CC BY
32i/h&iiaq-iishL
SLSbUUq-hSnhr&6flhL
^hULLU. UUiïb4nU3UL
C^ISC dfeujqqujjfib ipbipbuujljujb hujpujpbpnLfajriLbbbpfi
uiiíp¡inb¡i LuuiyjipLubip
CC Ufl-b4SPU8hL <UC4biiCn-h СЦРсНУЬШАЗЬ 4ЬРШК1ПИЭвПКЬС Ь4 LiULKjUSbUílMJQ
UriLjb hnrplmóp Ьфр1(ш0 £" « LunLippLujIib rffiipriLiíbbpli i¿bpinLÓnL-
[djuibp Li LjiublviuLphudiubp: Чилршрф[ £" пшп^Ьши^рф^ bpUriLj/a/i 2UJpdpb¡9wg¡i hш-ilLuifip i¿bp[ni¿Fnipjniti b dnq.b[un[npnid' ф6ш1]шцрш1]шЬ qnpó¡ipbbp[i фршп^шф: ЧшиЬшфршщЬи, фршпф[ £" d~LuilLubLuLiLujfib ¿ujppbpli únipbgmúp: lfnr¡.bibbp¡i hji-i¡Lub фш LjiublviuLphunLdbhp bb L]ujipujpi[b[ « uinLifipujjlib Ьш2ф1^2п11 i^Ju/uiqui ф-ipnLiSbbpfi duiu/ib, npnbp ifiLuuipnLiI bb, np pbLuLjLubnb ufiujúujbbbpnLÚ bu <C< Lunbip-plu]fib Иш2ф^2[1пЬ mbf) kuiL/uib i[uiipfauipuigJujb dfiifinid, fiul¡ COVID-19 ¡jmbbbuj qm-Juipuij/ib tybL/ip' ¡vnpuigbbinil « uinbippujjlib Ьш2ф1^2п11 uJnL¡ui щш^шитрцр:
<[llítiuipuinbp ujnhippujjfib Ьи^ф^Ь17 ujujpujbpujjfib Ьи^ф^Ь17 àmnujjm-
[ajmbbbpfi Иш2ф1]2ЬГ1' ЫщЬп!1^ ipbuujljujpujp l¡2fri~L, COVID-19, SARIMA únt}b[
JEL: F17, H62
"libpui6iu|3jiuíj: Lbpl|uijfiu q.|npui|iugduiti u|uijduititibprud hpl|pfi uinuitig-puijfiti duil|pninliinhuuil|uili gruguli^tibpfi u[bp[nLÔnL|3jnLlip U l|uitifuuiinbuduiti uprynLliplibpp r|.uintinLd bti n^ huii|uiuinfi, рш1ф np LnlimbunLpjriLlilibpfi puigru-pjmlip 1ю|шишЬ[ t t¡pl|ptibpfi intiinbunLpjnLtitibpfi u[bp2liupr).jnLlipfi и[рш шр-inuipfiti £ur\ui£uil|uitinL|3juiti tuil|uiti uiqr|.hgnL|3juiliQ: liu[b[fili, uipinuipfiti uinLinpuijfiti q.npônLlibnL|3jnLlifig шпши[Ь[шд.пу1| r|.puil|uiti шргугиЪрпи[ r|mpu
q.LU[nL bu|uiinuil|Q uuifiu|ni.d t bplipbbpfib' hP^bg mbmbunLpjnLbp hwpduipbg-bti|_nl uipinuipfib W2fuwphfi uiuihuibgbbpfib, fiul| «-fi bduib ijinpp, paig inbinb-urupjuidp bpl|pbbpfi haiJaip uipinuipfib ainUmnLpp r|.uinbnLd t qnp&fif!' npnu[ hair\|aaihaipu[nLJ bb uiqquijfib mbmburupjuib b uipinuir|.puib£>fi puiqduiquibbg-dwb gui&p duil|uipr|.uil|fi hbmbaibpnu[ wnwgwgnri hfidbuifubr|.fipbbpQ: COVID-19-nu[ u|wjiiuibuii|npi|w& bbpl|uijfiu 6qbuid'uiduijfib fipuii|ji6uil|nLd <K uinbm-piujfib hai2i|bl|2nfi (UK) dfimrudbbpfi L| aib fu aim burn Jb ainaiu[b[ piub uipr|.fiui-l|Lub t, £>uibfi np, dfiuijb COVID-19-fi t^)bl|Lnfi l|wbfuuimbuni.duijfib qbwhuiinui-L|aibb nLbbbai[nu[, l|l|uipnr|wbuib£> qbaihaimb[ « uipinuijDfib uinbmpfi u[pai huiduii|wpuil|fi aiq^bgrnpjaib ¿lul|iq:
