anempirical Study Strictly as per the compliance and regulations of :

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1 Global Journal of Researches in Engineering: J General Engineering Volume 16 Issue 2 Version 1.0 Type: Double Blind Peer Reviewed Inernaional Research Journal Publisher: Global Journals Inc. (USA) Online ISSN: Prin ISSN: Performance Assessmen of SARIMA Model wih Hol Winer s Trend and Addiive Seasonaliy Smoohing Mehod on forecasing Elecriciy Producion of Ausralia an Empirical Sudy By Md. Maiur Rahman Molla, S.M. Nuruzzaman, Dr. M. Sazzad Hossain & Md. Shohel Rana Islamic Universiy, Bangladesh Absrac- Ausralia is a leading developed counry which is indispensable a proper planning and managemen of power generaion. To ake a unique planning decision forecasing of elecriciy producion is badly in need so ha elecriciy generaion copes wih he demand of he elecriciy smoohly. The main ask of his sudy is o assess he performance of wo ime series models in forecasing elecriciy generaion in Ausralia. Two ime series forecasing mehods such as ARIMA and Hol-Winer s addiive rend and seasonaliy smoohing mehods are considered. Applying Theil s U-saisic as he key performance measure, he sudy concludes ha Holwiner s mehod is more appropriae model. Keywords: elecriciy producion, seasonal ARIMA, smoohing, forecasing, ime series analysis. GJRE-J Classificaion : FOR Code: p PerformanceAssessmenofSARIMAModelwihHolWinersTrendandAddiiveSeasonaliySmoohingMehodonforecasingElecriciyProducionofAusralia anempirical Sudy Sricly as per he compliance and regulaions of : Md. Maiur Rahman Molla, S.M. Nuruzzaman, Dr. M. Sazzad Hossain & Md. Shohel Rana. This is a research/review paper, disribued under he erms of he Creaive Commons Aribuion-Noncommercial 3.0 Unpored License hp:// creaivecommons.org/licenses/by-nc/3.0/), permiing all non commercial use, disribuion, and reproducion in any medium, provided he original work is properly cied.

2 Performance Assessmen of SARIMA Model wih Hol Winer s Trend and Addiive Seasonaliy Smoohing Mehod on forecasing Elecriciy Producion of Ausralia an Empirical Sudy Md. Maiur Rahman Molla α, S.M. Nuruzzaman σ, Dr. M. Sazzad Hossain ρ & Md. Shohel Rana Ѡ Absrac- Ausralia is a leading developed counry which is indispensable a proper planning and managemen of power generaion. To ake a unique planning decision forecasing of elecriciy producion is badly in need so ha elecriciy generaion copes wih he demand of he elecriciy smoohly. The main ask of his sudy is o assess he performance of wo ime series models in forecasing elecriciy generaion in Ausralia. Two ime series forecasing mehods such as ARIMA and Hol-Winer s addiive rend and seasonaliy smoohing mehods are considered. Applying Theil s U-saisic as he key performance measure, he sudy concludes ha Holwiner s mehod is more appropriae model. Keywords: elecriciy producion, seasonal ARIMA, smoohing, forecasing, ime series analysis. I. Inroducion A presen elecriciy has become a firs and foremos precondiion of macroeconomic developmen of a erriory. Each day, elecriciy plays key rolein keeping homes and business running smoohly, powers ransporaion ha ake people work, school and oher places, and supplies elecriciy o appliances in all secors. The demand of elecriciy especially in for indusrial secor need no o say. Wihou elecriciy no only a single day bu also a momen is unimaginable. A counry s economic growh direcly relaed o elecriciy producion. Tha s why susainable elecriciy producion badly in needs o fulfill he demand of households as well as indusry and communicaion secors. To manage such kind of demand of elecriciy a counry s power developmen board has o ake sophisicaed decision o produce elecriciy ha can cope wih demand wih supply of energy. Being a developed counry monhly elecriciy producion of Ausralia is a seasonal and rending behavior. So, elecriciy producion auhoriy of Ausralia should ake plan for proper managemen of producion wih demand. To overcome uncerainy of fuure producion smoohing or forecasing approach ime series analysis is he mos applied mehod. For Auhor ασ ρ Ѡ : Islamic Universiy, Bangladesh. maiur508@gmail.com predicing Ausralian elecriciy producion, we will use convenional smoohing mehods and well known ARIMA modeling. Hence we wan o show he comparaive performance of referred model. This paper is divided ino six secions. The secion one of his sudy is he inroducory par. The second secion of he sudy will presen forecasing approach where we presen saionariy, Hol s-winer rend and addiive seasonaliy, Box-Jenkins mehodology SARIMA modeling and accuracy measuremen approach. Secion hree is he empirical daa analysis and forecasing while secions four is he accuracy measuremen and finally conclusion Basic Terminologies: The following keywords are used hroughou he research approach. Saionariy: Saionariy means ha here is no growh or decline in he daa. The daa mus be horizonal along he axis. A ime series is said o be saionary if is mean and variance are consan over ime and he value of he covariance beween he wo ime periods depends only on he disance or gap or lag beween he wo ime periods and no he acual ime is compued. Suppose y be a sochasic ime series hen, ( ) E y y var ( ) ( ) 2 2 = µ = E y µ = σ Hol s-winer s rend and addiive seasonaliy mehod The basic equaions of Hol-Winers rend and addiive seasonaliy mehod are as follows: Level LL = αα(yy SS ss ) + (1 αα)(ll 1 + bb 1 ) Trend: bb = ββ(ll LL 1 ) + (1 ββ)bb 1 Seasonal: SS = γγ(yy LL ) + (1 γγ)ss ss Forecas: FF +mm = LL + bb mm + SS ss+mm Where s is he lengh of seasonaliy (e.g., number of monhs or quarers in a year), LL represens he level of he series, bb denoes he rend, SS is he seasonal componen, and FF +mm is he forecas for m period ahead. Box-Jenkin s mehodology and ARIMA modeling 7

