Research Article SARIMA-Orthogonal Polynomial Curve Fitting Model for Medium-Term Load Forecasting

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1 Discrete Dyamics i Nature ad Society Volume 216, Article ID , 9 pages Research Article SARIMA-Orthogoal Polyomial Curve Fittig Model for Medium-Term Load Forecastig Herui Cui, Pegbag Wei, Yupei Mu, ad Xu Peg School of Ecoomics ad Maagemet, North Chia Electric Power Uiversity, Baodig 713, Chia Correspodece should be addressed to Herui Cui; cuiherui1967@126.com Received 21 Jue 216; Accepted 4 October 216 Academic Editor: Paolo Rea Copyright 216 Herui Cui et al. This is a ope access article distributed uder the Creative Commos Attributio Licese, which permits urestricted use, distributio, ad reproductio i ay medium, provided the origial work is properly cited. Seasoal compoet has bee a key factor i time series modelig for medium-term electric load forecastig. I this paper, a seasoal-arima model is developed, but the parameters of the SAR ad the SMA tur out to be quite osigificat i most cases durig the model order selectio. To address this issue, the hybrid time series model based o the HP filter is utilized to extract the spectrum sequeces with differet frequecies ad aalyze iteractios amog various factors. Fially, a itegrative forecast is made for the electricity cosumptio from Jauary to November i 214. The empirical results demostrate that the method with HP filter could reduce the relative error caused by the iteractio betwee the tred compoet ad the seasoal compoet. 1. Itroductio To a certai extet, the medium-term power cosumptio is affected by the seasoal factors, the historical cosumptio, ad cosumptio peaks caused by uexpected evets. Accordig to the curret predictio techiques, these factors aretemporarilycategorizeditothelog-termtred(l), the seasoal fluctuatio (S), the cycle volatility factors (C), ad the irregular volatility factors (I). The iflueces of these factors superimpose o each other ad thus that became a difficult problem i model costructio. I recet years, may researches have bee coducted i the field of the above four fluctuatio factors i power load forecastig. The eural etwork method is ofte used to make predictios o electric load [1, 2], whereas, cosiderig the data volume, the time sequece model is more i lie with the characteristics of the sequece tha the eural etwork model [3]. Azadeh et al. [4] combied the seasoal fluctuatio ad the oliearity of forecastig with the fuzzy system ad data miig techiques to aalyze the mothly electricity demad i Ira. The SVM model ca also be exploited to aalyze the effect of the seasoal fluctuatio ad thelog-termtred[5].thesigificattredsequececabe aalyzed through the GM(1, 1) model combied with eural etwork method [6 8]. It follows that the characteristics such as tred ad seasoal oes are the key factors which affect the accuracy of the load forecastig i the medium-term load forecastig. The SARIMA model which could elimiate theeffectsofseasoalfactoradirregularchagefactors is more suitable for the mothly electricity cosumptio forecastig [9, 1]. The decompositio method of sequece is ofte used to aalyze the superimposed effect produced by seasoal chage tedecy ad the log-term growth ad declie tred [11]. Amog them, the applicatio of Hodrick- Prescott (HP) filterig method has the certai superiority i the series decompositio [12, 13]. The seasoal-arima model is able to take all seasoal fluctuatio of sequece ito full accout. However, due to the iteractio of the four fluctuatios, L, S, C, ad I, ad the iteractio betwee the seasoal factors ad the oseasoal factors, the seasoal parameters are osigificat i practical applicatios i most cases. HP filter is based o the spectral aalysis to separate the data sequeces ad relieve the superimposed impact of the fluctuatios. I this paper, by usig the HP filter we get the sequece {G} with sigificat tred ad the sequece {C} with sigificat periodicity. With separated modelig ad itegrative aalysis, the model ca successfully relieve the mutual ifluece of the chagig tred ad improve the precisio of predictio. Besides, to cope with the model order problems, the paper has coducted a log-memory test o the origial data sequece. The result shows that the sequece does ot meet the stadard radom

