Classification based Expert Selection for Accurate Sales Forecasting

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1 Inernaional Journal of Compuer Applicaions ( ) Classificaion based Exper Selecion for Accurae Sales Forecasing Darshana D. Chande Compuer Engineering Deparmen, Governmen polyechnic, Thane M.Vijayalakshmi Informaion Technology deparmen V.E.S.I.T, Chembur ABSTRACT Forecasing mehods used in pracice vary from domain o domain. This Paper focuses on sales forecasing. Mos of he series considered here are composed of hree componens- Trend, seasonaliy and irregular. A series has been decomposed ino is hree componens and muliple forecasers (Expers) have been applied on each componen. Then hese forecasers are recombined, using Caresian produc of heir forecass, o generae a se of Expers. A classificaion based scheme is proposed o idenify a final good se of Expers which can be used in various combinaions o creae forecas for each series. Furher i has been demonsraed ha his forecasing sysem succeeds in producing a forecas ha is more accurae han he Hol Winer mehod, which is a sandard mehod of forecasing. General Terms Sales Forecasing, Times Series, Daa Mining Keywords--Decomposiion,, Classificaion, Decision Tree, Expers, Combinaion 1. INTRODUCTION Sales forecasing is an imporan par of supply chain managemen. Timely and accurae sales forecass are crucial in bridging he gap beween supply and demand. So he selecion and implemenaion of he proper forecas mehodology is very imporan in sales forecasing. The primary goal of Time series forecasing is o improve he forecasing accuracy. We have employed various kinds of pre-processing like decomposiion. The series has been decomposed ino muliple componens such as Trend, seasonaliy and Irregular componen. Each of hese componens is individually forecased and heir forecass are combined back o come up wih final forecas. The decomposiion mehod has been used in which he componen series has been buil a each poin wih he help of some pas poins. Muliple forecasers are used and opinion is aken from heir forecass. For his he model is seleced by deermining he bes model based on cerain crieria and ha model is used for combining. Combinaion Mehod is used, as a single model selecion is associaed wih he insabiliy problem [4] when limied daa is available or when wo or more models are performing well [17]. In such circumsances, a sligh change in he daa may resul in he selecion of differen model. This inconsisency of model selecion may resul in high risk in final forecas. Combining reduces he risk of forecasing. In our work we have used muliple Expers (forecasers) for forecasing individual componen series, which gives muliple forecass for each componen. We hen ake Caresian produc of individual componen forecass which ulimaely gives us a very large number of Expers (of he order of 10 5 ).The availabiliy of such a large number of Expers has enabled us o combine based on frequency and rank. The ouline of he paper is as follows. In Secion 2, we presen Lieraure Survey. In Secion 3, we inroduce our Decomposiion followed by combining approach. We reviewed he basic forecasing models used here and some erms used in Daa Mining relevan o his paper. In Secion 4, he decision ree used in our algorihm is presened which shows he way we have classified he Expers. In Secion 5, he Resuls are discussed; he sudy of effec of filering ou he poorlyperforming forecasers is presened along wih comparison wih sandard mehod. I also inroduces a heurisic based on idenificaion of he good and bad individual rend, seasonal and irregular componen models derived from he classes of good and bad forecasers. A summary of our main resuls and conclusions are included in Secion LITERATURE SURVEY There are wo main approaches o forecasing- Quaniaive mehods (objecive approach) and Qualiaive mehods (subjecive approach).quaniaive forecasing mehods are based on analysis of hisorical daa and assume ha pas paerns in daa can be used o forecas fuure daa poins. Qualiaive forecasing echniques employ he judgmen of Expers in specified field o generae forecass. They are based on educaed guesses or opinions of expers in ha area. There are wo ypes of quaniaive mehods: Time-series mehod and explanaory mehods. 