A Hybrid Neural Network and ARIMA Model for Energy Consumption Forecasting

Transcription

1 84 JOURNAL OF COMPUTERS, VOL. 7, NO. 5, MAY 202 A Hybrid Neural Nework and ARIMA Model for Energy Consumpion Forecasing Xiping Wang Deparmen of Economy and Managemen, Norh China Elecric Power Universiy, Baoding 07003, China wxpmm@26.com Ming Meng Deparmen of Elecrical Engineering, Norh China Elecric Power Universiy, Baoding 07003, China mmwxp@26.com Absrac Energy consumpion ime series consiss of complex linear and non-linear paerns and are difficul o forecas. Neiher auoregressive inegraed moving average (ARIMA) nor arificial neural neworks (ANNs) can be adequae in modeling and predicing energy consumpion. The ARIMA model canno deal wih nonlinear relaionships while he neural nework model alone is no able o handle boh linear and nonlinear paerns equally well. In he presen sudy, a hybrid mehodology ha combines boh ARIMA and ANN models is proposed o ake advanage of he unique srengh of ARIMA and ANN models in linear and nonlinear modeling. The empirical resuls wih energy consumpion daa of Hebei province in China indicae ha he hybrid model can be an effecive way o improve he energy consumpion forecasing accuracy obained by eiher of he models used separaely. Index Terms arificial neural neworks, ARIMA model, hybrid model, energy consumpion, ime series, forecasing I. INTRODUCTION Energy consumpion forecasing is he basis for making an energy developmen plan in decision making. So, i is criical o model and forecas i accuraely. This is rue especially for Hebei province in China. Since he inroducion of reform and an open-door policy, Hebei has experienced rapid economic growh. The consumpion of primary energy has also been increasing coninuously. Even wih an annual growu rae of 7.7% during he periods. The oal energy consumpion amouns has magnified by approximaely 7.76 imes from million ons of sandard coal in 980 o million ons of sandard coal in accordingly, one-off energy consumpion including coal, crude oil and naural gas had rising rend wholly. Recenly, he energy consumpion in Hebei province accouns for approximaely 0% of he counry s oal energy consumpion. Corresponding auhor. Tel.: / ; wxpmm@26.com Manuscrip received January, 20; acceped May, 20. The rapid growh of energy consumpion along wih he low efficiency of energy use, he paern of exensive economic growh and he backward managemen mode, he energy shorage problem confroned by Hebei is increasingly serious. The primary energy consumpion has oupaced is producion since 988. Nowadays, more han 50% of he energy has o be ransferred from oher provinces or o be impored from abroad. Furhermore, along wih he coninuous economic developmen and he acceleraion of indusriailizaion and urbanizaion processes, he energy consumpion will increase even more rapidly. I is hus clear ha he problem of balance of energy supply and demand deeply hreaens he susainable developmen of Hebei. Given his fac, he accuracy of energy consumpion forecasing is imporan no only for making scienific energy plan bu also for he susainable developmen of Hebei province. A sound forecasing echnique is essenial for energy consumpion forecasing. Mulivariae modeling along wih co-inegraed echniques or regression analysis has been used in a number of sudies o analyze and forecas energy consumpion [-3]. One limiaion of mulivariae models is ha hey depend on he availabiliy and reliabiliy of daa on independen variables over he forecasing period, which requires furher effors in daa collecion and esimaion. On he oher hand, univariae ime series analysis provides anoher modeling approach, which only requires he hisorical daa of he variable of ineres o forecas is fuure evoluion behavior. The univariae Box Jenkins auoregressive inegraed moving average (ARIMA) analysis has been widely used for modeling and forecasing many medical, environmenal, financial, and engineering applicaions [4 6]. Alhough ARIMA models are quie flexible in ha hey can represen several differen ypes of ime series, heir major limiaion is he pre-assumed linear form of he model. ARIMA models assume ha fuure values of a ime series have a linear relaionship wih curren and pas values as well as wih whie noise, so approximaions by ARIMA models may no be adequae for complex nonlinear real-world problems. However, real world sysems are ofen nonlinear, hus, i is doi:0.4304/jcp