2 2 Discrete Dyamics i Nature ad Society walk process, which puts forward ew ideas with the power load forecastig. The purpose of this paper is to desig a accurate predictio model. Ad the remaiig parts of the paper are orgaized as follows. Sectio 2 itroduces the priciple of the method. Sectio 3 describes the process of the power load forecastig by usig the traditioal method ad the improved method ad discusses the results. The last sectio makes some coclusios of this paper. 2. Forecastig Models 2.1. SARIMA Model. SARIMA (Seasoal Autoregressive Itegrated Movig Average), which is deoted as SARIMA (p,d,q)(p,d,q) S, is based o the traditioal ARIMA(p, d, q) model, ad it ca elimiate the periodicity ifluece i a predictio process ad thus is a widely applied model for forecastig seasoal time series [14, 15]. The formula ca be described as follows: φ p (L) Φ P (L s ) (1 L) d (1 L s ) D y t =θ q (L) Θ Q (L s )ε t, where L is the backward shift operator. The itegers p, q, P, adq are the order of φ p (L), θ q (L), Φ P (L s ),adθ Q (L s ), respectively. The itegers d ad D are the umber of regular differeces ad seasoal differeces, respectively, ad, for a ostatioary time series y t, (1 L) d y t could come to a statioary series by usig the differece operator 1 L. L satisfies the formula L k y t =y t k.theformulas φ p (L) =1 φ 1 L φ 2 L 2 φ 3 L 3 φ p L p, θ q (L) =1 θ 1 L θ 2 L 2 θ 3 L 3 θ q L q (2) are polyomials i L of degrees p ad q.adtheformulas Φ P (L s )=1 Φ 1 L s Φ 2 L 2s Φ 3 L 3s Φ P L Ps, Θ Q (L s )=1 Θ 1 L s Φ 2 L 2s Θ 3 L 3s Θ Q L Qs (3) are polyomials i L of degrees P ad Q. Adε t which is a curret iterferece with variace σ 2 ad mea = is cosidered as the estimated residual at time t. Atthesame time, ε t is a idepedet ad idetically distributed ormal radom variable. I the process of the seasoal time series aalysis, there are three questios that eed to be aalyzed. (1) Statioary Test. The statioarity of the time series {y t } is the premise for buildig the S-ARIMA model. Whe it meets the coditio that μ, σ 2,adγ l are costats i formula (4), we ca defie {y t } as weakly statioary or covariace statioary: E(y t )=μ, var (y t )=σ 2, cov (y t,y t 1 )=γ l. (1) (4) The ADF uit root test ca be used to test whether the sequece {y t } is statioary or ot. If the sequece is ostatioary, the differece trasformatio would be used util the differece sequece is statioary. The statioary sequece with differetial trasformatio is defied as w t = Δ d y t. (2) Seasoal Aalysis. Before we make the seasoal aalysis, the autocorrelatio fuctio should be defied. It ca be expressed as follows: ρ k = t=k+1 (w t w) (w t k w) t=1 (w t w) 2, (5) where w t is a statioary sequece ad w is the average of the sequece {w t }. By judgig the autocorrelatio fuctio ad thecofideceiterval,theperiodicityadthecycles of {w t } could be obtaied. Accordig to the additive model which is defied as (6), the sequece {w t } cabeseasoallyadjusted: w t =TC t +S t +I t, (6) where TC t meas log-term tred ad cycle volatility, S t meas seasoal fluctuatio, ad I t meas irregular volatility. (3) Model Order Selectio ad Model Predictio. Firstly, theseasoallyadjustedsequeceisdefiedas{w SA }.The lag itervals for edogeous fuctio ad the cofidece iterval of the autocorrelatio fuctio ad the partial autocorrelatio fuctio should be aalyzed i order to determie the order of AR(p), MA(q), SAR(P), ad SMA(Q)adbuild the ARIMA(p, d, q)(p, D, Q) S model. The, accordig to the priciple of miimum mea square error, the predictio is the coditioal expectatio of y T+1,aditcabeexpressed as follows: y T (l) =E(y T+l y T,y T 1,...,y 1 ) ; (7) whe the higher-order problem exists i the ARIMA(p, d, q)(p,d,q) S model, we ca make the log-memory test for the statioary sequece {w t } R/S Method of ARFIMA Model. The log-memory aalysis, which is specific to the radom walk process, is put forwardbyh.e.hurstitheresearchoftherelatioship betwee the reservoir of water flow ad the storage capacity i Ad he puts forward the rescaled rage aalysis (R/S) for the log-memory aalysis. The the researchers ofte use this method for fiacial sequece aalysis ad build the Autoregressive Fractioally Itegrated Movig Average (ARFIMA) model [16, 17]. The aalysis procedure of R/S method is show i the followig paragraph. Firstly, the sequece {w t } is divided ito the ifiite umber of itervals, ad the legth of each iterval is.every iterval is defied as follows: w t, = t u=1 (w u M ), (8)