2.1 Time Series Inroducion A ime series is a sequence of observaions aken sequenially in ime. I can be seen as being composed of hree componens: Trend (Change in he mean of ime series), Seasonaliy (repeiion of a paricular paern of observaions afer cerain fixed ime inerval) and Irregular componen (random noise). This calls for decomposiion mehods ha will generae individual componens series from he original series. These mehods form one imporan par of he lieraure on forecasing. There exiss various decomposiion mehods e.g. Hol-winer mehod, Exponenial smoohing mehod, ARIMA ec. ha are used o ge hese componen series from he original series. Some of hem are discussed in nex secion. A ime series can be broken down ino is individual componens. The decomposiion of ime series is a saisical mehod ha breaks a ime series down ino is componens (Trend, Seasonal, Cyclical, and Random). 2.2 Basic Time Series Mehods Basic Time series mehods use hisorical daa as he basis of esimaing fuure oucomes. The Trend cycle can be esimaed by smoohing he series o reduce he random variaion (irregular componen). A widely used echnique is "smoohing". This echnique, when properly applied, reveals more clearly he 31

2 Inernaional Journal of Compuer Applicaions ( ) underlying rend, seasonal and cyclic componens. Smoohing echniques are used o reduce irregulariies (random flucuaions) in ime series daa. They provide a clearer view of he rue underlying behaviour of he series. Smoohing mehods are Averaging Mehods, Exponenial smoohing mehods, Box-Jenkins or ARIMA ec. Simple moving average akes cerain number of pas periods and adds hem ogeher; hen divide by he number of periods. Simple Moving Averages (MA) is effecive and efficien approach if he daa is saionary. Exponenial smoohing mehods is a widely mehod used of forecasing based on he ime series iself. An ES is an averaging echnique ha uses unequal weighs; however, he weighs applied o pas observaions decline in an exponenial manner. Double exponenial smoohing is beer a handling rends. Triple Exponenial Smoohing is beer a handling parabola rends. Hol's linear exponenial smoohing (LES) is an exension of simple exponenial smoohing. This mehod is used when a series has no seasonaliy and exhibis some form of rend. This is an exension of exponenial smoohing o ake ino accoun a possible linear rend. Oher mehods Ho-winer and ARIMA are discussed in nex secion. 2.3 Combinaion Normally here are many forecasing mehods ( Expers ) available, and so one has o decide wheher o selec only a single Exper or o combine he forecass of differen Expers in some way o ge he final forecas. The forecas accuracy can be subsanially improved hrough combinaion [3][16] of muliple individual forecass. The reason behind his was assumed o be ha one Exper could no enirely capure he deails of underlying process bu muliple Expers could capure differen aspecs of i and so should give beer resuls. Moving o he mehods used for decomposiion and combining, lo of work has already been done [15]. 2.4 Daa Mining Daa mining is he process ha aemps o discover paerns in large daa ses. The overall goal of he daa mining process is o exrac informaion from a daa se and ransform i ino an undersandable srucure for furher use. The daa mining sep migh idenify muliple groups in he daa, which can hen be used o obain more accurae predicion resuls. 2.5 Classificaion Classificaion is a daa mining funcion ha assigns iems in a collecion o arge caegories or classes. The goal of classificaion is o accuraely predic he arge class for each case in he daa. A classificaion ask (Figure 1) begins wih a daa se in which he class assignmens are known. Classificaions are discree and do no imply order. The simples ype of classificaion problem is binary classificaion. In binary classificaion, he arge aribue has only wo possible values. Muliclass arges have more han wo values. In he model build (raining) process, a classificaion algorihm finds relaionships beween he values of he predicors and he values of he arge. Differen classificaion algorihms