3 Performance Assessmen of SARIMA Model wih Hol Winer s Trend and Addiive Seasonaliy Smoohing Mehod on forecasing Elecriciy Producion of Ausralia an Empirical Sudy The general ARIMA model proposed by Box and Jenkins (1970) is wrien as ARIMA (p, d, q) bu when he characerisic of he daa is seasonal behavior hen i said o be SARIMA. And he seasonal ARIMA model is wrien as very formal noaion like his ARIMA (pp, dd, qq) (PP, DD, QQ) mm Non-seasonal Seasonal Par of he model par of he model AR: p = order of he auoregressive par I:d = degree of differencing involved MA: q = order of he moving average par m = number periods per season The basis of he Box-Jenkins modeling in ime series analysis is summarized he following figure and consis of hree phases: idenificaion, esimaion and esing, and applicaion. 8 Figure 1.1 : Schemaic represenaion of he Box-Jenkins mehodology for ime series modeling

4 Performance Assessmen of SARIMA Model wih Hol Winer s Trend and Addiive Seasonaliy Smoohing Mehod on forecasing Elecriciy Producion of Ausralia an Empirical Sudy Assessmen Approach: The validiy of he forecasing in ime series analysis can be assessedvia couples of approaches such as Mean error (ME), roo mean square error (RMSE), mean absolue error (MAE), mean percenage error (MPE), mean absolue percenage error (MAPE), mean square error (MSE), Mean absolue scaled error (MASE) and The il s U saisic. Percenage Error: If YY is he acual observaion for ime period and FF is he forecas for he same period, hen he percenage error is defined as PPPP = ( YY FF YY ) 100 Mean Percenage Error (MPE): nn MMMMMM = 1 nn PPEE =1 Mean Absolue Percenage Error: MMMMMMMM = 1 nn PPEE nn =1 If smaller he any above index is considered he beer forecasing echnique. Theil s U Saisic: I is defined as follows: Where FFFFEE +1 = FF +1 YY YY UU = nn 1 =1 (FFFFEE +1 AAAAEE +1 ) 2 nn 1 (AAAAEE +1 ) 2 =1 (forecas relaive change) And AAAAEE +1 = YY +1 YY (acual relaive change) YY If UU < 1: he forecasing echnique being used is beer han he naïve mehod. The smaller he U saisic is considered he beer forecasing echnique. II. Empirical Resuls Now, i is revealed o us ha he above figure of monhly Ausralian elecriciy producion exhibis an addiive seasonal and seadily increasing rend paern. Obviously he daa series is non-saionary. Before model building firs and foremos ask is o differeniae he original daa firs difference as well as seasonal firs difference. Figure: Time series plo of firs difference of he original daa Obviously, firs difference of original ime series daa is now of saionary. The model SARIMA (0, 1, 1) (0, 1, 2) [12] has chosen on he basis AIC & BIC crierion. The minimum of AIC & BIC ha model is aken as he ulimae model for forecasing. 9 Fig: 1. 2 : Ausralian monhly elecriciy producions from January, 1980 o Augus, 1995 Figure: 1.3 : Forecasing he elecriciy producion of Ausralia

