Time Series Forecasting Using Artificial Neural Networks under Dempster Shafer Evidence Theory and Trimmed-winsorized Means

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1 Internatonal Journal of Informaton and Computaton Technology. ISSN Volume 3, Number 5 (2013), pp Internatonal Research Publcatons House rphouse.com /jct.htm Tme Seres Forecastng Usng Artfcal Neural Networks under Dempster Shafer Evdence Theory and Trmmed-wnsorzed Means Har Teja.A 1 and S.Vasundra 2 1 CSE Department, JNTUACEA, AP, INDIA. 2 CSE Department, JNTUACEA, AP, INDIA. Abstract Artfcal neural networks are adequate for multple jobs n desgn recognton and machne-learnng. Contrastng to the tradtonal approaches for tme seres evaluaton, a synthetc neural system needs advce regardng the tme seres data and could be placed on a comprehensve varety of ssues. For the use, we conducted experments to obtan the approprate gudelnes for a forecastng system. The artfcal neural networks whch were dscovered had provded a better forecastng effcency under well known feature selecton approach. An Accurate tme seres forecastng usng whch s sgnfcant to demonstrate the approach wthn the past contnues n the drecton to nfluence the future as well as to schedule our daly actons. At present, a huge lterature s n progress on the usage of artfcal neural networks (ANNs) n many forecastng applcatons. In ths regard the proposed artfcal neural networks based on Tme Seres Forecastng use Dempster Shafer evdence theory and trmmed- Wnsorzed means for feature selecton. A comparatve study between these two methods, wth a set of referenced tme seres wll be shown. Keywords: Tme seres Forecastng; Dempster Shafer; Trmmed- Wnsorzed; Artfcal Neural networks; Machne Learnng. 1. Introducton Normally, the gudelnes of the typcal approach [7] are based on frequency range and the auto connecton of tme seres. The utlzaton of artfcal neural networks for tme sequence analyss reles just about the data whch were dscovered. A synthetc neural system s strong enough to sgnfy any knd of tme seres, as multple layer feed

2 384 Har Teja.A & S.Vasundra forward systems wth an adequate amount of hdden models and one or more hdden layers are capable of approxmatng functon [5, 6] to any consderable. The forward and backward paths of the completely connected feed forward network may be appled by nternal and external products of matrces and vectors n several outlnes of APL code. For the applcaton, we choose to make use of a completely joned, layered, feed forward artfcal neural system wth a sngle hdden layer and the back-propagaton learnng algorthm[1,2]. The fundamentals of the method for understandng n neural nets were set by [2]. Artfcal neural nets contan many smple processng devces (called Processng factors or neurons) grouped n levels. Each layer s recognzed from the ndex l=o,...,m. The processng elements are nterlocked as follows, Conversaton between processng elements s permtted for processng elements of nearby levels [3]. Neurons n a level cannot convey, each neuron has a partcular actvaton level 'a' as shown n Fg.1, Data s processed by the network from the exchange of servce levels between neurons. Fgure 1: Interchangng of actvaton values among neurons. The output value of the -th neuron n sheet l s denoted by ( l ), It s calculated wth the formula = g( a l ), ( l ) where g( a l ) s a monotone growng functon. For nstance, let us consder the 1 functon g(y) as the squashng functon where g( y). y 1 e The commencement level a l of the neuron n layer l s consdered by a f ( u ), ( l) ( l)

3 Tme Seres Forecastng Usng Artfcal Neural Networks under 385 Where f( u ( l) ) s the actvaton functon (n our case the characterstcs functon s used). The net nput u l of neuron n layer l s projected as follows, l, ( l ) n ( l ) ( l ) ( l 1) ( l) ( j j ) j 1 u Where l s the weght of neuron j n layer l 1 connected to neuron n layer ( l 1) j j the output of neuron j n layer l 1. l s a prejudce allege that s removed from the total amount of the weghted actvatons. 2. Implementaton The tme seres modelng and forecastng classfcaton was mplemented usng core 2 duo processor wth 4 GB RAM of an auxlary workstaton. The system conssts of two man components: A toolkt of APL functons that constran the neural network and log parameters and results of the replcaton runs to APL component fles. A graphcal user nterface that allows the user to navgate durng the smulatons and to evaluate the actual tme seres generated by the neural network. Fgure 2: User nterface of the forecastng system. Fg. 2 portrays a dsplay dump of the nterface, the damaged lne dsplays the real tme sequence and the strong lne sgnfes the network's output. The outlook data s dvded from the hstorc data - the network's tranng set - by the vertcal bar n the

4 386 Har Teja.A & S.Vasundra best quarter of the chart, the menu n the top left part of number 3 enables the person to choose a perspectve of the network's forecastng capacty at dfferent countres through the entre learnng stage. By lookng at the record fles of the smulator runs, current and prevous outcomes could be assessed and compared. 2.1 The Tranng Sets As test bed for our forecastng program we utlzed two well-known tme sequence from [7], the monthly totals of nternatonal flght passengers (thousands of passengers) from 1949 to 1960, as well as the daly closng costs of share nventory. Table 1: Propertes of tme seres. Tme Seres n Share Prce Grd power unt Prce Where s the standard devaton, s the mean and n s the number of observatons. Followng secton wll explan about how a neural network learn a tme seres. 2.2 Back-Propagaton Algorthm The neural network sees the tme seres X1,....,Xm n the form of many mappngs of an nput vector to an output value. Ths technque was presented n [5]. Fgure 3: Learnng a Tme Seres.