3 Discrete Dyamics i Nature ad Society 3 where M is the average of the iterval w u ad w t, is the cumulative deviatio of the iterval w u.thetheletterr ca be used i deotig the differece betwee the maximum w t, ad the miimum w t,,adtheletters ca be used i deotig the stadard deviatio of the sequece {w u },sothe formula of R/S aalysiscabeexpressedasfollows: K () H = R S = max (w t,) mi (w t, ) (1/) t=1 (w t w) 2, (9) where H, which is the Hurst Idex, is defied as the idex of ad K is a costat. The logarithm should be take o both sides of the equatio, ad adjust the equatio as follows: H= (log (R/S) log (K)). (1) log () ThetheHurstIdexcabeworkedoutbytheOLS method. Fially, the log memory ca be judged by the stadard as follows [18]: H<.5 H =.5.5<H<1 {w t }: mea reversio process {w t }: stadard radom walk process {w t }: log memory process; (11) whe.5<h<1, the origial sequece is likely to have a log memory [19]; however, whether there is a ARFIMA model which is suitable for most of the medium-term load forecastig caot be guarateed [2] Orthogoal Polyomial Curve Fittig. Orthogoal polyomial curve fittig is the improvemet of the Ordiary Least Square (OLS). There is a premise that the idepedet variables must be accurate values before usig the OLS method, but it is ot reasoable i most cases. Whe the error of the idepedet variables reaches a certai extet, the predictio model with OLS method would produce a certai error. I view of this situatio, the orthogoal polyomial curve fittig is proposed. Ad its basic priciple is that the square sum of the orthogoal distace from all poits to the fittig curve is miimum. I the OLS method the fittig polyomial ca be expressed as follows: y t =f(a, x t ), t=1,2,..., (12) which is fitted by the least square criterio: the distace square sum betwee the predicted value ad actual value is miimum, ad it ca be expressed as follows: mi e 2 t = mi (y t y t ) 2 = mi (y t a a 1 x t a x t )2 ; (13) the the udetermied coefficiets ca be got by the mea value theorem. This orthogoal polyomial curve fittig method is improved o the basis of OLS method, ad the errors of the depedet variable ad the idepedet variable are cosidered to build forecastig model. Ad the fittig polyomialcabeexpressedasfollows: y t =f(a, x t ), t=1,2,..., (14) where x t is the predicted value of the idepedet variable x t. The orthogoal distace error ca be expressed as follows: ε t = δ 2 t +σ2 t, (15) where δ t ad σ t are the radom error of x t ad y t,respectively. The the criterio of the orthogoal polyomial curve fittig ca be expressed as follows: mi ε 2 t = mi [δ 2 t +(y t a a 1 x t a x t )2 ]. (16) Combiig the orthogoal polyomial with the OLS method, the multiomial model ca rise to the imitative effect. The objective fuctio ca be expressed as follows: D= i=1 d(p i,l) 2, (17) where P i represets the real poit, L represets the fitted curve, ad d(p i,l) represets the orthogoal distace from therealpoitstothefittedcurve. The parameter equatio of fitted curve L cabedefied as follows: x(γ)=α+γcos θ, (18) y(γ)=β+γsi θ, where {α, β} is a poit of fitted curve L ad θ is the icluded agle of the taget to the abscissa axis, so the objective fuctio ca be expressed as follows: D= i=1 ((x i α) si θ (y i β)cos θ) 2. (19) Theweshouldtakeitspartialderivativewithrespectto α, β, adθ i order to calculate the miimum error ad the fittedcurve.theequatiosetcabeexpressedasfollows: D α = 2(x α) si2 θ+(y β)si 2θ = D β =(x α) si 2θ 2 (y β)cos2 θ= D θ =( (x i α) 2 (y i β) 2 si 2θ) t=1 t=1 2( (x i α)(y i β))cos 2θ =, t=1 (2) where x ad y are the mea values of the sequeces {x} ad {y}.

