999 an 000 (aroun 0%) an a perio of sagnaion aferwars. he weighs w reflec hese phenomena, hey increase from 994 o 00 an are nearly consan aferwars. Figure : Annual growh rae for aggregae averising expeniure for Europe (ADE) for he perio (bar char, scale on he lef y-axis ) an weighs w use in he calculaion of issimilariy D (line char, scale on he righ y-axis ).

4 64 Kaarina Košmelj an Vesna Žabar Figure : Denrogram obaine by War s meho. Figure 3: wo-imensional scaerplo of counries obaine by orinal muliimensional scaling.

5 A Mehoology for Ienifying ime-ren Paerns 65 Differen clusering mehos were use an Figure presens he enrogram obaine by War s meho. I shows ha, on he firs level, 8 counries are clusere ino wo clusers: he firs cluser conains Cyprus, Hungary, Greece, Slovenia, Czech Republic, Polan an Slovaia, while he remaining counries are in he secon cluser. On a lower level, here are four clusers, as presene in able. he resuls for he ifferen clusering mehos are ienical excep for Greece, which joine eiher Cluser 3 or Cluser 4. he resuls obaine by orinal muliimensional scaling (ALSCAL in SPSS) show ha a wo-imensional represenaion is saisfacory. We presen he map of he counries in Figure 3 o offer a eeper insigh ino he clusering resuls. he clusers are allocae along he x-axis, Cluser is on he lef, followe by Cluser an Cluser 3, Cluser 4 on he righ; however, Greece is allocae far-off. o gain a eeper unersaning of he resuls, we uneroo a eaile analysis of he counries wihin each cluser. Firs we ploe he ime series for each cluser (see Figures 4 an 5 in Appenix 3). he srange jumps in some ime series (see Lavia an Greece) can be explaine by he change in efiniion of averising spening (for example, aa for averising spening in Lavia in inclue proucion coss) an we i no ae hese values ino furher analysis. able : Linear regression for he ime series wihin each cluser obaine by War s meho. he inercep presens he preice value for AD/GDP % in 994, while he slope inicaes he average change per year. Cluser Members Inercep Slope Commen Lihuania, Luxembourg, Russia, urey 0.93*** 0.04*** Very slow growh from a very low inercep. Ausria, Belgium, Denmar, Esonia, Finlan, France, Germany, Irelan, Ialy, Lavia, Neherlans, Norway, Porugal, Spain, Sween, Swizerlan, Unie Kingom 0.745*** No growh from a meium inercep. 3 Czech Republic, Greece, Polan, Slovaia, Slovenia 0.55*** 0.099*** Inensive growh from a low inercep. 4 Hungary, Cyprus 0.998*** 0.*** Very inensive growh from a high inercep. Legen: *** p<0.00 Daa for Lavia for Daa for Greece for hese plos show a linear ren in all four clusers an we herefore analyse he ime series wihin each cluser using he linear regression moel. he resuls are summarise in able. he inercep presens he preice value for 994, whereas he slope inicaes he average change per year in he perio. he inercep is significanly ifferen from zero for all four clusers; he slope is posiive an significan in all clusers excep in Cluser.

