Research Article The Prediction for Shanghai Business Climate Index by Grey Model

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1 Reserch Journl of Applied Sciences, Engineering nd echnology 7(4): , 04 DOI:0.906/rjset.7.69 ISSN: ; e-issn: Mwell Scientific Publiction Corp. Submitted: September 4, 03 Accepted: October 30, 03 Published: April, 04 Reserch Article he Prediction for Shnghi Business Climte Inde by Grey Model Weisi Zhng nd Hongyn Li College of Mngement, Shnghi University of Engineering Science, Shnghi 060, Chin Abstrct: his study predicts Shnghi Business Climte Inde from the third qurter of 03 to the first qurter of 04 by Grey Model. Business climte inde (enterprise integrted production business inde) is the judgments nd epecttions inde to the development of n enterprise in the future. By compring the forecsting ccurcy of three grey models, i.e., GM (, ) model, Verhulst model nd the DGM (, ) model, the results show tht the forecsting ccurcy of GM (, ) model is higher thn Verhulst model nd DGM (, ) model. And GM (, ) model is used to predict Shnghi business climte inde in the net three qurters. Keywords: Business climte inde, GM (, ) model, grey model INRODUCION Business climte inde (enterprise integrted production business inde) is the judgments nd epecttions inde which is bsed on integrted production nd mngement of the enterprise nd comprehensively reflects the production nd opertion of enterprises. Climte inde is n indictor tht reflects the stte or trend for prticulr socil group or n economic phenomenon. Climte inde vlues re between 0 nd 00, its threshold is 00. When the climte inde is greter thn 00, it indictes tht the sitution tends to rise or improve nd the closer to 00, the better; when climte inde is less thn 00, it indictes tht the sitution tends to decline or deteriorte nd the closer to 0, the worse. Business sentiment survey which is conducted by periodiclly investigting the responsible persons through periodic smple surveys. According to the compny's business sitution nd the persons responsible for the judgment of the mcroeconomic environment nd epecttions to compile climte inde, it cn reflect the mcroeconomic nd business conditions ccurte nd timely, the forecst movements in economic development s survey method. It is to dpt to Chin's socilist mrket economic development in the new sitution, lern from the eperience of Western countries nd set up sttisticl survey system in dvnce, it is to enhnce the timeliness of sttisticl services nd epnd the scope of sttisticl services, improve the qulity of sttisticl services of new investigtions. he form of the business sentiment survey, minly qulittive, quntittive, supplemented by combintion of qulittive nd quntittive indictors of economic system in order to determine the mcroeconomic environment of the enterprise nd micro business conditions determine the intention of combining survey content. High hed of its informtion, objectivity, relibility nd continuity, both in terms of time or in the inde re set up for the shortcomings of trditionl sttisticl methods. Grey system theory is composed by professor of Huzhong University of Science nmed Deng (98, 989) in the erly 980s nd hs lredy hve considerble development in bout three decdes. Grey system theory hs been widely used in severl res, such s griculturl, industril nd environmentl system. Grey system theory is n importnt prt of predictive models nd hs been populrized in the time series prediction due to its simplicity nd bility nd high ccurcy to chrcterize n unknown system, using s little s four points. In recent yers, the grey system theory hs been widely used to forecst in vrious fields nd demonstrted stisfctory results. For instnce, Che nd Chen (003), hd used improved GM (, ) model for power demnd forecsting. Pin et l. (003), hd pplied grey model to nlyze humn nd vehicle fctors for iwn freewy trffic ccidents. Wu nd Chen (005), hd used the Grey Model GM (, to conduct cse study on internet ccess popultion forecst. Zhou et l. (006), hd used trigonometric grey prediction pproch to forecsting electricity demnd. Lu (007), hd used grey model to nlyze nd forecst the Rod trffic sfety improvement in Netherlnds. Hung nd Wng (007), hd used Grey Model-GM (, ) to predict the urbn trffic ccidents. Lin et l. (009), hd presented the dptive nd high precision grey forecsting model to predict the stock Corresponding Author: Hongyn Li, College of Mngement, Shnghi University of Engineering Science, Shnghi 060, Chin his work is licensed under Cretive Commons Attribution 4.0 Interntionl License (URL: 976

