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B@5=40 CAB0=02;820NB =0 >A=>25 3@0D8G5A:>3> 87>1@065=8O, ?CB5< >A@54=5=8O ?>:070B5;59 48=0<8:8, =0 >A=>25 AB0B8AB8G5A:>9 ?@>25@:8 38?>B57K > ?>AB>O=AB25 ?0@0<5B@0 B@5=40. 07@01>B:0 ?@>3=>7>2 =0 1075   ?@>8AE>48B 2 =5A:>;L:> MB0?>2. -;5<5=BK   =0=>AOBAO =0 :>>@48=0B=>5 ?>;5; A;8 3@0D8G5A:>5 ?>AB@>5=85 =5 405B G5B:>3> ?@54AB02;5=8O > 70:>=><5@=>AB8 87<5=5=8O ?@87=0:0 2> 2@5<5=8, B> ?@8<5=ONBAO A?5F80;L=K5 AB0B8AB8G5A:85 ?@85<K >1@01>B:8 40==KE (A3;06820=85 ?> A:>;L7OI59 A@54=59, >?@545;5=85 ?>A;54>20B5;L=KE @07=>AB59 8 ?@.); K18@0NB 8 @0AAG8BK20NB ?0@0<5B@K 0=0;8B8G5A:>9 DC=:F88 2840 ^t =f(t), >B@060NI59 48=0<8:C 87<5=5=8O ?@>3=>78@C5<>3> ?>:070B5;O yt 2> 2@5<5=8. !3;06820=85 2@5<5==>3> @O40 B<5B8<, GB> ?C=:B 2 ?@54AB02;5==>9 AE5<K ?@>3=>78@>20=8O <>65B 2K?>;=OBL 42>O:CN @>;L: >= <>65B 1KBL :0: ?>43>B>28B5;L=K< MB0?>< 4;O 40;L=59H59 >1@01>B:8 ?@54AB02;5==KE 40==KE (B.5. 4;O 2K?>;=5=8O MB0?0 3  @0AG5B0 ?0@0<5B@>2 ?@>3=>78@CNI59 DC=:F88 ^t), B0: 8 A;C68BL 2?>;=5 A0<>AB>OB5;L=K< <5B>4>< ?@>3=>78@>20=8O, B.:. >= 40QB >?@545;5==>5 ?@54AB02;5=85 > E0@0:B5@5 B@5=40. 0AA<>B@8< 420 A?>A>10 A3;06820=8O. 5B>4 A:>;L7OI59 A@54=59 !CBL <5B>40 A>AB>8B 2 70<5=5 D0:B8G5A:8E 7=0G5=89 ?>:070B5;O 8E CA@54=5==K<8 25;8G8=0<8. >@O4>: ?>AB@>5=8O. CABL y1, y2, ..., yn - 48=0<8G5A:89 @O4. ;O >?@545;5=8O A:>;L7OI59 A@54=59 ?>A;54>20B5;L=> @0AAG8BK20NB AC<<C m (=5G5B=>5 G8A;>) M;5<5=B>2 @O40. > >B45;L=K< AC<<0< >?@545;ONB A@54=85 0@8D<5B8G5A:85, :0640O 87 :>B>@KE <5=O5B A2>N 25;8G8=C ( A:>;L78B ) ?> <5@5 C25;8G5=8O t. 081>;55 G0AB> =0 ?@0:B8:5 ?@8<5=ONBAO B@5E- 8 ?OB8G;5==K5 A@54=85. $>@<C;K @0AG5B0: yt = (yt-1 +yt+yt+1)/3, t=2,3, ... , (n-1) (2.2) yt =(yt-2 + yt-1 +yt+yt+1+ yt+2)/5, t=3,4, ... , (n-2) (2.3) A;8 A:>;L7OI0O A@54=OO >?@545;O5BAO ?> G5B=><C G8A;C M;5<5=B>2, B> >=0 =5 <>65B 1KBL ?@8?8A0=0 @50;L=><C 7=0G5=8N t. 5 >?@545;ONB 2 2 MB0?0: A=0G0;0 =0E>4OB A@54=85 4;O ?@><56CB:>2 (t-1,t) 8 (t, t+1), 0 70B5< ?>;CG5==K5 25;8G8=K AC<<8@CNB 8 2=>2L 8A?>;L7CNB 4;O @0AG5B0 A@54=59. '0I5 8A?>;L7C5BAO 2KG8A;5=85 ?> 4 G;5=0< @O40: yt =1/2[(yt-2+yt-1 +yt+yt+1)/4+(yt-1+yt+yt+1+ yt+2)/4], t=3,4,.. ,(n-2) (2.4) @8<5@ 2.1.  B01;8F5 2.1 ?@54AB02;5= >1J5< @50;870F88 :>=48B5@A:8E 8745;89 B>@3>2K< ?@54?@8OB85< 2 B5G5=85 3>40. 0==K5 =0=5A5=K =0 3@0D8: @8A. 2.1. 0: A;54C5B 87 MB>3> 3@0D8:0 MB>B ?>:070B5;L E0@0:B5@87C5BAO 4>AB0B>G=> 1>;LH8< @071@>A>< B>G5:. >MB><C ?@8<5=8< : =5<C <5B>4 A:>;L7OI59 A@54=59. 57C;LB0BK @0AG5B>2 2=5A5=K 2 B01;8FC 2.1. 8 ?>:070=K =0 @8A. 2.1. "01;8F0 2.1. 5AOF (2 CA;>2=KE 54.) 1J5< @50;870F88 :>=4. 8745;89, B. "@5EG;5==K5 AC<<K "@5EG;5==K5 A:>;L7OI85 A@54=85 OB8G;5==K5 AC<<K OB8G;5==K5 A:>;L7OI85 A@54=851137,32132,2411,5137,23142,0415,1138,4689,2137,84140,9419,7139,9692,2138,45136,8418,0139,3695,3139,16140,3412,4137,5687,3137,57135,3409,6136,5680,1136,08134,0403,0134,3678,2135,69133,7402,6134,2673,2134,610134,9403,9134,6680,6136,111135,3412,9137,612142,7  8A. 2.1. @0D8: : ?@8<5@C 2.1. 5B>4 :>=5G=KE @07=>AB59 !D5@0 ?@8<5=5=8O - A;CG09, :>340 48=0<8:0 87<5=5=8O 8AA;54C5<>9 ?5@5<5==>9 >B>1@0605BAO >4=8< 87 ?>;8=><>2 k-3> ?>@O4:0: ^t =a0 +a1 t+a2t2 + ... + aktk (2.5) A>15==>ABL <5B>40 - ?>A;54>20B5;L=>5 >?@545;5=85 A?5F80;L=KE ?>:070B5;59 - @07=>AB59, A@548 :>B>@KE @07;8G0NB @07=>AB8 ?5@2>3>, 2B>@>3> 8 B.4. ?>@O4:>2: (t1 =yt+1 - yt (t=1,2,3, ... , n-1); (2.6) (t2=(t+11 -(t1 = yt+2 - 2yt+1 + yt (t=1,2,3, ... , n-2); (2.7) (t3=(t+12 -(t2 = yt+3 - 3yt+2 +3yt+1 - yt (t=1,2,3, ... , n-3); (2.8) 8 B.4.  >A=>25 <5B>40 :>=5G=KE @07=>AB59 ;568B >4=> 87 A2>9AB2 ?>;8=><0 AB5?5=8 k >1@0I0BL 2 =C;L @07=>AB8 (t+1k+1 8 ?@84020BL >48=0:>2>5 7=0G5=85 @07=>ABO< (t+1k . @8<5@ 2.2. > 40==K< >1J5<0 ?@>872>4AB20 E;510 =0 ?@54?@8OB8OE M:>=><8G5A:>3> @09>=0 70 8 ;5B =5>1E>48<> >?@545;8BL 70:>=><5@=>ABL 2K@01>B:8 ?@>4C:F88 70 0=0;878@C5<K9 ?@><56CB>: 2@5<5=8. 0AAG8B05< ?5@2K5 8 2B>@K5 @07=>AB8 (A<. B01;8FC 2.2). "01;8F0 2.2 >4, t@>872545=> E;510 yt, BKA. B5@2K5 @07=>AB8 (t1B>@K5 @07=>AB8 (t217,61,1028,71,1039,81,10,1410,91,2-0,1512,11,10613,21,10714,31,1 815,4   0: A;54C5B 87 40==>9 B01;8FK, 01A>;NB=K5 C@>2=8 ?5@2KE @07=>AB59 4;O 2A5E 7=0G5=89 t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t = f(t) A B0:8< @0AG5B><, GB>1K :204@0BK AC<<0@=KE >B:;>=5=89 D0:B8G5A:8E 7=0G5=89 @O40 (yt) >B =0945==KE ?> AB0B8AB8G5A:>9 <>45;8 (^t) 1K;8 1K <8=8<0;L=> 2>7<>6=K<8, B> 5ABL: ((yt - ^t)2 = min (2.9) 70?8A02 C@02=5=85 ?@O<>9 2 2845 ^t = a+bt 8 ?>4AB0282 53> 2 (2.9), ?