Goba Joura of Pure ad Appied Mahemaics. ISSN 097-768 Voume, Number 06, pp. 6-67 Research Idia Pubicaios hp://www.ripubicaio.com ARAR Agorihm i Forecasig Eecriciy Load Demad i Maaysia Nor Hamizah Miswa *, Nor Hafizah Hussi, Rahaii Mohd Said, Khairum Hamzah & Emy Zairah Ahmad Facuy of Egieerig Techoogy UiversiiTeia Maaysia Meaa Hag Tuah Jaya, 7600 Duria Tugga Meaa Absrac Eecriciy oad demad has grow more ha four-fod over he as 0 years period. The purpose of he curre sudy is o evauae he performace of ARAR mode i forecasig eecriciy oad demad i Maaysia. ox-jeis Auoregressive Iegraed Movig Average ARIMA wi be used as a bechmar mode sice he mode has bee prove i may forecasig coex. Usig Roo Mea Square Error RMSE as he forecasig performace measure, he sudy cocudes ha ARAR is more appropriae mode. Keywords: Load forecasig, ARAR, ARIMA Iroducio ARAR agorihm is acuay a adapaio of ARARMA agorihm which he idea is o appy seeced memory-shoreig rasformaio, ad he fi a ARMA modes o he rasformed series []. ARAR agorihm is oe of he usefu forecasig echiques for a wide rage of rea daa ses. However, he appicaio of ARAR mode i forecasig eecriciy oad demad is si o widespread as compared o commoy used mode, which is ARIMA based o ieraure. Fog Li Chu [] sudied ARAR modes ad is usefuess as a forecas geeraig mechaism for ouris demad for ie major ouris desiaios i he Asia Pacific Regio. The forecas of ARAR mode was compared o Seasoa ARIMA SARIMA modes. ased o RMSE ad MAPE vaues, ARAR mode ca be deemed as credibe aeraive for forecasig i ourism demad area. Mahedra Shia ad ug Lerd Ng [] forecased he oa feriiy i Maaysia by usig ARAR agorihm ad ARIMA modes. They foud ha ARAR mode was he
6 Nor Hamizah Miswa e a mos appropriae modes for forecasig feriiy rae i Maaysia. igimeg [4] used Time Series modes i modeig ad forecasig houry wid producio i Swede. She used specra aaysis, seasoa ui roo ad HEG es, SARIMA ad ARAR agorihm o he warm ad cod seaso series. As a resu, ARAR agorihm ouperformed SARIMA modes for warm seaso ad for cod seaso, hese wo modes have simiar forecasig reds. I his paper, ARAR agorihm wi be used i forecasig Maaysia eecriciy oad demad ad is performace wi be compared o ARIMA modes. Mehodoogy ARAR Agorihm The ARAR agorihm is basicay he process ha appied memory shoreig rasformaio ad fiig he auoregressive mode o he rasformed daa. I is used o predic he fuure daa from exisig sequece daa. The agorihm was iroduced by rocwe ad Davis 000 ad i cosiss of hree phases hroughou he process. Phase : Memory Shoreig Process This phase ivoves he process of rasformaio from a og-memory series o a shor-memory series. This process coiues ui he rasformed series is cassified as shor-memory ad saioary. The agorihm for decidig amog he og-memory L, medium-memory M ad Shor-memory S ca be described as foows: For each,,...,5, is cacuaed ad we choose he vaue ha miimizes he equaio beow, mi y I he case of ad 0.9, we use equaio beow, ˆ I he case of or ad 0. 9, we use equaio beow, ˆ 4 If 0. 9, he series is shor-memory. Afer he shoreig-memory rasformaio is achieved, he shor-memory series is defied by, S,,... 6
ARAR Agorihm i Forecasig Eecriciy Load Demad i Maaysia 6 Phase : Fiig Auoregressive Mode The ex sep i his phase is o fi a auoregressive process o he mea correced series, S S,..., where S deoed by he sampe mea of S S,...,. The Auoregressive mode is fied usig he mode 4 beow, 0, ~ WN where Noe ha he coefficie ad whie oise variace are cacuaed by usig ue-waer s equaio as show beow, ad 0[, where ad,..., 0,,, are he sampe auocovariaces ad auocorreaios of he series } {. For each,, such ha m, he coefficie ca be compued by choosig m= or 6. Phase : Forecas The as sep i ARAR agorihm is o forecas usig he combiaio bewee he equaio obaied from phase ad phase. Phase is he memory-shoreig process ad phase is he fiig he auoregressive mode o he mea correced series. The memory-shoreig fier obai from he firs phase ca be expressed as : 4...... S 4 Noe ha is he poyomia i he bacward shif operaor. The auoregressive modes o he mea correced series obai from phase ca be expressed as: 5 The ARAR Mode is obaied by combiig equaios 4 ad 5, such ha : 6 S 6