UnLjb hnr).u[ai6fi ba|aimail|p « UK u[bp[nL6nL|3jnLbp b hbaipaiu[np qaipqai-grudbbpfi l|uibfuuimbuni.db f hai2i|h ainbb[nu[ COVID-19-|n t^)bl|Lnp: Uju fubr).fipp [nL6b[nL haiJaip hai2i|Lupl|u[b[ bb « UK 2wpdpb|auigfi grngaib^bbpp, L|ainnLgu[b[ bb uujrj. 2Lupdpb|aaigp bl|uipuiqpnrL tLjntinJbmp|nL| Jnr).b[bbp b r).paibg hfiduib u[pai l|aiLnaipu[b[ bb l|uibfuuimbunujbbp: COVID-19-fi t^)bl|Lnp hai2i|h ainbb[nl haiJaip l|aiLnaipu[b[ t CC UK L|ainnLgu[ai5paijfib u[bp[nL6nL|3jnLb, r).pai puir|wr|.pfi£bbpfi haiJaip r^rnpu bb pbpu[b[ tdu|fipfil| inbuwl|wpwp ^h^-bbp, b nLbbbai[nu[ wnwgfib bnuidujuil|fi hwdbduimiiuib puiquT wuipuibpuijfib hai2i|bl|2nfi r).ba|pnLJ COVID-19-|n t^jbLjiriQ maipai6u[b[ t uidpnri2 l|wpuibmfibui-jfib 2P2Lubfi u[pai, fiul| SainaijnLpjnLbbbpfi hai2i|bL|2nfi haiJaip gnLgaipbpu[b[ t uiriuibSfib dnmbgnLif hai2i|h ainbb[nu[ r).pai puir|wr|.pfi£bbpQ (ap^aili1 qpnuai-2P2nL|3jnLbp) b r).paibg u[bpaipbpjai[ bpl|pbbpfi u|ui2mnbuil|uib hiujinuipuipru-pjmbbbpp:
q-puiljuitinLpjuiti uiljtiuiplj: Upmuipfib ainbmpfi 2wpd-pb|aiugfi i|bp|nL&nL-pjaib b liuibfuuiinbuduib hfiiibuifubr|.fipbbpQ [aijb inuipui&nLd rubbb fib^u|bu uul|Lur|.tiJ|iluL|ujIj, aijba|bu t[ dfigwqquijfib b huidu^fuwphuijfib i|>fibwbuwl|wb, uinbinpuijfib l|uiqduil|bpu|nL|3jnLbbbpfi 2P2wbuil|nLd: LbpL|aijaigbbbp dfigwq-quijfib b uiqquijfib JnmbgnLJbbpp:
bu[pna|aiL|aib ^iP-fi hpwu|wpuil|ui& «^Ludui2fiiLuphujjfib uinLLppfi ^LubfyLU-ipburiLdp: flLqqujLjfi dnipbgnidb [ibrj.rj.biJ «bbpphfig-ilhph» dnLpbgnnitibpfi» (Forecasting world trade direct versus "bottom-up" approaches, 2008) W2fuw-innLpjnLbnLii1 uipinuipfib uinbmpfi l|wbfuuimbuduib haiJaip oqmaiqnp6u[b[ bb miuppbp Jrir^bLbbp1 wi|innnbqpbufinb, u|uipq q&uijfib nbqpbufinb b paiqJai-qnp&nb: Cum hbr|j^bwl|bbpf^, LiaipfiaidaiJL|bm l|uibfuuimbuni.dbbpfi haiJaip uii|b|ji aipr).jnLbaiu[bm t ctuiduibuil|uijfib 2wp£>bpni( u[bp[nL6nL|3jnLbp, guib qnp-Snbaijfibp, hbmbaipaip, i|bp2buil|uib bqpail|aignL|3jnLbbbpp L|aimaipu[b[ bb uujrj. Jnr).b[bbpfi aipryriLbpbbpfi hfiduib u[pai:
«UfigLuqqujjfiti LunUippfi LjuibfuLuipburiLiJ: ctLudLubuj^Lujfib 2iup^bpfi dnipb-gmd» (Forecast international trade: A time series approach, 2009) hnr|.i|ui&nLiF hbr|jibwl|bbp 11. '-ib^/i, 11. f)-npn[r}fi U 11. fd-pimiiliiujli ba|winiul|Q wpinwpfib ainbmpfi 2Lup^pb|aaigfi LiaipfiaidaiJlibm l|wbfuwinbuni.db t: ULjrj. fubr).pfi [mS-dwb haiJaip bpaibp oqmaiqnp6b[ bb dwdwbwl|aijfib 2Luppbpfi u[bp[nL6nLpjaib
1 https://www.ecb.europa.eu/pub/pdf/scpwps/ecbwp882.pdf?a2fb2b6f2fea0495378226a016ddc387
2 https://www.econ-jobs.com/research/36056-Forecasting-international-trade-A-time-series-approach. pdf
irhau.2q-u.3hL SLSbuuq-hsnwa-snKb 87
