A New Algorithm about Market Demand Prediction of Automobile

Transcription

1 Ieraoal Joural of areg Sudes; Vol. 6, No. 4; 04 ISSN 98-79X E-ISSN Publshed by Caada Ceer of Scece ad Educao A New Algorhm abou are Demad Predco of Auomoble Zhmg Zhu, Tao Che & Tamao She Busess School, Hoha Uversy, Cha School of aageme & Egeerg, Najg Uversy, Cha Correspodece: Zhmg Zhu, Wes Focheg Road No. 8, Jagg Dsrc, Hoha Uversy, Boxue buldg, Najg, Jagsu, Cha. E-mal: zhmgzhu@6.com Receved: Aprl 3, 04 Acceped: ay, 04 Ole Publshed: July 8, 04 do:0.5539/jms.v64p00 URL: hp://dx.do.org/0.5539/jms.v64p00 Absrac A exesve evaluao herarchy model of auomoble shor-erm demad was esablshed o preve he dsadvaages of prevous models maly for sgle me seres. The defo of exesve correlao evaluao was proposed, ad he he mehod was dscussed o reflec he correlao of facors o auomoble demad. Ulzg exesve slls, facors ad sub-facors were represeed as correlao egemarx whch could esure he level of each facor s flueces o auomoble demad. The shor-erm hsorcal daa was predced whle was compared wh exsg daa, he resuls show ha he predcve error s less ha 6%, whch cofrms he valdao of predcve model. Ths sudy provdes he foudaos for goverme s macroecoomc corol ad auomoble maufacurers produco. Keywords: auomoble, shor-erm demad, predco, exesve correlao evaluao, couous me model. Iroduco The demad aalyss of auomoble s maly characerzed by he followg feaures: here are oo may affecg facors o demad chages, he facors are very complex, ad he relaoshp bewee he prmary ad secodary varables s chageful whch s dffculy quaave aalyss accuraely; eawhle he daa quay volved demad aalyss s large, a he same me, he requremes for he meless of he aalycal algorhm ad arhmec operao cos s hgh (Su, 00). Durg he process of research, we fd ha whe forecasg he demad, our domesc auomoble maufacurers usually use smple aalyss ool wh bacward mehods; wha s more, hey also aalyze he quaave ad qualave separaely. Usually he uceray of demad ofe maes predco cocluso whch drew from he modelg mehod usasfacory. Therefore, s mperave for us o esablsh a effecve auo demad forecasg model. The ey po o he mplemeao of scefc predco depeds o wheher he qualave mehod ad he quaave mehod are coeced closely, whch requres o rea he quaave mehod as a foudao ad comprehesvely aalyze he predced objec qualavely (Bao, 0). Hece, he paper proposes a dyamc couous me seres predco model based o qualave aalyss. Ths model cosss of wo pars, oe s quaave forecas model based o dyamc couous me model, whch we f ew sequece by ag advaage of he dyamc couous me model ad lear abou he hsorcal daa of demad, ad gve he quaave predco of produc demad. The oher s he exesve herarchy aalyss ad evaluao model of flueal facors based o produc demad, cocludg he correlao dex model abou he flueal facors hrough he aalyss of he flueal facors abou auomoble mare demad. Ths paper combes he wo models from each par, esablshes a fal predco model hrough quaave model whch based o qualave aalyss, ad gves a more objecve predco resul accordg o ha.. Tme Couous odel of Dyamc Sysem. Tme Couous odel of Dyamc Sysem Owg o our coury s macro-corol o auomoble dusry, s hard o esablsh a predco model of shor-erm car sales reds by radoal predco mehod. The esablshed predco models such as ARIA, ANN, Hol-wer, all of hese, o he bass of a large amou of hsorcal daa, searchg for he causales whch fluece he fuure red, so ha hey could forecas by esablshg relaed exrapolao ype model (Zuo & Gao, 0). The essece of car sales forecas s o sudy he me varao law of a dyamc sysem, whch s o deduce he fuure chages of he sysem accordg o he exsg saus daa. Ad he dyamc 00

