Magdalena Zachłod-Jelec – Związki dynamiczne między konsumpcją, dochodem i aktywami. Wnioski dla Polski

Bank i Kredyt 42 (6), 2011, 49–84 www.bankandcredit.nbp.pl www.bankikredyt.nbp.pl

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=JRGQLH ]H Z]RUHP  UHODFMD GïXJRRNUHVRZD PLÚG]\ NRQVXPSFMÈ D ERJDFWZHP SU]\EOLĝR QHJR GRFKRGHP ] SUDF\ L DNW\ZDPL MHVW UöZQD Z SU]\EOLĝHQLX ZDĝRQHM VXPLH ]G\VNRQWRZDQHJR WHPSD Z]URVWX GRFKRGX ] SUDF\ L VWRS\ ]ZURWX ] DNW\ZöZ SRPQLHMV]RQHM R WHPSR Z]URVWX NRQ VXPSFML2]QDF]DWRĝHZ]URVWLORUD]XNRQVXPSFMLLERJDFWZDZLÈĝHVLÚ]Z\ĝV]\PRF]HNLZDQ\P ZRNUHVLHtWHPSHPZ]URVWXGRFKRGX]SUDF\]QLĝV]\PRF]HNLZDQ\PWHPSHPZ]URVWXNRQVXPS FML]Z\ĝV]\PRF]HNLZDQ\P]ZURWHP]DNW\ZöZOXE]HZV]\VWNLPLZVSRPQLDQ\PLF]\QQLNDPL ïÈF]QLH3UDZDVWURQDIRUPXï\Z\UDĝD]DWHPUDFMRQDOQHRF]HNLZDQLDNRQVXPHQWöZ/HWWDX/X GYLJVRQ3RQDGWRMHĂOLSUDZDVWURQDUöZQDQLDWZRU]\]PLHQQÈJHQHURZDQÈSU]H]SURFHV RFKDUDNWHU]HVWDFMRQDUQ\PDNRQVXPSFMDGRFKöGLDNW\ZDVÈJHQHURZDQHSU]H]SURFHV\QLHVWDFMR QDUQHWR]DFKRG]LUHODFMDNRLQWHJUDFMLPLÚG]\NRQVXPSFMÈGRFKRGHP]SUDF\LDNW\ZDPLRSRVWDFL t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_r A r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1

(

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(

at i

(

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lt i t i

)

i i w t t t t a npy E r y c c , , 1 1 1 1

(

)

t t t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1

[

]

T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x

[

t t t

]

T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0

[

]

T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

y t y t y t y t yt y y t c npy fa c npy fa D npy = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

a t a t a t a t at a a t c npy fa c npy fa D fa = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 09 1 3 08 q t q t D D