4 4 Discrete Dyamics i Nature ad Society 2.4. Hodrick-Prescott Filter. Hodrick ad Prescott first put forward Hodrick-Prescott filter (HP filter) method i the paper aalyzig the ecoomic cycle about postwar America. The method regarded the time series as the spectrum for aalyzig[14,15].itdividedthesequeceitotwogroups, adtheirrelatioshipwiththeorigialsequeceiscouted as y t =g t +c t, (21) where the sequece {G} with log-term tred is deoted as G = {g 1,g 2,...,g } ad the sequece {C} with short-term volatility is deoted as C = {c 1,c 2,...,c }.Theseparatio process must satisfy the miimum loss fuctio priciple: mi { (y t g t ) 2 t=1 +λ [(g t+1 g t ) (g t g t 1 )] 2 }, t=1 (22) where λ=σ 2 1 /σ2 2,whereλ is the smoothig parameter ad σ 2 1 ad σ2 2 represet the stadard deviatio of the sequece {G} ad the sequece {C}, respectively. Whe λ icreases, estimated total tred chages i relatio to the chage i the sequece which is reduced. It meas that λ takes the high umber, the estimated tred is more smooth, ad whe λ treds to ifiity, estimated tred will be close to the liear fuctio. As a geeral rule of thumb, whe we aalyze the mothly data, λ ca be defied as λ = 144. I this paper, the HP filter is applied to the oseasoally adjusted series, ad the origial sequece is divided ito two sequeces with the sigificat spectral frequecy ad buildig the model more accurately by weakeig the mutual effect betwee the two sequeces Error Estimatio Methods. There are five basic error estimatio methods; simultaeously, the model ca be evaluatedbyrelativeerror(re),meaabsolutepercetageerror (MAPE), root mea square error (RMSE), ad mea absolute error (MAE), which ca be expressed as follows: RE i = y i y i y i 1%, MAPE = 1 RMSE = 1 MAE = 1 y i y i 1% i=1 y i, i=1 (y i y i ) 2, y i y i. i=1 (23) 2.6. Sequece Aalysis ad Combiatio Model Buildig. The improved model is based o separatig the origial sequece by filterig aalysis. The accordig to the characteristics of each sequece, the models ca be established for forecastig. The detailed process is as follows. (1) Accordig to the HP filterig priciple, the origial sequece {y t }, defied as the superpositio of the waves with differet frequecies, ca be divided ito the sequece {G} ad the sequece {C}. (2) The sequece {G} is defied as a fuctio of time T, ad its scatter-plot ca be draw. The error term from each poit to the fittig curve is deoted as δ 1,δ 2,...,δ, σ 1,σ 2,...,σ. The the orthogoal polyomial with the OLS method is used for makig polyomial curve fittig to miimize the sum of squared errors mi ε 2 t = mi [( δt 2 +σ2 t )2 ]. (3) Accordig to the polyomial fittig i the previous step, the sequeces predictios ca be got ad defied as g t. (4) The statioary property of the sequece {C} is tested. If it was statioary, the correlatio aalysis ca be used o the sequece; otherwise, the differetial trasform is coducted o the sequece {C} util it is statioary. The statioary sequece is deoted as {w c }. (5) Through the correlatio aalysis of the seasoal fluctuatio, the autocorrelatio ad movig average items ca be acquired [18, 2]. Accordig to the result, the ARIMA model ca be defied as y c =φ 1 p ε c. (L) φ 1 P (L)(1 L) d (1 L s ) D θ q (L) Θ Q (L) (24) (6)TheratioalityoftheARIMAmodelistestedbythe residual sequece. (7) Accordig