>;CG8<: ((yt - a-bt)2 =min (2.10)  @0AA<0B@8205<>< CA;>288 <8=8<870F88 7=0G5=8O ?5@5<5==KE yt 8 t 70 ?@54?@>3=>7=K9 ?5@8>4 O2;ONBAO 8725AB=K<8, 0 ?0@0<5B@K a 8 b -=58725AB=K<8 :>=AB0=B0<8. ;O 8E =0E>645=8O =04> ?@8@02=OBL =C;N G0AB=K5 ?@>872>4=K5 >B (2.10) ?> :064>9 8A:><>9 :>=AB0=B5 2 >B45;L=>AB8. >A;5 A>>B25BAB2CNI8E ?@5>1@07>20=89 ?>;CG0NB A8AB5<C C@02=5=89, :>B>@CN =07K20NB =>@<0;L=>9. ;O ;8=59=>3> B@5=40 ^t = a+bt =>@<0;L=K5 C@02=5=8O: ((yt= na + b(t, ( (2.11) ((ytt = a(t + b(t2 >4AB0282 2 A8AB5<C (2.11) 8<5NICNAO 8AE>4=CN 8=D>@<0F8N (yt 8 t) @0AAG8BK20NBAO ?0@0<5B@K ?@>3=>78@CNI59 DC=:F88 0 8 b. !><=>68B5;L n - 4;8=0 2@5<5==>3> @O40. "0:65 <>6=> ?>;CG8BL =>@<0;L=K5 C@02=5=8O 4;O :204@0B8G=>3> B@5=40 ^t = a+bt+At2, :>B>@K5 2K3;O4OB B0:: ((yt=na+b(t+A(t2, ( ( (ytt =a(t + b(t2 + A(t3, (2.12) ( ( (ytt2 =a(t2 + b(t3 + A(t4, 0AAG8B02 2A5 AC<<K 8 @5H82 A8AB5<C >B=>A8B5;L=> 0, b 8 A, ?>;CG8< C@02=5=85 ?0@01>;8G5A:>3> B@5=40. @8<5@ 2.4..  B01;8F5 2.3 ?@54AB02;5=K 40==K5, E0@0:B5@87CNI85 48=0<8:C 2K?CA:0 ?@>4C:F88 $8=;O=488 ( <;= 4>;;.) 70 17 ;5B. @>25AB8 @0AG5B ?0@0<5B@>2 ;8=59=>3> 8 M:A?>=5=F80;L=>3> B@5=40, ?>AB@>8BL 3@0D8:8 @O40 48=0<8:8 8 B@5=4>2. "01;8F0 2.3 #A;>2=K9 3>41J5< 2K?CA:0 ?@>4C:F88, <;= 4>;;.yttt28=59=K9 B@5=411415014150,0019404,88321400428008,00410928,02331308839264,00912451,16341251850072,001613974,30351347167355,002515497,44361361781702,003617020,583716356114492,004918543,723820037160296,006420066,863921748195732,008121590,0031023298232980,0010023113,1431126570292270,0012124636,2831223080276960,0014426159,4231323981311753,0016927682,5631423446328244,0019629205,7031529658444870,0022530728,8431639573633168,0025632251,9831738435653395,0028933775,123B>3>36703039247111785367030,051 ;O >?@545;5=8O G8A;>2KE 7=0G5=89 :>=AB0=B C@02=5=8O (3.11) C4>1=> ?>;L7>20BLAO B01;8F59 2.3. ?@545;82 2A5 AC<<K 8 ?>4AB0282 8E 2 A8AB5<C =>@<0;L=KE C@02=5=89 367030,0 = 17( a + b (153 3924711,0 = a (153 + b (1785 =0945< A2>1>4=K9 G;5= C@02=5=8O a =7881,74 8 :>MDD8F85=B ?@>?>@F8>=0;L=>AB8 b = 1523,14. "0:8< >1@07><, ?@>3=>7=0O <>45;L 8<55B 284 ^t = 7881,74 +1523,14 ( t >4AB02;OO 7=0G5=8O t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yt = a+b/tt =1/tyt = a+bt AB5?5==0Oyt=atb>30@8D<8@C5< lnyt=lna+blnt; Lnyt=yt ; Lna =a ; Lnt =t yt = a +bt -:A?>=5=F80;L=0Oyt=aet>30@8D<8@C5< lnyt=lna+t; Lnyt=yt ; Lna =a ;yt = a +t  >38AB8G5A:0Oyt=1/(a+be-t)1/yt= a+be-t ; 1/ yt= yt ; e-t=t yt = a +bt  @>AB0O <>48D8F8@>20==0O M:A?>=5=F80;L=0O yt=a-be-te-t=t yt = a -bt   A;8 4;O >?8A0=8O 8AE>4=>9 :@82>9 A @02=K< >A=>20=85< <>6=> 8A?>;L7>20BL =5A:>;L:> 0=0;8B8G5A:8E DC=:F89, B> 4;O 2K1>@0 7028A8<>AB8, =081>;55 B>G=> >B>1@060NI59 =01;N405<CN 48=0<8:C, @5:><5=4C5BAO ?@8<5=OBL A?5F80;L=K5 AB0B8AB8G5A:85 ?>:070B5;8. 081>;55 @0A?@>AB@0=5==K5 87 =8E: (2>AB->AB0B>G=0O 48A?5@A8O, (>AB-A@54=55 :204@0B8G=>5 >B:;>=5=85, V-:>MDD8F85=B 20@80F88, r- :>MDD8F85=B ;8=59=>9 :>@@5;OF88, Ry/t - 8=45:A :>@@5;OF88, d -:>MDD8F85=B 45B5@<8=0F88. 5@2K5 B@8 ?>:070B5;O A2O70=K <564C A>1>9: (2>AB= EMBED Equation.2 (y   EMBED Equation.2 )2/n; (>AB =  EMBED Equation.2  ; V = ( (>AB/yA@)(100% (745AL yA@  A@54=OO 0@8D<5B8G5A:0O yA@= EMBED Equation.2 yt / n).  :0G5AB25 C@02=5=8O B@5=40 A;54C5B 8A?>;L7>20BL BC 7028A8<>ABL, C :>B>@>9 7=0G5=8O (2>AB, (>AB, V - <8=8<0;L=K. =45:A :>@@5;OF88 - 405B >B=>A8B5;L=CN >F5=:C AB5?5=8 1;87>AB8 B@5=40 : B>G:0< 8AE>4=>9 :@82>9. 1I55 >B:;>=5=85 D0:B8G5A:>3> 7=0G5=8O ?5@5<5==>9 >B A@54=53> C@>2=O <>6=> ?@54AB028BL :0: AC<<C 42CE A;0305<KE: yt  yA@=( yt   EMBED Equation.2 ) + ( EMBED Equation.2  yA@), 8;8 A>:@0I5==> (>1I=(>AB+(t, 345 (>1I  (yt  yA@)  >B:;>=5=85, 87<5@ONI55 >1ICN 20@80F8N 70 AG5B 459AB28O 2A5E D0:B>@>2; (>AB=( yt   EMBED Equation.2 )  >AB0B>G=0O 20@80F8O, E0@0:B5@87CNI0O >B:;>=5=85 <564C 8AE>4=K< 8 @0AG5B=K< 7=0G5=8O<8 ?5@5<5==>9 yt; (t=( EMBED Equation.2   yA@)  >B:;>=5=85 7=0G5=8O DC=:F88 >B A@54=53> C@>2=O. 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"0:8< >1@07><, 8AE>4=K5 40==K5 ;CGH5 >?8AK20NBAO M:A?>=5=F80;L=K< B@5=4><. !;54>20B5;L=>, 2 40==>< ?@8<5@5 4;O @0AG5B0 ?@>3=>7=KE 7=0G5=89 ;CGH5 8A?>;L7>20BL M:A?>=5=F80;L=K9 B@5=4. 0AG5B 2>7<>6=>9 >H81:8 ?@>3=>70. @>3=>7=K5 @0AG5BK, 2K?>;=O5<K5 A 8A?>;L7>20=85< M;5<5=B>2 >48=>G=>3> 2@5<5==>3> @O40, 7025@H0NBAO 53> 25@8D8:0F859, B> 5ABL >F5=:>9 53> 4>AB>25@=>AB8. B:;>=5=8O >1KG=> 2>7=8:0NB 87-70 42CE >A=>2=KE ?@8G8=: 0 7028A8<CN ?5@5<5==CN 2>7459AB2C5B =5 B>;L:> 0@3C<5=B t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t=f(t), ?>AB@>5==>9 ?> 2K1>@>G=K< 40==K<, @0A?