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Transcription

1 5 8 [9] ARMA,! ** % & ' * #,-! #$% &'! ARMA, ' - / #'! /! - 4$!,- - - '$ #!!! ' - 78 & 5! 6! #$ &'! %,- 9 5 # 6 <# / 6 ' 6! -! >$ - - '$ #! 6 Pde 4 5% C-ble Kumer 4 SACF #@ -! 5% /!! 4? /4 4 &8 6 / A SPACF * / / 5/ 6/!4 B 5/ /5 6 B **

2 ' - '$ #! [] Some Idenificion Mehods of Mixed Model ARMA, nd is Probbilisics Properies when Deecing Rndom rror belong o Poisson Disribuion ABSTRACT Mos of he ime series h pper in mny economicl geophysicl nd oherphenomens re driven by non-gussin rndom error, so he im of his pper is o invesige some of he probbilisic properies of Gussin nd non-gussin mixed model ARMA,, nd he idenificion mehods of his model The reserchers hve heoreiclly derived he chrcerisic funcion he firs four momens nd he skeweness nd Kurosis coeficiens for for Gussin disribuion nd non-gussin disribuion poisson nd simulion experimen were used o confirm he ccurcy of he heoreicl resuls, We hve lso declred he idenificion smple uocorrelion funcion SACF nd Kumr mehod c-ble depending upon he pde pproximion nd we hve suggesed mehod depending upon he exended smple pril uocorrelion funcion SPACF o scerin he efficiency of suggesed mehod * ' A A! / ',- 8 8', / F'! G-!4 H!! 8' >!% 'F! 5% #/ - 4 #/ % ' >!/!! ' G- 4 I 5 6% K&! >8' J' #/ F,- G- 6 ' 6 - H! # Box & Jenkens A % 97 4 &

3 [] 5 8 ARMA ' # G- > 4!! - & K4! K % A! 9 - G- F'!!! 979 6% Nelson nd Grnger!! - / #'! G- 7A! #$ &'! % ARMA, '!,- ARMA, ' -! '$ / / #'! 5% #! 4!! #$ &'! % ARMA, ' - &' G-!! 4 * 5% & /!!! 6! - >/ 4! ARMA ' - ' 4! J! > >! 5%! %@ /! [4] Nelson nd Grnqer % 8 5 [] Andel /! 98 6%!!! >! &'!! 6 Cuchy $ plce 9! [5] Sim /! % > G- O ' 5%,-! 6! >P!ARMA, -! >A8 44/ >! H! [7] Swif & Jncek /! % 6 ' B & J ARMA 5% % -!

4 ' - '$ #! []! J'! Y! / - &8 % / 6 ' 6 T Z! 4$ [6] Sofi & Thnoon /! % MA, MA,/ -! / 6 #$ &'! % ' ' 5 [] A Nsir & Jfr /! 997 6%,/ % P [] /! 6 6%!! #$% &'!! MA,/ - 78 &!!! /! 6 O8 6 / 6 '!! 6% $!!! ARMA, ' - #' / 4,- P / 4 { ;, m, m, } ARMA ' - P p p q ~ µ, µ q { } 6 / >!! 8!! >- 4 #$ &' / Bckwrd Shif operore 8' / 6 '! 5% p B B, B B B B B B B q q B P % - Gussin K! ARMA p, q 9-5% Non! -! #$ F'! - - Gussin

5 [4] % ARMA p, q - 4 $ 4/ # ' B, B -@ Ouside of Uni Circle / AR - / P! ARMA p, q ' -! B I B, where B B 5% / B 5%! P! ARMA p, q - %! 98! 5% / MA,/, 4, % 4 ARMA,! 5 ARMA, 5% / P q p %! B B 5 P 5% / B / 6 '! B B B B % >- Whie noise! Q$ #$ &' /! ~ N,,/ P! ARMA, -!,-

6 ' - '$ #! [5] B B or B where B B B or B B B, B 6 5% / P ARMA, ' - -' O% 7 / - / P! ARMA, -! 98! 8 ARMA, * * 6 ' -! '$ > % # %, -! 4 # G- A ARMA p,q 984 6% Tio Tsy / SACF JP >! 4 4 > 4 5% 4 G- - [9 ] P! - / - OS % Z ARMA p P Z ep, ; p,, n -! > $ n Z / p,q % / -! P - #$ F' 9 e p,

7 [6] 5 8 ' -! '$ > ' J' % Kuldeep Kumr! &@ 4 ARMA, Pde 4 5% 4 G- > % / [8],/ P! - / P! 4 ARMA, p,q 6 >A% 4 G- P c 6 ' 6,- { c p,q p,q,,,} ARMA p,q ' -! '$ 5% 44/ G- /4 4 P 6 '!,- #@ -! k k if k k i k k, k, k, if k,, nd for,,, k Z m W k k, k k k, k #@ -! 7/ % %! SPACF W m, m m, Z M! m W m, for m o w Z / F p,q! ARMA 44/ - - p, q P! AR -

8 ' - '$ #! [7] - '$ SPACF 4 ' G- 5% %!!,- 6 / ARMA, ' m Z AR! 5,,, 8 7A MA! 5 98! % m 4 4 / ARMA p,q - m ± for m o w p, IJKMN q OPQ Z IPRSTUV IJKMN WV! 64 5 $ x! 5%! >/

9 [8] ~ N, 4$! OF!! #$ &' > - ' &'! 4 P 8 x { exp isx } w here i s x x s s s s exp S x S exp S P $ exp S O% '! % A! 4 &'! &' / F O% ARMA, -! O% # exp! S 4! ~ p $ / ~ p $!! #$ &' > - p m f / $! Poisson dis $ exp $ /! f,,,,, o w

