# Fortified financial forecasting models: non-linear searching approaches

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2 Anoher model ha i ofen very effecive in generaing foreca when here i a ignifican eaonal componen i he exponenially weighed moving-average (EWMA forecaing model. A each poin in ime, he EWMA model eimae a moohed average from pa daa, an average from pa daa, an average rend gain, and he eaonal facor. Thee hree componen are hen combined o compue a foreca [3]. II. Smoohing echnique are higher form of naϊve forecaing model which aume ha an underlying paern can be found in he TS of a variable ha i being foreca. I i aumed ha hee hiorical obervaion repreen no only he underlying paern bu alo random variaion. By aking ome form of an average of po obervaion, moohing echnique aemp o eliminae he diribuion ariing from random variaion in he erie and o hoe he foreca on a moohed average of everal pa obervaion [8, 9]. A. Moving average. If a daa erie poee a large random facor, in an effor o eliminae he effec o hi randomne, a erie of recen obervaion can be average o arrive a a foreca. Thi i he moving average mehod. A number of oberved value are choen, heir average i compued, and hi average erve a a foreca for he nex period.. Simple MA may be defined a: Ŷ+ = = + [ ] = + Δ = (9 = + + Where i Δ [7].. Weighed moving average may be viewed a a cenered MA, where he obervaion in a equence don receive equal weigh. Ŷ + =[Σw y ], Where i he revere of he um of he weigh, and i he number of obervaion in a moving average. The greaer he number of obervaion ued in moving average, he greaer he moohing effec becaue each new obervaion receive le weigh (/ a increae. Hence, generally, he greaer he randomne in he daa erie and he lower he change in he underlying paern, he more preferable i i o ue a relaively large number of pa obervaion in developing he foreca. The choice of an appropriae MA period, ha i, he choice of, hould be baed on a comparion of he reul of he model in forecaing pa obervaion. One crieria ha i ofen ued for uch comparaive purpoe i he minimizaion of he average foreca error, or roo mean quare error. RMSE = m [ Σd ] = m = ( y y Where m i he number of ime period [8]. B. ir-order exponenial moohing. To foreca a aionary ime erie wih he exponenial moohing model, we fir mooh he ime erie wih a MA imilar o hoe decribed in order o iolae he yemaic or mooh componen of he erie. We hen projec hi mooh componen ino he fuure. The MA employed by he exponenial moohing model for aionary TS i a pecial ype of weighed MA. The mooh componen of a aionary ime erie may be conidered a a ucceion of eimae of he underlying mean level of he aionary proce. Updae he moohed eimae: = y + ( = + ( = + ( = + d + ( 3 + ( k =, k =,,3,... Where i he moohed eimae for he curren period, i he moohed eimae for he proceeding period -, y i he obervaion for he curren period, i he moohing conan, and Ŷ +k he foreca for k period ahead. Thee model weigh he mo recen obervaion by 0<<, and he pa forecaing by (-. A large indicae ha a heavy weigh i being placed on he mo recen obervaion [8]. C. Double exponenial moohing Model. Daa ha are colleced over ime frequenly exhibi a linear rend when a linear rend i no apparen in he daa, ingle exponenial moohing i well uied a a forecaing echnique. How if a rend i preen in he daa, DES i more appropriae for obaining foreca han i ingle ES. The DES i cloely relaed o he rend analyi echnique of imple linear regreion, in which he foreca for +, given TS up o and including ime. In DES, he coefficien a and b are conidered o be funcion of ime and are updaed a each ucceive obervaion become available. Thee updaed coefficien are given by he following expreion: ŷ + =a +b (+ b =[(-](S -S ( ( a =S - -b S S =y +(-S - ( =S +(- S S ( Where i a moohing conan choen o minimize he um of he quared foreca error, S i he ingle moohed aiic compued recurively, S ( i he double moohed aiic alo compued recurively, and he iniial value S 0 and S ( 0 are obained uing he relaed equaion a follow: S 0 = 0 -[(-/]b 0 S ( 0 = 0 -[(-/]b 0 The quaniie 0 and b 0 are iniial value of he regreion coefficien. If daa are available, ay, o ime,

5 be ued nonlinear opimizaion mehod for finding forecaing value of inere variable baed on line earching mehod. The iniial difference of forecaing mehod i mainly on adjuing he daa mechanim for opimal predicion of variable; hereby, he aricle fir analyzed differen kind of forecaing echnique epecially on adjuing variaion componen power, hen i followed ome baic decen mehod o minimize he ime erie reidual in relaion o acual value of variable. Becaue of making aionary ime erie advanage of hee mehod, i ha ried o how how o inegrae hi characeriic for generaing forified forecaing daa. REERECES [] J. Sco, Armrong, Reearch of forecaing: a quarer cenury review, Inerface, January-ebruary 986, Pp [] M. S., Bazaraa, H.D. Sherali and C.M. Shey, onlinear programming: heory and algorihm,..: John Wiley & Son, 993. [3] C. Gourieroux, & J. Jaiak, inancial economeric, ew Jerey: Princeon Univeriy Pre, 00. [4] M.R. Hamidizadeh, onlinear programming, Tehran: SAMT Publihing Co., 00. [5] J., Kowalik, and M.R. Oborne, Mehod for unconrained opimizaion problem,..: Elevier, 968. [6] D. G. Luenberger, Linear and nonlinear programming, Maachue: Addion-Weley Publihing Co., Reading,989. [7] J.R. McGuigan, & R.C. Moyer, Managerial economic, S. Paul: We Publihing Co., 989. [8] J.R. McGuigan, R.C. Moyer, and.h. Harri, Managerial economic: applicaion, raegy, and acic, Cincinai: Souh-Weern College Publihing, 999. [9] J. eer, W. Waerman & G.A. Whimore, Applied aiic, Boon: Allyn and Bacon, Inc., 988. [0] J.. Traub, Ieraive mehod for he oluion of equaion,.j.: Prenice-Hall Englewood Cliff, 964. [] D. j. Wilde, and C.S. Beighler, oundaion of opimizaion,.j.: Prenice-Hall Englewood Cliff, 967. [] W.I. Zangwill, onlinear programming via penaly funcion, Managemen Science vol. 3, no 5, 967, pp [3] V. Zarnowiz, Recen work on buine cycle in hiorical perpecive, Journal of Economic Lieraure, June 985, pp

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