2 JOURNAL OF COMPUTERS, VOL. 7, NO. 5, MAY unreasonable o assume ha a paricular realizaion of a given ime series is generaed by a linear process. Recenly, arificial neural nework (ANN) echniques have also gained populariy in energy demand forecasing [7]. The major advanage of neural neworks is heir flexible nonlinear modeling capabiliy. Wih ANNs, here is no need o specify a paricular model form. Raher, he model is adapively formed based on he feaures presened from he daa. This daa-driven approach is suiable for many empirical daa ses where no heoreical guidance is available o sugges an appropriae daa generaing process. However, using ANNs o model linear problems have yielded mixed resuls, and hence, i is no wise o apply ANNs blindly o any ype of daa [8]. In his paper, a hybrid model by combining ARIMA and ANN is proposed for energy forecasing. The moivaion of he hybrid model comes from he following perspecives [9]. Firs, i is ofen diffcul in pracice o deermine wheher energy consumpion series under sudy is generaed from a linear or nonlinear underlying process or wheher one paricular mehod is more effecive han he oher in ou-of-sample forecasing. Thus, i is diffcul o choose he righ echnique for heir unique siuaions. Typically, a number of differen models are ried and he one wih he mos accurae resul is seleced. However, he final seleced model is no necessarily he bes for fuure uses due o many poenial influencing facors such as sampling variaion, model uncerainy, and srucure change. By combining differen mehods, he problem of model selecion can be eased wih lile exra effor. Second, real-world ime series are rarely pure linear or nonlinear. They ofen conain boh linear and nonlinear paerns. If his is he case, hen neiher ARIMA nor ANNs can be adequae in modeling and forecasing ime series since he ARIMA model canno deal wih nonlinear relaionships while he neural nework model alone is no able o handle boh linear and nonlinear paerns equally well. Hence, by combining ARIMA wih ANN models, complex auocorrelaion srucures in he daa can be modeled more accuraely. Third, i is almos universally agreed in he forecasing lieraure ha no single mehod is bes in every siuaion. This is largely due o he fac ha a real-world problem is ofen complex in naure and any single model may no be able o capure differen paerns equally well. For example, in he lieraure of ime series forecasing wih neural neworks, mos sudies use he ARIMA models as he benchmark o es he effeciveness of he ANN model wih mixed resuls. Many empirical sudies including several large-scale forecasing compeiions sugges ha by combining several differen models, forecasing accuracy can ofen be improved over he individual model wihou he need o find he rue or bes model. Therefore, combining differen models can increase he chance o capure differen paerns in he daa and improve forecasing performance. The res of he paper is organized as follows. In he nex secion, he ARIMA and ANN modeling approaches o ime series forecasing were reviewed, and hen he hybrid mehodology is inroduced. Empirical resuls from he real daa se is repored in Secion 3. Secion 4 conains he concluding remarks. II. METHODOLOGY A. The ARIMA Model Inroduced by Box and Jenkins, he ARIMA model has been one of he mos popular approaches for forecasing. In an ARIMA model, he fuure value of a variable is assumed o be a linear funcion of several pas observaions and random errors. Tha is, he underlying process ha generae he ime series has he form: y = θ0 + ϕy + ϕ2 y ϕ p y p. () + ε θε θ2ε 2 θqε q where y and ε are he acual value and random error a ime, respecively; ϕ i ( i =,2,, p) and θ j ( j =,2,, q) are model parameers. p and q are inegers and ofen referred o as auoregressive and moving average orders, respecively. Random errors, ε, are assumed o be independenly and idenically disribued wih a mean of 2 zero and a consan variance of σ. Equaion () enails several imporan special cases of he ARIMA family of models. If q = 0, hen () becomes an AR model of order p. When p = 0, he