Time Series Prediction Method of Bank Cash Flow and Simulation Comparison

Transcription

1 Algorihms 204, 7, ; doi:0.3390/a Aricle OPEN ACCESS algorihms ISSN Time Series Predicion Mehod of Bank Cash Flow and Simulaion Comparison Wen-Hua Cui, Jie-Sheng Wang * and Chen-Xu Ning School of Elecronic and Informaion Engineering, Universiy of Science and Technology Liaoning, Anshan 4044, Liaoning, China; s: cwh@julong.cc (W.-H.C.); NCX @63.com (C.-X.N.) * Auhor o whom correspondence should be addressed; s: wang_jiesheng@26.com or wangjiesheng@usl.edu.cn; Tel.: ; Fax: Exernal Ediors: Kenji Suzuki Received: 25 Sepember 204; in revised form: 5 November 204 / Acceped: 4 November 204 / Published: 26 November 204 Absrac: In order o improve he accuracy of all kinds of informaion in he cash business and enhance he linkage beween cash invenory forecasing and cash managemen informaion in he commercial bank, he firs moving average predicion mehod, he second moving average predicion mehod, he firs exponenial smoohing predicion and he second exponenial smoohing predicion mehods are adoped o realize he ime series predicion of bank cash flow, respecively. The predicion accuracy of he cash flow ime series is improved by opimizing he algorihm parameers. The simulaion experimens are carried ou on he realiy commercial bank s cash flow daa and he predicive performance comparison resuls show he effeciveness of he proposed mehods. Keywords: ime series predicion; moving average predicion; exponenial smoohing predicion. Inroducion In recen years, he ime series modeling and predicion have been one of he mos acive research opics in he academic research and engineering pracice [ 4]. The ime series is usually a chronological series of observed daa (informaion) according o he ime sequence, whose values are sampled a he invariable ime inervals. Researchers ofen predic fuure changes based on he hisorical daa. For

2 Algorihms 204, 7 65 example, according o he siuaion in he pas or he curren period of he marke sales, he changes of sock prices, he populaion growh and he bank s deposi and wihdrawal, he changes of he marke sales, he changes of sock prices, he populaion growh and he bank s deposi and wihdrawal in he fuure are prediced. The ime series forecasing affecs he life of people everywhere, so i has an imporan pracical significance and research prospecs in every field of oday's sociey, which is also an imporan direcion in he compuer applicaion field [5 8]. The bank cash flow forecasing managemen informaion sysem is designed o creae a sysem managemen plaform for he predicion and analysis of he commercial bank cash flow. I will realize he cash flow daa saisics summary, he cash flow shor-erm and long-erm predicion, he summary and saisical analysis comprehensively and scienifically of he business informaion, he operaional informaion and he managemen informaion relaed o he commercial bank cash flow under hree levels: secondary branches (Cash Operaion Cener), branch (Business Library) and Nework. Is purpose is o provide effecive daa all levels of organizaion o analyze and assess cash business operaion condiions. Also i will provide effecive sysem managemen means for he cash operaion managers and decision-making people a all levels. Aiming a he exised problem in he analysis of commercial bank cash flow, four ime series predicion mehods are used o se up he predicion models. The simulaion resuls show he effeciveness of he proposed mehods. The paper is organized as follows. In Secion 2, he ime series predicion mehods of bank cash flow are inroduced. The simulaion experimens and resuls analysis are inroduced in deails in Secion 3. Finally, he conclusion illusraes he las par. 2. Time Series Predicion Mehods of Bank Cash Flow The ime series predicion mehod analyzes he prediced arge s changes wih he ime on he imes series composed of he hisorical daa according o he chronological order. The predicion mehod is quaniaive and he relaed mahemaical model is esablished for exrapolaion [9 5]. Based on he circulaion daa of bank cash, four predicion mehods of he various cash operaing specific modules are designed for providing he decision-making basis of he business plan in commercial bank. The flowchar of he ime series predicion mehods of bank cash flow is shown in Figure. The simulaion environmen is described as follows: Windows 7 operaing sysem, Inel processor (2.5 GHz, 4G memory) and Malab 200 simulaion sofware. 2.. The Firs Moving Average Predicive Mehod The moving average mehod is a predicive echnique developed on he basis of he arihmeic average. The arihmeic average mehod can only reflec he average of a se of daa and canno reflec he change rend of he daa. However, he basic idea of he moving average mehod is iem by iem based on ime series daa by aking a cerain number of cycles of daa o be averaged every ime, successive advancing in chronological order. In each propulsion cycle, he forward cycle daa is rejeced, a new cycle daa is added and he average value is calculaed [6]. Se X is he acual value of he cycle. The firs moving average value is calculaed by he following equaion. N X X X N M N X i/n N i 0 ()