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П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – –               JG]LHȟt  R]QDF]DVNïDGQLNORVRZ\DSRRV]DFRZDQLXSDUDPHWUöZSRZ\ĝV]HMUHODFMLNRLQWHJUDF\MQHM ļUHV]W\]RV]DFRZDQHMUHODFMLGïXJRRNUHVRZHMNWöUH]JRGQLH]UR]ZDĝDQ\PPRGHOHPWHRUHW\F] Q\PZ\UDĝDMÈUDFMRQDOQHRF]HNLZDQLDNRQVXPHQWöZSR]RVWDïHR]QDF]HQLDEH]]PLDQ-HGQRF]H ĂQLHSUDZÈVWURQÚUöZQDQLDPRĝQD]LQWHUSUHWRZDÊMDNRRV]F]ÚGQRĂFL]SU]HFLZQ\P]QDNLHP ZUR]XPLHQLX&DPSEHOOD 2PöZLRQHSRZ\ĝHMUHODFMHPDMÈFKDUDNWHUGïXJRRNUHVRZ\:RGQLHVLHQLXGRG\QDPLF]Q\FK PRGHOLNRQVXPSFMLZOLWHUDWXU]HUR]UöĝQLDVLÚGZDSRGHMĂFLDRSDUWHQDUöZQDQLX(XOHUDSRGHM ĂFLH((RUD]QDIXQNFMLNRQVXPSFMLZSRVWDFLUöZQDQLD]PHFKDQL]PHPNRUHNW\EïÚGHPSRGHM ĂFLH&)(&3RGVWDZRZ\PNU\WHULXPSR]ZDODMÈF\PUR]UöĝQLÊREDSRGHMĂFLDMHVWHJ]RJHQLF]QRĂÊ ]PLHQQ\FK=JRGQLH]SRGHMĂFLHP((NRQVXPSFMDMHVW]PLHQQÈVïDERHJ]RJHQLF]QÈZ]JOÚGHPSD UDPHWUöZ VWUXNWXU\ GïXJRRNUHVRZHM FR R]QDF]D ĝH QLH Z\ND]XMH PHFKDQL]PX NRUHNW\ EïÚGHP ]RE&DPSEHOO(LWUKHLP-DQVHQ1\PRHQ5öZQDQLHG\QDPLF]QHNRQVXPSFMLZW\P SRGHMĂFLXPRĝQD]DWHPRNUHĂOLÊMDNRWU\ZLDOQH]SXQNWXZLG]HQLDPHFKDQL]PXNRUHNW\EïÚGHPļ VNïDGQLNNRUHNW\EïÚGHPMHVWQLHLVWRWQ\ZW\PUöZQDQLX:\MDĂQLDWRUöZQLHĝGODF]HJRZOLWHUDWX U]HUöZQDQLHWDNLHNZDOLILNXMHVLÚMDNRSRGHMĂFLHRSDUWHQDUöZQDQLX(XOHUD=JRGQLH]UöZQDQLHP

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(XOHUDSURFHVJHQHUXMÈF\ORJDU\WPNRQVXPSFMLMHVWERZLHPPDUW\QJDïHPFRR]QDF]DĝHSU]\URVW ORJDU\WPXNRQVXPSFMLMHVWUöZQ\VNïDGQLNRZLORVRZHPXRFKDUDNWHU]HLQQRZDFML]RE+DOO 'HDWRQ=NROHLZSRGHMĂFLX&)(&NRQVXPSFMDQLHPRĝHE\Ê]PLHQQÈVïDERHJ]RJHQLF]QÈ OHF]PXVLEUDÊXG]LDïZNRU\JRZDQLXRGFK\OHñRGUöZQRZDJLGïXJRRNUHVRZHM6NïDGQLNNRUHNW\ EïÚGHPSRZLQLHQE\ÊLVWRWQÈ]PLHQQÈZUöZQDQLXG\QDPLF]Q\PNRQVXPSFMLD]PLHQQ\PLVïDER HJ]RJHQLF]Q\PLPRJÈE\ÊGRFKöG]SUDF\LOXEDNW\ZD]REWDEHOD5HODFMÚNRLQWHJUDFML]DSLVD QÈZ]RUHPPRĝQD]DOLF]\ÊGRREXSRZ\ĝV]\FKSRGHMĂÊ =HZ]JOÚGXQDQLHVWDFMRQDUQRĂÊSURFHVöZJHQHUXMÈF\FKDQDOL]RZDQHV]HUHJLF]DVRZHGOD3RO VNLSRWZLHUG]RQÈRGSRZLHGQLPLWHVWDPL_{GRRNUHĂOHQLDGïXJRRNUHVRZ\FK]ZLÈ]NöZSRPLÚG]\} NRQVXPSFMÈDERJDFWZHPJRVSRGDUVWZGRPRZ\FK]RVWDQLHZ\NRU]\VWDQDSURFHGXUDZQLRVNRZD QLD]DSURSRQRZDQDSU]H]-RKDQVHQDRSDUWDQDPHWRG]LHQDMZLÚNV]HMZLDU\JRGQRĂFLGRHVW\PDFML ZHNWRURZHJRPRGHOXNRUHNW\EïÚGHP9(&0-RKDQVHQ]REWDNĝH-XVHOLXV2JöOQÈSR VWDÊPRGHOX9(&0]KRSöěQLHQLDPLSR]LRPöZ]PLHQQ\FK9(&0K]D:HOIH]REWDNĝH -XVHOLXVPRĝQD]DSLVDÊQDVWÚSXMÈFR t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_r A r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1