model reduces o an MA model of order q. One cenral ask of he ARIMA model building is o deermine he appropriae model order (p, q). Based on he earlier work, Box and Jenkins [2] developed a pracical approach o building ARIMA models, which has he fundamenal impac on he ime series analysis and forecasing applicaions. The Box Jenkins mehodology includes hree ieraive seps of model idenificaion, parameer esimaion, and diagnosic checking. The basic idea of model idenificaion is ha if a ime series is generaed from an ARIMA process, i should have some heoreical auocorrelaion properies. By maching he empirical auocorrelaion paerns wih he heoreical ones, i is ofen possible o idenify one or several poenial models for he given ime series. Box and Jenkins proposed o use he auocorrelaion funcion (ACF) and he parial auocorrelaion funcion (PACF) of he sample daa as he basic ools o idenify he order of he ARIMA model. In he idenificaion sep, daa ransformaion is ofen required o make he ime series saionary. Saionariy is a necessary condiion in building an ARMA model used for forecasing. A saionary ime series is characerized by saisical characerisics such as he mean and he auocorrelaions rucure being consan overime. When he observed ime series presens rend and heero scedasiciy, differencing and power ransformaion are applied o he daa o remove he rend and o sabilize he variance before an ARIMA model can be fied. Once a enaive model is idenified, esimaion of he model parameers is sraighforward. The parameers are

3 86 JOURNAL OF COMPUTERS, VOL. 7, NO. 5, MAY 202 esimaed such ha an overall measure of errors is minimized. This can be accomplished using a nonlinear opimizaion procedure. The las sep in model building is he diagnosic checking of model adequacy. This is basically o check if he model assumpions abou he errors, ε, are saisfied. Several diagnosic saisics and plos of he residuals can be used o examine he goodness of fi of he enaively enerained model o he hisorical daa. If he model is no adequae, a new enaive model should be idenified, which will again be followed by he seps of parameer esimaion and model verificaion. This hree-sep model building process is ypically repeaed several imes unil a saisfacory model is finally seleced. The final seleced model can hen be used for predicion purpose. B. The Arificial Neural Neworks Model Arificial neural neworks(ann) can be described as an aemp by humans o mimic he funcioning of he human brain. The models are analyical echniques modeled afer he processes of learning in he cogniive sysem and he neurological funcions of he brain and are capable of predicing new observaions (of specific variables) from oher observaions (of he same or oher variables) afer execuing a process of so-called learning from exising daa. The models can be buil wihou explicily formulaing he possible relaionship ha exiss beween variables. Theoreical resuls show ha ANNs are also able o sufficienly approximae arbirary mappings o he desired accuracy if given a large enough nework. In his sense, ANN may be seen as mulivariae, nonlinear and nonparameric mehods, and hey should be expeced o model complex nonlinear relaionships much beer han he radiional linear models [0]. Single hidden layer feedforward nework is he mos widely used model form for ime series modeling and forecasing []. The model is characerized by a nework of hree layers of simple processing unis conneced by acyclic links. The relaionship beween he oupu (y ) and he inpus (y,..., y p ) has he following mahemaical represenaion: q y = ω + ωg( ω + ω y ) + e 0 j 0 j i, j i j= i= p. (2) Where ω j ( j=,2,,q) and ω i, j (i=0,,2,,p; j=,2,,q) are he model parameers ofen called connecion weighs; p is he number of inpu nodes and q is he number of hidden nodes. The sigmoid funcion is ofen used as he hidden layer ransfer funcion, ha is, sig( x) = (+ exp( x) ). (3) Hence, he ANN model of (2), in fac, performs a nonlinear funcional mapping from he pas observaions (y,..., y p ) o he fuure value y, i.e. y = f( y,..., y, ω) + e. (4) p Where ω is a vecor of all parameers and f is a funcion deermined by he nework srucure and connecion weighs. Thus, he neural nework is equivalen o a nonlinear auoregressive