use differen echniques for finding relaionships. These relaionships are summarized in a model, which can hen be applied o a differen daa se in which he class assignmens are unknown. Figure 1. Classificaion and Predicion Process Classificaion models are esed by comparing he prediced values o known arge values in a se of es daa. The hisorical daa for a classificaion projec is ypically divided ino wo daa ses: one for building he model; he oher for esing he model. Classificaion problem is known as supervised learning, while clusering is known as unsupervised learning. Differen classificaion algorihms are Decision rees, K-neares neighbour algorihm, Neural neworks [13], Memory (Case) based reasoning, Bayesian neworks, Geneic algorihms ec. 2.6 Decision Tree In daa mining, a decision ree is a predicive model which can be used o represen boh classifiers and Regression models. The decision ree refers o a hierarchical model of decisions and heir consequences. The decision maker employs decision ree o idenify he sraegy mos likely o reach he goals. When a decision ree is used for classificaion ask, i is referred o as Classificaion ree. Classificaion rees are used o classify an objec or an insance o a predefined se of classes based on heir aribues. The use of decision ree is very popular echnique in daa mining. Decision rees are self-explanaory. They are usually represened graphically as hierarchical srucures, making hem easier o inerpre han oher echniques. 2.7 Challenges A single model selecion is associaed wih he insabiliy problem [7].A sligh change in he daa may resul in he selecion of differen model. This inconsisency of model selecion may resul in high risk in final forecas. Combining reduces he risk of forecasing. So no single Exper can give perfec forecas for all ype of ime series. The forecas accuracy can be subsanially improved hrough combinaion of muliple individual forecass [8].So in his projec we have combined muliple Expers and filered ou he bes Expers o ge he final more accurae forecas. 32

3 Inernaional Journal of Compuer Applicaions ( ) 3. DECOMPOSITION AND COMBINING A ime series is a sequence of observaions recorded a successive inervals of ime. I is ofen he case ha adjacen observaions are dependen. These dependencies are capured by various ime series models such as Hol Winer, ARIMA, ec. Any ime series is a composiion of many individual underlying componen ime series. Some of hese componens are predicable whereas oher componens may be almos random which can be difficul o predic. Decomposing a series ino such componens enables us o analyse he behaviour of each componen and his can help o improving he accuracy of he final forecas given by Brockwell [1],Makridakis [2]. A ypical sales ime series can be considered o be a combinaion of four componens (i.e. rend componen, cyclic componen seasonal componen, and irregular componen). The Seasonal componen models paerns of change in a ime series wihin a year. These paerns relae o periodic flucuaions of consan lengh, end o repea hemselves each year. The Trend represens changes in he level of he series. The Cyclic componen refers o paerns, or waves, in he daa ha are repeaed afer approximaely equal inervals wih approximaely equal inensiy, wih period normally larger han seasonal period. Usually he rend and cyclic componen are ogeher reaed as he Trend componen. The Irregular componen refers o variaions no covered by he above componens. 3.1 Decomposiion model Mahemaical represenaion of he decomposiion approach is: Where D is he ime series value (acual daa) a period. S is he seasonal componen (index) a period. T is he rend cycle componen a period. IC is he irregular (remainder) componen a period. The decomposiion could be addiive if he magniude of seasonal flucuaions do no vary wih he level of he series. We have a muliplicaive decomposiion if seasonaliy flucuaes and increases and decreases wih he level of he series. Muliplicaive model is more prevalen wih economic series since mos seasonal economic series have seasonal variaion which increases wih he level of he series. Furher experimens carried ou on a sample se of sales series has