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ENFS@FQ@SP A[QKS@NFU ;

Ujnrt @ftrncuet`nf tn tjaYastr`etac Xaetnr Kutnramrass`va Lncab (YXKY) nh

Enft`fu`ty Aqukt`nfs hnr Enft`funus KssurkfeaAr`g vkf Galpaf, Utucaft Laliar, @AAA , 2 ar`gvkfgalpafD`aaa.nrm 6

Hnftys Jnmasejnnb H`fkfe`aab Lkfkmalaft, Hnftys Qf`vars`ty nh Kppb`ac Ue`afeas

Kistrket Enft`funus kssurkfea ekf usa enft`fu`ty aqukt`nfsiy lncab`fm prac`etnrs hnr rapnrtac qukft`t`as `f ius`fass prneassstaps. Nfa nh tja iast lncabs hnr tjasa enft`fu`ty aqukt`nfs `s tjaYastr`etac Xaetnr Kutnramrass`va Lncab (YXKY). @f tj`s lncabbkms kra ast`lktac cur`fm tja lncab fm prneass ks nppnsac tnpraca f fm xac bkms `f tja iks`e XKY lncab. Hurtjarlnra,fnf-enrrabktac vkr kibas kra axebucac hrnl tja fkb lncab tnl`f`l`za tja nvarkbb pnstar`nr Y 9 nh tja lncab.

@fcax Sarls Enft`funus kssurkfea, enft fu`ty aqukt`nfs,YXKY, Yastr`etac Xaetnr Kutnramrass va lncab, cktk kfkbys`s.

@. @FSYNCQES@NF

E NFS@FQ@SP A[QKS@NFU kra k hufcklaftkb pkrt nh ebkss`ekb pjys`es, iut tja kppb`ekt`nf nh tjasa aqukt`nfs`f tja abc nh fkfea jks fnt iaaf axpbnrac `f catk`b. @f tja`rpkpar nf enft`fu`ty aqukt`nfs Gnmkf at kb. jkva prnv`cac tjatjanry kfc k fuliar nh snbut`nfs hnr kppby`fm tjasa aqukt`nfsks k tnnb `f tja enft funus kssurkfea cnlk`f. W ;\ Nfa nh

tjasa snbut`nfs `s tja Uuisat Xaetnr Kutnramrass va Lncab(Uuisat XKY) nr Yastr etac Xaetnr Kutnramrass va Lncab(YXKY). Sj`s lncab wks `lpbalaftac `f tja UKU bkfmukma.@f tj`s pkpar tja lncab `s `ftrncueac.

Ouby ;3, 94;5

@@. ENFS@FQ@SP A[QKS@NFU

Enft`fu`ty aqukt`nfs kra k hufcklaftkb pkrt nh ebkss ekbpjys`es. Sjasa aqukt`nfs caser`ia tja trkfspnrt nh k enfsarvacqukft ty, wj`ba s`lubtkfanusby afsur fm enfvarskt`nf nh tj`squkft`ty (b`ga lkss kfc/nr afarmy). Keenrc`fmby s`l`bkr rabk-t`nfs ekf ia ca fac hnr tja trkfspnrt nh qukft`t`as w`tj`f ksystal `f tja fkfe kb cnlk`f. Hnr axklpba tja lnvalaft nh rapnrtac qukft`t`as iatwaaf staps `f tja gay ius`fass prneassasekf ia caser`iac w`tj enft`fu`ty aqukt`nfs.

Sja tarl enft`fu`ty aqukt`nfs wks en`fac iy Xkskrjaby` kfcJkbpar `f ;00;, wjaf tjay lncabac tja nw nh i`bb`fm cktk ktKS&S. W9\ Kbtjnumj Xkskrjaby` kfc Jkbpar prnpnsac enft`fu-`ty aqukt`nfs lnra tjkf 94 yakrs kmn, b`ttba rasakrej jks iaafparhnrlac nf tja kppb`ekt`nf `f prket`ea kfc `lpbalaftkt`nfnh k caeaft enft fu`ty aqukt`nfs lncab. Aspae kbby rasakrejhneus`fm nf tja XKY lncab jks iaaf rkraby parhnrlac `f tjabkst twn caekcas. Nfby Czafm W5\ kfc Gnmkf at kb. W;\ jkva

kbsn enfs`carac tja XKY lncab `f tja`r pkpars.

@f lnst ius`fassas tja nw nh mnncs `s tja lnst `lpnrtkftiks`s hnr ravafua raenmf`t`nf. Ks suej, `t ekf ia usac tn prn-v`ca av`cafea hnr tja enlpbatafass, t`lab`fass kfc keeurkeynh tja rapnrtac ravafua. @h tja enft`fu`ty aqukt`nfs jnbc hnrk eartk f ius`fass prneass, nfa ekf kssart tjkt tjara kra fnbakgkmas hrnl tja trkfsket`nf nw, `.a. tja `ftamr`ty nh tja

nw nh mnncs ekf ia kssartac. Sjarahnra, enft`fu`ty aqukt`nfsprnv`ca k latjnc tn av`cafea tja `ftamr`ty nh tja iks`s hnrravafua raenmf t`nf, wj`ej lkgas tjal k vkbukiba tnnb `fenft`funus kssurkfea.