model. Noe ha expression (2) implies one oupu node in he oupu layer, which is ypically used for one-sep-ahead forecasing. The simple nework given by (2) is surprisingly powerful in ha i is able o approximae arbirary funcion as he number of hidden nodes q is sufficienly large. In pracice, simple nework srucure ha has a small number of hidden nodes ofen works well in ou-ofsample forecasing. This may be due o he over-fiing effec ypically found in neural nework modeling process. An overfied model has a good fi o he sample used for model building bu has poor generalizaion abiliy for daa ou of he sample. The choice of q is daa dependen and here is no sysemaic rule in deciding his parameer. In addiion o choosing an appropriae number of hidden nodes, anoher imporan ask of ANN modeling is he selecion of he number of lagged observaions, p, he dimension of he inpu vecor. This is perhaps he mos imporan parameer o be esimaed in an ANN model because i plays a major role in deermining he (nonlinear) auocorrelaion srucure of he ime series. However, here is no heory ha can be used o guide he selecion of p. Hence, experimens are ofen conduced o selec an appropriae p as well as q. Once a nework srucure (p,q) is specified, he nework is ready for raining--a process of parameer esimaion. As in ARIMA model building, he parameers are esimaed such ha an overall accuracy crierion such as he mean squared error is minimized. Various ypes of algorihms have been found o be effecive for mos pracical purposes. Levenberg Marquard opimized raining algorihms is used in his sudy. The esimaed model is usually evaluaed using a separae hold-ou sample ha is no exposed o he raining process. This pracice is differen from ha in ARIMA model building where one sample is ypically used for model idenificaion, esimaion and evaluaion. The reason lies in he fac ha he general (linear) form of he ARIMA model is pre-specified and hen he order of he model is esimaed from he daa. The sandard saisical paradigm assumes ha under saionary condiion, he model bes fied o he hisorical daa is also he opimum model for forecasing. Wih ANNs, he (nonlinear) model form as well as he order of he model mus be esimaed from he daa. I is, herefore, more likely for an ANN model o overfi he daa. There are some similariies beween ARIMA and ANN models. Boh of hem include a rich class of differen models wih differen model orders. Daa ransformaion is ofen necessary o ge bes resuls. A relaively large sample is required in order o build a successful model. The ieraive experimenal naure is common o heir modeling processes and he subjecive judgemen is someimes needed in implemening he model. Because of he poenial overfiing effec wih boh models, parsimony is ofen a guiding principle in choosing an appropriae model for forecasing.

4 JOURNAL OF COMPUTERS, VOL. 7, NO. 5, MAY C. The Hybrid ARIMA-ANN Model Boh ARIMA and ANN models have achieved successes in heir own linear or nonlinear domains. However, none of hem is a universal model ha is suiable for all circumsances. The approximaion of ARIMA models o complex nonlinear problems may no be adequae. On he oher hand, using ANNs o model linear problems have yielded mixed resuls. Hence, i is no wise o apply ANNs blindly o any ype of daa. Since i is difficul o compleely know he characerisics of he daa in a real problem, hybrid mehodology ha has boh linear and nonlinear modeling capabiliies can be a good sraegy for predicing energy consumpion. By combining differen models, differen aspecs of he underlying paerns may be capured [2-3]. I may be reasonable o consider he energy consumpion series o be composed of a linear auocorrelaion srucure and a nonlinear componen. Tha is, Y = L + N. (5) Where L denoes he linear componen and N denoes he nonlinear componen. Boh of hese wo parameers have o be esimaed from he ime series daa. Firs ARIMA model is used o capure he linear componen, hen he residuals from he linear model will conain only he nonlinear relaionship. Le e denoe he residuals a ime from he linear model, hen: e = Y YF. (6) Where YF is he prediced value of he ARIMA model a ime. The diagnosic check of he residuals is imporan o deermine he adequacy of he ARIMA models. An ARIMA model