Multi-level Forecasting Error Controlling Method: A Demonstration in System Energy Demand Forecasting

Transcription

1 Muli-level Forecasing Error Conrolling Mehod: A Demonsraion in Sysem Energy Demand Forecasing Hui-Min Wang * and Yunchang Jeffrey Bor ** Energy demand forecasing is he foundaion of almos all energy-relaed policies for all counries. How o provide energy demand forecasing wih a reasonable Energy Balances form has become a fundamenal work of many imporan energy-relaed research sudies as well as policy making, such as long-erm invesmen in energy supply faciliies, CO 2 emissions conrol, and he carbon ax burden among indusries, energy efficiency, and energy susainable index. The key problem of muli-level energy saisical forecasing is conrolling he sysem forecasing error wihin a reasonable manner for boh he by-energy and by-secor caegories of daa. The sum of he forecasing errors urns larger and larger when energy consumpion daa are divided ino much more deailed sub-sraums. The presen paper develops a muli-level forecasing error conrolling mehod o perform sysem forecasing on a family ree of demand-side energy consumpion daa. Once he weighed adjusmen process has been carried ou, he sums of he forecasing values of he energy sub-caegory iems will be equal o he forecasing values of he oal secondary energy daa in he ime base. The presen paper also akes Taiwan s Energy Balances real daa as an example o demonsrae he mehods in shor-erm energy demand sysem forecass. Keyword: Muli-level sysem forecasing, energy demand daa, forecasing error conrol, Energy Balances 1. INTRODUCTION Energy is he mos crucial elemen for economic aciviies and is also he essenial condiion o mainain a high qualiy of living. The degree of economic developmen and living sandard of one counry can be evaluaed by he average energy consumpion per capia. Therefore, he whole world pays significan aenion o energy-relaed issues, such as energy demand and supply, energy price shocks, energy securiy, and he 3E (economy-energyenvironmen) problems. Because of he above-menioned reasons, building a reliable energy demand forecasing sysem so as suppor a sufficien energy supply for an economy is one of every counry s op prioriy issues. Energy demand forecasing is he foundaion of almos all energy-relaed policies in all counries. The general seps of consrucing an energy demand forecasing sysem is o firs observe he changes in energy and is srucure among * Ph.D. suden, Insiue of Public Healh, Naional Yang-Ming Universiy, Taipei, Taiwan. ** Research Fellow, Chung-Hua Insiuion for Economic Research. bory@mail.cier.edu.w 1

2 users. The nex sep is o process an accurae predicion of energy demand. The srucure analysis includes boh he dimensions of he by-energy caegory and he by-secor caegory of energy demand. The Energy Balances syle of energy demand forecasing provides a basis for a governmen s decision-making concerning all energy-relaed policies. A good predicion resul no only depends on he good predicion mehod, bu i also needs o be dependen on he complee daa collecion. Energy Balances, consruced by IEA (Inernaional Energy Agency, 2003), has been adoped by all OECD (Organizaion of Economic Cooperaion and Developmen) counries and has widely been acceped by mos counries for heir energy saisics, alhough he definiion of energy iems and he classificaion of secors are dispuable in differen regions. The key poin of Energy Balance is o record he energy demand and supply of a counry in some saisical period (e.g., wihin a year or a monh). Basically, he saisics conain wo broad caegories of daa classificaion: by-energy caegory and by-secor caegory. This is one of he reasons why he energy saisics are called Energy Balances. Anoher reason is ha he energy saisics provide a hea balance of energy ransformaion from primary energy o secondary energy. Baseline forecasing of energy demand is he foundaion source of energy securiy as well as economic developmen. When one conducs he forecasing of energy demand, i is usually found ha he forecas of energy demand canno mach he rule of Energy Balances. Taking he by-energy caegory daa as an example, he oal energy consumpion is divided ino coal and coal producs, peroleum producs, naural gas, and elecriciy. Obviously, he sums of he forecass of hese four energy sub-caegories will no equal he forecass of he oal energy consumpion. The same siuaion happens o he forecasing errors: he sum of he forecasing errors becomes larger and larger when energy consumpion daa are divided ino much more deailed sub-sraums. In order o solve he balance of he energy demand forecas and conrol he sysem forecasing error a a minimum level or wihin a small range, he presen paper develops a muli-level forecasing error conrolling mehod o perform he sysem forecasing on a family ree of demand-side energy consumpion daa. The sums of he forecasing disaggregaed values of he energy sub-caegory iems will equal he forecasing values of he aggregae energy consumpion in he ime base afer he weighed adjusmen process has been carried ou. 2. DATA STRUCTURE AND METHOD Before inroducing he muli-level forecasing error conrolling mehod, we need o describe he daa srucure. A muli-level forecasing error conrolling mehod is applied o a muli-level sysem daa srucure. In general, a muli-level sysem daa srucure can be decomposed ino sub-caegory series of daa. In his paper, demand-side energy 2