indicaed ha seasonal muliplicaive model performs beer han he addiive model [15][20].In his research we shall hus use he muliplicaive decomposiion model. A mehod used in forecasing a single componen is referred o as an aomic forecaser. A forecaser for he original series is a riple made up of he aomic forecasers for each componen. The se of such riples is he Caresian produc of he ses of forecasers for he T, S and I componens. Each such riple of aomic forecasers (T, S, I) is called an Exper. In his work, a oal of 86 Trend models (aomic forecasers), 33 Seasonal models and 34 Irregular componen models have been used. These are mosly ARIMA and seasonal ARIMA models of differen orders. The Caresian produc of he Trend, Seasonal and Irregular models gives rise o 96,492 Exper forecass per poin. The Appendix includes a lis of aomic forecasers used in his work. Two of he bes known mehods of forecasing seasonal daa (such as reail sales) are he Hol- Winer mehod and seasonal ARIMA which is briefly reviewed nex. 3.2 Basic Forecasing Models Hol-Winer Mehod The Hol-Winer s mehod [1] is used for he ime series ha has boh rend and seasonal componens. In addiion o Hol parameers, suppose ha he series exhibis muliplicaive seasonaliy hen HW mehod is used as by B. Menzes [15]and Venugopal [20]. Winers smoohing mehod can remove seasonaliy and makes long erm flucuaions in he series sand ou more clearly. There are wo varians of his mehod, addiive and muliplicaive. Muliplicaive Seasonaliy The seasonaliy is muliplicaive [2][3] if he magniude of he seasonal variaion increases wih an increase in he mean level of he ime series. I is addiive if he seasonal effec does no depend on he curren mean level of he ime series. For muliplicaive seasonaliy he updaing equaions are:: Y L (1 )( L 1 b 1) S S F m s b ( L L Where s is he number of periods in one cycle of seasons e.g. number of monhs or quarers in a year. There are hree smoohing parameers α, β, and γ which all mus be posiive and less han one. To iniialize we need one complee cycle of daa, i.e. s values. Then se 1 Ls ( Y1 Y2... Ys ) s To iniialize rend we use s + k ime periods. 1 ys 1 y1 ys 2 y2 ys s ys bs ( ) s s s s If he series is long enough hen a good choice is o make k = s so ha wo complee cycles are used. However we can, a a pinch, use k = 1. Iniial seasonal indices can be aken as k Sk k 1, 2,..., s Ls The parameers α, β, γ should lie in he inerval (0, 1), and can be seleced by minimising MAD, MSE or. Addiive Seasonaliy The equaions are L ( Y S F 1 Y (1 ) S L m Y ) (1 ) b s L b m S s m s b ( L L 1 S ( Y L ) (1 ) S L b m S ) (1 )( L ) (1 ) b s m s b 1 Where s is he number of periods in one cycle. ) 33

4 Inernaional Journal of Compuer Applicaions ( ) The iniial values of Ls and bs can be as in he muliplicaive case. The iniial seasonal indices can be aken as Sk Yk Ls k 1, 2,..., s The parameers α, β, γ should lie in he inerval (0, 1), and can again be seleced by minimising MAD, MSE or Auoregressive Inegraed Moving Average (ARIMA) The Auoregressive Inegraed Moving Average (ARIMA) models [1][2], or Box-Jenkins mehodology, are a class of linear models ha is capable of represening saionary as well as nonsaionary ime series. ARIMA mehodology of forecasing is differen from mos mehods because i does no assume any paricular paern in he hisorical daa of he series o be forecas. Models for ime series daa can have many forms. When modelling variaions in he level of a process, hree broad classes of pracical imporance are he auoregressive (AR) models, he inegraed (I) models, and he moving average (MA) models. These hree classes depend linearly on previous daa poins. Combinaions of hese ideas produce auoregressive moving average (ARMA) and auoregressive inegraed moving average (ARIMA) models. Seasonal ARIMA models a paern ha repeas seasonally over ime. I is classified as an ARIMA (p,d,q)x(p,d,q) model, where P is he number of seasonal auoregressive (SAR) erms, D is he number of seasonal differences, Q is he number of seasonal moving average (SMA) erms Non Seasonal ARIMA Models are classified as an "ARIMA (p,d,q)" model, where: p is he number of auoregressive erms, d is he number of non seasonal differences, and q is he number of lagged forecas errors in he predicion equaion. 