is no sufficien if here are sill linear correlaion srucures lef in he residuals. However, diagnosic check of he residuals is no able o deec any nonlinear paerns in he ime series daa. For his reason, even if he residuals pass he diagnosic check and he model is an adequae one, he model may sill no be sufficien in ha nonlinear relaionships have no been appropriaely modeled. Any significan nonlinear paern in he residuals will indicae he limiaion of he ARIMA. Therefore, he residuals can be modeled by using ANNs o discover nonlinear relaionships. Wih n inpu nodes, he ANN model for he residuals will be: e = f ( e, e 2,, e n) + u. (7) Where f is a nonlinear funcion deermined by he neural nework and u is he random error. Noe ha if he model f is no an appropriae one, he error erm is no necessarily random. Therefore, he correc model idenificaion is criical. Denoe NF as he forecas from (7), hen he combined predicion will be: YF = LF + NF. (8) In summary, he proposed mehodology of he hybrid sysem consiss of wo seps. In he firs sep, an ARIMA model is used o analyze he linear par of he problem. In he second sep, a neural nework model is developed o model he residuals from he ARIMA model. Since he ARIMA model canno capure he nonlinear srucure of he daa, he residuals of linear model will conain informaion abou he nonlineariy. The resuls from he neural nework can be used as predicions of he error erms for he ARIMA model. The hybrid model explois he unique feaure and srengh of ARIMA model as well as ANN model in deermining differen paerns. Thus, i could be advanageous o model linear and nonlinear paerns separaely by using differen models and hen combine he forecass o improve he overall modeling and forecasing performance. Ⅲ. APPLICATION OF THE HYBRID MODEL TO ENERGY CONSUMPTION FORECASTING A. ARIMA Modeling Taking he energy consumpion (EC) of Hebei from 980 o 2008 as he example. Because of many facors influencing he energy demand, such as he growh of he economy, he indusry framework, people s income level, he weaher, he governmen s policy and so on, he hisorical daa of he energy consumpion of Hebei from 980 o 2008 was increasing over ime and was no saionary, as shown in figure Figure Energy consumpion of Hebei from 980 o 2008 (million ons of sandard coal). (C,T,K) TABLE I. TEST OF THE UNIT ROOT HYPOTHESIS ADF saisic Criical value % 5% 0% X (C,T,) Y (C,N,) Z (N,N,) C,T and K indicae he model saisics wih inercep, rend and he number of lags, N indicaes wihou rend or inercep To eliminae he heeroscedasiciy, he logarihmic and hen differenial funcion of EC was compued o obain is saionary series. The logarihmic series of EC was X, Y and Z were he -order difference and he 2- order difference series of X respecively. Then examined he ime series properies of he daa using ADF (Augmened Dickey Fuller) es. The resuls are given in

5 88 JOURNAL OF COMPUTERS, VOL. 7, NO. 5, MAY 202 able I. I can be seen from able I ha X has a uni roo in levels and is saionary in second difference. Afer Z was idenified as saionary, he bes fi AR parameers and MA parameers should be esimaed according o is parial auocorrelaion (PAC) funcion and auocorrelaion (AC) funcion, respecively. Figure 2 shows he AC and PAC of Z. I was obvious ha he AC energy consumpion daa ses for each parameer were normalized o he range of [0, ]. The number of neurons in he inpu and oupu layers have been se as 4 and respecively. In order o deermine he opimum number of hidden nodes, a series of differen opologies were used. Compared wih he raining resuls, i was found ha he raining se had he Figure 2 The AC and PAC graph of Z funcion died off smoohly a a geomeric rae afer one lag and he PAC declined geomerically afer one lag. Therefore, he parameers of AR and MR can be chosen as for he ARIMA model. However, in he pracical fiing process, any oher AR/MA parameers could be seleced. For insance, he AR parameers can be defined as or 4, he MA parameers can be defined or 7. Afer fied, ARIMA(,2,) has been found o be he mos parsimonious among all ARIMA models. Once he ulimaely fies model was idenified, he equaions form of he model could be obained: Z = Z -.438μ. The series Z was he 2-order difference of X, The series X was he