3 Algorihms 204, So he predicive value of he nex period ( + ) is: ˆ () X M (2) where N is he number of seleced daa for calculaing he firs moving average value and Xˆ is he predicive value of he nex period ( + ). Figure. Flowchar of he ime series predicion mehods of bank cash flow. Based on he colleced daa in a commercial bank from January o April in 20and 202, he firs moving average mehod is adoped o realize he ime series predicion of bank cash flow. The cycle number of he moving average in 20 is 2 5 and he coninuous sample poins are 00. The opimal moving average value for he seleced daa is N = 6 and he simulaion resuls are shown in Figure 2. The cycle number of he moving average in 202 is 2 5 and he coninuous sample poins are 00. The opimal moving average value for he seleced daa is N = 2 and he simulaion resuls are shown in Figure 3. I can be seen from Figures 2 and 3 ha he random flucuaions of bank acual cash flow values is larger, bu he random flucuaions are reduced significanly afer he firs moving average calculaions. The more used monhs by calculaing he average, ha is o say he greaer N, he sronger of he smoohing degree and he more small flucuaion. However, in his case, he reacion velociy on his change rend for he acual daa is slower. Conversely, if N is se lower, he reacion velociy on his change rend for he acual daa is more sensiive, bu he smoohing degree is less and i is easy o reflec he random inerference as he rend. Therefore, he choice of N is very imporan, which should be seleced according o he specific siuaion. When N is equal o he cycle of change, he influence of periodic change can be eliminaed. In pracice, he mean square error S of predicion for pas daa is generally adoped o be he crierion for choosing N. However, because of he accumulaion of errors, he predicive error is bigger for he predicion of more disan periods. Therefore, he firs moving average mehod is usually adaped o he

4 Algorihms 204, saionary model and only a period predicion (i.e., predicing he + period). So when he basic mode of prediced variables changes, he adapabiliy of he firs moving average mehod will be relaively poor. Figure 2. Predicive resuls of he firs moving average mehod in x 07.5 Raw daa Predicive value.4 Invenory limi (Yuan)) Sample poins Figure 3. Predicive resuls of he firs moving average mehod in x 07 Raw daa Predicive value Invenory limi (Yuan) Sample poins

5 Algorihms 204, The Second Moving Average Predicive Mehod The second moving average mehod is o carry ou he moving average again based on he firs moving average mehod, ha is o say he predicion model is esablished on he basis of he firs moving average values and he second moving average values o calculae he prediced value. As menioned above, he average value calculaed by he firs moving average mehod has a lag deviaion. Especially when here is a linear rend in he ime series daa, he firs moving average value is always behind he observaion value. The second moving average mehod is proposed o revise his lag deviaion by esablishing he mahemaical model having he linear ime relaionship of he predicive arge o obain he predicive values. The second moving average predicive mehod can solve he conradicion of he prediced value lagging behind he acual observed values, which are suiable for forecasing he ime series wih he phenomenon having he obvious change rend. A he same ime, i also reains he advanage of he firs moving average mehod. Se M (2) is he second moving average value in period, Y is he acual value of he cycle. The second moving average mehod is described as follows. M M Y Y... Y (3) n () n M M... M (4) n () () () (2) n where M () is he firs moving average value in period, M (2) is he second moving average value in period, n is he number of seleced daa for calculaing he firs moving average value. In order o eliminae he influence of lag error on he predicion resuls, he linear rend model wih he hyseresis error rule on he basis of he firs and second moving average values is esablished. M () and M (2) are used o esimae he inercep a and slope of he linear rend model. The calculaion ˆ bˆ formulas are described as follows. () (2) aˆ 2M M 2 b M M N ˆ () (2) ( ) Then he linear rend predicion model is esablished as: yˆ ˆ ˆ a b (6) where is he curren period, τ is from o forecas period number, yˆ is predicive value in period + τ, a ˆ is he esimaed value of he inercep, b ˆ is he esimaed value of he slope. In order o carry ou he research on he second moving average mehod for predicing he bank cash flow ime series, he same daa in he firs moving average mehod are adoped. The cycle number of he moving average in 20 and 202 is 2 5 and he opimal moving average value for he seleced daa is N = 3. The simulaion resuls are shown in Figures 4 and 5. I can be seen from Figures 4 and 5 ha he prediced effec of he second moving average mehod is beer han he firs moving average mehod. So i is more suiable for he predicion he ime series wih linear rend changes. (5)