(

)

(

at i

(

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lt i t i

)

i i w t t t t a npy E r y c c _{, , 1} 1 1 1

(

)

t t t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1

[

]

T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x

[

t t t

]

T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0

[

]

T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

y t y t y t y t yt y y t c npy fa c npy fa D npy = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

a t a t a t a t at a a t c npy fa c npy fa D fa = 0 + 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 091 3 08 q t q t D D

∑

∑

∑

∑

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П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – –             JG]LH x_t  ŘZHNWRUp]PLHQQ\FKVWRFKDVW\F]Q\FK ȕļPDFLHU]rOLQLRZRQLH]DOHĝQ\FKED]RZ\FKZHNWRUöZNRLQWHJUXMÈF\FKx_t ĮļPDFLHU]GRVWRVRZDñGRWUDMHNWRULLUöZQRZDJL ī_k  ļPDFLHU]SDUDPHWUöZNUöWNRRNUHVRZ\FK D_t  ļZHNWRUJ]PLHQQ\FKGHWHUPLQLVW\F]Q\FK ĭļPDFLHU]SDUDPHWUöZ]ZLÈ]DQ\FK]H]PLHQQ\PLGHWHUPLQLVW\F]Q\PL İ_t  ļZHNWRUELDïRV]XPRZ\FKVNïDGQLNöZORVRZ\FK 0RGHOZSRVWDFLPRĝQDX]\VNDÊZZ\QLNXSURVW\FKSU]HNV]WDïFHñPRGHOX9$5 t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_r A r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1

(

)

(

at i

(

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lt i t i

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i i w t t t t a npy E r y c c _{, , 1} 1 1 1

(

)

t t t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1

[

]

T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x

[

t t t

]

T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0

[

]

T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

y t y t y t y t yt y y t c npy fa c npy fa D npy = 0 + 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

a t a t a t a t at a a t c npy fa c npy fa D fa = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 091 3 08 q t q t D D

∑

∑

∑

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П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – –      JG]LH t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_rA r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1 ( ) ( at i ( ) lt i t i) i i w t t t t a npy E r y c c , , 1 1 1 1 ( ) _{t t} t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1 [ ]T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x [t t t]T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0 [ ]T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , [ t y t a t ] y t y t y t y t yt y y t c npy fa c npy fa D npy = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , [ t y t a t ] a t a t a t a t at a a t c npy fa c npy fa D fa = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 091 3 08 q t q t D D

∑

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П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – – ŘPDFLHU]PQRĝQLNöZGïXJRRNUHVRZ\FKPQRĝQLNöZFDïNRZLW\FK Ȇ_k  ŘPDFLHU]SDUDPHWUöZRLQWHUSUHWDFML]EOLĝRQHMGRPQRĝQLNöZSRĂUHGQLFK SR]RVWDïHR]QDF]HQLDEH]]PLDQ

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9(&0bPRĝQDSU]HGVWDZLÊQDVWÚSXMÈFRZV]\VWNLH]PLHQQHZ\UDĝRQRZFHQDFKVWDï\FKbU ZXMÚFLXper capitaļV]F]HJöïRZHGHILQLFMH]PLHQQ\FKV\VWHPRZ\FKSRGDQRZ$QHNVLH t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_r A r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1

(

)

(

at i

(

)

lt i t i

)

i i w t t t t a npy E r y c c , , 1 1 1 1

(

)

t t t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1

[

]

T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x

[

t t t

]

T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0

[

]

T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0 + 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

y t y t y t y t yt y y t c npy fa c npy fa D npy = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

a t a t a t a t at a a t c npy fa c npy fa D fa = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 09 1 3 08 q t q t D D

∑

∑

∑

∑

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П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – – JG]LH fa_t  ŘORJDU\WPDNW\ZöZILQDQVRZ\FKQHWWRZSRVLDGDQLXJRVSRGDUVWZGRPRZ\FK

