ISSUES RELATED WITH ARMA (P,Q) PROCESS. Salah H. Abid AL-Mustansirya University - College Of Education Department of Mathematics (IRAQ / BAGHDAD)

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1 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK ISSUES RELATED WITH ARMA PQ PROCESS Sl H. Ai AL-Msnsiy Univesiy - Collee Of Ecion Deen of Meics IRAQ / BAGHDAD ABSTRACT: Sose e n ARMA ocess wi wie noise eo ocess. Le n e e cceisic fncions of n esecively. In is e enel fol o eesen in es of is oine. By sin is fol we invesie o e isiion of ARMA ocess wee i s wie noise follow Nol Ccy invese Gssin n G isiions. Inse of e iionl l eo n esy enel fol o eeine e coefficiens fo e csl ARMA ocess will e esene lso. KEYWORDS: Ai ol Cceisic ncion Csl ncion ARMA PQ. Meics Sec Clssificion: 6M 7M 9B8 INTRODUCTION Aoeessive scees wi ovin vee eo es of e fo. Wee ve een consiee. Te ocess is clle n oeessive ovin vee ocess of oe o iefly ARMA wee is seence of wie noise i.i.. no viles. Alenively. cn e wien s. Wee n eesen e oos of. Sose n e e cceisic fncions of n esecively Anel 98 eesene n AR ocess in es of is wie noise ocess s follows. Ten e woe e followin elionsi eween e cceisic fncion of is ocess n e cceisic fncion of wie noise ocess s 9

2 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK Piesley 98 ee wi AR ocess n eesene is ocess in es of i's wie noise s.5 Ten one cn wie e followin elionsi eween n fo AR ocess.6 Si in 986 sie e evio of AR ocess wee e esils isie s G n weill. In 99 Si sie e evio of AR ocess wee e esils isie s G n ee ees exonenil. In 99 Al-os n Al-zi sie e oeies of ARMA- enelize oisson ocess esecilly fo covince ix inveiiliy n eession evio. Si in 99 iscsse e oens of AR ocess wi esils isie s loisic. In 99 si sie e oe esiion n ionsic cecin fo AR ocess wee e esils isie s loisic ye nen G exonenil n Llce. In 997 Alzi Al-wsel n Al-ncwi se e silion o coe eween xi lielioo esio n Yle-wle esio fo AR enelize oisson ee. In 998 e se ove eseces se silion o coe on Yle-wle esio coniionl les se esio xi lielioo esio n oen esio fo AR Binoil ee. Ai woe e elionsi eween n fo AR ocess s follows.7 Wee.8 n conine nil ssiion of s l l l. Deenin on e followin fol e eive fo eesenion of AR ocess in es of i's wie noise ocess

3 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK Te fis ol of is e is o eive enel fol o eesen in es of fo ARMA ocess. An ARMA ocess is csl fncion of if i cn e wien s e MA ocess. Wee e coefficiens sisfy. So e secon ol of is wo is o fin enel fol o eeine in es of s ' n s '. REPRESENTATION O ARMA PROCESS IN TERMS O IT'S WHITE NOISE isly e fol of ARMA cn e wien s. B B B. Also we cn wie ARMA ocess s.

4 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK B B B. ARMA ocess cn e wien in es of i's wie noise s follows.5.6

5 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK Siilly ARMA ocess cn e wien s.7

6 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK Since c c c fo evey consns c n en 5.8

7 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK 5 By sin e se en we cn enelize e ove esls o e followin enel fol fo eesenion of ARMA ocess in es of i's wie noise.9. Wee fo. An so on nil we ec o l l l wee l is osiive inee ne.