4. THE PROPOSAL We are using Classificaion mehod of Daa Mining for forecasing he ime series. All our hypoheses are esed on real life monhly sales series from sandard library (Table 6). We use he mehod of decomposiion and combining o ge he final forecas. 4.1 Preliminaries Our proposal uses decomposiion as pre-processing. Afer decomposing he given ime series, we use 86 Trend Expers, 33 seasonal Expers, 34 irregular Expers. Their Caresian produc gives us around forecass and heir combinaion gives he final forecas. Model combining has been explored in several papers [9][16]. Our experimens are performed on abou 25 series aken from he Time Series Library [19] and he Economic Time Series Page [18][19]. The series represen monhly sales daa over years of diverse iems such as wine, beverages, jewellery, gasoline and single family homes. They capure he vagaries ofen encounered in demand sales series. Abraham is highly regular, Dry is less so, Hsales exhibis a low-frequency cyclical naure and Swee has highly anomalous behaviour in he midsecion. For demand sales, he mos widely used error mehod for a forecasing model/mehod is he Mean Absolue Percenage Error () defined by Here is he forecas of poin and is he acual value a poin. 4.2 Classificaion Based Forecasing The Decision Tree mehod of classificaion [5][12][14] has been used o caegorise he models. Firsly APE values calculaed for all he models and afer soring on APE value, op models are seleced as Good and boom as Poor performer and divided hem in differen classes considering heir frequency and rank. The crieria used for classificaion is shown in he ree (Figure 2). Expers having Coun > avg.-1% Rank>10200 All Expers in Good (min. APE) Forecass Discarded: No used for Furher Processing Class Label: BEST Class Label: GOOD Filering Bes (Removing BAD) Class Label: EXCELLENT forecass generaed by combining 86*34*33(TSI) Expers Expers having Coun <= avg.-1% quoe Rank<=10200 Class Label: BAD Figure 2. Decision Tree Discarded: No used for furher Processing 4.3 The Basic Algorihm / Pseudo code Le n be he oal number of poins in he series. We use he firs n1 poins o learn one or more ses of good Expers and hen use hese o forecas he las n2 poins of he series. Toal inpu: 96492(86*34*33) models Sample aken: Top and Boom, of 96492(Afer Soring on ) We have n=96492, n1=20000, n2=24 Expers having Coun > avg. All Expers in Bad (max.ape) Forecass Expers having Coun <= avg. Training Phase: For each poin,, of he series beween i = 1 o n Idenify he op n1 Expers and boom n1based on heir Then find ou he frequency of each Exper in he se of op Also calculae Rank for each Exper Then using Decision ree algorihm, based on Rank and frequency idenify he BEST, Good and Bad Expers as per he applied condiion Find ou he for hese Expers In he nex sep find ou hose Expers which survive afer filering Bes These are he Excellen (Ei) Expers which gives min. for mos of he series 34

5 Inernaional Journal of Compuer Applicaions ( ) Denoe hese ses of Expers E1, E2, ec Choose he Ei wih he bes for forecasing in he esing phase. Tesing Phase: For each poin, in he inerval comprising he las n2 poins of he series Compue he forecas for poin of each Exper in he se E Compue he mean of hese E forecass as he forecas a poin Compue for he las n2 poins. 5. DISCUSSION OF RESULTS Muliple Expers have been used for he sales series and also for he individual componens of he series obained afer applying basic decomposiion. The models considered for consrucing he Exper are ARIMA (including Seasonal ARIMA) models of various orders and various Exponenial Smoohing Models such as Hol Winer Model, Hol Model, Seasonal Exponenial Smoohing, Ec in SPSS Tool. Some Appropriae ransformaion like logarihmic ransformaion is ofen used for ime series ha show exponenial growh or variabiliy proporional. Then Caresian produc of all componens is done o ge he final forecas. In his way we have 86*34*33= forecas for each poin of daa. Finally, we have seleced bes (min APE) forecas wih heir Exper ids as he final daase for Bes