to the ARIMA model, the sequeces predictios ca be got ad deoted as c t. (8) The fial predictio result ca be obtaied based o the priciple of HP filter: y t = g t + c t. (25) The improved model will produce twice predictio error i the aalysis. I theory, there is the possibility of icreasig the errors ad reducig the predictio accuracy. But i the actual aalysis, the HP filter method weakes the mutual ifluece of factors (icludig the log-term tred ad the seasoal fluctuatio) ad utilizes itegrative forecastig for models with the differet characteristics of the sequece {G} ad the sequece {C}. Ithisway,thetredofthesequece ca be effectively fitted ad the ifluece o the seasoal tred ca be reduced. Fially higher predictio accuracy ca be achieved. Accordig to the above steps, the specific process of the improved model is show i Figure Empirical Aalysis The example chooses the research data about electric power cosumptio from Jauary 24 to November 214 i Chia, the data i Jauary 24 to December 213 for model buildig, ad the data i Jauary 214 to November 214 for testig the predictio error.

5 Discrete Dyamics i Nature ad Society 5 Iput {y} HP filter Sequece G Sequece C Curve fittig Defie the error terms δ ad σ mi{ (δ 2 t +σ2 t )} i=1 Yes Seasoal test No ARIMA model Statioarity test No Differece trasform Yes Seasoal adjustmet Yes No Polyfit y G = f(t) Adjust the fittig parameters Residual error sequece test Forecast ĝ t No statioarity ARIMA model meaigless Forecast Statioarity Combied forecast Figure 1: Model flow chart based o HP filter Figure 2: Mothly electricity cosumptio of Chia from Jauary 24 to December TheForecastigoftheSeasoal-ARIMAModel. Figure 2 plots the mothly electricity cosumptio data from Jauary 24 to December 213; as we ca see, the itercept ad the tred exist i the origial sequece, ad the sequece is ostatioary. The result of the ADF uit root test with itercept ad tred o the sequece is show i Table 1. The ADF uit root test demostrates that the origial sequece is ostatioary ad the first-order differece of the origial sequece is statioary uder the 5% sigificat level. Through observatio of the autocorrelatio fuctio of the first-order differece sequece, we discover that the sequece s seasoal cycle is 12. Therefore, the additive model is used to adjust the seasoal tred of the sequece. The aalysis of the partial autocorrelatio ad the autocorrelatio is show i Figure 3. O the basis of the 95% cofidece level, the cofidece iterval of the correlatio coefficiet is

6 6 Discrete Dyamics i Nature ad Society Autocorrelatio Partial correlatio AC PAC Q-Stat Prob Figure 3: Autocorrelatio figure ad partial autocorrelatio figure. Table 1: Augmeted Dickey-Fuller uit root test o d(ele). Augmeted Dickey-Fuller test statistic t-statistic Prob Test critical values: 1% level % level % level Prob. is the P value; the smaller the P value, the larger the sigificace. idicates to reject the origial hypothesis uder the cofidece level of 95%. [ 2, 2 ] = [.183,.183]. (26) Combied with Figure 3, we ca fid that partial autocorrelatio coefficiet i 1, 2, 11 ad the autocorrelatio coefficiet i 1, 11, 13 areotithecofideceiterval.basedo the autocorrelatio diagram ad the partial autocorrelatio diagram, OLS method is adopted to establish the seasoal- ARIMA