Enft`fu`ty aqukt`nfs kra iksac nf j`stnr`ekb cktk nh qukft`-t`as `f tja sapkrkta staps nh ius`fass prneassas. Hnr axklpba,tja skbas eyeba ekf ia lncabac ks tjraa sapkrkta staps? ra-ea v`fm tja nrcar hrnl tja eustnlar, sj`pp fm mnncs tn tjaeustnlar kfc `fvn`e`fm hnr tja nrcarac kfc sj`ppac mnncs. Nh enursa tja qukft`ty nh nrcarac mnncs tncky w`bb sjnw up `ftja `fvn`e`fm stap k eartk`f klnuft nh ckys bktar. Sja ck`by

nw nh mnncs iatwaaf tjasa staps ekf ia ca fac ks k eartk`fqukft`ty [ kfc bkm iatwaaf tja staps .

K. Iksa Lncab

@f tj`s pkpar wa w`bb hneus nf tja skbas eyeba, w`tj tja tjraaprav`nusby ca fac prneass staps. Sja enft`fu`ty aqukt`nfs hnrtja skbas eyeba ekf ia raprasaftac ks Aqukt`nf ;. @f tj`s lncabnrcar t `s tja qukft`ty nrcarac kt t`la t , tja tarls kra F ; trkfs`t`nf vaetnrs hnr k lubt vkr`kta b`fakr lncab kfc tjaL tarls kra F ; vaetnrs enftk f`fm ck`by kmmramktas nh qukft`t`as hnr tja m`vaf c`lafs`nf.

nrcar t < nn L (nrcar ) + sn L (sj`ppac ) + `n L (`fvn`eac )sj`ppac t < ns L (nrcar ) + ss L (sj`ppac ) + `s L (`fvn`eac )`fvn`eac t < n` L (nrcar ) + s` L (sj`ppac ) + `` L (`fvn`eac )

(;)Akej nh tjasa sui-aqukt`nfs lncabs k prac`etnr hnr tja rapnrtacqukft t`as `f k spae` e stap `f tja ius fass prneass. Ksprav`nusby ca fac, tja qukft`t`as kra rabktac tn qukft`t`as `ftja ntjar prneass staps iy k t`la cabky (bkm). Hnr axklpba,`h nrcars kra sj`ppac `f axketby nfa cky, w`tjnut axeapt`nf,kfc `fvn`e`fm `s parhnrlac s`lubtkfanusby w`tj sj`pp`fm, tjarasubt`fm prac`etnrs ekf ia ca fac ks Aqukt`nf 9

nrcar t < ; sj`ppac t +; + 9 `fvn`eac t +;sj`ppac t < ; nrcar t ; + 9 `fvn`eac t

`fvn`eac t < ;

nrcar t ; + 9

sj`ppac t

(9)

mailto:erikvankempen@ieee.orgmailto:erikvankempen@ieee.org

7/28/2019 Short Introduction to the Restricted Vector Autoregressive Model (RVAR) of Continuity Equations for Continuous Ass

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ENFS@FQ@SP A[QKS@NFU 9

I. Iks`e Xaetnr Kutnramrass`va Lncab

@f tja iks`e Xaetnr Kutnramrass`va Lncab (XKY) tja lncab`s ast`lktac npt`l`z`fm hnr tja nvarkbb Y9 iy try`fm c`hharaftbkms hnr tja prneass staps. Nfby tja lkx`lkbby axpaetac bkm`s prnv`cac tn tja kbmnr`tjl kfc `t tjaf tr`as tn fc tja iast

tt`fm lncab iy `tarkt`fm trnumj kbb bkm pnss`i`b`t`as. Sja axketbkms cn fnt jkva tn ia gfnwf pr`nr tn lncab`fm ks tja iast

tt`fm bkms kra catarl`fac wj`ba lncab`fm.Nfa ekf aks by ufcarstkfc tjkt `t `s fnt kbwkys tr v`kb tn

catarl`fa bkms pr`nr tn tja lncab`fm prneass, a.m. bkms `f tjapurejks`fm eyeba kra j`mjby capafcaft nf tja pnb`e as kfcprneassas kt tj`rc pkrt`as. Sjarahnra, tja XKY lncab ekf iak pnwarhub tnnb hnr lncab`fm enft`fu`ty aqukt`nfs `h bkms ekffnt ia praca fac tr`v`kbby.