2 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 sysem model ca be expressed by a hgh order dffereal equao. If he dyamc behavors of car sales are observed by couous me, we call me couous model of dyamc sysem. Accordg o he feaures of shor-erm chages of auo sales, he rule of accumulave chages of sales ca be expressed by -h order dffereal equao (Zhao, 99). Accordg o me couous model of dyamc sysem pu forward by Shpeg Zhao, we ca express wh -h order dffereal equao: d d x a d Abbrevaed as D (, h), where x (,,, h )s accumulaed me seres of prmve me seres The followg hree mahemacal models are gog o be used: Frs, s order lear dyamc model wh sgle sequece D (, ) model: dx d d x ax b 0 h b x where a, μ are cosa. Secod, s order lear dyamc model wh wo sequeces (D (, ) model: () ( ) dx ( ) ( ) ax bx (3) d Where x s oce accumulaed sequece of { x } seres, a ad b are cosa. Thrd, s order lear dyamc model wh hree sequeces (D (, 3) model: dx d ( ) ax ( ) bx ( ) cx ( ) 3 (4) Where 3 x s oce accumulaed sequece geeraed from sequece { x 3 }, a, b ad c are cosa.. Daa Processg Oce accumulaed geerag operao process daa before we esablsh flucua ecoomc sequece model, whle a verse accumulaed geerag operao s usually used o resore he predced value geeraed from he prevous model. Ecoomc sequece X s oegave sequece (.e., each compoe x ( ) 0), hus X s moooe creasg. Lu Zhu pos ou ha afer accumulaed geerag operao sequece X possesses beer properes ha he orgal sequece X,.e., has beer smoohess, ad flucua sequece geeraes moooe ew sequece, whch weaes he radomess of sample value sequece (Lu, 009). Through accumulaed geerag operao, me seres ( ) x, x ( ) 0,,,, ge moooe creasg x ( ) x ( ). The orgal me seres s oegave, ad s daa amplude chages rregularly, bu he geeraed me seres s o oly oegave, bu also moooe creasg, amely daa amplude chage has cera regulary. Compared wh he orgal sequece, geeraed sequece has a ehaced deermacy. Dervable everywhere s he characersc of smooh couous fuco, bu 0

3 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 sequecex ( ) cosss of dscree sgle pos, hus usually has o dervave, herefore we ca' research smoohess of sequece x ( ) wh dervave. We sudy he characerscs of smooh couous fuco by he followg pos of vew. Hypohess : f a sequece has roughly smlar characerscs wh smooh ad couous fuco, he sequece s cosdered o be smooh. Defo : assume ha X () s couous fuco defed oa, b, ser eror pos oa, b. a b Now o b a, here s a dvso,,,,,,,,,,,. We use o express he legh of.tae ay po o seres X x( ), x(),, x( ), X x ), x( ),, x( ) sequece. Le max 0 (, we ge x (), hus we have, s recorded as lower boudary po, assume ha d s a dsace fuco -dmesoal space, X * s he represeave sequece for specfed fuco. No maer how me zoe a, b s dvded ad how eror po small me erval s seleced, whe 0 here are: for ay eror po sequece X, X j, d X*, X dx*, X j ; () dx*, X dx*, X Tha we call x() smooh couous fuco. 0 Theorem : assume a sequece X ( x, x(),, x( ), x( )), Z s a mea sequece geeraed,amog whch z ( ) 0.5x( ) 0.5x( ),,,,. X * s from X, Z z( ), z(),, z( ) a represeave sequece for a dervave fuco, ad d s a dsace fuco -dmesoal space. We sll call X afer deleg x ( ) from X, f he followg codos s sasfed, we call X smooh sequece. K s suffcely large, x ( ) x( ) ; max () x ( ) x( ) x * ( ) z( ). * max, () s called sequece smoohess codos Theorem : assume ha X s oegave sequece, X x, x (),, x, ( r ) ( r) ( r) ( r) x ( ) 0 ad x ( ) a, b,,,. X ( x, x (),, x ( )) s r-h accumulaed 0