8 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK 6 THE CHARACTERISTIC UNCTION O ARMA PROCESS By sin e enel fol in.9 we cn wie in es of fo ARMA ocess s follows i E i E i E. ex ex ex Exle Sose is n ARMA ocess n i's wie noise follow nol isiion wi cceisic fncion } / ex{ i en e cceisic fncion of cn e wien s i i } / ex{ } / ex{ ex ex i i So e isiion of will e N N

9 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK 7 As secil cse if = en e isiion of ARMA ocess will e nol wi en n vince. ARMA will isie lso s nol wi en n vince. Exle Sose is n ARMA ocess n i's wie noise follow Ccy isiion wi cceisic fncion } ex{ i en e cceisic fncion of cn e wien ccoin o. s i i ex ex ex ex i i So e isiion of will e Ccy As secil cse if = en e isiion of ARMA ocess will e Ccy wi ees n.

10 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK 8 ARMA will isie lso s Ccy wi ees n. Exle Le e n ARMA ocess n i's wie noise follow Invese Gssin IG isiion wi cceisic fncion } ex{ / i en e cceisic fncion of cn e wien ccoin o. s i i / / ex ex ex ex / / / / i i So e isiion of will e / / IG As secil cse if = en e isiion of ARMA ocess will e Invese Gssin wi ee /. ARMA will isie lso s Invese Gssin wi ee /. Exle

11 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK 9 Le e n ARMA ocess n i's wie noise follow G isiion wi cceisic fncion i en e cceisic fncion of cn e wien ccoin o. s i i Te ove fol oes no ssin ny iionl oiliy isiion of so one cn se e nieness elion eween e oiliy isiion n i's cceisic fncion o fin e oiliy isiion of. COEICIENTS O THE CAUSAL ARMA PROCESS If we se e nsfoion eion.9 cn e ewien s. Ten fo e ove eion n eion. we cn excly eeine e vles of o e. Exles 5 ollowin secil cses of ARMA s exles o escie e ove wo. A ARMA ocess

12 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK o eion. we cn wie e ARMA oel s 5. If we ssie in n 5. cn e ewien s. By esecively ssiions s we i ove n en coe e eslin eion wi eion. we cn e 5. : : Accoin o e iionl eo. Te vles of in 5. cn e oine sily y sin o enel fol since fo. we cn wie 5. If en n so if en n so on fo e oe vles of. B ARMA ocess o eion. we cn wie e ARMA oel s

13 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK 5. If we ssie in n 5. cn e ewien s By esecively ssiions s we i ove n en coe e eslin eion wi eion. we cn e 5.5 : Accoin o e iionl eo. Te vles of in 5.5 cn e oine sily y sin o enel fol since fo. we cn wie 5.6 If en n so if en n so on fo e oe vles of.

14 Eoen Jonl of Sisics n Poiliy Vol. No..9- Mc Plise y Eoen Cene fo Resec Tinin n Develoen UK REERENCES Ai S. H. "Genel fol o eesen e cceisic fncion of AR ocess y es of i's wie noise cceisic fncion" AL-Qisy Jonl fo econoic n inision sciences Vol. no..-8. Al-os M. n Al-Zi A.99 "Soe oeessive ovin vee ocesses wi enelize oisson inl isiions" Ann.lns.M.vol.5No..-. Al-Wsel l & Al-Zi A. n Al-Ncwi H.998 "Esiin e ees of e Binoil AR ocess" Alie M. & co. vol Al-Zi A. & Al-Ncwi n H. Al-wsel l. 997" Esiin e ees of e enelize oisson AR ocess" J.sis. co. Si.vol Anel J. 98 "A inl isiions of oeessive ocess" Pe Confeence Of Infoion Teoy. Bocwell P. n Dvis R. "Inocion o ie seies n foecsin " secon e. Sine-Vel New Yo USA. Piesley M. 98 "Secl nlysis n ie seies" Aceic Pess Cony. Si C. 986" Silion of weill n oeessive siony ocess" Co. S. Sil. vol.5 no..-6. Si C. 99 "is oe oeessive oels fo n exonenil ocesses" J.Al.Po. vol Si C. 99 "is oe oeessive loisic ocesses" J. Al. Po. vol Si C. 99 "Moelin non nol fis oe oeessive ie seies" J.Of oecsin vol

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