3 consumpion daa are used o demonsrae he muli-level sysem daa srucure, for example. Energy Daa Srucure The Energy Balances, which are published periodically by he Bureau of Energy, Taiwan, ROC, conain wo broad caegories of daa classificaion: caegory. by-energy caegory and by-secor In he demand-side energy consumpion daa, he oal secondary energy consumpion is divided ino coal and coal producs, peroleum producs, naural gas, and elecriciy. Coal and coal producs and peroleum producs can hen be furher divided ino sub-caegory iems. This is all aribued o he energy caegory. The by-secor caegory records he amoun of energy consumpion for each energy iem in every secor. The presen paper uses mahemaical noaion o demonsrae and clearly undersand he daa srucure. Suppose he oal energy consumpion can be se as he firs level ime series, he noaion of he oal energy consumpion is T, where indicaes he ime uni and i may be uni per annual, per quarer, or per monh. The second level ime series are coal and coal producs, peroleum producs, peroleum producs, naural gas, and elecriciy. The noaion of hese four energy sub-caegory are C O G and E, respecively, where also indicaes he ime uni. The hird level ime series are he deailed iems of coal and coal producs and peroleum producs, respecively. The noaion of he deailed iems of coal and coal producs is SubC 1, SubC2, L, SubCn, where n indicaes he numbers of he deailed iems of coal and coal producs. SubC 1 can be seam coal, and SubC 2 can be coking coal, for insance. Similarly, he noaion of he deailed iems of peroleum producs is SubO 1, SubO2, L, SubOm, where m indicaes he number of he deailed iems of peroleum producs. SubO 1 can be he gasoline, and SubO 2 can be diesel, for insance. Finally, he las level is he energy consumpion in every secor (e.g., fuel oil consumpion in each secor). In he sysem daa srucure of energy demand, here is relaionship of Balance beween each level. iems of he second level. The balance means ha he value of he firs level can be divided ino he energy iems of he hird level, and so on. each level can be shown as follows: Level 1 Level 2 Level 3 M Level p The value of he second level also can be divided ino he energy T The mahemaic expression of he relaionship beween T = C + O + G + E C = SubC + SubC + L+ SubC 1 2 n (1) O = SubO + SubO + L+ SubO 1 For illusraion purposes, a marix form can be used o represen he daa srucure of sysem energy demand daa, such as Table In Table 1 he columns express he energy m