>;0305BAO ;8=8O @53@5AA88, :>B>@CN <>6=> ?>;CG8BL, 5A;8 8A?>;L7>20BL 2 ?@>F5AA5 2KG8A;5=89 M;5<5=BK 2A59 35=5@0;L=>9 A>2>:C?=>AB8. '5< H8@5 4>25@8B5;L=0O 7>=0, B5< ACI5AB25==55 @07;8G8O 2 ?0@0<5B@0E 2K1>@>G=>9 8 35=5@0;L=KE ;8=89 @53@5AA88. >@O4>: ?>AB@>5=8O 4>25@8B5;L=>9 7>=K >AB@>8< 4>25@8B5;L=CN 7>=C =0 ?@8<5@5 ;8=59=>9 7028A8<>AB8 yt = a + bt. !=0G0;0 >?@545;ONBAO A;CG09=K5 >H81:8 4;O ?0@0<5B@>2 a 8 b. 0AG5BK 254CBAO ?> D>@<C;0<:  EMBED Equation.3 ; (2.16)  EMBED Equation.3 ; (2.17) 745AL ma  A;CG09=0O >H81:0 ?0@0<5B@0 a; mb  A;CG09=0O >H81:0 ?0@0<5B@0 b; D>AB  >AB0B>G=>5 A@54=55 :204@0B8G=>5 >B:;>=5=85: 8A. 2.9. >=0 4>25@8B5;L=>9 25@>OB=>AB8  EMBED Equation.3  'B>1K CAB0=>28BL, =0A:>;L:> 25;8:8 @0AE>645=8O <564C ?0@0<5B@0<8 C@02=5=89, E0@0:B5@87CNI8E 2K1>@>G=CN 8 35=5@0;L=CN A>2>:C?=>ABL, <>6=> 8A?>;L7>20BL t  :@8B5@89 !BLN45=B0. $0:B8G5A:85 7=0G5=8O MB>3> ?>:070B5;O @0AAG8BK20NBAO ?> D>@<C;0<: ;O a  EMBED Equation.3  (2.18) ;O b  EMBED Equation.3  (2.19) 0AG5B=K5 7=0G5=8O tD A>?>AB02;ONBAO A A>>B25BAB2CNI8<8 B01;8G=K<8 25;8G8=0<8 tT , =0945==K<8 4;O k = n  2 AB5?5=59 A2>1>4K 8 ?@8=OB>9 4>25@8B5;L=>9 25@>OB=>AB8 0,95 8;8 0,99. A;8 tD > tT , B> A2>1>4=K9 G;5= C@02=5=8O B@5=40 a 8 :>MDD8F85=B @53@5AA88 b AG8B0NBAO AB0B8AB8G5A:8 7=0G8<K<8 8 <>3CB ?@8<5=OBLAO 4;O >B>1@065=8O B5=45=F88 87<5=5=8O ?5@5<5==>9 yt, A;>682H59AO 2 35=5@0;L=>9 A>2>:C?=>AB8. A;8 65 tD < tT , B> 2>7<>6=>ABL =5A>2?045=8O 70:>=><5@=>AB59 2 2K1>@>G=>9 8 35=5@0;L=>9 A>2>:C?=>ABOE 25AL<0 25;8:0. K2>4K 5B>4K =5?>A@54AB25==>9 M:AB@0?>;OF88 >B=>AOBAO : G8A;C =081>;55 ?@>ABKE <5B>4>2 ?@>3=>78@>20=8O. =8 >A=>20=K =0 87CG5=88 48=0<8:8 87<5=5=8O M:>=><8G5A:>3> O2;5=8O 2 ?@54?@>3=>7=>< ?5@8>45 8 ?5@5=5A5=88 =0945==>9 70:>=><5@=>AB8 2 1C4CI55. >AB>8=AB20<8 <5B>40 O2;O5BAO H8@>:0O C=825@A0;L=>ABL 2KG8A;8B5;L=>9 AE5<K, =57=0G8B5;L=0O B@C4>5<:>ABL @0AG5B=>3> 0;3>@8B<0. !;54C5B >B<5B8BL 8 =54>AB0B:8  =5>1E>48<>ABL 8A?>;L7>20=8O 107>2KE 40==KE 70 1>;LH>9 ?@><56CB>: 2@5<5=8, A=865=85 4>AB>25@=>AB8 ?@>3=>70 ?@8 C25;8G5=88 A@>:0 53> C?@5645=8O. ;O ?@>3=>78@>20=8O 8A?>;L7C5BAO 2@5<5==>9 @O4, ?@54AB02;ONI89 A>1>9 48A:@5B=K5 7=0G5=8O :0:>3>-;81> ?>:070B5;O 2 B5G5=88 >?@545;Q==>3> 2@5<5=8, B.5. A>AB>OI53> 87 42CE 7=0G5=89 (yi) - C@>2=59 @O40 8 <><5=B0 2@5<5=8 (t). 45O <5B>40 2 B><, GB>1K =09B8 B5=45=F8N 2 87<5=5=8OE ?@87=0:0 8 ?@>4;8BL MBC B5=45=F8N 2 1C4CI55. ;O MB>3> 8A?>;L7CNBAO :@82K5, =0945==K5 ?> <5B>4C =08<5=LH8E :204@0B>2 8 ?>4>1@0==K5 ?> A?5F80;L=K< AB0B8AB8G5A:8< E0@0:B5@8AB8:0<.  :>=F5 @0AAG8BK205BAO 2>7<>6=0O >H81:0 ?@>3=>70. >=OB=>, GB> B0:>9 ?@>3=>7 8<55B A<KA; :0: :@0B:>A@>G=K9, =0 ?5@8>4, 2 >B=>H5=88 :>B>@>3> <>6=> ?@8=OBL, GB> E0@0:B5@8AB8:8 87CG05<>3> O2;5=8O ACI5AB25==> =5 87<5=ONBAO. -B> B@51>20=85 G0AB> >:07K205BAO @50;8AB8G=K< 2A;54AB285 4>AB0B>G=>9 8=5@F8>==>AB8 2=5H=59 A@54K. 4=0:> 8 1>;LH8=AB2> ?@>3=>7=KE >H81>: A2O70=> A B5<, GB> 2 <><5=B D>@<C;8@>20=8O ?@>3=>70 2 1>;55 8;8 <5=55 O2=>9 D>@<5 ?>4@07C<520;>AL, GB> ACI5AB2CNI85 B5=45=F88 A>E@0=OBAO 2 1C4CI5<, GB> @54:> >?@024K205BAO 2 @50;L=>9 M:>=><8G5A:>9 8 >1I5AB25==>9 687=8. @5<5==K5 @O4K ?><8<> ?@>AB>9 M:AB@0?>;OF88 <>3CB 8A?>;L7>20BLAO B0:65 2 F5;OE 1>;55 3;C1>:>3> ?@>3=>7=>3> 0=0;870, =0?@8<5@, >1J5<0 ?@>406. &5;LN 0=0;870 2 40==>< A;CG05 O2;O5BAO @07;>65=85 2@5<5==>3> @O40 ?@>406 =0 3;02=K5 :><?>=5=BK, 87<5@5=85 M2>;NF88 :064>9 A>AB02;ONI59 2 ?@>H;>< 8 55 M:AB@0?>;OF8O =0 1C4CI55.  >A=>25 <5B>40 ;568B 845O AB018;L=>AB8 ?@8G8==>-A;54AB25==KE A2O759 8 @53C;O@=>ABL M2>;NF88 D0:B>@>2 2=5H=59 A@54K, GB> 45;05B 2>7<>6=K< 8A?>;L7>20=85 M:AB@0?>;OF88. 5B>4 A>AB>8B 2 @07;>65=88 2@5<5==>3> @O40 =0 =5A:>;L:> :><?>=5=B  D>@<C;0 (2.1). >?@>AK 4;O A0<>?@>25@:8  GQ< >A=>2=0O 845O <5B>4>2 M:AB@0?>;OF88? 'B> B0:>5 B@5=4? A=>2=0O 2KG8A;8B5;L=0O AE5<0, 8A?>;L7C5<0O 4;O ?>AB@>5=8O ?@>3=>70.  G5< 70:;NG05BAO >A>15==>AB8 A3;06820=8O ?> <5B>4C A:>;L7OI59 :@82>9? >340 ?@8<5=O5BAO A3;06820=85 ?> <5B>4C :>=5G=KE @07=>AB59? 3> >A>15==>AB8 8 D>@<C;0 4;O 2KG8A;5=89. 5B>4 =08<5=LH8E :204@0B>2. @82548B5 2K2>4 A8AB5<K =>@<0;L=KE C@02=5=89 4;O ;8=59=>9 8 :204@0B8G=>9 DC=:F88. 0:85 :@82K5 G0I5 2A53> 8A?>;L7CNBAO 4;O M:AB@0?>;OF88? >?@>1C9B5 A2O70BL D>@<C :@82KE A :>=:@5B=K<8 ?@>F5AA0<8, ?@>8AE>4OI8<8 2 @50;L=>AB8. 0:><C ?@>F5AAC 1>;LH5 A>>B25BAB2C5B B0 8;8 8=0O DC=:F8>=0;L=0O 7028A8<>ABL? !?>A>1K ;8=50@870F88 :@82KE. ;O G53> ?@8<5=ONBAO A?5F80;L=K5 AB0B8AB8G5A:85 ?>:070B5;8? 'B> B0:>5 4>25@8B5;L=0O 25@>OB=>ABL 8 4>25@8B5;L=K9 8=B5@20;? !E5<0 @0AG5B0 2>7<>6=>9 >H81:8 ?@>3=>70. 0745; 2.2. !B0B8AB8G5A:>5 <>45;8@>20=85 1I85 ?