dtipnr|.litipp Li LÎnr|.b[tjbpQ^ [oiq.bpfi pui2fuL|LuônLpjLuli, u[til|Lnnpail|aili aiu[mnntiq.-ptmfiuijfi U ARIMA dnr|.ti|litipp: <tir|jiliLul|litipp tiqpail|aigpti[ till, np Ii2l|luô dn-r).tl[lltipp P LU l|aiL| Lull fill LUpr).jnLllLUL[tlLn till, U l|UlllfllLULntlUL|nrL LUpr).jnLliplltrpll LUjrj. Jnr).ti[litipnL[ 62q-Phm ^ ^nLn hP^LiLulirupjuilip, |nti^LL|bu IiluU lirujlipuili LuprynL-liLuijtïLn bti, nppuili, op[iliLul|, Updmjpfi dfigwqquijfili h|nLÎtiLur|.puudfi (U.U<) l|fi-U LU dj LU l| LUJ [ill LL|LUppbpLul|LulinL[BJLU Jp h p LU LL| LU p LU l| l|n World Economic Outlooks-rud mbr^ qmuiô l|LulifuLumtiunLdlitipp: Upuiuipfili uinLmpfi l|wlifiiLU-LnbunLd, hflJlll|LUÔ d" LU J LU II LU l| LUJ [ill 2LUPptipfl LÎnr|.b[tjbp|n l|pLU, fipLul|LuliLugpti[ till IiluU luj[ h br^lnti lu L)ti bp :
«PLutjq[Lur}b2li [ltirfhiutinLp tjbpdnLÔdujtj huiduip IjLutjfuLULpbudujtj h lu Jim-uiLULfiuiu/vuih dnijbiji npn2riLd» hnr|.L|LuônLd J (Identifying an appropriate forecasting model for total import of Bangladesh, 2011) S. tuuitip gliliLupl|ti[ t Puiliq|Lur|.ti2h plir).hLulinLp litipdnLÔdLuli lil|LupLuqpduili huiduip dnr|.ti|ji npnliduili fulir|.fipp: <br|jiliLul|Q l|Luliq t Lunti[ duiduiliuil|Lujfili 2Lunpt"Ph dnmbgduili i|pLU, duiuliuiL[npLuu|tiu* Puiliq[uir|.ti2h libpdnLÔduili l|uilifiiLULntiudLuli huiduip l|LunnLgtiL t SARIMA, <n|p-riLfili|atipufi U i(til|LnnpLul|Luli WL|LnnritiqptiufiLujfi dnr|.ti|litipp:
« 'VujLjjlULpLut/jl LU nil Ifp LUJ fib h^^b^lt1 djl LfnLdtlbpjl L(bp[nLÔnL[&jnLtj, ijLuti-¡vuiLfibunLd. LpbuLuijLuti Ll tdu/fipfilj hbLpuiqnLpnLpjnLli» (Forecasting the trend analysis of trade balance of Pakistan: A theoretical and empirical investigation, 2016) hnr>L[Luôr)Ld4 hbr|jiliLul|litip U. H-uj^p, L 3mhp U 9-, U[fih L[bpLnLÔbL till 'TlLulifiumLulifi UK d"LudujliLuL|Luj[ili 2UJPPh 2UJpd'plipuigp, L|LunnLgti[ till duidui-IiluL|luj[iIi 2luPPD lil|LupuiqpnrL pp till r|.LUj fill Ll ARIMA dnr).ti[litip, npnlig hfiduili l|pLU l|LULTlLUpb[ bb l|LullfuLULntlUnLdlltip:
ULnUmpfi huidu^fuuiphuijfili l|uiqduil|tipu|nLpjnLliti (U^) hP u|LU2LnnliLU-L|luIi l|LujpnLd hpujLL|LupLuL|b[ t uipmuipfili uinLuipti dfiuirudlltipfl L[bpLUpbpjLU[ l|inpàLUqflLnLul|Lull l|LullfuLULntlUnLlî tipLnLJpfl qLUpqLUgJluIi lifl JDUlllfl UgtlllLU-pni|: ^LullfllLUmtlUnLJlltipp l|LULr)LUpL[tl[ till QULTl LnLUpLUÔLU2P2LulllltIp^^, 20202021 pp. huiduip5: 1-|nLnLupLji|bL t quipquigduili 3 mtiuLul|fi ugbliuip1 u|uimdui-l|Ulll (tiptl LL|Luhu|LullL|jl 2UJPPh Wnl|UI dfiuirudp), |WL|uiLntlULul|Lull U hnntlLntlULU-l|Luli: bl|' [LUl|LULntlULuL|Lull, U' hnntlLntlUaiL|Lull UgtlllLUplltipfl U|LUpLUqLUjnLli 2020 p. l|LulifuLULntiuL[nLJ t Lulil|nLij, fiul| 2021-filT tuil|Luli lu6: 2020 p., pum |LUL|uiLntlULul|Lull UgtlllUipfl, l|UlllfllLULntlUL|nLd t huidu^fuuiphuijflll LUnlimpfl 12.9%-ni| Lulil|nLiJ, fiul| pum hnntILntIULuL|Lull^^, 31.9%-ni| Lulil|nLJ: 2021 p., pum [Lui|LumtiuLuL|Luli ugtiliuipfi, l|LulifuLumbuL[nLJ t huidu^fuuiphuijfili uinLuipfi 21 3%-ni| lu6, fiul| pum hnntïLntïULul|Lullt^, 24.0%-nL[ lu6:
« LiluLjpnLpbLpbuuiLjuib L[bp[nLÔnLfdjnlIi, dnr}b[uiL[npnLd Ll L/Luti/vLULpbunLd» LU2fuuiLnnLpjnLlinLd (U. id-uiLluiryuiti Ll riLpfctibp, 2014)6 <K uipmuipfili huimL|ui-ôfi L[bp[nLÔnLpjnlIiIi [ipLul|LuliLugL[b[ t CC plir).hLulinLp Lupuiuihuillduill, lltipJnLÔ-JluIi Ll LunUmpLujfili hui2L|til|2nfi, LULLjpLulipLujfili lu p m lu h lu li JluIi, libp JnLÔJujli U
3 http://ijtef.org/papers/109-F497.pdf
4 http://hrmars.com/hrmars_papers/Forecasting_the_Trend_Analysis_of_Trade_Balance_of_ Pakistan_A_Theoretical_and_Empirical_Investigation1.pdf
5 https://www.wto.org/english/news_e/pres20_e/pr855_e.htm
6 Sb'u U. rd-uiiluiqjuiti li nip|i2tibp, U~wl|pniiibiiitiuwl|wb uj^bp[nLÔnLfajnlLi, Jnr|.b|wi|npnLJ b L|ujb-fuujmbunLJ/Lri88, «UJpbprj.» Jujmbbuj2ujp, «Sbmbuujq.bm» hpujm., 2014, t"g 34-50:
hu2i|bl|2nfi inuiphl|uiti duduitiuil|uijfiti 2wp£>bpfi hfiduiti и[рш (2007-2012 2r|]auijuil|uiti 2Lupdpli|augfi gruguilif^tibpfi Иш21|шр1|пи[:
«^LujLuuLpujhfi СшЬршщЬцтщшЬ ipbipbuiuLjiub quipquigduiti qhpiuljiu-inL¡ajnLbbhp¡i qtnuhuiLfinLiIß h Ljiubfviuiphunniß» ui2fuuiinnL|3jnLlinLd (U. id-ш-¿/шгцшЬ U riLpfotibp, 2015)7 1|шшшри[Ь[ t СС uipinuipfiti intiinbuuil|uiti qnpôru-titmLpjiuti i[bp[nLÔnLpjnlIj, npfi 2P2LuliLul|nLd Иш21|шр1|и[Ь[ tili uipinuipfiti uinLin-pfi grugfi^libpfi 2Lupdpli|augfi ini[jui|tjbpQ U inhuuil|uipuip l^finhbpp:
<uidui2fuLuphuijfiti puitil|fi (<P) huijuiuinuitijuiti qpuiubtijuil|fi «T-diliupfib
puiphLfinfunLdtibpfi hiury&iuhiupduib ujiuipbh ИЬшрш^прт^гнЬ» ш2|г1ш1пш1ф-
nLr|_tjpÖnnJ^ (2017-2018 |Э|Э.) tibpl|uijuigi|ui& bli « duil|pndfi2Lui|uijpQ, ш1|1|1|ш[-i|nq фпфп^т^пЛ^Ьрр U hbmuiqui quipquigrudtibpQ: 4uiinuipi(uiô t duil|pn-intiinbuuil|uiti hfidtiuil|iuti gruguli^tibpfi 2Lupdpli|augfi U l|uinni.gi|uiÔ£>fi, uijr|. рфи^1 uipinuipfiti huiini|uiôfi gnigmli^libpfi1 uipinuihiutiduiti, tibpdruôduiti, uinLinpuijfiti hui2L|hdliuignpr|.fi, pti|auigfil| Иш2ф i|bp|ruôrupjrutj: SriLjg t inpi|uiô uijr|. griLguli^tibpfi 2Lupdpli|augp 2013-2017 U r|.fiinuipl|i|uiô bti hbmuiqui dfimnLiRjbpQ:
« l|btiinpntiuil|uiti puitil|p (4P) hnuidujuil|uijfili u|uippbpuil|uitinL|3juidp hpuiu|iupuil|i|nq «9-bujófi hiu2iJhipilnL[ajnLbnLií»9 uilir|.piur|.uipâtïL t ^ intiinb-urupjuiti и[рш l|npnliuii|jipnLufi uiqr|.bgnL|3juiti l|uitifuuiinbuduiti hfidtiuifutir|.pfiti: Cum « ЧР-fi' huil|uióqtiuid'uiduijfiti dfignguinrudtibpfi U dfigujqquijfiti пщ1т-puihnupbpfi tii|uiqduiti hbmliulipnu[ qqui|jinphti l|l|p6uiini|f) int¡r|uil|uiti ша|-puitiplibpfi U ôuinuijnLpjnLtilibpfi til|uiinduidp а|шИш1|2шр1|р:
üjua|fiunu[, qpuil|uitinL|3juiti u[bp[nLÔnL|3jnLlip фшитш^ t, np duiduitiuil|ui-jfiti 2Luppbpnu[ uipinuigfili uinLinpfi i|bp|nLÔnL|3juiti U l|uitifuuiinbuduiti db|anr).-tihpp ¿bti q^grud qnpôntiuijfititibpfiti, uii(h|jiir liuipduiduidlibinnLd (dfiti^L 1 inui-pfi) г|.рш1ф ши[Ьф uipr|.jnLtiuii|bin bli:
<binuiqninmpjuiti dbpnrmipuitinLpjmti: « UK L|bPLnL^nL~
pjuiti U l|uitifuuiinbudiuti 1ю|штш1|пи[ oqmuqnpôu[b[ bli « uipinuihuitiduiti, tibpdruôduiti, uinlunpuijfiti hui2L|hdtiuignpr|.fi uiduuil|uiti, bnuidujuil|uijfiti U inui-pbl|uiti ипи[|ш[1|Ьрр: Si|jui|tibpfi huiduip uiqpjrup hti ИшЬгфишдЬ[ « 4P u|ui2-inntiuil|uiti l|uij£>rud hpuiu|uipuil|i|nq i|]i6uil|uiqpnL|3jnLtiQ, duiutiuii|npuiu|bir « ^бшршфЬ hu2i|bl|2nfi i|ji6uil|uiqpnL|3jnLtiQ1J: Oqmuqnpôu[b[ bli uiu|puitipuijfiti uipinuihiutiduiti U tibpdruàduiti uiduuil|uiti ini[jui|tibpQ trading.economics nb-urupufig11 U « i|ji6uil|uiqpuil|uiti l|ndfiinbfi (>-L4)' uduul|uli a|uppbpuL|ulinL-pjmdp Ирша|шрш1|и[п^ upmupfili unUmpu2P2mliunnL|3juli duufili шфш[-libpp1=:
<hinuiqnini|nq duduliul|uhuLnu[uôli plir).qpl|nLd t 2000-2019 |ai|uil|uili-libpp: UfiguLjujgfi qIj in p n Lpj n lIj q a|ujduiliuii|npL|uiô t hbmliju[ huliqudulig-
7 Sh'u U. rd-uiiluqjuti U nip|i2tibp, <ли|шитшЪ|п <mbpmujbmnL[ajmb тЬтЬиш1|шЬ qmpq.mgJmb q.bpml|mjnL[ajnLbbbp|i qbiuhujuinulp b L|mbfummbunLJp, bp., «liJpbpr|.» 11штЬЬш2шр, 4-[nLfu 1, 3-pr|. щшршс).ршф, «Sbmbumq.bm» Иршип., 2015, t"g 26-35:
8 http://documents.worldbank.org/curated/en/581091517210462491/pdf/122979-WP-Armenian-PUBLIC-Armenia-report-add-series.pdf
9 https://www.cba.am/Storage/AM/downloads/parberakan/DVQ/Gnach_I_20.pdf
10 https://www.cba.am/am/SitePages/statexternalsector.aspx
11 https://tradingeconomics.com/armenia/exports, https://tradingeconomics.com/armenia/imports
12 https://armstat.am/en/
libpnu[. r|.puili liuifunpr|.nrL duJuliul|uhmLnu[u6nLJ inlnntjurupjuili U, htiinLui-puip, ht¡inuiqnini|nrL bpUnLj|afi fufiuin uilil|uijnLlinL|3jnLli, ini[jui|litjpfi puiguil|ui-JnL|3JnLtl, r|.puilig futir|ui|3jni.pduill, huiJulr|.pti|jinL|3jLull futíП-hn I-1 ht¡infunphpr|.ui-jfili 1;фЫ|т: Si[jui|litjpp 1|ш[ыша|штршити[Ь[ U liuifuliuil|uili iÍ2Lul|duili till bti-|эшр1|и[Ь[ MS Excel1J 6puiqpuijfili фш|эЬ|эпи[, fiul| hu^uipl|litjpp 1|штшри[Ь[ till R 3.6.0 6puiqpuijfili фш|эЬ|эпи[14:
Urujli hnr|.u[uj6nLJ 1фршги|Ь[ t i|ji6uil|uiqpuil|uili u[bp[nL6nL|3jujli Ll dnr|.tj|ui-i|npduili qnp&fi£>uil|uiqd: <tjinuiqninnL|3juili liu|uiinuil|fig Ь|ЬЬ|П1{' int¡fulifil|ui-L|ixiti i|tjp|nL&nL|ajuili qnp&fiplibpp 1фршги|Ь[ bli uijli hfidliu^npduidp, np duidui-liiul|uijfili 2ШРРЬ ршг\шг).р^1|Ьрр qnp&nliuijfili L|bpa|nu[ bli lil|uipiuqpni.d 2ШР~ pp1 шпшЬд г|.рш1ф uilii|uilitj|ni.. lapblir^p1 tjpl|uipuiduidl|t¡in qnp&nlilihpfi uiqr|.tj-gnLpjnLlip, uЬqnllШJllnL|ЭJnLllp, l|uip6uiduidl|hin, L|br\6 фпфп^ш^ш^ЬЬрр1 u|ui-hiujfili qnp&nlilihpp, a|ujppbpuj2p2ujliujjfili рш^шг^р^р1 inlnnt¡uuil|uili u|uippt¡-рш2р2ш1ф ujqr).bgnL|3jnLlip, fiul| u|uiinuihuil|uili рш^шг^р^р1 JliuiguiS, Иш2ф ^uinlii|ui&, n^ ор^и^шф, a|uiLnuihuil|uili qnp&nlilitipp: Чштшри[Ь[ t СС UK duiduiliuil|uijfili 2ШРРЬ Ц.ЬрLnL&nL|3jnlIi' 2шРс''С^1эш9Ь 2rLI®aiJai'-la|t| ^ pwqfiuui-jfili gruguilif^tipfi dfigngnip, i|uipfiuigfinli i|tjp|nL&nL|3jnLir 2ШРРЬ Lnuiinuilin-r|uil|uilinL|3juili uiuinfi6uilifi U puj2fuiiujli Й1ф duiufili r|.uiinnr|nL|3jnLlilitjp uilit¡|nL huiduip: ULjr). u[bp[nL6nL|3jujli hfiduili и[рш plimpu[b[ t ^K UK duiduiliuil|uijfili 2шррр u|uipuipn|uijfili |эрЫ|гф16 U l|t¡ri& фпфп[иш1|ш1ф lífigngnil lil|uipuiqpt¡|nL Jnr).b[p: UjlirnhbrnU, 1|штшри[Ь[ t utiqnliuijlinL|3juili i|t¡p|nL&ni.|3jnLir huiul|uiliui-|_nl huiduip ubqnliuijfili qnp&nlifi uiqr|.tjgnL|3jnLlili puin t¡nuidujuil|litjpfi17: <Ьтш-qninrupjuili u[bp2nLJ 1фршги|Ь[ t ctuiduiliuil|uijfili 2ШР£>Ь 2шРс''Р^|эшдр liL|uipui-qpnri uidt¡liuiól|nLli qnp&hpkbpfig и1Ы|рл SARIMA (p,d,q)(P,D,Q)[m]1s dnr>t¡Lp, npp libpuinrud t Jh £>ш1ф dnr|.t¡[ uii|innntjqptjufinli, ишИпг\ Jfigfilifi, filiinti-qpduilT qni.duipui& r|.puilig utiqnliuijfili r).puUnpnLJlibpp (uhqnliuijfili uii|innntjq-pbufiui, г).р[1фт, ишИпг\ dfigfilifi ршг\шг).р^): 4uilifuuiint¡uni.dlitjpli fipuil|uiliuig-и[Ь[ hli fili^a|t¡u итшди[ш6 Jnr).b[libpfi h|nduili и[рш (uiqpt¡quigi|ui&), uijliu|t¡u t[ oqmu[b[nu[ duiuliuiinduili Лзрпгфд: Чш1|[иштЬии[Ь[ bli ht¡inuiqnini|nrL t¡pLni.j|afi ршг\шг).р^1|Ьрр:
4bpLnLdnL|3jnLti: Luifu « UK 2ШРС''Р^1ЭШ9Ь 2ШРРЬ T-binbpdlitjiugiliuS i[bp[nL&nLpjпlIi t 1|штшри[Ь[ 2Lupdpli|aujgfi, u[ujpfiujgfiujjfi grugujli^libpfi U ut¡-qnliujjlinLpjujli hujJuj|au[bpfi Jfi2ngnu[: Uju u[bp[nL6nL|3jnLlip mi|b[ t bpUnLj|afi 2ujpdpli|aujgfi a|uihuijfili, L|bmujjfili qliujhujmujLiujlilibp, oqlib[ t u|uiinl|tjpui-gmJ L|UjqiIb[nL lipuj puj2fuiiujli inhupfi, hujJujubnnLpjujli ujumfi6ujlifi U ubqn-liuijfili u[ujppujq6fi Jujufili: UjlirnhbrnU 1|штшри[Ь[ t CC Ul^ 2ШРС''Р^1ЭШ9Ь 2ШР"