4 caegory and he oal energy consumpion. The rows express he secor caegory and he oal energy consumpion. There are i h iems in columns and j h iems in rows. Table 1. The sysem daa srucure of energy consumpion Mehod In order o realize he applicaion of he muli-level forecasing error conrolling mehod more specifically, he presen paper akes Taiwan s Energy Balances as an example o illusrae he adjusing process of his mehod. This sudy also akes EnFore (Energy Forecasing Sysem), which is developed by Bor e al from (Bor e al 2004) so as o forecas he energy demand and supply and energy-relaed environmenal impacs. EnFore is a decision suppor sysem which is based on boh he fundamenal aspecs of demand and supply plus 3E (energy-economy-environmen), and he ime dynamics facor. The sysemic purpose of EnFore is o build a complee energy, economic, environmenal, long-erm planning and naional forecasing sysem. The EnFore sysem uses he ineracive model among several sub-sysems, including EnFore-D (demand forecasing subsysem), EnFore-S (supply planning subsysem), EnFore-CO 2 (CO 2 emission conrol subsysem), EnFore-DSS (policy simulaion subsysem), and EnFore-I (energy index subsysem). These ogeher wih he principle of an energy daabase provide decision makers wih various kinds of decision references and model funcions. The maerial daa oupus of he EnFore-D subsysem can be divided ino monh, quarer, and yearly. The key forecasing mehod is he hybrid forecas mehod of combining he ime series mehods and economerics o choose he bes forecasing model (i.e., he leas forecasing error oupu). Figure 1 shows he basic flow char of he hybrid mehod and he muli-level forecasing error conrolling mehod of energy demand forecasing in he EnFore sysem. The procedure of forecasing in EnFore-D is mainly divided ino four seps. Firs, he presen paper applies univariae ime series models and economerics models in he by-energy caegory and by-secor caegory daa, respecively. The MAPE (Mean Absolue Percenage Error) crierion of predicion is hen used o choose he bes forecasing model. In he EnFore-D subsysem, here are he exponenial smoohing mehod, Box and Jenkin s ARIMA mehod, 4

5 Specral analysis, he linear regression model, and he Hodrick-Presco filer mehod for univariae ime series models, and a naural logarihm OLS regression model for he economerics model. Figure 1. Energy Demand Forecasing in EnFore Sysem Hybrid Mehod Read in Secondary Energy Daa Qualiaive Analysis By energy, By secor Exogenous Variables GDP, Producion Index, Populaion, Energy Price Index By Energy Time Series Models By Secor Economerics Model Muli-level Forecasing Error Conrolling Mehod Energy Balance Sysem Forecasing Oupu The hybrid forecas mehod means ha every energy iem will uilize each of he above-menioned forecas mehod o se up he prediced candidae model, and hen according o he MAPE crierion of he predicion efficiency of every candidae model he bes forecasing model is seleced. However, in shor-erm and mid-erm forecasing (monhly and quarerly energy demand forecasing), he economerics mehod has been excluded; ha is, only ime series mehods are applied. Because of he cycle rend and he srucure of shor-erm and mid-erm energy consumpion daa, he presen paper chooses he above univariae ime series mehods o enhance he forecas precision. On he oher hand, long-erm forecasing focuses on policy analysis and he long-erm secoral srucure change of he indusry. The economerics model serves beer in explaining he background of economical and populaion changes. The mahemaical expression of he MAPE crieria is as follows. 5

6 MAPE = 1 n n = 1 F A A, (2) where F indicaes he forecasing of period, A is he realized observaion of period, and n is he number of forecasing periods. If he number of MAPE is smaller, hen i shows a sronger accurae abiliy of he forecasing model. For he nex sep, he presen paper uses he ou-sample es for selecing he bes model from he firs sep in order o forecas every disaggregaed energy caegory. EnFore-D conducs a full-sample forecasing of all caegories. Nex, afer he bes model has been idenified, The las sep carries ou he muli-level forecasing error conrolling mehod and oupus he Energy Balances ype of he energy demand forecass. Because he energy daa have he Energy Balances characerisic shown in Table 1, he original forecasing value of energy demand will obviously no conform wih he balance principle. For example, he sum of he forecasing value of coal and coal producs, peroleum producs, naural gas, and elecriciy will no equal he forecasing value of oal energy consumpion. In order o solve he balance problem afer forecasing, he presen paper develops he muli-level forecasing error conrolling mehod o adjus he forecasing resuls of every level o mee he balance principle. The adjusing process of he muli-level forecasing error conrolling mehod is mainly based on he nes-level-apporioned principle, which carries ou he apporionmen of every level of forecas. The nes-level-apporioned principle apporions he forecasing value of he oal energy consumpion o he second level: coal and coal producs, peroleum producs, naural gas, and elecriciy. The second level, coal and coal producs and peroleum producs, also apporions he forecasing value of he shared second level o he hird level, respecively. The raio of apporionmen is he forecasing resul divided by he sum of ha level and period. The raio can be used as a muliplier o apporion he forecasing resul of ha period of ime. This adjused mehod also can apply o he forecasing value of secors. Once he weighed adjusmen process has been carried ou, he sum of he forecasing values of he energy caegory and secor caegory will saisfy he principle of Energy Balances. In order o measure he sysemaic forecas error afer adjusmen, he presen paper develops a new measure - adjused MAPE - which is abbreviaed as AMAPE. is as follows. 1 AMAPE = N N n [ = 1 i= 1 F i A A i i ] The formula, (3) where Fi indicaes he forecasing value of he i h energy caegory of period, Ai is he realized observaion of he i h energy caegory of period, N is he number of he forecasing periods, and calculaes he sysemaic forecas error of every level. 6 n is he number of energy caegories. The new measure, AMAPE, If he MAPE (or AMAPE) of he firs