logarihmic funcion of EC, so EC could be expressed as: 2 X- X Z-.438μ- EC = e By his model, he forecasing EC of each year was calculaed. Based on his, he residual beween he original sequence and prediced resuls e can be caculaed as: e = 2 X X + EC Z.438 μ e B. Neural Nework Modeling A hree-layer feedforward neural nework model was developed for he predicion of energy consumpion using an opimized Levenberg Marquard raining algorihm. The daa for he period beween 980 and 2008 were available for he modeling purposes. Energy consumpion ime series daa were divided ino wo independen daa ses. The firs daa se of 980 o 2005 was used for model raining, and he second daa se of 2006 o 2008 was used for model verificaion purposes. In he ANN modeling process, he inpu and oupu Figure 3 Training performance of ANN model. lowes error value when he number of hidden unis was 9. 9 is chosen as he number of hidden nodes. Thus he number of each layer s neurons in he nework was 4-9-, respecively. The parameers of he nework were chosen TABLE II. COMPARING THE PREDICTED RESULTS WITH ACTUAL VALUE Acual value ARIMA prediced value ANN prediced value ARIMA-ANN prediced value TABLE III. FORECASTING PERFORMANCE OF DIFFERENT MODEL ARIMA ANN ARIMA-ANN RMSE MAE MAPE 3.536% % 0.3% TABLE IV. FORECASTING RESULTS OF ENERGY CONSUMPTION FOR HEBEI PROVINCE FROM 2009 TO 203 Forecasi ng value Growh rae % 3.% 0.9% 7.8%.6%

6 JOURNAL OF COMPUTERS, VOL. 7, NO. 5, MAY as follows: he ransformaion funcion of hidden neuron was ansig and logsig was he oupu layer funcion. The sop crierion of error funcion was se o 0.00 and he maximum of number of ieraion was 000. Compuer program has been performed under MATLAB 7.0 environmen. Figure 3 demonsraes he ANN model raining performance for energy consumpion parameer. C. Hybrid Modeling The proposed algorihm of he hybrid sysem consised of wo seps. In he firs sep, o analyze he linear par of he problem, an ARIMA model was employed. In he second sep, he residuals from he ARIMA model were modeled by using a neural nework model. Since he ARIMA model canno deec he nonlinear srucure of he energy consumpion ime series daa, he residuals of linear model will conain informaion abou he nonlineariy. The oupus from he neural nework can be used as predicions of he error erms of he ARIMA model. The hybrid model uilizes he unique feaure and srengh of ARIMA model as well as ANN model in deermining differen paerns. Therefore, i may be favorable o model linear and nonlinear paerns separaely by using differen models and hen combine he predicions o improve he overall modeling and predicing performance. In he hybrid modeling algorihm, he inpu and oupu energy consumpion daa ses for each parameer were normalized o he range of [0,]. In he modeling process, he hybrid model was rained o adjus he model so ha he model prediced energy consumpion parameers mach well wih observed daa. The verificaions resuls of lised in able II Table II indicaes ha he hybrid model predicion resuls reasonably mach he observed energy consumpion. D. Compaison of Model Performance To evaluae he performance of he forecasing capabiliy, he hree evaluaion ssisics: roo mean square error (RMSE), mean absolue error (MAE) and mean absolue percenage forecas error (MAPE) o each model are used. They are expressed as below: n 2 ( ) / i= n RMSE = Y YF n MAE = Y YF / n i= n i= MAPE = ( Y YF ) / YF / n 00% Where Y and YF are he i-h acural and forecasing values, respecively. And n is he oal number of predicions. Table Ⅲ repors he RMSE, MAE and MAPE for he year of 2006 o 2008 from he hybrid, ANN and ARIMA models. From able III, i can be seen ha he error levels in he case of he hybrid model are lower han in he oher wo cases, which leads us o he conclusion ha he hybrid neural nework presens a beer adapabiliy and consequenly produces beer resuls as well. Therefore, we can predic he energy consumpion daa of Hebei province from 2009 o 203 wih he hybrid model and he forecasing resuls of energy consumpion from 2009 o 203 are shown in able IV. As shown by predicion, he energy consumpion in Hebei province will coninue o increase for he nex 5 years. In 203, he energy consumpion will reach o million ons of sandard coal, a he average