4 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 geerag me sequece of X, whe r s suffcely large, for ay 0, here exs N, N, ( r ) x ( ) he followg equao s esablshed ( r ),ha s, for he bouded oegave sequece, x ( ) afer may mes accumulaed geerag operao,he geeraed sequece s suffcely smooh,ad smooh rao ( ) 0( ) Theorem 3: assume ha X s a oegave sequece, X ( x x, x (),, x x( )), x ( ) 0 ad x ( ) a, b,,,,. X x, x (),, x ( ) s oce accumulaed geerag sequece of X, Z z, z (),, z ( ),where z ( ) 0.5x ( ) 0.5x ( ) s adjace mea 0, geeraed sequece of X,he for ay N, here are ( ) x ( ) x (),, here s a posve eger N,ad for ay, x z ( ) ( ) Boh he accumulaed geerag operao ad he mea geerao ca mprove he smoohess of he sequece, we ca use wo ds of mehods hrough combao, eve f we mpleme a mea geerao afer accumulaed geerag operao. 3. Herarchy Evaluao odel of Iflueal Facors 3. Facors Affecg he Auo are The followg facors affec he fuure reds of he auomove mare ad dusry: polcal facors, ecoomc facors, socal facors ad echcal facors. Through he aalyses o Cha's auo dusry he pas, prese ad fuure, we fd ha: polcal facor s he guaraee for healhy developme of auomove dusry; ecoomc facor s he foudao for he auomove dusry o ae off; echcal facor s he prerequse for prospery of he auomove dusry; socal facors s he ey o creae he auomove cosumer mare (Feg, 004; Wag & a, 006). Accordg o he relevace of facors ha affec he demad for cars (Ca, 999), we esablsh a herarchy evaluao model of auomoble demad facors as follows: 03

5 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 car demad X X X P m P m H L H L H L H L H L H L m Fgure. Car demad flueal facors evaluao model Where,(,,, m) represe macro flueal facors, for sace ecoomc, socal, echologcal ad oher facors affecg he demad for cars,,,, Preprese he sub-facors ha affec macro facors. H,, L respecvely represe hgh, medum ad low degree of he fluece of sub-facors. X, X, X dcae dffere ypes of auomobles. Rule : rules o esablsh herarchy evaluao model I he fucoal herarchy, a complex sysem s decomposed accordace wh he basc relaoshp amog s compoe elemes; () The hghes level herarchy coas oly oe eleme: he overall goal. Oher levels ca coa a umber of elemes; (3) There s o lm for levels he herarchy; (4) Whe favorg comparso ca o be carred ou bewee cera elemes, a approprae ew level mus be sered. (5) Herarchy s flexble, ad ca be modfed a ay me order o adap o he ew gudeles. 3. Evaluao odel Based o Aalyc Herarchy Process If R represes he egemarx of car demad flueal facors, represes he facors affecg he demad for auomobles, c represes varous momes, ( ) s membershp degree of v, here v s he correspodg value of c (he flueal facors of he demad for auomobles). Assume ha possesses m facors, ad marx cosss of her shared momes ( v xj ) ( x,,, m; j,,, ), he followg marx called he egemarx of auomoble demad. m c ( ) ( ) ( ) m Rm c ( ) ( ) ( m) (5) c ( ) ( ) ( m) Defo : Esablsh sequeal egemarx R f for cars demad forecas ad real sequeal egemarx R r whch cludes mulple flueal facors. Where x ( j),,,, ; j,,, mrepreses he me f 04