:HNWRU Dt   ]DZLHUD ]PLHQQH GHWHUPLQLVW\F]QH ]DVWRVRZDQH Z PRGHOX Z\UD] ZROQ\ WU]\

VFHQWURZDQH ]PLHQQH VH]RQRZH t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_r A r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1 ( ) ( at i ( ) lt i t i) i i w t t t t a npy E r y c c , , 1 1 1 1 ( ) _{t t} t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1

[

]

T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x

[

t t t

]

T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0

[

]

T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , [ t y t a t ] y t y t y t y t yt y y t c npy fa c npy fa D npy = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , [ t y t a t ] a t a t a t a t at a a t c npy fa c npy fa D fa = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 09 1 3 08 q t q t D D

∑

∑

∑

∑

∑

П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – –  RUD] GZLH GRGDWNRZH ]PLHQQH ]HURMHG\QNRZH t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_rA r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1 ( ) ( at i ( ) lt i t i) i i w t t t t a npy E r y c c , , 1 1 1 1 ( ) _{t t} t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1

[

]

T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x

[

t t t

]

T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0

[

]

T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , [ t y t a t ] y t y t y t y t yt y y t c npy fa c npy fa D npy = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , [ t y t a t ] a t a t a t a t at a a t c npy fa c npy fa D fa = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 091 3 08 q t q t D D

∑

∑

∑

∑

∑

П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – – ZSURZDG]RQHZFHOXVNRU\JRZDQLDQLHVWDELOQRĂFLV]HUHJXDNW\ZöZILQDQVRZ\FKQHW WRZNRñFRZHMF]ÚĂFLSUöE\Z]ZLÈ]NX]NU\]\VHPILQDQVRZ\P3DUDPHWU\PRGHOXV]DFRZDQRQD SUöELH,bNZDUWDïļ,,bNZDUWDïU:DQDOL]LHUR]ZDĝDQRUöĝQHPLDU\DNW\ZöZJRVSRGDUVWZ GRPRZ\FKZ3ROVFHWDNĝHQLHILQDQVRZ\FK1LH]GRïDQRMHGQDN]QDOHěÊUHODFMLNRLQWHJUDF\MQHMGOD NRQVXPSFMLGRFKRGXLDNW\ZöZQLHILQDQVRZ\FKZLÚFHM]RE=DFKïRG-HOHF 2WU]\PDQ\PRGHOZVWRSQLX]DGRZDODMÈF\PVSHïQLD]DïRĝHQLDHVW\PDFML01:PRGHOX9$5 ZV]F]HJöOQRĂFLZV\VWHPLHEUDNLVWRWQ\FKHIHNWöZDXWRNRUHODFMLLKHWHURVNHGDVW\F]QRĂFLUHV]W1LH PDSRGVWDZGRRGU]XFHQLDKLSRWH]\]HURZHMQRUPDOQRĂFLUHV]WQDSR]LRPLHLVWRWQRĂFLZDUWRĂÊ VWDW\VW\NLWHVWRZHMWHVWXLORUD]XZLDU\JRGQRĂFLZ\QLRVïDDSUDZGRSRGRELHñVWZR]QLÈ]ZLÈ ]DQH0RĝQD]DWHPSU]\MÈÊĝHUHV]W\]UöZQDñRV]DFRZDQHJRPRGHOXVSHïQLDMÈ]DïRĝHQLD HVW\PDFML01:PRGHOX9$5 3RRWU]\PDQLXSRSUDZQLHZ\VSHF\ILNRZDQHJRPRGHOXSU]HSURZDG]RQRWHVWOLF]E\ED]RZ\FK ZHNWRUöZNRLQWHJUXMÈF\FKQDSRGVWDZLHPRGHOX9(&0RSRVWDFL t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_r A r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1

(

)

(

at i

(

)

lt i t i

)

i i w t t t t a npy E r y c c _{, , 1} 1 1 1

(

)

t t t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1

[

]

T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x

[

t t t

]

T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0

[

]