and Good models and (max APE) forecass wih heir Exper ids as final daase for Bad models classificaion. Based on frequency of model appeared we calculaed coun and also a rank. Then a classificaion of series has been done by applying Decision ree algorihm on 50% and 70% of daa as raining daa and form Bes, Good (from op 20000) and Bad(from boom 20000) classes. The average values of for 50% and 70% daa are given in he Table 1. Table 1. Average values for 50% daa 50% 50% 50% Training Training Training daa Bes daa good daa Bad Class class class Abraham Beer Clohing Dry Equip Forif Furniure gasoline grocery Hsales Jewellary Merchandise Moorpars Newcar Paper Red Rose Shoe Sofware Spaper spark sores swee oal wine Table 2. Average values for 70% daa 70% 70% 70% Training Training Training daa daa Bes daa Bad Good class class class Abraham Beer Clohing Dry Equip forif Furniure gasoline grocery Hsales Jewellary Merchandise Moorpars Newcar paper red rose Shoe Sofware spaper spark sores swee oal wine From Table 1.and 2 i is clear ha values of for 50% of raining daa is also near o ha of 70% raining daa, so for our algoriham,50% raining daa is sufficien. 35

6 Inernaional Journal of Compuer Applicaions ( ) Finally he Bes model has been filered and Bad models have been removed, he models which survived afer filering are pu in he class Excellen and which gave minimum for mos of he series. comparison wih Hol winer is shown in he Table 3 and he resul was 7.17% improvemen over he sandard Hol-winer mehod. Table 4 shows improvemen of over Hol-Winer. Table 3. Comparison wih Hol-Winer wih HW wih Bes class Afer Filering Abraham Beer Clohing Dry Equip Forif Furniure Gasoline Grocery Hsales Jewellary Merchandise Moorpars Newcar Paper Red Rose Shoe Sofware Spaper Spark Sores Swee Toal Wine Table 4. Improvemen over Hol-Winer wih HW Afer Filering % Improvemen over HW Abraham Beer Clohing Dry Equip Forif Furniure gasoline Hsales Jewellary Merchandise Moorpars Newcar rose Shoe Sofware spaper spark swee oal wine Bad performing series grocery paper red sores From Table 4,i is clear ha our mehod is giving poor resul(higher ) for he series RED, Paper,grocery and sores.bu i has very good resul for Abraham, clohing, Dry, equip, Forif, Hsales, moorpars, spaper and swee. Some sample Graphs are given in Figure 3,4,5 and Figure 6. 36

7 Sales Values Inernaional Journal of Compuer Applicaions ( ) Table 5. Resuls of Filering Models-Dry SeriesError! No a valid link. Figure 3: Abraham series Final forecas accuracy on average. The challenge lies in being able o selec a se of consisenly good models for a series. We zoomed in on he T, S and I componen models comprising each good Exper a a poin and idenified he frequenly occurring T, S and I models a each poin. The Decision Tree mehod of Classificaion has been applied on he ses for each componen yielding he good ses, T, S and I. Afer classifying he Bes models, he produc of he averages of he forecass of he models in T, S and I were used as he final forecas (since we have used a muliplicaive model of ime series decomposiion). We sudied wo approaches. In he firs, we idenified a good se of Expers over a raining period using boh 50% and 70% of raining daa and used hese Expers o forecas he series in he es phase (las 24 poins of a series). The oher approach is o idenify a se of poorly performing forecasers and filer hese from he oal pool of Expers. The resuling se is used o forecas he series in he es phase. These resuls indicae ha he laer approach yields lower. These approaches yield sufficien improvemens of abou 7.17% over Hol-Winer forecasing.as in he Table ACKNOWLEDGEMENT We would like o hank our college and Principal for sponsoring us for he Higher educaion. Table 6. Descripion of various Time Series Figure 4: Red series Final forecas Dry Series Forecasing 70% Daa Monhs Original Figure 5: Dry series forecas Before filering Figure 6: Dry series forecas Afer filering 70% Bes 70 % Good 70%Bad 6. SUMMARY AND CONCLUSIONS Combining models for sales forecasing helps reducing he risk involved in rusing a single forecas and improves forecasing abraham beer clohing Dry Equip forif furniure