6 66 Kaarina Košmelj an Vesna Žabar A eeper insigh ino ime-ren paerns reveals several ineresing issues. In Cluser we observe a very low saring poin (0.3%) an he en-year growh of 0.%; hence he percenage of AD in GDP increase from 0.3% in 994 o 0.5% in 004. he four counries (Lihuania, Luxembourg, Russia an urey) can be characerise by a slow change from a very low saring poin. his cluser incorporaes he awaening counries. Cluser incorporaes 7 counries where AD represens abou 0.7% of GDP an is consan hroughou he perio. he cluser members are he mos evelope European Union counries along wih he wo Balic counries of Esonia an Lavia. his cluser consiss of he sable counries. he wo Balic counries come ou as a surprise, an explanaion for Esonia can be foun in Ilić, 000. In Cluser 3 we observe inensive growh from 0.5% in 994 o.5% in 004. he resuls show ha Greece iffers from he oher four cluser members (Czech Republic, Polan, Slovaia, an Slovenia). hese counries were caniaes for he European Union in he perio uner suy, Greece joine in 00 while he ohers followe in 004. he main characerisic of he cluser is inensive growh from a low saring poin. his cluser consiss of he cachingup counries. Cluser 4 has he highes saring poin (%) an he highes growh in he enyear perio (. %). he wo counries, Cyprus an Hungary, were very propulsive an ha very inensive growh from he highes saring poin. his cluser is he leaing cluser. Accoring o Manrai e al. (00), Hungary has he mos evelope averising inusry. 5 Conclusions his suy enquire ino wheher here are ifferen ime paerns of he raio AD/GDP % for 8 European counries in he perio. he answer is affirmaive. Furher, we invesigae which counries have similar paerns across ime. wo muliimensional saisical approaches were use for his purpose: cluser analysis an muliimensional scaling on ime-varying aa. A proximiy marix was calculae using he issimilariy beween wo ime series. I aes ino accoun he orer of ime poins, he informaion on he fixe ime poins, an he weighs which are arbirary. Since informaion on averising expeniure for he whole of Europe is very imporan, is growh rae was incorporae ino he calculaion of he weighs. he resuls show ha issimilariy hols grea power when i comes o ienifying ifferen ime paerns. We ienifie four clusers of counries wih similar ren paerns in he perio: awaening counries (Russia, Luxembourg, Lihuania an urey);

7 A Mehoology for Ienifying ime-ren Paerns 67 sable counries (Lavia, France, Ialy, Porugal, Sween, Belgium, Irelan, Denmar, Esonia, he Unie Kingom, Germany, Swizerlan, he Neherlans, Norway, Ausria, Finlan an Spain); caching-up counries (Greece, Slovenia, Czech Republic, Polan an Slovaia); an leaing counries (Cyprus an Hungary). o sum up, he new exploraory approach enables a eeper insigh ino imeren paerns of averising expeniure in he counries uner suy. References [] Euromonior (006): Worl Mareing Daa an Saisics. [] Ilić, M. (000): Čas velie rasi in čas umirjanja. Mareing magazin, 0, 7, 8-9, Ljubljana. [3] Košmelj, K. an Baagelj, V. (990): Cross-secional approach for clusering ime varying aa. Journal of Classificaion 7, [4] Manrai, L.A., Manrai, A.K., an Lascu, D.-N. (00): A counry-cluser analysis of he isribuion an promoion infrasrucure in Cenral an Easern Europe. Inernaional Business Review, 0,

8 68 Kaarina Košmelj an Vesna Žabar Appenix able : Daa for AD/GDP% for 8 European counries in he perio AU BEL CYP CZE DNK ES FIN FRA DEU GRC HUN IRL IA LVA LU LUX NLD NOR POL PR RUS SVK SVN ESP SWE CHE UR GBR

9 A Mehoology for Ienifying ime-ren Paerns 69 Appenix he issimilariy D beween ime series x an y is base on a compoun ineres moel. D is obaine in a sepwise manner using he issimilariies an he weighs a ime poins,,,. he value of D a ime poin is D, i is base on is previous value D -, on an as follows: D D D D D K K D D K K K In his scheme, represens he income, incorporaes he informaion on he ineres rae an D he balance a a paricular ime poin. o summarise, D can be expresse as he weighe sum of : w D D wih he weighs w which are he proucs of he weighs :,,, w s s K w.

10 70 Kaarina Košmelj an Vesna Žabar Appenix 3 Cluser Lihuania Luxembourg Russia urey AD/GDP % Cluser AD/GDP % France Germany Irelan Ialy Lavia Figure 4: ime-series for he percenage of averising expeniure in gross naional prouc (AD/GDP %) for Cluser an Cluser. Noe: for Cluser only 5 ou of 7 ime-series are ploe.

11 A Mehoology for Ienifying ime-ren Paerns 7 Cluser Czech Greece Polan Slovaia Slovenia AD/GDP % Cluser Cyprus Hungary AD/GDP % Figure 5: ime-series for he percenage of averising expeniure in gross naional prouc (AD/GDP %) for Cluser 3 an Cluser 4.