T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

y t y t y t y t yt y y t c npy fa c npy fa D npy = 0 + 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

a t a t a t a t at a a t c npy fa c npy fa D fa = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 091 3 08 q t q t D D

∑

∑

∑

∑

∑

П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – –             JG]LHƠ  MHVWZHNWRUHPSDUDPHWUöZGRVWRVRZDñRZ\PLDU]H3  =  rPöZLÈF\PRW\PNWöUH]PLHQ QHLMDNGRVWRVRZXMÈVLÚZV\VWHPLHSRMHJRZ\WUÈFHQLX]WUDMHNWRULLUöZQRZDJLȕR]QDF]DZHNWRU 3  =  rSDUDPHWUöZUHODFMLNRLQWHJUDF\MQHMDr  ļU]ÈGNRLQWHJUDFML6NïDGQLN t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_rA r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1 ( ) ( at i ( ) lt i t i) i i w t t t t a npy E r y c c , , 1 1 1 1 ( ) _{t t} t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1 [ ]T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x [t t t]T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0 [ ]T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , [ t y t a t ] y t y t y t y t yt y y t c npy fa c npy fa D npy = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , [ t y t a t ] a t a t a t a t at a a t c npy fa c npy fa D fa = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 091 3 08 q t q t D D

∑

∑

∑

∑

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П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – – MHVWWRZHNWRUR Z\VNïDGQLNNRUHNW\EïÚGHPUöZQRZDJLZSRSU]HGQLPRNUHVLHtŘ

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QDUQRĂFL]PLHQQ\FKZFHOXVSUDZG]HQLDZDĝQRĂFLZQLRVNöZGRW\F]ÈF\FKVWRSQLD]LQWHJURZDQLD SURFHVöZVWRFKDVW\F]Q\FKJHQHUXMÈF\FK]PLHQQHZFKRG]ÈFHZVNïDGUR]ZDĝDQHJRV\VWHPX1D SRGVWDZLH Z\QLNöZ W\FK WHVWöZ PRĝQD ZQLRVNRZDÊ ĝH ZV]\VWNLH SURFHV\ JHQHUXMÈFH ]PLHQQH Xĝ\ZDQHZDQDOL]LHPRJÈE\ÊX]QDQH]D]LQWHJURZDQHVWRSQLDSLHUZV]HJR,-HGQRF]HĂQLHĝD GHQ]SURFHVöZQLHZ\ND]XMHWUHQGRVWDFMRQDUQRĂFL1DVWÚSQLHVSUDZG]RQRF]\PRĝQDZ\ïÈF]\Ê WUHQGGHWHUPLQLVW\F]Q\]ZHNWRUDNRLQWHJUXMÈFHJR']LÚNL]DVWRVRZDQLXWHVWXLORUD]XZLDU\JRGQR ĂFLRUR]NïDG]LH&KLNZDGUDW]MHGQ\PVWRSQLHPVZRERG\VWZLHUG]RQRĝHQLHPDSRGVWDZGRRG U]XFHQLDKLSRWH]\]HURZHMRZ\ïÈF]DOQRĂFLWUHQGXGHWHUPLQLVW\F]QHJR]SU]HVWU]HQLNRLQWHJUXMÈFHM SU]\JUDQLF]Q\PSR]LRPLHLVWRWQRĂFLWHVWXUöZQ\P2]QDF]DWRSU]\MÚFLHQLHRJUDQLF]RQHJR GRSU]HVWU]HQLNRLQWHJUDF\MQHMZ\UD]XZROQHJRFRMHVWX]DVDGQLRQH]HZ]JOÚGXQDLVWQLHQLHWUHQ GXOLQLRZHJRZORJDU\WPDFK]PLHQQ\FKV\VWHPRZ\FKļ]REZ\NUHV3RQRZQLHSU]HSURZDG]RQR WHVW\U]ÚGXNRLQWHJUDFML=DSUH]HQWRZDQHSRZ\ĝHMZQLRVNLGRW\F]ÈFHU]ÚGXPDFLHU]\ƗSR]RVWDMÈ ZPRF\]REWDEHODGROQDF]ÚĂÊ .ROHMQ\PHWDSHPVSUDZG]HQLDDGHNZDWQRĂFLRV]DFRZDQHJRPRGHOXGïXJRRNUHVRZHJRMHVWDQD OL]D VWDELOQRĂFL VWUXNWXU\ GïXJRRNUHVRZHM =DVWRVRZDQ\ WHVW VWDELOQRĂFL ORJDU\WPX ZLDU\JRGQR ĂFLRUD]Z\QLNLWHVWöZVWDELOQRĂFLSDUDPHWUöZZHNWRUDNRLQWHJUXMÈFHJRơ LbZHNWRUDGRVWRVRZDñƠ ]REQS-XVHOLXVZVND]Dï\ĝHSDUDPHWU\VWUXNWXU\GïXJRRNUHVRZHMPRGHOX9(&0bVSHï QLDMÈZ\PöJVWDELOQRĂFL]RE=DFKïRG-HOHF =JRGQLH]UH]XOWDWDPLRV]DFRZDñSDUDPHWUöZVWUXNWXU\GïXJRRNUHVRZHMZUDPDFKUR]ZDĝD QHJRV\VWHPXZHNWRUNRLQWHJUXMÈF\ơ dla t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_r A r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1 ( ) ( at i ( ) lt i t i) i i w t t t t a npy E r y c c , , 1 1 1 1 ( ) t t t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1