64 Nor Hamizah Miswa e a The fia mode obaied i equaio 6 is he used o forecas. Figure : ARAR Agorihm process Forecas Accuracy Crieria The mos adequae mode for ARIMA forecasig which has bee se as a bechmar for his sudy wi be compared wih ARAR mode usig he forecasig accuracy crieria. RMSE has bee seeced o be oe of he powerfu forecas accuracy crieria which are give by he foowig equaio y yˆ RMSE Where y ad ŷ are he acua observe vaue ad he prediced vaues, resecivey, whie is he umber of prediced vaue. Resus ad Discussio Figure shows he iear red aaysis for he origia eecriciy oad demad daa. The po suggess ha he origia daa se is o saioary. Therefore, he firs differece y y yˆ is appied o he origia daa. 64
ARAR Agorihm i Forecasig Eecriciy Load Demad i Maaysia 65 Figure : Liear Tred Aaysis of he origia daa. Afer he series is saioary, he we appy he secod sep for ARAR agorihm which is fiig auoregressive mode. R saisica sofware has bee used o aayze he daa. ased o he resu from he sofware, i is suggess hahe opima ags for he fied mode are, 7, 4 ad. Afer ha, he fied mode is used o forecas he daa. Here, we se o forecas up o 0 sep head. The forecasig graph ad resu are show i Figure ad Tabe respecivey. Figure : Forecasig po for he firs differece daa usig ARAR agorihm ARIMA modes were seup as he bechmars for his sudy. ased o he po ad
66 Nor Hamizah Miswa e a he sigifica spie, he foowig ie modes have bee esimaed ad ideified usig R saisica sofware. The poeia modes are show i Tabe beow. Tabe : The is of he poeia ARIMA modes MODEL AIC RMSE MODEL AIC RMSE ARIMA,, 5.8060 67.957 ARIMA,, 4 5.68860 590.0 ARIMA,, 5.767 69.5779 ARIMA4,, 5.7980 608.654 ARIMA,, 4 5.7509 6.7 ARIMA4,, 5.74896 607.9474 ARIMA,, 5.7787 64.096 ARIMA4,, 4 5.6840 584.76 ARIMA,, 5.74956 6.74 The esimaed ARIMA mode for forecasig he eecrica oad wih heir correspodig AIC vaues is give i Tabe. I is show ha he ARIMA 4,, 4 has he miimum AIC ad RMSE vaues. I is show ha ARIMA 4,, 4 is bes mode modeig ad forecasig amog he oher ARIMA modes Comparaive Performace for ARAR ad ARIMA Modes RMSE wi be used as a forecas accuracy crierio i order o measure he performace of he bes modes from ARAR ad ARIMA modes. The RMSE vaues are abuaed i Tabe. Tabe : Comparaive performace for ARAR ad ARIMA modes. EST FORECASTING MODELS RMSE ARAR 46.84 ARIMA4,, 4 584.76 From Tabe, he owes RMSE vaues are from ARAR mode. Hece, ARAR modes are he bes modes for modeig ad forecasig eecriciy oad demad daa i Maaysia as compared o ARIMA modes. Cocusio The forecasig of eecriciy oad demad has become oe of he major fieds of research i rece years. This paper preses a aemp o forecas he oad demad by usig ARAR modes. ARIMA modes have bee seeced as bechmar sice he modes has bee exesivey used i may areas i ime series, especiay for oad forecasig. ARAR has bee cosidered as he bes mode as compared o ARIMA mode due o he owes RMSE vaue. This mode ca be used i forecasig he eecriciy oad demad i Maaysia for he fuure.. 66
ARAR Agorihm i Forecasig Eecriciy Load Demad i Maaysia 67 Acowedgemes The mai auhor woud ie o acowedge he suppor of he Facuy of Egieerig Techoogy FTK, Uiversii Teia Maaysia Meaa UTeM. Refereces [] Peer J. rocwe ad Richard A. Davis, Iroducio o Time Series ad Forecasig, Spriger Scieces & usiess Media, 006 [] Fog Li Chu, 008, Aayzig ad Forecasig Tourism Demad wih ARAR Agorihm, Tourism Maageme, 96 ; 85-96 [] Mahedra Shia ad ug Lerd Ng, 05, Forecasig he Toa Feriiy Rae i Maaysia, Paisa Joura of Saisics, 5; 547-556 [4] iagimeg, 00, Modeig ad Forecasig Houry Wid Power Producio i Swede, D-Leve i Saisics [5] Heio Hah, Sija Meyer-Nieberg ad Sefa Pic, 009, Eecric Load Forecas Mehods: Toos for Decisio Maig, Europea Joura of Operaioa Research 99, 90-907
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