7 level is smaller han AMAPE, hen i shows ha he combined hybrid forecas mehod and muli-level forecasing error conrolling mehod can reduce he sysemaic forecas error. The benefis of he above new procedure are o guaranee ha he forecasing error has been conrolled in a reasonable small range and o provide balanced forecass for all caegories of energy demand daa. EXAMPLE AND RESULT In order o illusrae he applicaion of he muli-level forecasing error conrolling mehod more specifically, he presen paper akes Taiwan s Energy Balances daa as he inpu of he EnFore-D subsysem. In he EnFore-D subsysem he energy demand daa adop he IEA srucure as in Table 1, divided ino a by-energy caegory and by-secor caegory. There are 23 energy iems in he by-energy caegory, including oal secondary energy consumpion. In he by-secor caegory here are 20 secor iems in oal. There are four levels of daa srucure in he EnFore-D subsysem. The firs level is he oal energy consumpion. The second level can be divided ino coal and coal producs, peroleum producs, naural gas, and elecriciy. The hird level includes he deailed iems of coal and coal producs and peroleum producs. There are five deailed iems in coal and coal producs and hireen deailed iems in peroleum producs. The final level is he energy consumpion of every secor. The hisorical daa srucure beween levels fis he balance principle as inroduced in he above secions. For simpliciy, he presen paper shows he resul of shor-erm (monhly) energy demand forecasing only. Oher wo ypes of mid-erm and long-erm energy demand forecasing resuls are similar. Basically, he number of candidae forecasing models is he same as he number of forecasing mehods used in he EnFore-D sysem. In a way, one can say ha he muli-level forecasing error conrolling mehod developed by his paper is independen o he forecasing models. The more mehods ha are used in he energy demand forecasing, he more candidae forecasing models ha are needed o be consruced for comparing he forecasing errors. Of course, more ime and cos would be spen on producing he saisfacory and balanced forecasing resul if more forecasing mehods were used. Two o six differen forecasing mehods are usually used in he EnFore-D sysem. Some researchers like o adop only wo forecasing mehods - for insance, he exponenial smoohing mehod and Box & Jenkin s ARIMA mehod - o es he muli-level forecasing error conrolling mehod, simply because hey believe ha he wo mehods would be good enough o produce a reliable forecasing resul or hey jus wan o save he forecasing cos in he job of shor-erm energy demand forecasing. As such, he wo candidae forecasing models should be buil o compare he forecasing errors. Afer ha, he MAPE measures will be calculaed for hese wo candidae forecasing models for every energy iem. The 7

8 smaller MAPE measure of hese wo candidae forecasing models would be he bes forecasing model for specific iems. Please noe ha i is no necessary ha all iems have he same bes forecasing mehod (even when here are wo forecasing mehods only in his case). I is quie possible and reasonable ha some iems will have a smaller forecasing error for he exponenial smoohing mehod, and some will prefer Box & Jenkin s ARIMA mehod. This kind of resul is quie accepable for he proposed sysem forecasing mehod. Table 2 illusraes he forecas error of every level of energy caegory. The lengh of he daa in Table 2 begins from January 1982 and ends a March Since welve daa poins are kep for he ou-sample es and error measuremen, he presen paper keeps he daa from January 1982 o March 2002 o build he candidae forecasing models. The bes model will be used o predic 12 monhs from April 2002 o March Finally, AMAPE is also calculaed o evaluae he sysemaic forecasing error. In Table 2, he AMAPE measure of he firs level of oal secondary energy consumpion is , which is smaller han he AMAPE measure of he second level of oal secondary energy consumpion, (abou 26.3% improved). From he same Table 2, i is obvious ha he hird levels of he AMAPE measure of coal and coal producs and peroleum producs are much bigger, and , respecively. The AMAPE measure of he oal secondary energy consumpion is smaller han he AMAPE measure of every sub-level. In fac, his is same as he resul of he by-secor caegories. This resul shows ha combining he hybrid forecasing mehod and muli-level forecasing error conrolling mehod can really reduce he sysemaic forecas error and produce he Energy Balances syle of forecasing a he same ime. Firs lelve of oal secodary energy consumpion Second level of oal secodary energy consumpion Third level of coal & coal producs Third level of peroleum producs Year Monh Forecasing error Forecasing error Forecasing error Forecasing error AMAPE(%) 8