>;>65=8O 0: 3>2>@8;>AL 2 ?@54K4CI5< @0745;5 ACI=>ABL <5B>4>2 ?@>3=>7=>9 M:AB@0?>;OF88 70:;NG05BAO 2 87CG5=88 48=0<8:8 87<5=5=8O M:>=><8G5A:>3> O2;5=8O 2 ?@54?@>3=>7=>< ?5@8>45 8 ?5@5=5A5=8O =0945==>9 70:>=><5@=>AB8 =0 =5:>B>@K9 ?5@8>4 1C4CI53>. 1O70B5;L=K< CA;>285< ?@8<5=5=8O M:AB@0?>;OF8>==>3> ?>4E>40 2 ?@>3=>78@>20=88 A;54C5B AG8B0BL ?>7=0=85 8 >1J5:B82=>5 ?>=8<0=85 ?@8@>4K 8AA;54C5<>3> ?@>F5AA0, 0 B0:65 =0;8G85 CAB>9G82KE B5=45=F89 2 <5E0=87<5 @0728B8O. -B>B A?>A>1 >1;0405B >?@545;5==K<8 4>AB>8=AB20<8, A@548 :>B>@KE =57=0G8B5;L=0 B@C4>5<:>ABL 2KG8A;8B5;L=>3> 0;3>@8B<0, C=825@A0;L=K5 @0AG5B=K5 AE5<K. @><5 C:070==KE 4>AB>8=AB2, >= 8<55B =5A:>;L:> ACI5AB25==KE =54>AB0B:>2, > :>B>@KE 3>2>@8;>AL 2 ?@54K4CI5< @0745;5. 0A?@>AB@0=5==>9 <5B>48:>9 ?@>3=>78@>20=8O B5E 8;8 8=KE ?@>F5AA>2 8 O2;5=89 A;C68B <>45;8@>20=85. >45;8@>20=85 AG8B05BAO 4>AB0B>G=> MDD5:B82=K< A@54AB2>< ?@>3=>78@>20=8O 2>7<>6=>3> O2;5=8O =>2KE 8;8 1C4CI8E B5E=8G5A:8E A@54AB2 8 @5H5=89. ?5@2K5 4;O F5;59 ?@>3=>78@>20=8O ?>AB@>5=85 >?5@0F8>==KE <>45;59 1K;> ?@54?@8=OB> 2 M:>=><8:5. >45;L :>=AB@C8@C5BAO AC1J5:B>< 8AA;54>20=8O B0:, GB>1K >?5@0F88 >B>1@060;8 E0@0:B5@8AB8:8 >1J5:B0, ACI5AB25==K5 4;O F5;8 8AA;54>20=8O. >MB><C 2>?@>A > :0G5AB25 B0:>3> >B>1@065=8O - 045:20B=>AB8 <>45;8 >1J5:BC - ?@02><5@=> @5H0BL ;8HL >B=>A8B5;L=> >?@545;5==>9 F5;8. >=AB@C8@>20=85 <>45;8 =0 >A=>25 ?@5420@8B5;L=>3> 87CG5=8O 8 2K45;5=8O 53> ACI5AB25==KE E0@0:B5@8AB8:, M:A?5@8<5=B0;L=K9 8 B5>@5B8G5A:89 0=0;87 <>45;8, A>?>AB02;5=85 @57C;LB0B>2 A 40==K<8 >1J5:B0, :>@@5:B8@>2:0 <>45;8, A>AB02;ONB A>45@60=85 <5B>40 <>45;8@>20=8O. 06=K< :;0AA>< <0B5<0B8G5A:8E <>45;59, 8<5NI8E ?@8:;04=>5 7=0G5=85 2 ?@>3=>78@>20=88, O2;ONBAO AB0B8AB8G5A:85 <>45;8, A@548 :>B>@KE >A=>2=>5 <5AB> ?@8=04;568B <5B>40< @53@5AA8>==>3> 8 :>@@5;OF8>==>3> 0=0;870. 53@5AA8>==K9 0=0;87 8A?>;L7C5BAO 4;O 8AA;54>20=8O D>@< A2O78, CAB0=02;820NI8E :0G5AB25==K5 A>>B=>H5=8O <564C A;CG09=K<8 25;8G8=0<8 87CG05<>3> A;CG09=>3> ?@>F5AA0. >AB>8=AB2>< @53@5AA8>==>3> <5B>40 A;54C5B AG8B0BL 53> C=825@A0;L=>ABL, H8@>:89 2K1>@ DC=:F8>=0;L=KE 7028A8<>AB59, 2>7<>6=>ABL 2:;NG5=8O 2 AB0B8AB8G5A:CN <>45;L 2 :0G5AB25 A0<>AB>OB5;L=>9 ?5@5<5==>9 D0:B>@0 2@5<5=8. B;8G85 <5B>4>2 AB0B8AB8G5A:>3> <>45;8@>20=8O >B M:AB@0?>;OF8>==KE O2;O5BAO ?>AB@>5=85 ?@>3=>7=>9 <>45;8, E0@0:B5@87CNI59 7028A8<>ABL 87CG05<>3> ?0@0<5B@0 >B @O40 D0:B>@>2 =0 =53> 2;8ONI8E, 2 B> 2@5<O :0: <5B>4K M:AB@0?>;OF88 1078@CNBAO =0 ?@>H;>< >?KB5, :>B>@K9 ?@>4;5205BAO 2 1C4CI55. A=>2>9 MB8E <5B>4>2 O2;O5BAO ?>=OB85 :>@@5;OF8>==>9 A2O78. >@@5;OF8>==0O A2O7L - =5?>;=0O AB0B8AB8G5A:0O A2O7L, ?@8 :>B>@>9 :064><C >B45;L=><C 7=0G5=8N =57028A8<>9 ?5@5<5==>9 <>65B A>>B25BAB2>20BL >?@545;5==>5 <=>65AB2> 7=0G5=89 DC=:F88. ;O =0G0;0 @0AA<>B@8< B.=. 02B>:>@@5;OF8>==K5 AB0B8AB8G5A:85 <>45;8. 0<5G0=85. B<5B8< 206=CN >A>15==>ABL ?@8<5=O5<KE <>45;59 (:0: 02B>:>@@5;OF8>==KE, B0: 8 42CE- 8 <=>3>D0:B>@=KE).  =8E <K 8A?>;L7C5< =5 ?@>AB> =5:85 ?>:070B5;8 y, x 8 B.?., :>B>@K5 =5>1E>48<> A?@>3=>78@>20BL. 0==K5 <>45;8 <K CA;>6=O5< B5<, GB> 2 :0G5AB25 ?>:070B5;59 <K @0AA<0B@8205< 2@5<5==K5 @O4K, C65 8725AB=K5 =0< ?> ?@54K4CI5<C @0745;C. -B> A45;0=> 4;O B>3>, GB>1K ?>:070BL 548=AB2> ?@>F5AA>2 ?@>3=>78@>20=8O, >A=>20==KE =0 <0B5<0B8G5A:>9 AB0B8AB8:5. =K<8 A;>20<8, 5A;8 =01;N405BAO 87<5=5=85 ?>:070B5;59 y 8 x ?> 2@5<5=8 (B.5. yt = f1(t), xt = f2(t)), B> ?>A;5 ?>?KB>: =5?>A@54AB25==>3> M:AB@0?>;8@>20=8O <>6=> ?@8<5=8BL : =8< AB0B8AB8G5A:>5 <>45;8@>20=85. 2B>@53@5AA8>==K5 <>45;8 ?@>3=>78@>20=8O. >=OB85 02B>@53@5AA88 @8 ?@>3=>78@>20=88 =5:>B>@KE ?>:070B5;59 A;54C5B CG8BK20BL =0;8G85 CAB>9G82>9 A2O78 8AA;54C5<>3> ?@87=0:0 A 53> 7=0G5=8O<8 2 ?@>H;>< 8 1C4CI5<. 0?@8<5@, @50;870F8O 28==K<8 702>40<8 ?@>4C:F88 7028A8B =5 B>;L:> >B C@>60O MB>3> 3>40, => 8 >B =0?@02;5=8O 8A?>;L7>20=8O 28=><0B5@80;>2 2 1C4CI5< (A:>;L:> 70:;04K205BAO 4;O 40;L=59H53> E@0=5=8O). 708<>A2O7L <564C ?>A;54>20B5;L=K<8 M;5<5=B0<8 48=0<8G5A:>3> @O40 ?@54AB02;O5B G0AB=K9 A;CG09 :>@@5;OF8>==>9 7028A8<>AB8 8 =>A8B =0720=85 02B>:>@@5;OF88. #@02=5=85, 2K@060NI55 25;8G8=C ?5@5<5==>9 yt 4;O 2@5<5=8 t G5@57 7=0G5=8O MB>9 ?5@5<5==>9 2 <><5=BK (t-1), (t-2), (t-3), ... , (t-p), =07K205BAO C@02=5=85< 02B>@53@5AA88. #@02=5=85 02B>@53@5AA88 2 ;8=59=>9 D>@<5:  EMBED Equation.2  (2.20)  :0G5AB25 0@3C<5=B0 8 DC=:F88 2 (3.1) 8A?>;L7C5BAO >4=0 8 B0 65 ?5@5<5==0O. #@02=5=85 02B>@53@5AA88 (#) ?@8=OB> :;0AA8D8F8@>20BL ?> :>;8G5AB2C M;5<5=B>2, 2:;NG5==KE 2 ?@02CN G0ABL (3.1). 07;8G0NB C@02=5=8O 02B>@53@5AA88 ?5@2>3> ?>@O4:0 (4.2), 2B>@>3> ?