6 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 seres for cars demad predco, ad x ( j),,,, ; j,,, mrepreses he acual me seres, we have r c xr xr x r Rr c xr() xr() xr() cm xr( m) xr( m) xr( m) c xf xf x f R f() f() f() f c x x x cm xf( m) xf( m) xf( m) 3.3 Correlao Rgh Egemarx 3.3. Characerscs of Oe-Layer Correlao Rgh If Rw represes wegh marx fluecg all facors of each predcve objec ad represe he weghs of -h facor of each predcve objec. The we have (6) (7) w (,,, ) Rw w w w w (8) 3.3. Characerscs of Two-Layer Correlao Rgh Demad for cars coas mul-layer flueal facors, hece s correspodg wegh should be dvded o several layers. Tae wo layers as a sample, he res ca be doe he same maer, here s: w w w w R w (9) cc c cc c cc c w ww w ww w ww w Where c sads for he -h secodary flueal facor whch belogs o he -h ma flueal facor herarchy model of auomoble demad, we use w (,, ;, p ) o express her correspodg rgh Correlao Degree Egemarx By correlao rasformao of he correspodg degree of membershp of auomoble demad forecasg sysem, we ge he respecve correlao coeffce o cosruc he egemarx of he correlao coeffce, wre as R, amely m c m R c m (0) c m 05

7 Ieraoal Joural of areg Sudes Vol. 6, No. 4; Predcve Learg Algorhm Based o Exeso Correlao Evaluao ad Dyamc Couous Tme odel 4. Correlao Trasformao Algorhm I s evde () ha he degrees of membershp abou each flueal feaure are que dspersve. Tha s adverse for overall facors comparso. So s ecessary for us o focus o a value. Geerally we use weghed ceralzed processg (Ca, Yag, Che, & L, 008). Here, we have a ew mehod o deerme he wegh,.e. summae characersc values of facors dffere momes, ad he mpleme ormalzao process o he characersc values of each facor. The we ca oba he correlao coeffce of every facor, ceer upo he auomoble sales, fgure up he dsace bewee facors each mome ad car sales, ad fally do he mea reame o dsace each mome of he same facor, amely he correlao degrees bewee he demad for auomobles ad varous facors. The seps are as follows: Sep Oba he arhmec mea value of each facor, amely: m ( ) m m m j j m ( ) m m m j j m ( ) m m m j j Sep Impleme ormalzao reame o each facor s characersc degree () m m c j j mj j j j m c R j j mj j j j m c j j mj j j j Sep 3 Ceer o, m, calculae dsace bewee,,,,,,, m ad, m d (, ),,,,,, m;m. () 06

8 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 d d dm m c j j j j mj j j j j j j j m r c j j j j mj j j j j j j j m c j j j j mj j j j j j j j (3) Sep 4 Comprse correlao degree r bewee auomoble demad flueal facors,,,,,,, m ad facor, m r j j j (4) j j j j j j j j j j j j r r r Where r,,,,,,, m represe correlao degrees bewee -h flueal facors of auomoble demad forecas sysem ad he -h em. 4. Demad Saus Aalyses Based o Exeso Theory ad Herarchy Evaluao odel Sep Aalyss of he relaoshp bewee facors he auomoble demad sysem, esablsh he herarchcal srucure of he sysem; Sep Process me seres of he varous flueal facors wh algorhm 3., he ge correlao degrees bewee facors ad auo demad; Sep 3 Calculae correlao degrees bewee he varous facors ad demad arge, he sor; Sep 4 Sudy he mpac of varous facors o he demad for cars wh correlao degree as he evaluao of dcaors. 4.3 Soluo of Predcve odel (Choose odel as a Sample) Sep Process seres{ x ( ) } by meas of accumulaed operao Sep Impleme mea value reame o seres{ x ( ) Sep 3 Solve (6) by leas square mehod x ( ) ( 0 ) ) x ( ) ( (5) }, he model urs o a ( ) ( x ( ) x ( )) x (6) 07