2 Res. J. App. Sci. Eng. echnol., 7(4): , 04 inde in iwn. Kycn et l. (00), hd used Grey System heory-bsed models in time Series prediction. Zhu (00), hd used the composite grey BP neurl network forecsting model to motor vehicle ftlity risk in Chin. Mo nd Sun (0), hd pplied the Grey- Mrkov model in forecsting fire ccidents in Chin. Becuse the fctors tht ffect the business climte inde re comple nd uncertin, therefore, to forecst the business climte inde, here re lot of known informtion, there re lso lot of unknown informtion, which cn be regrded s grey system, so it cn be nlyzed by using grey system theory. In this study, we first introduce the concept of business climte inde nd then we introduce the GM (, ) model, Verhulst model nd the DGM (, ) model of the bsic concepts nd compre these three models predict ccurcy of the results. Finlly, predicts Shnghi Business Climte Inde from the third qurter of 03 to the first qurter of 04 by the GM (, ) model. MEHODOLOG Grey models: he most common grey prediction model is GM (, ), hen we cn use the rw sequence to mke the Accumultion Generting Opertion (AGO). he AGO revel the hidden regulr pttern in the system development. Before the lgorithm of GM (, ) is described, the rw series is ssumed to be: = {, (),, ( } where n is the totl number of modeling. he AGO formtion of (I) is defined s: = {, (),, ( } () ( k ) k = m ( m ) ( k =,,, = (3) And P = (, b ) = ( B B ( ) ( ) ( + ()) ( ) ( ) B= ( () + (3)) M ( ) ( ) ( ( n ) + ( ) = ( ) ( 3 ) M ( n ) M (6) (7) Applying the Inverse Accumulted Genertion Opertion (IAGO). Nmely: b ( k+ ) = ( k+ ) ( k) = ( e )[ ] e = ( k =,3, L,. k (8) he Verhulst model ws first introduced by Germn biologist Pierre Frnois Verhulst. he min purpose of Velhulst model is to limit the whole development for rel system. For n initil time sequence: = {, (),, ( } he GM (, ) model cn be constructed by estblishing first order differentil eqution for (k) s: d + = b (4) prmeters nd b re clled the developing coefficient nd grey input, respectively. In prctice, prmeters nd b re not clculted directly from Eq. (4). herefore, the solution of (4) cn be obtined by using the lest squre method. ht is: b k b ( k + ) = [ ] e + ( k =,3,, (5) 977 he initil sequence construct the Verhulst model: d + = b( ) is used to directly (9) where is development coefficient nd b is grey ction quntity. he solution of the prmeter vector =, cn be obtined by utilizing the lest squre method. P = (, b ) = [( AM ( AM ] ( AM

3 Res. J. App. Sci. Eng. echnol., 7(4): , 04 And ( + ()) A = ( () + (3)) M ( ( n ) + ( n )) [ ( + ())] B = [ ( () + (3))] M (0 ) [ ( ( n ) + ( )] ( () ( (3) () = M ( ( ( n ) (0) () () () (3) B = M ( M ( () ( (3) () = M ( ( ( n ) According to (4), we hve: b k b b + k+ = e + k+ + ) ( ) ( ( ) ( ) (5) (6) (7) he prediction vlues of originl sequence cn be obtined by pplying inverse AGO to. Nmely: he resolution of (9) is: ( k+ ) = ( k+ ) = ( k) ( k = 0,, L, ( k ) = b + + [ b ( k= 0,, L, k ] e (3) he DGM (, ) model is single sequence second-order liner dynmic model nd is fitted by differentil equtions. Assume n originl series to be : = {, (),, ( } A new sequence is generted by the Accumulted Generting Opertion (AGO): = {, (),, ( } Cse study: In this section, the GM (, ), the Verhulst model nd the DGM (, ) re used for comprison. he business climte inde in Shnghi from the second qurter of 0 to the second qurter of 03 is dopted to demonstrte the effectiveness nd prcticbility of these models. he business climte inde in the second qurter of 0 to the third qurter of 0 is employed to set up the three grey prediction models nd the business climte inde from the fourth qurter of 0 to the second qurter of 03 is used s set to compre the three models ccurcy. he evlution criterion is the Men Reltive Percentge Error (MRPE), which mesures the percent of prediction ccurcy: ( k ) k = m= (0 ) ( m) ( k =,,, Setting up second-order differentil eqution: d P = (, b ) d + = ( B = b B (4) 978 MRPE = n n k= [ (0 ) (0 ) ( k ) ( k ) ( k ) ] he rel nd predictive vlues re shown in ble. So we cn compre the forecsting ccurcy nd reltive error of the three models. he corresponding clculted results (the men error in the different stge) re shown in ble. ble demonstrtes tht the reltive error of the GM (, ) prediction model is smller thn the others. From ble, it cn be seen tht the MRPE of the GM (, ) model, the Verhulst model nd the DGM (, ) model from the fourth qurter of 0 to the second qurter of 03, respectively re 6.3,.36 nd 7.8%.