13 https://www.microsoft.com/en-us/
14 https://www.r-project.org/
15 https://univer-nn.ru/statistika/pokazateli-dinamiki-temp-rosta-i-prirosta/
16 Shu Кремер Н.Ш., Путко Б.А., Эконометрика: учебник, М„ ЮНИТИ-ДАНА, 2002. Глава 6, tg
133-149:
17 Sb'u Статистическое моделирование и прогнозирование: учеб. пособие, Е.М. Марченко и др., Владим. гос. ун-т им А.Г. и Н.Г. Столетовых. Владимир, Изд-во ВлГУ, 2018, t"g 45-58, http://e. Iib.vlsu.ru/bitst ream/123456789/7365/1/01751, pdf:
1H Sb'u Cryer J.D., Chan K.S., Time Series Analysis, Springer, Texts in Statistics, 2008 (Second Edition, ISBN-978-0-387-759558-6), Chapter 9, 10, tg 191-245, https://iink.springer.com/content/pdf/10.1007%2F978-0-387-75959-3.pdf:
pfi uinnfuuiuinfil| i[bp[nLÔnLpjnLlj^ dnrç.b|uii|nptï|nil duiduitiuil|uijfltl 2ШПРЬ Рш~ г\шг).р^1|Ьрр:
о
2000 200: 2002 2003 2004 2005 2006 2007 2003 2000 20:0 20: : 20:2 20:3 20!-! 20: 5 201 ó 20:7 20:г 2019
-500
-:ооо
-1500 -2000 -2500 -3000 -3500
C)-6uiu|uiinl]bp 1. СС LLC hui2ilbifbuignpr).[i ¿uipdpbpuigi] 2000-2019 pp. (iî[b ULTb г1П[шП)п
Я-0шо|шш1|Ьр 1-fig bpLrud t, np hhinuiqnini|nrL dudutjul|uihuiini|uiônLd <K UK a|uil|uiunLpr|.Q r).puUnpb[ t шб|п dfiinrud: Cuippfi uiriuii|b|uiqnLjti uipdbpp qpuligu[b[ t 2002 p.' -459.46 d[li Ш-ГЬ r>n|uip, lii[uiquiqnLjV 2008 p.' -3127.49 J[li U.U"L г).п[шр, npp hbmuqnLnu[nq dudutjul|uihuiini|uiônLd « UK u|uil|uiunLpr|.fi umuii|tí|uiqnLjti puiguiuuil|uiti uipdbpti f 2008-2011 uuil|uiti dqtiuiduidfi hbmliulipnu[: UfigfilinLd hbmuqnLnu[nq duiduitiuil|uihuiin-i|uiôni.d « UK Иш21|ЬЛ|шдпрг).р bqb[ t -1537.90 ií[ti ULU~L г).п[шр duil|iupr|.ui-Ljnllî, fiul| dbr|.fiuitiuiti huii|uiuiup t -1659.25 d[ti ULUTL r|.n|uipfi: Uinuigi|nLd t, np r).fiLnupl|u[nq dudutjul|uihuiini|uiônLd « UK u|uil|uiunLpr|.fi 2ШР£>Ь Lupdbp-lihpfi 50%-p guiôp t bqb[ -1659.25 ULTb rpiLuipfig: -Рш1ф np Jhsh^D dbô t db-гфшЪифд, ша|ш li2Luliuil|ni.d t, np 2Luppli rutifi uitihuiduiubn pu^furud: Cuip-pfi uii|b|ji dbô updbplibpp qqi-u|ji uiqr|.bgnL|3jnLti bli mlibgb[ 2ШР£>Ь 2ШРС''Р^-|aiugfi ptir|.huitinLp a|uiinl|hpfi и[рш:
UTfigfili huii|b|ui6fi mbJo|p huii|uiuuip t 7.1%-|n, li2LU^iai'-lnL^ t' r).fiLnupl|u[nq dudutjml|uihuiini|uiônLd JfigfilimJ uidbti inuipfi « UK u|uil|uiunLpr|.ti шбЬ[ t 7.1%-пф UTfigfili ршдшр0ш1| Иши[Ь[шбр l|uiqdni.d t -75.77, li2LU^iai'-lnL^ t' dfigh" tirud uidbti inuipfi UK u|uil|uiunLpr|.ti uii|b|uitinLd t 75.77 d[ti U.UTL г).п[шрпи[: Ршдшр0ш1| huii|b|ui6fi inbdu|fi hfiduiti и[рш l|uitifuuiinbuni.dtibpQ hbinLjui[ti bli.