5 Performance Assessmen of SARIMA Model wih Hol Winer s Trend and Addiive Seasonaliy Smoohing Mehod on forecasing Elecriciy Producion of Ausralia an Empirical Sudy 10 Densiy Diagnosic Checking: we wan o compare he performance of he SARIMA wih Hol s-winer rend and addiive smoohing approach. Mehod RMSE MAE MAP E SARIMA * SES HOLT s SNAIVE HOLT WINTER * MAS E Theil s U * * We may say from he above accuracy measuremen able ha he performance of SARIMA (0, 1, 1) (0, 1, 2) [12] model is beer han Hol s-winer mehod. Now, we wan o represen he hisogram of he respecive mehod sequenially Hisogram of forecaser forecaserrors Figure: Hisogram of forecas error of SARIMA (0,1,1)(0,1,2)[12] model Densiy Hisogram of forecaser forecaserrors Figure: Hisogram forecas error of Hol-winer s rend and addiive seasonaliy model Commen: On he basis of above wo hisogram of forecas error, i is revealed ha he boh of wo error erms shape is approximaely normal disribuion. So, he boh of he error erm represen whie-noise. Bu he SARIMA (0, 1, 1) (0, 1, 2) [12] model exhibis beer normaliy of forecas error han counerpar. Whie Noise Tes: The following Table represens he whie noise assessmen of he error erm of he fied model Tes P-value HH 00 Decision Ljung-Box accep saionary KPSS 0.1 accep Saionary ADF 0.01 Do no accep Saionary Above whie noise esing approach suggess here is lack of correlaion in error erm. So, he model is well fied. III. Conclusion The main goal of his paper was he performance assessmen beween seasonal ARIMA modeling wih Hol Winers exponenial smoohing approach. The empirical analysis revealed ha SARIMA (0, 1, 1) (0, 1, 2) [12] were he beer model han counerpar References Références Referencias 1. Anderson, T.W. (1994), The saisical Analysis of Time Series, Willey India pv. Ld, New Delhi, India. 2. AKAIKE, h. (1974) A new look a saisical model idenificaion, IEEE ransacion and auomaic conrol, AC-19, AWAL, M.A. and M.A.B. Siddique (2011), Rice Producion in Bangladesh Employing by ARIMA Model, Bangladesh Agriculural Journal.

6 Performance Assessmen of SARIMA Model wih Hol Winer s Trend and Addiive Seasonaliy Smoohing Mehod on forecasing Elecriciy Producion of Ausralia an Empirical Sudy 4. BROCKWELL, P., J. and R.A.DAVIS (1996) An inroducion o ime series and forecasing, New York: Springer-Verlag. 5. Box, G.E.P., G.M. Jenkins, and G.C. Reinsell (1994) Time series analysis: Forecasing and conrol, 3 rd ed., Englewood Cliffs, NJ: Prenice-Hall. 6. BOX, G.E.P AND D.A. PIERCE (1970) Disribuion of he residual auocorrelaion in auoregressiveinegraed moving average ime series models, Journal of he American Saisical Associaion, 65, Chafield, C. and M. YAR (1988) Hol-Winers forecasing: some pracical issues, The Saisician, 37, Doughery, C.,(2011), Inroducion o Economerics, Oxpord Universiy Press Inc., Newyork. 9. DICKEY, D.A. and W.A. FULLER (1979) Disribuion of he esimaors for auoregressive ime series wih a uni roo, Journal of he American Saisical Associaion, 74, Faisal, F. (2012) Time Series ARIMA Forecasing of Naural Gas Consumpion in Bangladesh s power secor Elixir Inernaional Journal, Elixir Prod. Mg. 49(2012) Gujarai, D.N. (2014), Basic Economerics, Taa Mc Graw Hill Ediion, New Delhi, India. 12. LEPOJEVIC, V. and M. A. PESIC (2011) Forecaing Elecriciy Consumpion by Using Hols -Winers and Seasonal Regression Model, Universiy Servia Economic Organizaion, Vol.8 pp Makridakis, S., and S.C. Wheelwrigh and R. J. Hyndman ( ) Forecasin Mehod and applicaions, Willey and Sons (Asia). 14. PEGELS, C.C.(1969) Exponenial forecasing: some new variaions, Managemen Science, 12, No. 5,