gasoline grocery hsales jewellary merchandise moorpars newcar paper Red Rose shoe sofware spaper spark sores swee oal wine Descripion Monhly gasoline demand (Onario gallon millions) US reail sales: beer, wine liquor sores US reail sales: Clohing Sores Monhly Ausralian sales of dry whie wine (Thousands of lires) US reail invenories: Building maerials, Garden equipmen, supply sores (Million Dollars) Monhly Ausralian sales of forified wine US reail sales: Furniure Sores US reail sales: gasoline saion US reail sales: Grocery Sores Monhly sales of new one-family houses sold in he USA. US reail sales: Jewellery Sores US reail invenories: General merchandise sores US reail invenories: moor vehicles and par dealers US reail sales: New car dealers Monhly sale of prining and wriing paper. Monhly Ausralian sales of red wine Monhly Ausralian sales of rose wine US reail sales: Shoe sores US reail sales: Compuer and sofware sores CFE specialy wriing papers monhly sales Monhly Ausralian sales of Sparkling wine US reail invenories: Deparmen sores (million dollars) Monhly Ausralian sales of swee wine US reail invenories: oal Monhly Ausralian sales of wine 37

8 Inernaional Journal of Compuer Applicaions ( ) 8. REFERENCES [1] Brockwell, P.J. and Davis, R.A. (1991) Time series: Theory and Mehods, 2 nd Edn. Springer Inernaional Ediion. [2] Makridakis, S., Wheelwrigh, S., and Hyndman, R. (1998), Forecasing mehods and Applicaions, 3 rd Ediion. Wiley: NY. [3] Armsrong J. Sco, (2001), Combining Forecass. Principles of Forecasing: A Handbook for Researchers and Praciioners, J. Sco Armsrong (ed.): Norwell, MA: Lower Academic Publishers. [4] Baes, J. M., & Granger, C. W. J. (1969). Combinaion of forecass. Operaions Research Quarerly, 20: [5] Performance comparison of Rule based Classificaion Algorihm Prafulla Gupa, Durga Tosniwal, Inernaional Journal of Compuer Science & informaics,vol I, 2011 [6] Time-Series Classificaion based on Individualised Error Predicion Kriszian Buza, Alexandros Nanopoulos, Lars Schmid, h IEEE Inernaional Conference on Compuaional Science and Engineering. [7] Granger, C., & Ramanahan, R. (1984), Improved mehods of combining forecass, Journal of Forecasing 3: [8] Hand, D. J. (2009). Mining he pas o deermine he fuure: Problems and possibiliies. Inernaional Journal of Forecasing, 25(3), [9] Clemens Rober T. (1989), Combining forecass: A review and annoaed bibliography, Inernaional Journal of Forecasing 5: [10] YaohuiBai, Jiancheng Sun, JianguoLuo and Xiaobin Zhang Forecasing Financial Time Series wih Ensemble Learning, 2010 Inernaional Symposium on Inelligen Signal Processing and Communicaion Sysems (lspacs 2010) December 6-8,2010 IEEE [11] Learning Weighs for Linear Combinaion of Forecasing Mehods, Ricardo B. C. Prudencio and Teresa B. Ludermir, Proceedings of he Ninh Brazilian Symposium on Neural Neworks (SBRN'06) /06 $ [12] Join Segmenaion and Classificaion of Time Series Using Class-Specific Feaures Zhen Jane Wang and Peer Wille, Fellow, IEEE, ieee ransacions on sysems, man, and cyberneics par b: cyberneics, vol. 34, no. 2, april 2004 [13] The comparaive sudy on linear and non-linear forecascombinaion mehods based on neural nework Han Dongmei1,2, Niu Wen-qing1, Yu Changrui1,, /07/$ IEEE [14] Wind Power Ramp Evens Classificaion and Forecasing: A Daa Mining Approach Hamidreza Zareipour, Dongliang Huang, William Rosehar,, /11/$ IEEE [15] Menezes B., Seh A., and Singh R., (2007), Can a million Expers improve your sales forecass? European Symposium on Time Series Predicion, Helsinki, Finland, Feb. 7-9, 2007 [16] Zou H. and Yang Y., (2004), Combining ime series models for forecasing Inernaional Journal of Forecasing, 20 (1): [17] Timmermann, A. (2006), Forecas Combinaions, in eds. G. Ellio, C.W.J. Granger and A. Timmermann, Handbook of Economic Forecasing, Elsevier Press. [18] Economagic.com: Economic ime series page. hp:// [19] hp://daamarke.com/daa/lis/? q=provider:sdl granulariy:monhly [20] VenuGopal, (2007), Forecasing using consisen Expers, Maser s Thesis, Kanwal Rekhi School of Informaion Technology, Bombay, INDIA. 38

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