6 Algorihms 204, Figure 4. Predicive resuls of he second moving average mehod in x 07.5 Raw daa Predicive value.4 Invenory limi (Yuan)) Sample poins Figure 5. Predicive resuls of he second moving average mehod in x 07 Raw daa Predicive value Invenory limi (Yuan) Sample poins 2.3. The Firs Exponenial Smoohing Predicion Mehod The exponenial smoohing mehod is a ime sequence analysis predicion mehod developed from he moving average mehod. By calculaing he exponenial smoohing value, he fuure of phenomenon

7 Algorihms 204, is prediced wih he cerain ime series predicion model. Is principle is o calculae he exponenial smoohing values in any period wih he syle of weighed average by combining he acual observed value and he exponenial smoohing value in he previous period. The firs exponenial smoohing mehod is a weighed predicion, whose weigh coefficien is α. I need no sore all hisory daa, which can grealy reduce he daa sorage. Someimes, only a new observaion value, he laes prediced value and he weigh coefficien α can be used o realize he ime series predicion. When he ime series has no obvious rend change, he firs exponenial smoohing predicion mehod is effecive. Se X0, X,, Xn are he observaions of ime series and S (), S2 (),, Sn () are he exponenial smoohing values of observaions in ime. So he firs exponenial smoohing value is calculaed by he following equaion. () 2 S X ( ) X ( ) X 2... (7) where α is smoohing coefficien, 0 < α <. I can be seen form Equaion (7) ha he weigh coefficiens of he acual values X, X and X 2 are α, α ( α) and α ( α) 2, respecively. The daa is farher from he momen, wih he smaller weigh coefficien. Because he weigh coefficien is an index geomeric series, i is called he exponenial smoohing mehod. Equaion (7) can be changed slighly as: () S X ( ) X ( ) X 2... () (8) X ( ) S Equaion (8) can be rewrien as: Then he predicive value of nex cycle is obained: () () () S S ( X S ) (9) ˆ () S (0) X Xˆ ˆ ˆ X ( X X) () Seen from he Equaion (), he exponenial smoohing mehod solves a problem exising in he moving average mehod, i.e., hrere is no longer a need o sore he hisorical daa in pas N cycles. One only needs he mos recen observed value x, he mos recen prediced value X ˆ and he weigh coefficien α o calculae a new predicive value. The exponenial smoohing mehod is used o realize he unequal weighs daa handle wih differen imes by using he smoohing coefficien α. So he problem of chosing α is discuss as follows. () 0 < α <. (2) The selecion of he smoohing coefficien α is an imporan problem, which affecs he predicion resuls direcly. I is seleced according o he characerisics of he acual ime series and exper experiences. () When he flucuaion of ime series is no big and he long-erm rend is relaively sable, i is beer o selec a smaller α. The weigh of he pas predicive values can hen be aggravaed. Is value generally locaes he scope [0.05, 0.2]. (2) When he flucuaion of ime series is big and has an obvious endency of rapid change, i is beer o selec he big α, which can aggravae he weigh of he new predicive values. Is value generally locaes he scope [0.3, 0.7].

8 Algorihms 204, In order o carry ou he research on firs exponenial smoohing predicion mehod for predicing he bank cash flow ime series, he same daa in he above wo mehods are adoped. When he weigh coefficien is 0.9, he mean square error is minimum and he simulaion resuls are shown in Figures 6 and 7. I can be seen from Figures 6 and 7 ha he firs exponenial smoohing model predicion mehod need o find he bes value α hrough he repeaed experimens. However, even wih a bes value α, he accuracy of prediced resuls also is no ideal for he ime series wih larger rend. Figure 6. Predicive resuls of he firs exponenial smoohing predicion mehod in x 07.5 Raw daa Predicive value.4 nvenory limi (Yuan) Sample poins Figure 7. Predicive resuls of he firs exponenial smoohing predicion mehod in x 07 Raw daa Predicive value Invenory limi (Yuan) Sample poins

