Adeeb Ahmed Ali AL Rahamneh. Applied Statistics, Faculty of Business, AL Balqa Applied University, Jordan

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1 Middle-Eas Journal of Scienific Research 25 (7): , 2017 ISSN IDOSI Publicaions, 2017 DOI: /idosi.mejsr Using Single and Double Exponenial Smoohing for Esimaing The Number of Injuries and Faaliies Resuled From Traffic Accidens in Jordan ( ) Adeeb Ahmed Ali AL Rahamneh Applied Saisics, Faculy of Business, AL Balqa Applied Universiy, Jordan Absrac: This sudy aimed a esimaing he number of injuries and faaliies resuled from raffic accidens in Jordan for he period of ( ) by using he Single & Double Exponenial Smoohing, This sudy specifies he bes model which depends on he( MAPE, MAD, MSD) resuls, (Miniab) used o analyze he sudy daa, The sudy approved ha he Double Exponenial Smoohing is an appropriae model o measure and analyze injuries and faaliies in Jordan. Key words:double Exponenial Smoohing Faaliies Injuries Jordan Traffic Accidens Single Exponenial Smoohing INTRODUCTION selecion of he bes model of he ime series, Annual daa Inernaional grain prices, As well as he use of he Scienific research needs he ime series for effec of inerference on he chain daa and deermine he analysis, which represen he behavior and naure rank of he model by drawing funcions As well as he use of he changes ha occur o he phenomenon during of he effec of inerference on he chain daa and cerain periods of ime. Time series can herefore be deermine he rank of he model by drawing funcions used for planning and forecasing and ha he auocorrelaion funcion(acf) and parial auocorrelaion mehodology of ime series in general. I has funcion(pacf) become he mos common and used insrumen in a Aldalkhi, Sarmad Alwan [5]. This paper addressed a scienific communiy, ha mehodology proved o be number of saisical ools and how o use hem o conrol highly efficien in daa modeling of ime and invenories,the exponenial smoohing mehod was used forecasing [1]. o forecas he amoun of demand during he waiing One of he common mehods of forecasing and period, The bes mehod of forecasing was found o be planning is he Exponenial Smoohing mehods. The he single exponenial model. mehods is very imporan in he saisical mehods and Al Ajili, Saad Saber Mohammed, [2] This research procedures addressing noise and random errors [2], aims o analyze seasonal ime series using exponenial Exponenial Smoohing mehods can be defined in general smoohing models (Hol-Winer). in he case of as ha fine-uning or smoohing daa where inerference, muliplicaive and he addiive seasonal model.and he i is a kind of esimaion process, i is proven hrough he single and double exponenial seasonalas well ashe linear sudy of cases ha depend on ime or change wih ime. rendmodel. Saisicians develop a group of mehods and saisical Musa, Fares Jalal Abdullah, [6]. In his sudy, an mehods for use in forecasing and hese mehods o boo aemp was made whea producion modeling in Sudan exponenial mehod [3]. Hyndman [4] exended he in order o reach he model represens a paern which mehods of he exponenial smoohing and incorporaed indicaes i can be used o forecas he fuure, The he Damped Hol mehod. researcher applied he Arima models and he Exponenial Smoohing models o whea producion daa, Previous Sudies: Hamoooda, AllaAbdulsaar, [2]. In The model ha gave he bes fi for he series according his aricle, he wo mehods of exponenial smoohing o he crieria used is he Hol model for he exponenial were compared,and he impac of inerference in he smoohing. Corresponding Auhor: Adeeb Ahmed Ali AL Rahamneh, Applied Saisics, Faculy of Business, AL Balqa Applied Universiy, Jordan. 1544