>@O4:0 (4.3), C@02=5=8O ?>@O4:0 p.  EMBED Equation.2  (2.21)  EMBED Equation.2  (2.22) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  EMBED Equation.2  (2.23)  >1I5< A;CG05 ?@>F5AA D>@<8@>20=8O ?@>3=>70 A ?><>ILN # 45;8BLAO =0 3 AB0488: CAB0=02;8205BAO ?>@O4>: #; >?@545;ONBAO ?0@0<5B@K ?@>3=>78@CNI59 DC=:F88; @0AAG8BK20NBAO 7=0G5=8O ?5@5<5==>9 yt =0 ?5@A?5:B82C. ?@545;5=85 ?>@O4:0 C@02=5=8O 02B>@53@5AA88 B0:, C@02=5=85 02B>@53@5AA88 8<55B 284 (2.20), => :0:>9 ?>@O4>: MB> C@02=5=85 1C45B 8<5BL 2 :064>< :>=:@5B=>< A;CG05, O2;O5BAO ?5@2>9 AB04859 D>@<8@>20=8O ?@>3=>70. ;O @5H5=8O MB>9 7040G8 8A?>;L7CNBAO =5A:>;L:> <5B>4>2. 0AA<>B@8< 420 87 =8E. @0D8G5A:89 0=0;87 8AE>4=KE 40==KE. -B> =081>;55 ?@>AB>9 ?@81;865==K9 <5B>4. !B@>8BAO =5A:>;L:> 3@0D8:>2, ?> >AO< :>B>@KE >B:;04K20NBAO A>>B25BAB2CNI85 ?0@K 7=0G5=89 (yt, yt-1), (yt, yt-2), (yt, yt-3) 8 B.4. =B5@20;K 2@5<5=8 (t, t-k), (345 k=1,2,3,...), E0@0:B5@87CNI85 C40;5==>ABL A>?>AB028<KE C@>2=59 @O40 4@C3 >B 4@C30, ?@8=OB> =07K20BL ?@>4>;68B5;L=>ABLN 70?074K20=8O (7045@6:8). 5@8>4 70?074K20=8O k ?>:07K205B, G5@57 :0:>9 ?@><56CB>: 2@5<5=8 87<5=5=85 ?5@5<5==>9 yt-k >:065B 2>7459AB285 =0 yt . 7CG5=85 3@0D8G5A:8E ?>AB@>5=89 4;O @07=KE k ?>72>;O5B ?@81;865==> >F5=8BL =0?@02;5=85 8 A8;C A2O78 <564C 1;87;560I8<8 G;5=0<8 @O40. @8<5@. <5NBAO 40==K5 > 565ACB>G=>9 2K@01>B:5 E;51>1C;>G=KE 8745;89 =0 >4=>< 87 E;51>?5:0@=KE ?@54?@8OB89 (B01;.2.7). "@51C5BAO 2K?>;=8BL 3@0D8G5A:89 0=0;87 8AE>4=>9 8=D>@<0F88. 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hfh4OCJNHOJQJaJ"hgh4O6CJH*OJQJaJhgh4O6CJOJQJaJhfh4OCJOJQJaJhgh4OCJH*OJQJaJ~2<Xb ɵɩɵꚋ|m\mLmLmh#h4O6CJOJQJaJ h3h4OCJNHOJQJaJh3h4OCJOJQJaJhS~hS~CJOJQJaJhfh4OCJOJQJaJhg6CJH*OJQJaJhgCJOJQJaJ'h3hg6CJOJQJaJmH sH h3hgCJOJQJaJ"h3hg6CJH*OJQJaJ*h3hg6CJH*OJQJaJmH sH 8@z<փ&Jʇ̇7gdg(^gdS~(gd4O(7`7gdS~  & F^gd4O7d^7`gd4O77d^7`7gd(*77d^7`7gd4O$7d^7`a$gd4O  &(||(|2|4|6|||}}}}}}<~>~@~J~N~P~R~\~^~~~8|lhgh4O6CJOJQJaJhS~CJOJQJaJUh#h4O6CJOJQJaJ h3h4OCJNHOJQJaJ"hgh4O6CJH*OJQJaJ% j>hS~h4O6CJOJQJaJhgh4OCJH*OJQJaJh3h4OCJOJQJaJhS~h4O6CJOJQJaJ(= 1). !?CABO ACB:8 (k = 2) A8BC0F8O 87<5=O5BAO. =>2L ?>O2;O5BAO A?@>A =0 E;51>1C;>G=K5 8745;8O < 2K?CA: ?@>4C:F88 2>7@0AB05B. 02B>:>@@5;OF8>==>5 2708<>459AB285 <>6=> >1=0@C68BL 8 B>340, :>340 70?074K20=85 k = 3,4.5. & ACB:0<. 4=0:>, ?> <5@5 C25;8G5=8O k 7028A8<>ABL <564C ?5@5<5==K<8 yt - k 8 yt AB0=>28BAO <5=55 AB@>3>9, 0 @071@>A B>G5: =0 :>>@48=0B=>< ?>;5 2A5 1>;55 2>7@0AB05B. !;54>20B5;L=>, ?5@8>4 70?074K20=8O ?@8<5=8B5;L=> : CA;>28N @5H05<>9 7040G8 <>6=> ?@8=OBL @02=K< 42C< 4=O<. @>3=>7=0O <>45;L 02B>@53@5AA88 4>;6=0 8<5BL 284:  EMBED Equation.3  AG8A;5=85 02B>:>@@5;OF8>==>9 8 G0AB=>9 02B>:>@@5;OF8>==>9 :@82>9. ;O CB>G=5=8O E0@0:B5@0 02B>:>@@5;OF8>==>9 DC=:F88 =5>1E>48<> 4;O :064>3> 2>7<>6=>3> 8=B5@20;0 70?074K20=8O >?@545;8BL A ?><>ILN :>MDD8F85=B0 02B>:>@@5;OF88 (rk) A8;C 02B>:>@@5;OF8>==>9 A2O78: rk = ck/c0 , (2.24) 345 ck= EMBED Equation.2 ; c0= EMBED Equation.2 ; !>2>:C?=>ABL =0945==KE 7=0G5=89 rk >1@07C5B 02B>:>@@5;OF8>==CN DC=:F8N, ?>:07K20NICN :0: 87<5=O5BAO :>MDD8F85=B 02B>:>@@5;OF88 ?> <5@5 C25;8G5=8O ?5@8>40 70?074K20=8O. @8 =0E>645=88 02B>:>@@5;OF8>==>9 DC=:F88 :>MDD8F85=BK 02B>:>@@5;OF88 @5:><5=4C5BAO >?@545;OBL 4;O ?5@8>4>2 70?074K20=8O 2 480?07>=5 1 < k ( n/4. @8<5@. ;O ?@54K4CI53> ?@8<5@0 @0AAG8B05< :>MDD8F85=BK :>@@5;OF88 4;O 7045@65: k = 1, 2, 3, & , 10. ;O MB>3> 8A?>;L7C5< B01;8FK 2.7 8 2.8, 4>?>;=8< 8E @57C;LB0B0<8 2KG8A;5=89. "01;8F0 2.8 5AOFN;L=8 <5AOF0789101112131415161718#A;>2=K5 4=8, t123456789101112K@01>B:0 E;510, yt4,66,85,17,14,65,54,15,13,754,45,2 (yt  yA@)* (yk  yA@)0,163,240,014,410,160,250,810,011,6900,360,04(yt  yA@)* (yt - k  yA@), 4;O k=1-0,720,180,21-0,84-0,2-0,45-0,09-0,1300-0,12 -  -, k=2-0,043,78-0,041,050,360,051,1700,780 -  -, k=3-0,84-0,720,05-1,89-0,04-0,650-0,06-0,26 -  -, k=40,160,9-0,090,210,5200,540,02 -  -, k=5-0,2-1,620,01-2,730-0,3-0,18 -  -, k=60,360,18-0,1300,240,1 -  -, k=7-0,04-2,340-1,26-0,08 -  -, k=80,520-0,060,42 -  -, k=90-1,080,02 -  -, k=100,240,36 5AOFN;L=0G5=85 c0 (4;O 5 AB@>:8) 8 ck (4;O >AB0;L=KE)rk = c0/ ck=8 <5AOF01920212223242526#A;>2=K5 4=8, t1314151617181920K@01>B:0 E;510, yt4,15,44,65,936,83,15,9(yt  yA@)* (yk  yA@)0,810,160,160,8143,243,610,811,241,00(yt  yA@)* (yt - k  yA@), 4;O k=1-0,18-0,36-0,16-0,36-1,8-3,6-3,42-1,71-0,69-0,56 -  -, k=20,540,080,360,360,81,623,81,620,810,66 -  -, k=30-0,24-0,08-0,81-0,8-0,72-1,71-1,8-0,53-0,43 -  -, k=41,1700,240,181,80,720,760,810,400,32 -  -, k=5-0,09-0,520-0,54-0,4-1,62-0,76-0,36-0,47-0,38 -  -, k=60,810,040,5201,20,361,710,360,290,23 -  -, k=7-0,45-0,36-0,04-1,170-1,08-0,38-0,81-0,40-0,32 -  -, k=80,360,20,360,092,601,140,180,290,23 -  -, k=9-1,89-0,16-0,2-0,81-0,2-2,340-0,54-0,36-0,29 -  -, k=10-0,090,840,160,451,80,182,4700,320,26 2B>:>@@5;OF8>==0O DC=:F8O E0@0:B5@87C5BAO B5=45=F859 : C<5=LH5=8N ( 70BCE0=8N ) 01A>;NB=KE 7=0G5=89 rk ?