4 Res. J. App. Sci. Eng. echnol., 7(4): , 04 ble : Model vlues nd prediction error of business climte inde in Shnghi Shnghi business climte inde (the second qurter of 0-the second qurter of 03) GM (, ) Verhulst DGM (, ) Model building stge E-post building stge er Rel vlue Model vlue Error R (%) Model vlue Error R (%) Model vlue Error R (%) he second qurter of he third qurter of he fourth qurter of he first qurter of he second qurter of he third qurter of he fourth qurter of he first qurter of he second qurter of ble : MRPE for the three prediction models Stge GM (, ) Verhulst DGM (, ) he second qurter of 0 to the third qurter of he fourth qurter of 0 to the second qurter of Vlues of business climte inde in Shnghi Rel vlue GM (, ) model Verhulst model DMG (, ) model ime point from the beginning of the second qurter of 0 Fig. : Rel vlues nd models vlues ble 3: Forecsting vlues for business climte inde er Model vlues Rel vlues he fourth qurter of he first qurter of he second qurter of he third qurter of he fourth qurter of he first qurter of he effectiveness nd ccurcy of GM (, ) model is higher thn the Verhulst model nd the DGM (, ) model. Figure shows tht the GM (, ) model nd the DGM (, ) model hve the better forecsting precision from the second qurter of 0 to the second qurter of 03, but the GM (, ) prediction model seems to obtin the lowest men reltive percentge error, besides the GM (, ) model is more suitble to mke short-term prediction. So the GM (, ) model is used to predict business climte inde in Shnghi from the third qurter of 03 to the first qurter of 04 (ble 3). CONCLUSION In this study, we compre the ccurcy of three grey forecsting models by predicting business climte 979 inde in Shnghi. he grey system theory could del with the problems with incomplete or unknown informtion or problems with only few smples, so it is suitble to uses it in this study. he result shows tht the forecst vlue of GM (, ) model from the fourth qurter of 0 to the second qurter of 03 is more ccurte thn the Verhulst grey model nd the DGM (, ) model. Bsed on the bove nlysis, the GM (, ) model ppels to be the best model, becuse it is simply to pply nd ccurte to forecst, thus we use the GM (, ) model to forecst business climte inde in Shnghi from the third qurter of 03 to the first qurter of 04. ACKNOWLEDGMEN his study is supported by the Ntionl Nturl Science Founion of Chin (065, 470, 60755), Ntionl Socil Science Fund (BGL088), Shnghi Eduction Reserch nd Innovtion Key Project (4ZZ57). REFERENCES Che, C.H. nd C.. Chen, 003. Appliction of improved grey prediction model for power demnd forecsting [J]. Energ. Convers. Mnge., 44(4): Deng, J.L., 98. Control problem of grey system [J]. Syst. Control Lett., (5): Deng, J.L., 989. Introduction to grey system theory [J]. J. Grey Syst., : -4. Hung,.. nd. Wng, 007. Forecsting model of urbn trffic ccidents bsed on grey model-gm (, ) [J]. Chongqing Inst. echnol. Comput., 007: Kycn, E., O. Kynk nd B. Uluts, 00. Grey system theory-bsed models in time series prediction [J]. Epert Syst. Appl., 37():

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