2 Middle-Eas J. Sci. Res., 25 (7): , 2017 Munahil and Yunus [7] explained he rend seasonaliy of ime series, indeed he riple exponenial mehod (Winer's Mehod) model is beer han addiive model by using many crierions.mad, MAPE, MSE Safawi and Ghanem, [8] explained he comparison beween he Box-Jenkins mehod and Exponenial Smoohing mehods and compare he sandard based on he (MSE) (MAE) and (MAPE) Al-Tai and Al-Kurani, [9] menioned he reconciliaion of one of he ime series models, Predicion I is reached o he bes Models in he proporional because i has he less value for saisical sandard Akaike Informaion Crierion and Mean Square Error. Iniial Value: (Taylor, J.W. [10]) The smooh Exponenial mehods need an iniial value o sar o find a predicion algorihm, In mos cases, he firs real value is considered as he iniial value of he smoohing when using he simple exponenial. Parameers Esimaion: (Philipp K. Janer [11]) The esimaion parameers which is called a consan smoohing of he mos imporan seps in he forecasing process. The mehods of he exponenial smoohing depend on he value of he smoohing consan. The researchers disagreed on deermining he value of his fixed value, which is sandwiched beween zero and one. Choose he Model: There are several crieria for selecing he bes model among he esimaed models and hese crieria: (Sha'rawi, Samir Musafa, [12, 13]. Akaike Informaion Crierion 2 AIC (M) = nln + 2M Schwarz s Bayesian Informaion Crierion 2 SBIC (M) = nln + MLnn m: number of Parameers in he model Tes he Accuracy of he Predicive Resuls: The predicion of ime series assumes ha he ime series is a se of paerns and some random errors, which aims o separae he paern from he error by undersanding he direcion of he paern of daa in is long-erm increase or decrease and seasonaliy, any changes caused by seasonal facors and ha he goal of forecasing is o reduce he risk in he decision-making process and ha he more low error rae was accurae predicion [14]. There are several crieria by which o compare he mehods used o predic ime series. The lower hese values, he closer o he prediced values of he real values, Among he mos imporan of hese sandards [15, 16]. Mean Squared Error (MSE) n ( ) 2 X 1 X = MSE = n Roo Mean Squared Error ( RMSE) 1 n 2 RMSE = ( X ) 1 X n = Mean Absolue Percen Error ( MAP) 1 n X X MAP = [ ]*100 n = 1 X Mean Absolue Error ( MAE) 1 n MAE = [ X X ] where, n = 1 X X : is he acual observaion a ime : is he forecas value of X n: is he oal number of observaions Single Exponenial Smoohing: The smooh can be described by he following equaion simple exponenial equaion, [17]: (3) (4) (5) (6) F( + 1) = X() + (1 ) F() (7) Such ha X(): Represens he real value a ime(): F(): he forecas value a ime()represens: F( + 1): Represens he forecas value a ime(+1): Represens a fixed Sofening value limied and beween (0 1) This mehod is called exponenial smoohing o give he previous observaions weighs of unequal values and hese weighs are decreasing exponenially sequenially and can be illusraed by he following equaions: S = X + (1 ) X (8) 1 X : Represens he real value a ime() S : Represens he real value of predicion a ime(-1)

3 Middle-Eas J. Sci. Res., 25 (7): , 2017 S : Represens he real value of predicion a ime() : Represens a fixed Sofening value limied and beween (0 1) And repea he process of compensaion we ge S X (1 ) X (1 ) 2 (1 ) 3 1 X 2 X 3... (1 ) = S When subsaion (S ) in (S ) we ge: (11) 1 S = X + (1 )[ X + (1 ) s ] 1 2 When subsaion (S ) in (S ) we ge: 1 (9) j = (1 ) (1 ) j= 1 j + o S X S (12) S = X + (1 )[ X 1+ (1 )[ X 2 + (1 ) s 3].] (10) S : Represens he iniial value of he smooh process o The Pracical Side: Table (1) shows he number of injuries and faaliies resuling from raffic accidens in Jordan for he period ( ) Year Injuries Faaliies Source: The Hashemie Kingdome of Jordan, Minisry of Inerior, Public Securiy Direcorae, Jordan Traffic Insiue,,, Jordan Traffic Insiue. Annual Repor of Traffic Accidens for he Period ( ) [18] 1546