9 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 T T a ( B B) B Y ; - ( x () ) x - ( x (3) ()) x Where B (7) ( x ( ) ( )) x T a (a, μ) (8) Sep 4 Afer we ge a, μ, he aswer o model () s Sep 5 Impleme verse accumulaed operao The we ca ge he predced value T ( x (), x (3),..., x ( (9) Y )) ) e a a a x ( ) ( x (0) x ( ) x ( ) x ( ) 4.4 Sysem Predco Value of K omes he Fuure Sep Process measured radom sequece wh accumulaed operao ad mea value reame Sep If x ( ) s lear dyamc sysem wh sgle facor sequece, esablsh forecas model accordg o formula (),or f s lear dyamc sysem wh wo-facor sequece, esablsh forecas model accordg o formula (3), or f s lear dyamc sysem wh hree-facor sequece, esablsh forecas model accordg o formula (4); Sep 3 Solve he model wh 3.3; Sep 4 Ge he soluos by verse accumulaed operao, ad he he resuls are predced values of osaoary sequece. 4.5 Aalyss ad Forecas of Auomoble Shor-Term Demad Sep Qualavely aalyze flueal facor wh algorhm 3., ad he oba correlao coeffces of each demad flueal facor; Sep Process prmve correlao coeffce by ulzg algorhm 3., ge he wegh of each demad flueal facor; Sep 3 Aalyze ad forecas auomoble shor-erm demad wh algorhm 3., 3.3, Example Aalyses Aalyze he model he paper by ag car demad forecas aalyss whch comes from a cera area as a example. Se auomove hsory sales durg as he prmve daa, mpleme correlao aalyses o he auo demad flueal facors, he resuls ca help he goverme o mae macro-corol o auomoble dusry ad auomoble maufacurg eerprses o mae produco pla. The rego's car sales ad flueal facors of auomoble demad sascs are Table. () 08

10 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 Table. Numercal able of auomoble demad flueal facors year oal car sales gross domesc per capa proporo of he socal fxed real sales of premum (oe per capa urba ad rural (0 housad) produc (GDP) GDP hrd dusry asses socal hudred aual come resdes (oe (Yua) GDP (%) vesme cosumpo mllo Yua) (Yua) year-ed savgs hudred mllo (oe hudred (oe hudred balace Yua) mllo Yua) mllo Yua) (oe hudred mllo Yua) Daa source: Cha sascal yearboo, I pracce, here are may car demad flueal facors, cludg gross domesc produc (GDP), per capa GDP, proporo of he hrd dusry GDP, socal fxed asses vesme, real sales of socal cosumpo, per capa aual come, urba ad rural resdes year-ed savgs balace, premum ad oher facors, hs paper chooses he above facors o aalyss her fluece o car demad. Process daa Table accordg o algorhm 4. ad 4., respecvely we ge Table ad Table 3 ad Table 4. Table preses he correlao coeffces of demad facors sysem dffere momes, Table 3 shows he dsace from facors o car sales. Correlao coeffces for all mpac facors wh regard o car sales are show Table 4. Table 5 represes correlao degrees amog facors relave o car sales. Table. Facors correlao rasformao processg year oal car sales x ( ) 0 (GDP) x ( ) Per capa GDP x ( ) proporo of he hrd dusry GDP x ( 3 ) fxed asses vesme x 4 ( ) real sales of socal cosumpo x ( 5 ) premum per capa x 6 ( ) come x ( 7 ) savgs year-ed balace x 8 ( )

11 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 Table 3. Dsace bewee facors ad car sales year 0( ) ( ) 0 ( ) ( ) ( ) ( ) ( ) ( 08 ) Table 4. Correlao coeffces amog facors year ( 0 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Table 5. Correlao degrees of mpac facors correlao degree γ 0 γ 0 γ 03 γ 04 γ 05 γ 06 γ 07 γ Illusrae Table 5 wh Fgure., whch represes correlao degrees amog facors wh regard o auomoble sales, where we ca fd ha γ 04 >γ 08 >γ 0 >γ 0 >γ 05 >γ 07 >γ 06 >γ 03, hece fxed asses vesme has he closes correlao relaoshp wh auomoble sales, he secod close s premum. Thrd dusry GDP has he mmum fluece. 0