5 Tme Seres Forecastng Usng Artfcal Neural Networks under 387 A number of adjonng data ponts of the tme seres (the nput wndow X t to X t-s ) as shown n Fg.3 are planned to the nterval [0,1] and utlzed as servce levels for the models of the entre level. The problem useful for that back-propagaton learnng algorthm s currently computed by evaluatng the worth of the result unt together wth the value of the tme sequence at tme' t 1 '. Tranng a sensory network wth all the back-propagaton algorthm generally demands that representatons of the entre set (called one epoch) whch s offered for several tmes. To understand the perod of seres data, the representatons were offered n a random fashon, As reported n [5], pckng a random place for every portrayal's nput wndow ensures better system functonalty and prevents local mnma. 3. Comparson between Dvergent Feature Selecton Modelng s On comparng the results ganed under feature selecton methods called Dempster Shafer evdence theory and trmmed-wnsorzed means, the executon of the procedure uses the applcatons explaned by Jenkns and Box n Component V of ther classc [7]. The approach s known as an autoregressve ntegrated movng average method of order (p, d, and q). It s descrbed by Eqs (1-2) as follows, Xt d a( z) X b( z) U t t Where stands for n tme ordered values of a tme seres, t = 1... N for n observatons. Ut Is a sequence of random values called whte nose process. The backward dfference operator V s defned as Xt Xt Xt 1 (1 z) Xt (2) We fxed these feature selecton models for each tme seres and let t predct the next 20 observatons of the tme seres. The last 20 observatons were dropped from the tme seres and used to calculate the predcton error of the models. The followng feature selecton models were calculated for the power unt prce of the tme seres after a logarthmc transformaton as, (1 - Z) (1 - z 12 X ) t = ( , z 12 ) Ut and for the Share tme seres, (1 - X z) t = ( z) Ut In the forecasted errors of the man-made neural network (ANN), the artfcal neural network utlzng the logarthmc and change (ANN record,) n the feature selecton models opted are compared. The artfcal neural network utlzng the logarthmc and changed tme seres out-performed for both tme seres, whereas the "smple" artfcal neural network expected more precsely just for the Shares tme seres [4]. Ths behavor could be descrbed as, the bgger the data selecton n the tme seres, It results n a reduced precson for the untransformed place set. Logarthmc and dfferencng transformatons helped to remove the tendency and planned the tme seres data n to a smaller varety. (1)

6 388 Har Teja.A & S.Vasundra Table 2: Forecastng errors for ANN under Dempster Shafer evdence theory and Trmmed-Wnsorzed means. Tme seres Dempster Shafer evdence theory Trmmed- Wnsorzed means power unt prces Share prce Fgure 4: Fault proneness of ANN under Dempster Shafer evdence theory and Trmmed-Wnsorzed means. 4. Concluson and Future Work We've offered a predctng program for un-varant tme sequence that utlzes artfcal neural networks. These processng devces proved themselves to be feasble optons to classc approaches. The machne may be utlzed along wth other approaches for tme seres evaluaton or just as a standalone devce. Enhancement of the work may nclude the assessment wth addtonal TSA (tme seres analyss) approaches, development of hybrd process that blend the power of standard methods wth artfcal neural networks and the use of our program to multvarate tme seres. References [1] Wezhong Yan and Senor Member "Toward Automatc Tme-Seres Forecastng Usng Neural Networks " n the proceedngs of IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, VOL. 23, NO. 7, JULY 2012

7 Tme Seres Forecastng Usng Artfcal Neural Networks under 389 [2] G. P. Zhang and D. M. Klne, Quarterly tme seres forecastng wth neural networks, IEEE Trans. Neural Newt., vol. 18, no. 6, pp , Jun [3] S. Crone and P. Grafelle, An evaluaton framework for publcatons on artfcal neural networks n sales forecastng, n Proc. Int. Conf. Artfcal ntellgence., Las Vegas, NV, Jun. 2004, pp [4] S. D. Balkn and J. K. Ord, Automatc neural network modelng for unvarate tme seres, Int. J. Forecast., vol. 16, no. 4, pp ,2000. [5] Kurt Hornk, Maxwell Stnchcombe, and Halbert Whte. Multlayer Feed forward Networks are Unversal Approxmators. Neural Networks, 2: , [6] Halbert Whte. Economc predcton usng neural networks: the case of bm daly stock returns. In Proceedngs of the IEEE Internatonal Conference on Neural Networks, pages II , [7] George E. P. Box and Gwlym M. Jenkns. Tme Seres Analyss - forecastng and control. Seres n Tme Seres Analyss. Holden-Day, 500 Sansome Street, San Francsco, Calforna, 1976.

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