> <5@5 C25;8G5=8O ?5@8>40 70?074K20=8O k. 7 MB>3> A;54C5B, GB> @0AAG8BK20BL A;54C5B 02B>:>@@5;OF8>==K5 A2O78, :>B>@K5 E0@0:B5@87CNB 2708<>A2O7L C@>2=59 @O40, =0E>4OI8EAO 2 =5?>A@54AB25==>9 1;87>AB8 4@C3 >B 4@C30. -B> =03;O4=> ?>:070=> =0 @8A. 1.11.  EMBED Excel.Chart.8 \s  8A. 1.11. 57C;LB0B 2KG8A;5=8O 02B>:>@@5;OF8>==>9 DC=:F88 rk #AB0=>2;5=85 ?>@O4:0 ?@>3=>78@CNI59 DC=:F88 2B>:>@@5;OF8>==0O 7028A8<>ABL 405B :0G5AB25==CN >F5=:C ?>@O4:0 C@02=5=8O 02B>@53@5AA88. ;O CB>G=5=8O :>=AB@C:B82=KE >A>15==>AB59 ?@>3=>78@CNI53> C@02=5=8O F5;5A>>1@07=> 8A?>;L7>20BL B.=. G0AB=CN 02B>:>@@5;OF8>==CN DC=:F8N. 5 ?@8<5=5=85 >A=>20=> =0 B><, GB> ;8HL G0ABL :>MDD8F85=B>2 02B>@53@5AA88 aj, AB>OI8E 2 =0G0;5 ?>A;54>20B5;L=>AB8, ?@8=8<05B =5=C;52K5 7=0G5=8O. >MDD8F85=BK 1>;55 2KA>:>3> ?>@O4:0 2 1>;LH8=AB25 A;CG052 AB@5<OBAO : =C;52><C C@>2=N, ?>A:>;L:C 2708<>459AB285 G;5=>2 48=0<8G5A:>3> @O40, >BAB>OI8E 4@C3 >B 4@C30 =0 1>;LH>< @0AAB>O=88, =57=0G8B5;L=>. 'B>1K CAB0=>28BL ?>@O4>: 02B>@53@5AA88, F5;5A>>1@07=> 87<5=8BL 2K@065=8O (4.2)  (4.3).  :064>5 87 =8E =5>1E>48<> 225AB8 4>?>;=8B5;L=K9 ?>4AB@>G=K9 8=45:A k, E0@0:B5@87CNI89 :>;8G5AB2> ?5@5<5==KE yt-j 2 ?@02>9 G0AB8 C@02=5=89 02B>@53@5AA88:  EMBED Equation.2  (4.6)  EMBED Equation.2  (4.7)  EMBED Equation.2  (4.8) . . . . . . . . . . . . . . . . . . . . . . . . . . .  EMBED Equation.2  (4.9) @8 ?>4>1=>9 D>@<5 70?8A8 :>MDD8F85=BK akk 1C4CB AB>OBL =0 ?>A;54=5< <5AB5 2 2K@065=8OE (4.6)  (4.9). G5284=>, GB> ?> <5@5 C25;8G5=8O ?>@O4:0 C@02=5=8O |akk| ( min. 028A8<>ABL akk >B 2@5<5=8 70?074K20=8O =07K205BAO G0AB=>9 02B>:>@@5;OF8>==>9 DC=:F88. -B0 DC=:F8O ?>72>;O5B >?@545;8BL ?>@O4>: ?@>F5AA0 02B>@53@5AA88. >:070=>, GB> ?@8 02B>@53@5AA88 ?>@O4:0 p G0AB=0O 02B>:>@@5;OF8>==0O DC=:F8O =5 @02=0 =C;N 4;O 2A5E k(p 8 AB@5<8BAO : =C;N ?@8 k>p. A;8 @0AAG8B0BL =5A:>;L:> 7=0G5=89 akk 8 @0A?>;>68BL 8E 2 ?>@O4:5 C25;8G5=8O ?5@8>40 70?074K20=8O k, B> 8=45:AK ?>A;54=53> :>MDD8F85=B0 akk, ACI5AB25==> >B;8G0NI53>AO >B =C;O, >?@545;OB ?>@O4>: C@02=5=8O 02B>@53@5AA88 (k=p). "0:8< >1@07><, =5>1E>48<> >?@545;8BL, A:>;L:> G;5=>2 4>;6=> 1KBL 2 C@02=5=88 02B>@53@5AA88 (4.1) A ?><>ILN ?>AB@>5=8O G0AB>B=>9 :>@@5;OF8>==>9 DC=:F88, 4;O G53> =04> ?>AG8B0BL :>MDD8F85=BK akk. 081>;55 @0F8>=0;L=K< A?>A>1>< >?@545;5=8O ?0@0<5B@>2 C@02=5=8O 02B>@53@5AA88 (4.1) O2;O5BAO 8A?>;L7>20=85 <5B>40 =08<5=LH8E :204@0B>2 8 <8=8<870F8O >AB0B>G=KE 48A?5@A89 4;O :064>3> 87 2K@065=89 (4.6)  (4.9) 2 >B45;L=>AB8:  EMBED Equation.3  (4.10) 0: C65 1K;> ?>:070=>, ?@8<5=5=85 <5B>40 =08<5=LH8E :204@0B>2 A2>48BLAO : ?>AB@>5=8N A8AB5<K =>@<0;L=KE C@02=5=89.  40==>< A;CG05 >=8 1C4CB 8<5BL 284:  EMBED Equation.2  .................................................................................................................  EMBED Equation.2  ?@545;82 ?> 8AE>4=><C 2@5<5==><C @O4C 2A5 AC<<K, C:070==K5 2 =>@<0;L=KE C@02=5=8OE, 8 @5H82 A8AB5<C, <>6=> @0AAG8B0BL :>MDD8F85=BK 02B>@53@5AA88 01, 02, ... , 0 . @8<5@. @8<5=8B5;L=> : @0AA<>B@5==><C =0<8 ?@8<5@C ?>AB@>8< C@02=5=85 02B>@53@5AA88 2B>@>3> ?>@O4:0 (p = 2):  EMBED Equation.2  0AG5B AC<< 4;O C@02=5=8O 02B>@53@5AA88 2K?>;=8< 2 B01;8F5 1.10. "01;8F0 1.10 @5<O, (CA;>2=K5 4=8) tK@01>B:0 E;510 ytyt-1Yt-2y2t-1y2t-2ytyt-1ytyt-2yt-1yt-214,626,84,635,16,84,646,2421,1634,6823,4631,2847,15,16,826,0146,2436,2148,2834,6854,67,15,150,4126,0132,6623,4636,2165,54,67,121,1650,4125,339,0532,6674,15,54,630,2521,1622,5518,8625,385,14,15,516,8130,2520,9128,0522,5593,75,14,126,0116,8118,8715,1720,911053,75,113,6926,0118,525,518,87114,453,72513,692216,2818,5125,24,4519,362522,882622134,15,24,427,0419,3621,3218,0422,88145,44,15,216,8127,0422,1428,0821,32154,65,44,129,1616,8124,8418,8622,14165,94,65,421,1629,1627,1431,8624,841735,94,634,8121,1617,713,827,14186,835,9934,8120,440,1217,7193,16,8346,24921,089,320,4205,93,16,89,6146,2418,2940,1221,08A53>468,77480,32427,47464,29440,46 >4AB0282 @57C;LB0BK 2KG8A;5=89 2 A8AB5<C, ?>;CG8<:  EMBED Equation.3  BAN40  EMBED Equation.3  #@02=5=85 02B>@53@5AA88 2B>@>3> ?>@O4:0 8<55B 284:  EMBED Equation.3  (1.24) !>AB02;5=85 ?@>3=>7>2 A ?><>ILN C@02=5=89 02B>@53@5AA88 KG8A;5=8O A ?><>ILN C@02=5=89 02B>@53@5AA88 ?@>2>4OB 2 2845 <=>3>H03>2>9 ?