9 DISCUSSION The muli-level forecasing error conrolling mehod provided by his paper mainly resolves he daa when i conains muli-level sysem daa wih many sub-caegories and requess he balance forecass in every level. For energy demand forecasing, he sysem forecasing oupu should saisfy he balance condiion in Energy Balances afer he forecasing. From he empirical sudy, he resul is consisen o he basic principle of he muli-level sysemaic forecasing error conrol. In addiion, he hybrid forecasing mehod is oally independen o he forecasing models used in he sysem. This provides a good poin of flexibiliy for choosing forecasing models by general users, because mos of ime general users do no have sufficien knowledge abou various forecasing models and heories. As menioned above, energy demand forecasing is he foundaion of almos all energy-relaed policies in every counry. Providing energy demand forecasing wih he syle of Energy Balances plus under he condiion of a reasonable small sysemaic forecasing error is highly demanded from governmen agencies as well as professional researchers or consulans. The presen sudy in he EnFore-D sysem has shown ha combining he hybrid forecasing mehod and muli-level forecasing error conrolling mehod no only solves he balance problem of forecasing, bu he mehodology ruly decreases he sysemaic forecasing error so as o make he forecasing resul more accurae. In conclusion, alhough he presen paper does no show how o secure he minimum sysem forecasing error for he hybrid forecasing mehod in a heoreical manner, he suggesive new procedure sill provides a consisen mehod which is highly and widely applicable o almos every field. REFERENCE Aposol, T.M. (1975), Mahemaical Analysis, second ediion, Boson: Addison-Wesley Publishing Corporaion. Bor, Y.J. e al (2004), Energy Forecasing Sysem (EnFore): Link-up World Energy Marke and Energy Modeling, Taipei: Energy Commission, ROC. Box, George E.P. and G.M. Jenkins, (1976), Time Series analysis: forecasing and conrol, rev. ed. San Francisco: Holden-Day. IEA (2003), Energy Balances of OECD Counries, Paris: Inernaional Energy Agency. IEA (2003), Energy Balances of Non-OECD Counries, Paris: Inernaional Energy Agency. Fuller, W. A. (1976), Inroducion o Saisical ime Series, New York: Wiley Gardner, E.S. (1985), Exponenial Smoohing: he Sae of he Ar. Journal of Forecasing, Vol. 4, pp Granger, C.W.J. and P. Newbold, (1974), Superious Regressions in Economerics, Journal of Economerics, Vol. 12, pp Granger, C.W.J. and M. Hashem Pesaran, (2000), Economic and Saisical Measures of Forecas Accuracy, Journal of Forecasing Vol. 19, pp Gardner Jr., E.S. and McKenzie, E.,(1988) Model idenificaion in exponenial smoohing, Journal of he Operaional Research Sociey, 39, pp Ljung, G. and G. Box (1979), On a Measure of Lack of Fi in Time Series Models. Biomerika, 66, pp

10 Tashman, L. J. and Kruk, J. M. (1996), The use of proocols o selec exponenial smoohing procedures: a reconsideraion of forecasing compeiions, Inernaional Journal of Forecasing, 12, pp Venkaachalam, A.R. and Jeffrey E. Sohl (1999), An Inelligen Model Selecion and Forecasing Sysem, Journal of Forecasing Vol. 18, pp