9 Algorihms 204, The Second Exponenial Smoohing Predicion Mehod Because he firs moving average mehod and second linear moving average mehod all need sore a large amoun of hisorical daa, in order o compensae for his limiaion, he second linear exponenial smoohing model is developed, which only need o use hree daa values and a smoohing coefficien α. A he same ime, i also can make he weigh of pas observaions small. In mos cases, he use of second linear exponenial smoohing model is more convenien. The second exponenial smoohing predicion mehod is o carry ou anoher exponenial smoohing based on he firs exponenial smoohing predicion mehod, which has he advanages of simple calculaion, less sample requiremen, srong adapabiliy and he relaively sable prediced resuls. I canno predic lonely and mus cooperae wih he firs exponenial smoohing predicion mehod o build he ime series predicive mahemaical model. The weighed average of hisorical daa is as he prediced value of fuure ime. The second exponenial smoohing predicion mehod is described as follows. () () S ay( a)s ( ) (2) (2) () (2) S as ( a)s ( ) (3) where, S () is he firs exponenial smoohing value in period, S (2) is he second exponenial smoohing value in period and α is he smoohing consan. So he predicion model of he second exponenial smoohing mehod is described as follows. b F T a bt (4) () (2) a 2S S (5) () (2) ( a a)(s S ) (6) where F + T is he predicive value in period + T, T is he number of he fuure forecas period, a and b are he model parameers. Equaion (5) is used o add he difference beween he firs exponenial smoohing value and he second exponenial smoohing value on he firs exponenial smoohing value. Equaion (6) is adoped o add he rend change value. When predicing he period +, a rend change value b is added o he a. When predicing he period + T, he rend change value T b is added o he a. In order o carry ou he research on he second exponenial smoohing predicion mehod for predicing he bank cash flow ime series, he same daa in he above hree mehods are adoped. When he weigh coefficien is 0.5, he mean square error is minimum and he simulaion resuls are shown in Figures 8 and 9. I can be seen from Figures 8 and 9 ha because he second exponenial smoohing mehod considers he linear parameer changes in differen periods of he ime series, he exen of he prediced values fiing wih he original ime series is very good, which reflecs he variaion rends of he original ime series in differen ime periods. So i is more suiable for he predicion of ime series wih a linear rend.

10 Algorihms 204, Figure 8. Predicive resuls of he second exponenial smoohing mehod in x 07.5 Raw daa Predicive value Invenory limi (Yuan) Sample poins Figure 9. Predicive resuls of he second exponenial smoohing mehod in x 07 Raw daa Predicive value nvenory limi (Yuan) Sample poins 3. Simulaion Comparison In order o carry ou he performance comparison under he above menioned four ime series predicive mehods for bank cash flow, he simulaion curves are shown in Figure 0. I can be seen clearly ha he prediced resuls of he second exponenial smoohing mehod is beer han oher mehods.

11 Algorihms 204, Figure 0. Performance comparison resuls..6 x Invenory limi (Yuan) Raw daa 0.8 he firs moving average mehod he second moving average mehod 0.7 he firs exponenial smoohing mehod he second exponenial smoohing mehod Sample poins The predicion error is he deviaion beween he prediced resuls and he acual resuls, which deermines he predicion accuracy. The accuracy of he quaniaive predicion mehods has a lo of measurable indicaors. Suppose y, y2,, yn are he acual observed values of he prediced arge and yˆ ˆ ˆ, y2,..., y n are he prediced values. The absolue error of prediced poins is a ˆ y y,,2,, n (7) where a is he absolue error a he poin. Obviously, a is he mos direc measure index of predicion error, bu i is affeced by he measuremen uni of prediced objec. So i is unsuiable as he final measure indicaor of predicion accuracy. Relaive error of prediced poins a ˆ y y aˆ,,2,, n y y (8) where a is he relaive error a he poin, which is usually expressed as a percenage and measures he accuracy of he prediced values relaive o he observed value a he prediced poin. Predicion accuracy of he predicion poins A ˆ y y y, 0 y ˆ y y (9) A 0, y ˆ y y (20)

12 Algorihms 204, 7 66 where A is he predicion accuracy a he predicion poin. Mean square error (MSE) Mean square error (MSE) is a kind of convenien mehod o measure he average error o evaluae he degree of daa change, which is described as follows. 2 n MSE (y y) (2) n Four menioned mehods are used o carry ou he simulaion on he same prereaed experimenal. The simulaion resuls are shown in Table. The performance comparison resuls in Table also showed ha he second exponenial smoohing mehod obains he higher predicion precision of he cash flow ime series. Performance indicaors Table. Performance comparison resuls. Firs moving average mehod Second moving average mehod Firs exponenial smoohing mehod Second exponenial smoohing mehod MSE Absolue error Relaive error of (%) Predicion accuracy (%) Conclusions Four ime series predicive mehods are adoped o realize he real-ime predicion of cash flow in he commercial bank. By comparing he ime series predicive performance under four algorihms and analyzing he simulaion resuls in-deph, he second exponenial smoohing predicion mehod is he opimal predicion mehod. Acknowledgmens This work is parially suppored by he Program for China Posdocoral Science Foundaion (Gran No ), he Program for Liaoning Excellen Talens in Universiy (Gran No. LR204008) and he Projec by Liaoning Provincial Naural Science Foundaion of China (Gran No ). Auhor Conribuions Wen-Hua Cui paricipaed in he concep, design, inerpreaion and commened on he manuscrip. A subsanial amoun of Jie-Sheng Wang s conribuion o he draf wriing and criical revision of his paper was underaken. Chen-Xu Ning paricipaed in he daa collecion, analysis and algorihm simulaion. Conflics of Ineres The auhors declare no conflic of ineres.

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