4 Middle-Eas J. Sci. Res., 25 (7): , 2017 Table 2: Shows he value (MAPE, MAD, MSD) according o differen values ( ) using he Single Exponenial Smoohing for Injuries MAPE MAD MSD MAPE MAD MSD Double Exponenial Smoohing (Philipp K. Janer [11]): ' '' b = ( S S ) (16) The binary exponenial smoohing mehod is one of he 1 exponenial longiudinal smoohing mehods, which smooh's he ime series wice. The saisical sooh from '' S : Smooh from he second grade series he firs and second levels uses he predicion calculaion. The smooh of he second grade series equaion as in he In equaions (15), (16) he b ( ) represens he local following equaion: smooh level a ime (), while ( ) represens he smooh level of he general rend of he ime series(), '' ' '' S = S + (1 ) S b he (13) predicion is horizonal o ( ) and replaced( ) and ( ) in 1 ( S ' ) and ( S '' ), we ge: The iniial predicion ( ) for he seps The seps for he ime series for period () are: ' '' Y+ = (2 + ) S (1 ) S 1 + (17) 1 Y+ = + b (14) When = 1 Such ha: = 1,2,... 2 ' 1 '' Y+ 1 = ( ) S ( ) S (18) 1 1 ' '' = 2S S (15) The resuls shown in he able above show, based on a crierion ( Leas MAPE, MAD, MSD) ha he bes forecas is when he value of ( ) is equal o (0.9). Fig. 1: Represens Single Exponenial Smoohing Plo for Injuries 1547

5 Middle-Eas J. Sci. Res., 25 (7): , 2017 Table 3: Shows he number of injuries expeced during he years ( ) according o he use of he mehod Single Exponenial Smoohing Year Forecas Lower Upper Table 4: Shows he value (MAPE, MAD, MSD) according o differen values ( ) using he Single Exponenial Smoohing for Faaliies MAPE MAD MSD MAPE MAD MSD The resuls shown in he Table(4) above show, based on a crierion ( Leas MAPE, MAD, MSD) ha he bes forecas is when he value of ( ) is equal o (0.9) Fig. 2: Represens Single Exponenial Smoohing Plo for Faaliies Table 5: Shows he number of Faaliies expeced during he years ( ) according o he use of he mehod Single Exponenial Smoohing Year Forecas Lower Upper Table 6: Shows he value (MAPE, MAD, MSD) according o differen values ( ) & ( ) using he Double Exponenial Smoohing for Injuries MAPE MAD MSD MAPE MAD MSD

6 Middle-Eas J. Sci. Res., 25 (7): , 2017 Table 6: Coninued 0.3 MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD The resuls shown in he Table (6) above show, based on a crierion ( Leas MAPE, MAD, MSD) ha he bes forecas is when he value of ( ) is equal o (0.9) &( ) is equal o (0.7) Fig. 3: Represens Double Exponenial Smoohing Plo for Injuries 1549

7 Middle-Eas J. Sci. Res., 25 (7): , 2017 Table 7: Shows he number of Injuries expeced during he years ( ) according o he use of he mehod Double Exponenial Smoohing Year Forecas Lower Upper Table 8: Shows he value (MAPE, MAD, MSD) according o differen values ( ) & ( ) by using he Double Exponenial Smoohing for Faaliies MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD MAPE MAD MSD The resuls shown in he Table (9) above show, based on a crierion (Leas MAPE, MAD, MSD) ha he bes forecas is when he value of ( ) is equal o (0.9) & ( ) is equal o (0.1) 1550

8 Middle-Eas J. Sci. Res., 25 (7): , 2017 Fig. 4: Represens Double Exponenial Smoohing Plo for Faaliies Table 9: Shows he number of Faaliies expeced during he years ( ) according o he use of he mehod Double Exponenial Smoohing Year Forecas Lower Upper Resuls: The sudy showed ha he bes forecas of injuries resuled from raffic accidens in Jordan when using he Single Exponenial Smoohing) according o leas crieria of (MAPE, MAD, MSD) is when he value of ( ) is equal o (0.9). The sudy showed ha he bes forecas of faaliies resuled from raffic accidens in Jordan when using he Single Exponenial Smoohing) according o leas crieria of (MAPE, MAD, MSD) is when he value of ( ) is equal o (0.9) The sudy showed ha he bes forecas of injuries resuled from raffic accidens in Jordan when using he Double Exponenial Smoohing) according o leas crieria of (MAPE, MAD, MSD) is when he value of ( ) is equal o (0.9)& ( ) is equal o (0.1) The sudy showed ha he bes forecas of faaliies resuled from raffic accidens in Jordan when using he Double Exponenial Smoohing) according o leas crieria of (MAPE, MAD, MSD) is when he value of ( ) is equal o (0.9)& ( ) is equal o (0.1) The sudy proved ha he use of he double exponenial smoohing echnique for he fuure forecasing of injuries resuled from raffic accidens in Jordan is beer han using he Single Exponenial Smoohing echnique, The sudy proved ha he use of he double exponenial smoohing echnique for he fuure forecasing of faaliies resuled from raffic accidens in Jordan is beer han using he Single Exponenial Smoohing echnique, Recommendaions: The researcher recommends he subjec of injuries resuled from raffic accidens in Jordan is a grea imporance by researchers because he resuls have vial social and economic impacs. The researcher recommends he subjec faaliiesresuled from raffic accidens in Jordan he grea imporance by researchers because he resuls have vial social and economic impacs. The researcher recommends using he double exponenial smoohing echnique for he fuure forecasing of injuries resuled from raffic accidens in Jordan. The researcher recommends using he double exponenial smoohing echnique for he fuure forecasing of faaliies resuled from raffic accidens in Jordan 1551