model, ad the adjustmet of model parameters is based o the sigificace of correlatio coefficiet. The estimatio of parameter is show i Table 2. After determiig the model order through parameter sigificace testig, the time series model we obtai is ARIMA(2,1,11)(1,1,) 12.Ithismodel,theoseasoal autoregressive items are AR(1) ad AR(2), the oseasoal movig average items are MA(1) ad MA(11), ad the seasoal autoregressive items are SAR(1). Accordig to this model, the electricity cosumptio from Jauary to November i 214 could be forecasted ad the result is show i Table The Forecastig of the Seasoal-ARFIMA Model. I the process of model order selectio, MA(11) has sigificat ifluece o modelig ad predictig. This pheomeo shows that the error caused by the log-term observatios still iflueces the curret mothly electricity cosumptio to some extet. We ifer that the mothly electricity cosumptio may have the log-term memory characteristics, ad this cojecture is cofirmed by the log-term memory test usig R/S method which shows the Hurst expoet: (log (R/S) log (K)) H=, log () H =.837. (27) Accordig to the criteria,.5 <.837 < 1, we kow that the mothly electricity cosumptio has the log-term memory characteristic. Therefore the curret forecast is iflueced by the distat observatios Itegrative Model. The HP filter is applied to aalyze the origial sequece ad the smoothig parameter λ is assiged values as 144. Ad the decompositio results are show i Figure 4. The blue curve meas the origial sequece. The red curve meas the log-term tred, ad we ca fid that thegrowthrateofthepowercosumptioismailycostat from 24 to 213. The gree curve meas the cyclical ad

7 Discrete Dyamics i Nature ad Society 7 Table 2: The parameters estimate of the ARIMA model. ARIMA model AR(1) AR(2) AR(11) SAR(1) ARIMA(11, 1, 13)(1, 1, 1) 12 Coefficiet (t-statistic).742 ( 3.265).225 ( 1.699).345 (4.954).543 (4.956) ARIMA(2,1,11)(1,1,) 12 Coefficiet (t-statistic).368 ( 2.353).277 ( 2.488).66 ( 3.991) MA(1) MA(11) MA(13) SMA(1) ARIMA(11, 1, 13)(1, 1, 1) 12 Coefficiet (t-statistic) ( 17.58).421 ( 6.468).536 (7.11).41 (1.638) ARIMA(2,1,11)(1,1,) 12 Coefficiet (t-statistic).614 (5.127).341 (3.251) R 2 AIC SC ARIMA(11, 1, 13)(1, 1, 1) ARIMA(2,1,11)(1,1,) Electricity Tred Cycle Figure 4: HP filter diagram of the power cosumptio. irregular chage. Ad as time goes o, the fluctuatio rage is more sigificat. Accordig to HP filter, the origial sequece ca be separated ito the sequece {G} with the log-term tred ad the sequece {C} with other fluctuatio properties. The data separatio result usig HP filter is show i Figure5. We ca see thesequece {G} approximates a smooth curve, i which the curve of the sequece {C} fluctuates up ad dow aroud the zero. I the perspective of statistics, the sequece {G} ca be trasformed ito a sequece relatig to T. Let the idepedet variable T (T = 1,2,...,12)represet time ad let the sequece {G} represet the depedet variable of the system. A curve is fitted to describe the sequece {G} as a fuctio of T. It turs out that the best fittig is achieved whe the order of curve fittig is four ad the relative error of curve fittig is show i Figure 6. The fittig polyomial is G = t t t t (28) Sequece G Sequece C Figure 5: Data separatio based o HP filter. Accordig to the