E. Yastr`etac Xaetnr Kutnramrass`va Lncab

Gnmkf at kb. jkva sjnwf `f tja`r stuc`as tjkt tja XKY lncabc`c sjnw mrakt rasubts. Lnra `lpnrtkftby, tjay sjnwac tjkt tjaUuisat XKY lncab rasubtac `f avaf iattar rasubts.

Sja Uuisat XKY lncab trkfsbktas rnumjby tn npt`l`z`fm hnrY 9 nh tja prac`etnr iy axebuc`fm ufenrrabktac vkr`kibas hrnltja XKY lncab. Hnr axklpba, `h tja lakf bkm iatwaaf nrcarkfc sj`pp`fm `s bass tjkf k lnftj tja vkr`kiba sj`ppac t +581kfc kfy ntjar vkr`kiba sj`ppac t + w`tj 6 5; kra ralnvaciaekusa tjasa kra niv`nusby fnt enrrabktac vkr`kibas.

Sja Yastr`etac Xaetnr Kutnramrass`va Lncab (YXKY) fntnfby npt l zas hnr tja nvarkbb Y9 iy try`fm c`hharaft bkms,`t kbsn npt l`zas tja mnncfass nh tja t iy axebuc`fm tjaufenrrabktac vkr`kibas kfc ra`tarkt`fm tja XKY prneass.

@@@. KCXKFSKMAU

Sja YXKY lncab st`bb jks tja kcvkftkma nh tja XKY lncabnvar strueturkb lncabs kfc s`lubtkfanus aqukt`nfs iaeksua tjabkms cn fnt jkva tn ia xac pr`nr tn tja lncab`fm prneass.Sj`s `s k mrakt kcvkftkma hnr tja kfkbyst wjn parhnrls tjalncab`fm. Sja stap nh ast`lkt`fm bkms `s vary safs`t`va tn arrnrs`f `ftarpratkt`nf kfc jks afnrlnus `lpket nf tja rasubt fmlncab. Iy ralnv`fm tj`s stap hrnl tja lncab`fm prneass bassarrnrs kra `ftrncueac, rasubt`fm `f k lnra keeurkta prac`etnr.

Hurtjarlnra, tja rasubt`fm YXKY lncab `s lnst b`gaby tnjkva k j`mjar Y9 enlpkrac tn tja iks`e XKY lncab, wj`ejlakfs tjkt tja lncab `s k iattar prac`etnr `f tarls nh keeurkeyhnr tja rapnrtac qukft t`as. K j`mjar keeurkey ekf bakc tn

k bnwar cav`kt`nf axeapt`nf tjrasjnbc kfc tjus k slkbbarcataet`nf r`sg `f tja enft`funus kssurkfea cnlk`f.H`fkbby, tja rasubt`fm lncab `fenrpnrktas bass vkr`kibas kfc

ekf ia ufcarstnnc lnra aks`by. Fnt avary `fc`v`cukb enfearfacw`tj enft`funus kssurkfea `s kf axpart `f tja abc nh cktkkfkbys`s nr stkt`st`es. K slkbbar kfc lnra aks`by ufcarstkfckibalncab ekf jabp pntaft`kb usars nh tja lncab tn kckpt lnraqu`egby tn us`fm `t `f tja kssurkfea cnlk`f.

YAHAYAFEAU

W;\ K. Gnmkf, L. M. Kbbas, L. K. Xkskrjaby`, kfc O. ]u, Kfkbyt ekbprneacuras hnr enft funus cktk bavab kuc`t fm? Enft`fu`ty aqukt nfs,94;4.

W9\ L. K. Xkskrjaby` kfc H. I. Jkbpar, Sja enft`funus kuc t nh nfb`fasystals, Kuc`t`fm? K Onurfkb nh Trket`ea & Sjanry , vnb. ;4, fn. ;, pp.;;4;91, ;00;.

W5\ U. Czafm, K enlpkr`snf nh kfkbyt ekb prneacuras axpaetkt nf lncabsus`fm intj kmmramkta kfc c`skmmramkta cktk, Kuc t`fm? K Onurfkb nh Trket`ea & Sjanry , vnb. ;5, fn. Hkbb, pp. ;93, ;003.

Ar`g vkf Galpaf Ar`g (inrf Kpr`b 91, ;0:=) `s kbaeturar `f Utkt`st`es, AYT kfc Ius`fass @ftabb`mafeakt Hnftys Qf`var`ty nh Kppb`ac Ue`afeas `f A`fc-jnvaf, Sja Fatjarbkfcs. Tr`nr tn tj`s baeturasj`p, janitk`fac k Ikejabnr nh Ius`fass Kcl`f`strkt`nf `fKeenuftkfey.

J`s rasakrej `ftarasts kra `f tja kraks nh enft`fu-nus kssurkfea, slkrt kuc`t`fm, ius fass `ftabb`mafeakfc prneass l`f`fm.