[

]

T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x

[

_{t t t}

]

T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0

[

]

T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , [ t y t a t ] y t y t y t y t yt y y t c npy fa c npy fa D npy = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , [ t y t a t ] a t a t a t a t at a a t c npy fa c npy fa D fa = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 091 3 08 q t q t D D

∑

∑

∑

∑

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П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – – SU]HGVWDZLDVLÚQDVWÚSXMÈFRZQD ZLDVDFKSRGDQRZDUWRĂFLVWDW\VWNLt6WXGHQWD t t t W C = = = = = = = = = = = ≈ – – – – – – – – – – – – + + + – + + + + + + + + + + = , ) (_{T t} 1 t i t l t i i t t r_r A r_{r r} EY C + + + + + = = = _ _ _ _ _ _ _ _ _ , 0 1 1 1 1

(

)

(

at i

(

)

lt i t i

)

i i w t t t t a npy E r y c c _{, , 1} 1 1 1

(

)

t t t t a npy c 1 t t K k k t k t T t x x D x 1 1 1 t t K k k t k t x D x =1 I K k k T =1

[

]

T t t t npy fa c qi t D (i 1, 2, 3 ) 1 09 3 08 _, q t q t D D , 1 1 1 t t t t T t x x D x 1 t T_x

[

t t t

]

T t c npy fa x T ) 1 , 8 ( ) 4 , 28 (0,934 0,100 1 t t t t npy fa c = + + ) 1 , 13 ( ) 7 , 102 (,887 0,113 0

[

]

T t t t t t t c npy fa R p x = c t R t t t p R = + [ t y t a t ] c t c t c t c t ct c c t c npy fa c npy fa D c = 0 + 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

y t y t y t y t yt y y t c npy fa c npy fa D npy = 0 + 1 1 1 + 1 1+ 2 1+ 3 1+ + ,

[

t y t a t

]

a t a t a t a t at a a t c npy fa c npy fa D fa = 0+ 1 1 1 + 1 1+ 2 1+ 3 1+ + , , 09 1 3 08 q t q t D D

∑

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П П П Ф Ф ρ ρ ρ γ γ Δ Δ Δ Δ Γ Γ Δ Δ γ γ γ γ β α β α β α β β ε tc t t t npy fa c = + + ) 2 , 14 ( ) 6 , 119 (,894 0,106 0 ζ ζ ζ ξ ξ ξ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ α ξ ε ε ε Φ ∞ ∞ β β β α α α β β β γ γ γ γ γ γ γ γ γ γ γ γ γ γ γ – – – – – – – – – – – – – – – – – – – – – – – –

   

 

 

     

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