@>F54C@K, =0 :064>< MB0?5 :>B>@>9 >?@545;O5BAO 7=0G5=85 ?5@5<5==>9 yt 4;O >G5@54=>3> >B@57:0 2@5<5=8 (3>40, :20@B0;0, <5AOF0, 4=O 8 B.?.). A;8 ?5@8>4 C?@5645=8O @025= l 548=8F0<, B> =0 ?5@2>9 AB0488 @0AG5B>2 2KG8A;ONB 25;8G8=C ?>:070B5;O =0 <><5=B 2@5<5=8 t = n + 1. A MB>9 F5;LN 2 C@02=5=85 02B>@53@5AA88 ?>4AB02;ONB p ?>A;54=8E G;5=>2 8AE>4=>3> 48=0<8G5A:>3> @O40, 70B5< >?@545;O5BAO 25;8G8=0 ?>:070B5;O wt 4;O t = n + 2. ?@8 MB>< 2 :0G5AB25 >4=>3> 87 0@3C<5=B>2 8A?>;L7C5BAO ?5@5<5==0O wt = n+1, =0945==0O =0 ?@54K4CI5< MB0?5.  E>45 ?>A;54CNI8E 2KG8A;5=89 >?@545;ONBAO wt = n+3 ; wt = n+4 ; . . . , wt = n+l. ">G=>ABL ?@>3=>70 2 7=0G8B5;L=>9 AB5?5=8 7028A8B >B ?5@8>40 C?@5645=8O. '5< 1>;LH5 1, B5< 2KH5 2>7<>6=0O >H81:0 ?@>3=>70, B>< 7=0G8B5;L=55 @0AE>645=8O <564C @0AG5B=K<8 8 D0:B8G5A:8<8 7=0G5=8O<8 ?5@5<5==>9.  :0G5AB25 >4=>3> 87 ?@>AB59H8E :@8B5@852 045:20B=>AB8 C@02=5=8O 02B>@53@5AA88 8AE>4=><C 2@5<5==><C @O4C 8A?>;L7C5BAO ?>:070B5;L 01A>;NB=>3> A@54=53> >B:;>=5=8O |A@|, >?@545;O5<K9 ?> D>@<C;5:  EMBED Equation.3  (4.12) KG8A;5=8O |A@|, >ACI5AB2;ONB 4;O ?@54?@>3=>7=>3> ?5@8>40 2@5<5=8 ?CB5< A>?>AB02;5=8O @0AG5B=KE 8 8AE>4=KE C@>2=59 48=0<8G5A:>3> @O40. 8A?>;L7CO 40==K5 ?@54K4CI53> ?@8<5@0 (A<. B01;8FC 4-1), >?@545;8< >1J5< ?@>872>4AB20 E;51>1C;>G=KE 8745;89 4;O t=23 4=O. > C@02=5=8N 02B>@53@5AA88 (4.11) ?@5420@8B5;L=> @0AAG8B05< 2K?CA: ?@>4C:F88 70 420 ?@54H5AB2CNI8E 4=O:  EMBED Equation.3  ">340 ?@>3=>7 A C?@5645=85< l = 3 A>AB028B:  EMBED Equation.3  0945< 01A>;NB=CN A@54=NN >H81:C ?@>3=>70 (w23=3,074B) 8 A>?>AB028< 5Q A 0=0;>38G=K<8 >F5=:0<8, @0AAG8B0==K<8 4;O ?@>3=>7>2 A C?@5645=8O<8 l = 1 8 l = 2 4=O<. ;O MB>3> =5>1E>48<> A>AB028BL B01;8FC 8 A>AG8B0BL 01A>;NB=K5 A@54=85 >B:;>=5=8O. >?@>AK 4;O A0<>:>=B@>;O ?> B5<5 'B> ?>=8<05BAO ?>4 02B>:>@@5;OF8>==>9 A2O7LN <564C ?5@5<5==K<8?  G5< A>AB>8B >B;8G85 C@02=5=8O 02B>@53@5AA88 >B <>45;59 2840  EMBED Equation.2 =f(t)? 'B> ?>:07K205B ?5@8>4 70?074K20=8O k? 'B> ?>=8<05BAO ?>4 02B>:>@@5;OF8>==>9 8 G0AB=>9 02B>:>@@5;OF8>==>9 DC=:F8O<8? 0: >?@545;O5BAO ?>@O4>: C@02=5=8O 02B>@53@5AA88? 040=85 <5NBAO 40==K5 > A@54=8E @0AE>40E =0 :>=5G=>5 ?>B@51;5=85 70 8 ;5B (B01;.1.11). 0AAG8B0BL :>MDD8F85=BK 02B>:>@@5;OF88 ?5@2>3> 8 2B>@>3> ?>@O4:0. "01;8F0 1.11 tyt172838410511612714816 >=OB85 C@02=5=89 <=>65AB25==>9 @53@5AA88. =>65AB25==>9 =07K20NB ?@>3=>7=CN <>45;L, ?>AB@>5==CN A 8A?>;L7>20=85< =5A:>;L:8E 2@5<5==KE @O4>2, C@>2=8 :>B>@KE >B=>AOBAO : >4=>8<5==K< >B@57:0< 2@5<5=8 (40B0<).  >1I5< A;CG05 <=>65AB25==>5 C@02=5=85 @53@5AA88 8<55B 284:  EMBED Equation.2 = f(x1t,x2t,x3t,...,xpt) (5.14) @8 >B1>@5 ?@87=0:>2-0@3C<5=B>2, ?>4;560I8E 2:;NG5=8N 2 <=>65AB25==CN <>45;L, >A>1>5 7=0G5=85 ?@8405BAO B@048F8>==><C M:>=><8G5A:><C 0=0;87C, 2 E>45 :>B>@>3> 3;C165 8 ?>;=55 2KO2;O5BAO ACI5AB2>, =0?@02;5==>ABL 8 B5A=>B0 A2O78 <564C D0:B>@0<8.  ?@>F5AA5 >B1>@0 D0:B>@80;L=KE ?@87=0:>2, ?>4;560I8E 2:;NG5=8N 2 <=>65AB25==CN <>45;L, >A>1>5 2=8<0=85 A;54C5B C45;OBL 2KO2;5=8N 8 CAB@0=5=8N B.=. <C;LB8:>;;8=50@=>AB8, ?>4 :>B>@>9 ?>=8<05BAO =0;8G85 B5A=>9 :>@@5;OF8>==>9 A2O78 <564C 42C<O (:>;;8=50@=>ABL) 8 1>;55 (<C;LB8:>;;8=50@=>ABL) 0@3C<5=B0<8 2 <>45;8 (5.14). 4;O MB>3> >?@545;ONBAO :>MDD8F85=BK ?0@=>9 :>@@5;OF88 <564C ?@87=0:><8. !G8B05BAO, GB> ?>:070B5;8-0@3C<5=BK :>;;8=50@=K, 5A;8 25;8G8=0 :>MDD8F85=B0 :>@@5;OF88 ?@52KH05B 0,8. ;O CAB@0=5=8O :>;;8=50@=>AB8 =5>1E>48<> >AB028BL >48= D0:B>@ 87 G8A;0 4C1;8@CNI8E 4@C3 4@C30. 06=>5 7=0G5=85 2 E>45 AB0B8AB8G5A:>3> <>45;8@>20=8O 8<55B ?@028;L=>5 >?@545;5=85 >1I53> G8A;0 D0:B>@80;L=KE ?@87=0:>2 2 (5.14). =5>?@0240==>5 CA;>6=5=85 <>45;8 ?>2KH05B B@C4>5<:>ABL 2KG8A;5=89, 70B@C4=O5B 0=0;87 8 =5 >15A?5G8205B 70<5B=>3> ?>2KH5=8O 4>AB>25@=>AB8 ?@>3=>70. 0>1>@>B, C?@>I5=85 <>45;8 <>65B ?@825AB8 : >H81:0< 2 @0AG5B0E. !G8B05BAO, GB> 4;O ?>;CG5=8O >?B8<0;L=KE @57C;LB0B>2 :>;8G5AB2> D0:B>@80;L=KE ?@87=0:>2 4>;6=> 1KBL ?@8<5@=> 2 5 @07 <5=LH5 G8A;0 =01;N45=89, A>AB02;ONI8E 2K1>@>G=CN A>2>:C?=>ABL ?> :064>9 ?5@5<5==>9. ;O >?@545;5=8O D>@<K A2O78 <564C ?@87=0:0<8 7=0G8B5;L=>5 2=8<0=85 A;54C5B C45;OBL 3@0D8G5A:8< ?>AB@>5=8O<, >B@060NI8< 87<5=5=85 7028A8<>9 ?5@5<5==>9 ?>4 459AB285< :064>3> 87 D0:B>@>2 2 >B45;L=>AB8. A;8 MB0 A2O7L ;8=59=0, B> 8A?>;L7C5BAO ;8=59=>5 <=>3>D0:B>@=>5 C@02=5=85 @53@5AA88:  EMBED Equation.2 =a0+a1x1t,+a2 x2t,+...+apxpt (5.15) >MDD8F85=BK a1, a2, ... , ap =07K20NBAO :>MDD8F85=B0<8 G8AB>9 @53@5AA88. =8 ?>:07K20NB, :0: 87<5=8BAO 7028A8<0O ?5@5<5==0O yt ?@8 C25;8G5=88 8;8 C<5=LH5=88 D0:B>@0 =0 548=8FC ?@8 CA;>288, GB> 2A5 >AB0;L=K5 ?