12 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 Fgure. Correlao degrees of mpac facors Accordg o he forecas model ad mehod proposed by hs paper, forecas couous daa of car demad durg 000-0, ad compare hem wh he exsg daa, he resul s show Table 6. Table 6. Comparso bewee car demad forecas values ad acual values durg me acual value predced value absolue error relave error Predced resuls based o he above model are gve Table 6 reflecs ha wh he mehod hs paper we have a fe fg degree bewee predced seres ad prmve seres durg Excep for relave errors sascs of year 008, he ohers are corolled wh 6%, ha meas hs model ca forecas shor-erm me seres accuraely. A bg reaso of 008 predco error s he facal crss whch maes grea volaly o auomoble demad. I 009, reurs o ormal predcve error. The above aalyss resul shows ha we ca mae a effecve assessme o demad sysem, ad smulaeously acheve he purpose of car demad corol hrough he relaed ecoomc polces. 6. Cocluso Auomove dusry has become a mpora par of Cha's dusry, predco model proposed by hs paper has solved dffcul problems ha shor-erm forecas radoal predco mehod cao hadle wh; s also able o f ucera car demad chages wh hgher precso. By usg he predco model o forecas car demad he comg hree years, we ca see ha car demad wll grow couously, ad he growh rae wll also crease year by year.

13 Ieraoal Joural of areg Sudes Vol. 6, No. 4; 04 A he same me, he exesve evaluao model se up hs paper provdes auomoble eerprses ad goverme ageces wh a feasble ad effecve mehod for car demad forecas aalyss. The model aalyses ma facors of car demad flueal, ad sor hem accordg o he exe of he effecs. We foud ha amog varous flueal facors, fxed asses vesme ad he premum affec a lo. However, he hrd dusry GDP has lle effec. These aalyses wll help he goverme o mae macro-corol o auomoble demad ad he same o he auomoble maufacurers o mae produco pla. Refereces Bao, Y. J. (0). Iegraed Forecas o Car Owershp Rae of Urba Dwellers Cha: Based o Dffere Icome Levels. Techology Ecoomcs, 30, Ca, W. (999). Exeso heory ad s applcao. Chese Scece Bulle, 44, hp://dx.do.org/0.007/bf Ca, W., Yag, C. Y., Che, W. W., & L, X. S. (008). Exeso se ad exeso daa mg. Scece Press. Feg, B. (004). Key Facors Aalyss of Chese Auomoble Brad Developme. Taj Auo, 4, 6 9. Lu, Z. (009). Applcao of Grey Sysem Theory for Por Coaer Throughpu Forecasg. Hefe Uversy of Techology, 009. Su,. (00). Iflueal Facors, Tred ad Dsrbuoal Chage of Cars'Demad Emprcal Aalyss Based o he Household Prvae Cars Owershp. Joural of Shax Face ad Ecoomcs Uversy, 3, Wag, L. L., & a, X. (006). Aalyss o Ecoomerc odel of Demad of Chese Cvl Auomoble. Joural of Shax Ecoomc aageme Isue, 4, 6 8. Zhao, S. P. (99). A New ehod of Esablshg Tme Couous odel of Dyamc Sysem. Sysems Egeerg-heory & Pracce, 5, 4 9. Zuo, X. Y., & Gao, S. (0). Forecasg sysem aalyss for auomove mare quay demad based o per e. Joural of Shadog Uversy of Techology(Naural Scece Edo), 5, Copyrghs Copyrgh for hs arcle s reaed by he auhor(s), wh frs publcao rghs graed o he joural. Ths s a ope-access arcle dsrbued uder he erms ad codos of he Creave Commos Arbuo lcese (hp://creavecommos.org/lceses/by/3.0/).