9 Middle-Eas J. Sci. Res., 25 (7): , 2017 REFERENCESS 8. Safawi, Safa Younis, Iman Ibrahim Ghanem, Iraqi Journal of Saisical Sciences, 25: Al-Tai, Fadel Abbas, esimae he muliplier 9. Al-Tai, Fadel Abbas, Al-Kurani and Jihani Fakhri smooh parameers, wih simulaion, Journal of Saleh, The Predicion of Seasonal ARIMA Tanmia AL Rafidain Compuer Science and Model by using Exponenial Smoohing Mehods Mahemaics, No. 1, Baghdad, Iraq wih Applicaion, Iraqi Journal of Saisical Sciences, 2. Hamoooda, Alla Abdulsaar, Comparison 14: beween exponenial Smoohing model and 10. Taylor, J.W., Exponenial Smoohing wih a Inervenion mehod on inernaional prices of barley, Damped Muliplicaive Trend, Inernaional Journal College of Compuers Sciences and Mahemaics, of Forecasing, 19: Tikri Journal of pure science, 18(1): Philipp K. Janer, 2006 "Exponenial Smoohing" 3. Al Ajili, Saad Saber Mohammed, This research WWW. Toy Problems.og. aims o analyze seasonal ime series using 12. Sha'rawi, Samir Musafa, Inroducion o exponenial smoohing models( Hol - Winer).in he Modern Time Series Analysis, King Abdul Aziz case of muliplicaive and he addiive seasonal Press, Riyadh, Saudi Arabia model.and he single and double exponenial 13. Sha'rawi, Samir Musafa, Inroducion o seasonal as well as he linear rend model. Modern Time Series Analysis, King Abdul Aziz 4. Hyndman, R.J., A.B. Koehler, R.D. Snyder and Press, Riyadh, Saudi Arabia S. Grose, A sae space framework for auomaic 14. Kalekar, Prajaka S., Time Series Forecasing forecasing using exponenial smoohing mehods. Using Hol- Winers Exponenial Smoohing, Inernaional Journal of Forecasing, 18(3): <URL:hp:// doi: /s (01) ing.pdf> _ExponenialSmooh. (Accessed 6 Sepember 2011) 15. Muar, Thafer R., A proposed echnique for 5. Aldalkhi, Sarmad Alwan, Invenory Conrol he problem of selecing he bes forecasing model Sysem for Fas Moving Iems in Baghdad Elecriciy in ime series: A case sudy, Iraqi Journal of Disribuion Sae, Tanmia AL Rafidain, 86(29): Saisical Science, 14: Musa, Fares Jalal Abdullah, Use of Arima and 16. Liu, L.M., Time Series Analysis and Exponenial Smoohing Models for Forecasing nd Forecasing, 2 ed., Scienific Compuing Associaes Whea Producion in Sudan for he Period Crop., Illinois, USA. ( ) (Comperaive Sudy), Sudan Universiy 17. Samreen, Faima, Hybrid Sysem of Simple of Science and Technology, Faculy of Science, PhD Exponenial Smoohing and Neural Nework, FAST Thesis un published. naional universiy, Karachi, Marke Forces January, 7. Munahil, Daniel and Yunus Nadwa, Forecasing he Sales Volume of he Medical Produc 18. The Hashemie Kingdome of Jordan, Minisry of by he Triple-Herediary Mehod, Journal of Inerior, Public Securiy Direcorae, Jordan Traffic Educaion and Science, 25(4). Insiue, Jordan Traffic Insiue.Annual Repor of Traffic ccidens for he Period ( ). 1552