@87=0:8, 2:;NG5==K5 2 <>45;L, >AB0NBAO ?>AB>O==K<8. 0@O4C A ;8=59=>9 <>45;LN >?@545;5==>5 @0A?@>AB@0=5=85 ?>;CG8;8 =5;8=59=K5 <=>3>D0:B>@=K5 :>@@5;OF8>==K5 7028A8<>AB8. 7 :@82>;8=59=KE DC=:F89 G0I5 2A53> 8A?>;L7C5BAO AB5?5==0O DC=:F8O:  EMBED Equation.2 = EMBED Equation.2  (5.16) CB5< ;>30@8D<8@>20=8O AB5?5==>5 C@02=5=85 <>6=> ?@825AB8 : ;8=59=><C 284C:  EMBED Equation.2 =a0+a1x 1t,+a2 x 2t,+...+apx pt @>F5AA ?>AB@>5=8O 8 >A>15==>AB8 ?@0:B8G5A:>3> ?@8<5=5=8O <=>3>D0:B>@=KE <>45;59 7028A8B >B E0@0:B5@0 8=D>@<0F88, 8A?>;L7C5<>9 ?@8 2K?>;=5=88 @0AG5B>2.  E>45 2KG8A;5=89 <>3CB ?@8<5=OBLAO ?5@28G=K5 40==K5, >B@060NI85 A>AB>O=85 >1J5:B0 :0: 2 AB0B8:5, B0: 2 48=0<8:5. !B0B8G5A:>5 <>45;8@>20=85 ?@8<5=O5BAO 4;O 0=0;870 2708<>A2O759 <564C >1J5:B0<8 8 O2;5=8O<8. 8=0<8G5A:>5 <>45;8@>20=85, >A=>20==>5 =0 >1@01>B:5 A2O70==KE 2@5<5==KE @O4>2, ?>72>;O5B >?@545;8BL >1ICN =0?@02;5==>ABL 2 87<5=5=88 ?@87=0:>2, 1>;55 B>G=> >?@545;8BL 25;8G8=C 8AA;54C5<>3> ?>:070B5;O 2 1C4CI5<. ;O 8A:;NG5=8O 02B>:>@@5;OF88 <564C C@>2=O<8 @O4>2 <>3CB ?@8<5=OBLAO <5B>4K ?>A;54>20B5;L=KE @07=8F, $@8H0->C 8 ?@.  @O45 A;CG052 F5;5A>>1@07=> A>2<5AB=>5 8A?>;L7>20=85 AB0B8G5A:8E 8 48=0<8G5A:8E <>45;59. 081>;LH55 @0A?@>AB@0=5=85 ?>;CG8;8 425 2KG8A;8B5;L=K5 AE5<K ?@>3=>78@>20=8O A ?><>ILN <5B>4>2 <=>65AB25==>9 :>@@5;OF88 8 @53@5AA88. 5@20O AE5<0 >A=>20=0 =0 :>@@5;8@>20=88 >B:;>=5=89 >B B5=45=F89 87<5=5=8O ?@87=0:>2. 0: C65 ?>:07K20;>AL, 8A?>;L7>20=85 >B:;>=5=8O >A;01;O5B 2>7459AB285 02B>:>@@5;OF88 =0 @57C;LB8@CNI85 ?>:070B5;8. B>@0O AE5<0 ?@54?>;0305B ?>AB@>5=85 =5A:>;L:8E AB0B8G5A:8E <>45;59 (4;O :064>3> 3>40 ?@54?@>3=>7=>3> ?5@8>40), ?0@0<5B@K :>B>@KE ?@54AB02;ONBAO 2 2845 DC=:F89 2@5<5=8, ?>A;5 G53> @0AAG8BK20NBAO =081>;55 25@>OB=K5 7=0G5=8O ?@87=0:>2 2 ?5@A?5:B825. @8<5@. > 40==K< 70 20 <5AOF52 (B01;. 17) =5>1E>48<> ?>AB@>8BL C@02=5=85 @53@5AA88 7028A8<>AB8 ?@81K;8 ?@54?@8OB8O y (<;=. @C1.) >B F5= =0 AK@L5 x1 (BKA. @C1. 70 1 B) 8 ?@>872>48B5;L=>AB8 B@C40 x2 (54. ?@>4C:F88 =0 1 @01>B=8:0). "01;8F0 17 5AOFK@81K;L y&5=0 =0 AK@L5 x1@>872>48B5;L=>ABL B@C40 x21210800,0300,027201000,0500,033001500,0600,04950800,0500,05430900,0400,064201200,0500,071301100,0400,084301200,0500,09601300,0450,0105701100,0500,0115201400,0600,0122501300,0500,0138001200,0600,0142001200,0450,0153001400,0550,016501300,0450,0175501100,0500,0183601100,0450,0193201400,0550,0204201200,0500,0 ;O 2KG8A;5=8O ?0@0<5B@>2 <=>3>D0:B>@=>9 <>45;8 <>6=> 8A?>;L7>20BL  Excel. 04> 2>9B8 2 <5=N 2 =0;87 40==KE 8 2K1@0BL DC=:F8N 53@5AA8O. "0:65 :0: 2 ?@8<5@5 4;O 42CED0:B>@=>9 <>45;8 225AB8 2A5 8AE>4=K5 40==K5. >A;5 MB>3> 7040BL >1;0ABL 2K2>40 @57C;LB0B>2 DC=:F88 53@5AA8O. 57C;LB0BK @53@5AA8>==>3> 0=0;870 ?@54AB02;5=K =0 @8A. 14. + " 53@5AA8>==0O AB0B8AB8:0=>65AB25==K9 R0,995838766R-:204@0B0,991694848>@<8@>20==K9 R-:204@0B0,99!B0=40@B=0O >H81:022,8701;N45=8O20 8A?5@A8>==K9 0=0;87dfSSMSF=0G8<>ABL F 53@5AA8O21062001,05531000,521014,962,0628E-18AB0B>:178893,94523,17B>3>191070895 >MDD8F85=BK!B0=40@B=0O >H81:0t-AB0B8AB8:0P-=0G5=8586=85 95%5@E=85 95%86=85 95,0%5@E=85 95,0%Y-?5@5A5G5=85194,5337,115,246,63E-05116,22272,84116,22272,845@5<5==0O X 1-1,460,036033319-40,729425892,16E-18-1,54-1,39-1,54-1,395@5<5==0O X 23,930,09510352441,40311421,64E-183,734,133,734,13 8A.14. 57C;LB0BK ?@8<5=5=8O ?@>F54C@K 53@5AA8O 4;O <=>3>D0:B>@=>9 <>45;8 "0:8< >1@07><, C@02=5=85 @53@5AA88 8<55B 284: yt =194,534 - 1,468 x1t + 3,938 x2t . 0AA<0B@820O ?>A;54>20B5;L=>ABL >AB0B:>2 :0: 2@5<5==>9 @O4, <>6=> ?>AB@>8BL 3@0D8: 8E 7028A8<>AB8 >B 2@5<5=8.  A>>B25BAB288 A ?@54?>AK;:0<8 <5B>40 =08<5=LH8E :204@0B>2 >AB0B:8 (t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y (BKA. :BG) >B >1J5<>2 ?@>872>4AB20 ?@>4C:F88  - x1 (BKA. 54.) 8 ?@>4C:F88  - x2 (BKA. 54.). ?@545;8BL ?0@0<5B@K C@02=5=8O @53@5AA88. "01;8F0 18 5AOFK>B@51;5=85 M;5:B@>M=5@388, y@>872>4AB2> ?@>4C:F88 ( - x1) @>872>4AB2> ?@>4C:F88  - x2 11450650,0300,021562680,0365,031490550,0510,041800700,0500,051650660,0450,061500575,0500,071470550,0460,081610620,0480,091680670,0520,0101780710,0570,0111700655,0600,0121820750,0550,0131856740,0620,0141760685,0580,0151860720,0600,0 -:A?5@B=K5 <5B>4K ?@>3=>78@>20=8O. 0AA<>B@5==K5 2KH5 AB0B8AB8G5A:85 <5B>4K ?@>3=>78@>20=8O >15A?5G820NB =0456=K5 @57C;LB0BK ?@8 =0;8G88 4>AB>25@=>9 8AE>4=>9 8=D>@<0F88.  A;CG05, :>340 4;8=0 8AE>4=KE 48=0<8G5A:8E @O4>2 >:07K205BAO =54>AB0B>G=>9 (=5?>;=>B0 8=D>@<0F88), ;81> :>340 A2O7L <564C 8AA;54C5<K<8 O2;5=8O<8 =>A8B :0G5AB25==K9 E0@0:B5@, ?@8<5=ONBAO B.=. 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