fittig polyomial, the sequece from Jauary to November 214 ca be forecasted ad the results are show i Table 3. The sequece {C} is aalyzed based o the time series model. Ad accordig to the sigificace we ca adjust the parameters ad record i Table 4. Fially, the model is ARIMA(11, 1, 1)(, 1, ) 12. Accordig to ARIMA(11, 1, 1)(, 1, ) 12,thesequece{C} is forecasted ad the predictio results from Jauary to November 214 are show i Table 5. Fially, accordig to the HP filter priciple, y t = g t + c t, we get the predictio of electric cosumptio from Jauary to November 214, as show i Table Model Error Aalysis. Accordig to Table 6, we make a lie chart about the absolute value of the relative error asshowifigure7.exceptformarch,may,adjue, the relative errors of the itegrative model are smaller tha

8 8 Discrete Dyamics i Nature ad Society Table 3: Forecastig of {G}. Time Predictios Ja Feb Mar Apr May Jue Jul Aug Sep Oct Nov Figure 6: Relative error of the curve fittig about sequece {G} i Jauary 24 to December Table 4: The parameters estimate of the ARIMA model. Variable Coefficiet t-statistic AR(1) AR(2) AR(11) MA(1) R 2 =.394 AIC = SC = Table 5: Forecastig of {C} Q1 214Q2 214Q3 214Q4 Time Predictios Ja Feb Mar Apr May Jue Jul Aug Sep Oct Nov the SARIMA model. From the log-term forecast i July to November, the forecastig results of itegrative model are superior to the forecastig results of SARIMA model. I March, May, ad Jue, the optimizatio models of fittig values are ot optimized. O the oe had, this is the objective result of the experimetal data; o the other had, theimprovedmethodisotperfecteough.thepredicted data is i the large floatig i March; this fluctuatio is caused by the predictio of sequece {C}. Accordig to the predictio result, we make aalysis for the predictio error ad fill the result i Table 7. Through the comparative aalysis, it ca be discovered that the predictio accuracy of the improved model is sigificatly improved. AsshowiTable7,theMSEoftheimprovedmodel is the miimum, ad it meas the predictive ability of the improved model is the most stable. By observig the MAPE, the improved model is 1.817%, which is less tha 2.643% of Itegrative model SARIMA model Figure 7: Predictio ad origial data of the lie graph from Jauary to November i 214. the SARIMA model, ad it shows that the predictive results oftheimprovedmodelareclosetotherealvalue.themae error measuremet also shows the same result. 4. Coclusios I this paper, HP filter is utilized for adjustig the time sequece data. Thus the origial sequece is decomposed ito the sequeces with differet tred, ad the mutual iterferece betwee the differet fluctuatio items ca be relieved. Moreover the relative error of load forecastig is reduced ad the multistep predictio is guarateed. The testig result of the R/S method shows that the mothly electricity cosumptio has the property of logmemory process. This coclusio may be attributed to iterfereceoftheamoutofthedata.however,itheactual order aalysis, the higher-order AR or MA ideed affects the power load forecastig. Therefore, the log memory of the time series ca be cosidered for buildig the SARFIMA model i the midterm power load forecastig. Competig Iterests Theauthorsdeclaredthatthereisocoflictofiterests related to this paper.