annual growh rae of nearly 2.8% during he period of 2009 o 203. Therefore, policy measures, such as energy axes, invesmens in improved energy efficiency, or changes in oupu composiion mus be considered explicily. IV. CONCLUSIONS Forecasing energy consumpion is one of he mos imporan policy ools by he decision makers, specifically for Hebei province in China. I is a challenge for us o develop forecas ools wih he energy consumpion series obained due o he complex linear and non-linear paerens. Taking he shorage of ARIMA and ANN forecasing model ino accoun, his sudy proposes a hybrid model aking advanage of he unique srengh of ARIMA and ANN in linear and nonlinear modeling. The forecasing performance of each model is assessed by hree saisical measures: RMSE, MAE, MAPE. The resuls of he saisical measures sugges ha he hybrid model can be an effecive ool o improve he forecasing accuracy obained by eiher of he models used separely. Therefore, using he hybrid model, we predic he energy consumpion of Hebei province from 2009 o 203. The resuls demonsrae ha he energy consumpion in Hebei province will coninue o increase for he nex 5 years. In 203 he energy consumpion will reach o million ons of sandard coal, a he average annual growh rae of nearly 2.8% during he period of 2009 o 203. Therefore, policy measures, such as energy axes, invesmens in improved energy efficiency, or changes in oupu composiion mus be considered explicily. ACKNOWLEDGMENT This work was suppored in par by a gran from he Fundamenal Research Funds for he Cenral Universiies (09MR44) and he Social Science Foundaion of Hebei province under Gran HB0XGL2 REFERENCES [] Himanshu AA, Leser CH. Elecriciy demand for Sri Lanka: a ime series analysis. Energy 2008;33: [2] Hamzacebi C. 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7 90 JOURNAL OF COMPUTERS, VOL. 7, NO. 5, MAY 202 [6] Kucuk, G., Basaran, C. Reducing energy consumpion of wireless sensor neworks hrough processor opimizaions Journal of Compuers, v2, n5, p67-74, May 2007 [7] Pao HT. Forecasing elecriciy marke pricing using arificial neural neworks. Energy Conversion and Managemen 2007;48: [8] Tso GKF, Yau KKW. Predicing elecriciy energy consumpion: a comparison of regression analysis, decision ree and neural nework. Energy 2007;32(9):76-8. [9] G. Peer Zhang. Time series forecasing using a hybrid ARIMA and neural nework model. Neurocompuing 2003; 50: [0] H.T. Pao. Forecasing energy consumpion in Taiwan using hybrid nonlinear models. Energy 2009;34: [] G. Zhang, E.B. Pauwo, M.Y. Hu. Forecasing wih arificial neural neworks: he sae of he ar. In. J. Forecasing 998;4: [2] Durdu Omer Faruk. A hybrid neural nework and ARIMA model for waer qualiy ime series predicion. Engineering Applicaions of Arificial Inelligence 200; 23: [3] Theodoros Kouroumanidis, Konsaninos Ioannou, Garyfallos Arabazis. Predicing fuelwood prices in Greece wih he use of ARIMA models, arificial neural neworks and a hybrid ARIMA-ANN model. Energy Policy 2009; 37: Xiping Wang was born in Hebei, China, on November, 969. She graduaed from Hebei Normal Universiy, Shijiazhuang, China, in 992. She received he M.E. and Ph.D. degrees from Beijing universiy in 999 and Tianjin Universiy in 2005, respecively. Her research ineress are ime series forecasing, neural neworks, macroeconomy and managemen. Her research has been published in some Chinese journals. Currenly, her research projec was suppored by he Fundamenal Research Funds for he Cenral Universiies and he Social Science Foundaion of Hebei province under Gran HB0XGL2. Ming Meng was born in Hebei, China, on December 20, 967. He graduaed from he Deparmen of Elecrical Engineering, Tianjin Universiy, Tianjin, China, in 99. He received he M.E. and Ph.D. degrees from Norh China Elecric Power universiy in 2000 and Tianjin Universiy in 2005, respecively. His research fields include elecrical machines, power elecronics, elecric drives, and renewable energy sysem. His curren research ineress are elecrical machine design, elecrical machine conrol, novel elecrical machines and is conrol, applicaions of power elecronics in power sysems, wind energy, solar energy,analysis and conrol of power qualiy, disribued generaion and smar grids.