10 ' - '$ #! [9] &' G- $ > / $ or { exp is } s exp $ x s s! ARMA, - 5% / exp exp x s $ is exp is # 8- $! 6 '! 5 P 5% 6 5% / 4$ & s / s x exp i$ exp i$ 6 5% $ 98! J' 6!!/ µ $ i Vr $ i 5% / ARMA, -! ' $ i 7 64!!! 6

11 5 8 [] $ $ 8! #! #! #! # i $ $ $ , N ' % / & 9 G@ 5/ $ 5% O & 94 / 6 6 ' 6,- > SK { } { } 9 SK or SK µ µ µ µ 78 5/ Flness I, Coefficien of Kurosis /! 6 6 ' [ ] { } KU or KU µ µ µ µ -! 5/ - KU > - KU K/ 5/ <

12 ' - '$ #! [] 9 P %! 4!! 6 6 '! & 5% / SK KU 78, P $! & % / 6! 6 6 '! ARMA, ' - #! SK / # $! 78 KU # 4 4! # $! 4

13 [] > % <! 6 '! &@ - >' >A P U 4 6! 4 #$ % #/! - #$ P 5 / 6, ' - P 6 64! 6 6!,- 6 5% / ARMA, % 4 $ 4/, > n 5,, / 8' >% 6@/! 5! - 78 & 4 --!! ARMA, ' - - 4! &'! % N, N, 4! #$ &' 6 / P 64 [] Box Muller 4 6 '!! 6 6 / 6 5% / ' - /!@ 78 & 6 /!@ 64! 4 5% 9 I &' 64!@

14 ' - '$ #! [] 89 6 % ARMA, N, 4* 4 n, SK KU!@!@ , , , , ,

15 [4] 5 8 < 6!@ G- p $! &'! % 6 '! p $!! #$ &' 6! [] Reecion Mehod 4 6 5% / ARMA, ' - P & 6 5% / 6, 6 8' 64 5% / 5% 9 P 6 '!!@ 5% 4 P 6 '! 64 <#, 7A 6 p $ % ARMA,! n, SK KU , - 9 -,, - 7, 5 9, !@ !@

16 ' - '$ #! [5] <# G- >A% 6!! ARMA, - $ 5 8' 6 -' 6 n % 6@/! $ 78 & 7A p $, SK SK KU KU!@!@ R ARMA ARMA, * 4 - K4 Z 4 $ 4/ 6!@ G-, 8' 64,,- &@ - #! 6!@ 6 ' -! / 4 5% 7A 4! > 6@/! 5 / 5% # / ARMA, -

17 [6] 5 8 8' # ARMA, - n , -8, -8-4,, - 8, 6 9, 9 SACF C-ble SPACF ! SPACF /4 4 7A <# - C ble 4 A SACF 4 4 / ARMA 4! * # Percenge rror F'! 94 6 ' 6 > 6@/ 98! ARMA, ' -! / ',- 7A 4!

18 ' - '$ #! [7] ' -! / # F'! ARMA, n , -8, -8-4,, - 8, 6 9, 9 SACF C-ble SPACF @/ F'! 7A <# A,- 7A <#!-!- 6 5% - SACF 4 ARMA, ' -! / 4 6 SPACF /4 4 6@/ &'! 4 C - ble 4

19 [8] 5 8 %!!A 4 %6! 78 & 4! <# ' R &'! % ARMA, ' - & 64 <! #$ % ' -!@ &' 4,-! 4 7A <# ' R 4 $! &'! SPACF /4 4 7A <# ' - -! ARMA, ' -! / SACF 4 4 6@/ F'!! <# ' -4 ARMA, ' -! / 4 A 4 6 SPACF /4 4 6 SACF 4 C - ble - A Nsir, A M H & Jfr, H 997 Momens of low order MA Process Gussin nd Non Gussin, J of Adminisrive nd conomicl Sci he Sixh Sci Conference of Adminisrion nd conomics College - - Andel, J 98, Mrginl disribuion of Auoregressive Processes Ninh Prgue Conferece of Informion heory, Sisicl decision funcion nd Rndom Process, Czechoslovk Acdemy of Sciences, Insiue of Informion heory nd Auomion prgue

20 ' - '$ #! [9] - Fish mn, G S 97, Conceps nd Mehods in discree even digil Simulion, John Wiley nd sons, New York 4- Nelsn, H & Grnger, C W 979, xperience wih using he Box Cox Trns formion whom forecsing conomic Time Series, J of conomerics, vol 8, No 5- Sim, C H 987, A mixed Gmm ARMA, Model for River Flow Time Series, wer Resources Resech, Vol, No, pp Sofi, F B & Thnoon, B Y 994, Probbiiy Densiy Funcion of Some low order Moving Averge Models wih uniform Innovion, J of Tnmiy A- Rfidin, Vol 4, No 7- Swif, A & Jncek, G J 99, Forecsing Non Norml Time Series, J of forecsing, Vol, No 8- Kumr, k 987, Idenificion of ARMA mdels using Pde Approximion, Bullein of he Inernionl S Insiue Ne herlnds, Vol, Book, p Tsy, R S nd Tio, G C 984, Consisen simes of Auo regressive prmeers nd xended smple Auocorrelion funcion for sionry nd Non Sionry ARIMA models, JASA, Vol 79, No 84, p & T!% 6@ - / 6 '!!!!,/ ' - #'! / - &/ G /! ARMA,

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