9 Discrete Dyamics i Nature ad Society 9 Table 6: Electricity cosumptio forecastig results i 214. Model Moth Origial data Seasoal-ARIMA Combied seasoal-arima Predictio RE (%) Predictio RE (%) Ja Feb Mar Apr May Jue Jul Aug Sep Oct Nov Table 7: The error of forecast. SARIMA model Improved model RMSE (%) MAPE (%) MAE Ackowledgmets The authors sicerely ackowledge the fiacial support from the Natioal Natural Sciece Foudatio of Chia (o ). Refereces [1] M. Meg, D. Niu, ad W. Su, Forecastig mothly electric eergy cosumptio usig feature extractio, Eergies, vol. 4, o. 1, pp , 211. [2] B. Yag ad Y. Su, A improved eural etwork predictio model for load demad i day-ahead electricity market, i Proceedigs of the 7th World Cogress o Itelliget Cotrol ad Automatio (WCICA 8), pp , Chogqig, Chia, Jue 28. [3] S. S. Pappas, L. Ekoomou, D. C. Karamousatas, G. E. Chatzarakis, S. K. Katsikas, ad P. Liatsis, Electricity demad loads modelig usig AutoRegressive Movig Average (ARMA) models, Eergy, vol. 33, o. 9, pp , 28. [4] A. Azadeh, M. Saberi, S. F. Ghaderi, A. Gitiforouz, ad V. Ebrahimipour, Improved estimatio of electricity demad fuctio by itegratio of fuzzy system ad data miig approach, Eergy Coversio ad Maagemet, vol. 49, o. 8, pp ,28. [5] M. De Felice, A. Alessadri, ad F. Catalao, Seasoal climate forecasts for medium-term electricity demad forecastig, Applied Eergy,vol.137,pp ,215. [6] C. Hamzacebi ad H. A. Es, Forecastig the aual electricity cosumptio of Turkey usig a optimized grey model, Eergy, vol. 7, pp , 214. [7] D. Niu ad M. Meg, Research o seasoal icreasig electric eergy demad forecastig: a case i Chia, Chiese Joural of Maagemet Sciece,vol.8,o.2,pp ,21. [8]N.Dogxiao,C.Zhiye,X.Mia,adX.Hog, Combied optimum gray eural etwork model of the seasoal power load forecastig with the double treds, Proceedigs of the CSEE,vol. 22, pp , 22. [9] Y. Wag, J. Wag, G. Zhao, ad Y. Dog, Applicatio of residual modificatio approach i seasoal ARIMA for electricity demad forecastig: a case study of Chia, Eergy Policy, vol. 48, pp , 212. [1] Q. Zhaju, Medium ad log-term load forecastig based o cesus X12-SARIMA model, i Proceedigs of the CSU-EPSA, vol. 28, pp , 214. [11] Z. Ma ad Q. Shu, Short term load forecastig based o ESPRIT itegrated algorithm, Power System Protectio ad Cotrol,vol.43,o.7,pp.9 96,215. [12] X. Zhu, W. Lua, ad Y.-S. Zhu, Aalysis of macroecoomic time series by the HP filter, i Proceedigs of the 2d Iteratioal Coferece o E-Busiess ad E-Govermet (ICEE 11), pp , Shaghai, Chia, May 211. [13]Y.He,B.Wag,J.Wag,W.Xiog,adT.Xia, Correlatio betwee Chiese ad iteratioal eergy prices based o a HP filter ad time differece aalysis, Eergy Policy, vol. 62, pp , 213. [14] R. S. Pidyck ad D. L. Rubifeld, Ecoometric Models ad Ecoomic Forecasts, Chia Machie Press, 4th editio, [15] F. Huahua ad Z. Ligyu, EViews Statistical Aalysis ad Applicatio, Chia Machie Press, Beijig, Chia, 29. [16] C. W. Grager ad R. Joyeux, A itroductio to log-memory time series models ad fractioal differecig, Joural of Time Series Aalysis,vol.1,o.1,pp.15 29,198. [17] Z. Huimig ad L. Jig, Bayesia Ecoometric Model, Sciece Press, Beijig, Chia, 29. [18] A. Lahiai ad O. Scaillet, Testig for threshold effect i ARFIMA models: applicatio to US uemploymet rate data, Iteratioal Joural of Forecastig, vol. 25, o. 2, pp , 29. [19] N. Chaâbae, A hybrid ARFIMA ad eural etwork model for electricity price predictio, Iteratioal Joural of Electrical Power & Eergy Systems,vol.55,pp ,214. [2] R. S. Tsay, Aalysis of Fiacial Time Series,JohWiley&Sos, New York, NY, USA, 3rd editio, 21.

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