« UK (2020)= -2047.15 ií[li UUL гу^шр*,
« UK (2021)= -2122.92 úyh UUL r>nLuip
2019 2018-fi huidbduiin, « uinLinpuijfiti hui2L|hl|2nfi puiguiuuil|uiti hui2L|hdtiuignpr|.ti шбЬ[ t 24.25 d[ti UUL г).п[шрпи[ l|uid 1.3%-пф Uriuii|b|uiqnLjti Иши[Ь[шбр bqb[ t 2015 p.' 887.09 d[ti U.U"L г).п[шр, llu[шqшqnLJllp, 2008 p.1 -1220.64 J[li UUL г).п[шр: Utôfi inbdu|p puipâp t, fillip i|l|uijnLd t CC UK pui-guiuuil|uiti funpugJuli upuqugJuli duiufili:
2019 2000-h hmJbJum, « UK a|uil|uiunLpr>ti шбЬ[ t 1439.60 d[li UUL г>п[шрпи[ 1|ш J 270.7%-пф
19 https://www.cba.am/am/SitePages/statexternalsector.aspx
¿,J * ИпшЪд C0VID-19-|n 1;фЫ|т|1, Ь[эЬ 2шПЕЬ шфш!. JfiinnLdQ и^шИи^шЬфр:
Lduiti ÖUnu[ « UK tinuidujuiL|uij|nti duiduitiuiL|uijfiti 2ШПРЬ hwduip Liu huJ2i|ujpL|u[b[ bb 2Lupdpli|aujgfi puiqfiuuijfiti U 2Tpi-LijuiL|uiti grugujli^tibpp: ULju-o|bu, 2019 p. 4-prj. bnuidujuiL|ni.d, 2019 p. 3-pr). t¡nuidujuiL|fi huidtiduiin, « uinLinpuijfiti huJ2i|bL|2nfi puiguiuuiL|uiti hui2L[tidtiuignpr|.ti шбЬ[ t 499.03 d[ti ULUL г).п[шрпи[ 1|шй 123.1%-пф ULriiui|ti|uiqnLjti Иши[Ь[шбр Ьг|Ь[ t 2009 p. 1-fiti bniudujiuliruiT 495.22 d[ti ULUTL г).п[шр, lji|iuqiuq.nLjlj|V 2019 p. 4-pr). briuidujui-L|riLif -499.03 J[li ULUTL г).п[шр: UL6fi uii(ti|uigduiti mbJa|p, fiti^u|bu inuiptiL|uiti 2uipd"ptipuigfi 2ШР£>Ь T-bu^rud, (wónrj) t:
2019 p. 4-pr). ЬпшJujml|riLLÏ, 2000 p. 1-fiti hnuidujuiL|fi huidhduiin, « UL< u|uiL|uiuni.pr|.ti ши[Ь[шдЬ[ t 770.86 d[ti ULUTL г).п[шрпи[ 1|шй 577.5%-пф
UTfigfilirnJ « UL< t¡nuidujuiL|uijfiti duiduitiuiL|uijfiti 2ШР£>Р Ьг\Ь[ t -384,47 d|ti ULUTL г}п[шр|п duiL|uipr|.uiL|ni.d: UTfigfili t¡nuidujuiL|uijfiti huii|ti|ui6fi mbJojp hui-и[шишр t 2.5%-fi, lj2Ujljiul|nLd t' П.|птшр1|и[пг\ dudutjuiL|uihuiini|uiôni.d uidbti bnuidujiuL| « UL< u|uiL|uiuni.pr|.ti шбЬ[ t dfigfihrud 2.5%-nu[: Ufigfili bnuiiîujui-L|uijfiti puiguipâuiL| Иши[Ь[шбр L|uiqdni.d t -9.76, t^w^wLirud t' Ludhli bnuid-ujuiL| UL< u|uiL|uiuni.pr|.ti uii(ti|uitini.d t dfigfihrud 9.76 d[ti ULUTL г).п[шрпи[: üuipd[itipuig|i 2uipg|i i[ujp|iuig|inti i[bpLiu6iu|3jiutj
« UL< duiJujIiuiL|uijfill 2ШР13Ь l[lupLug|nnti i|hp|nLÔnLpjuiti huiduip hui2-u[ujpL|u[b[ tili i|uipfiuigfiuijfi puiguipâuiL| nl huipuipbpuiL|uiti grugujli^tibpp U pui2fuduiti griLgujli^tibpp:
>-Luipfiuigfiuijfi ршфр huii|uiuuip t 2668.02-fi, li2LU^LU'-lnL^ t' 2шТфЬ tu|uiquiqnLjti U uiriuii|tï|uiqni.jti uipdbptitipfi dfigU uinL|ui t 2668.02 d|ti ULUTL r|.n|uipfi
Ufigfili qôuijfiti 2br\nLdp huii|uiuuip t 714.61-fi, li2uitiuiL|ni.d f 2ШРРЬ jrupuipuitiyrup uipdbp djruufig тшррЬрфш! t dfigfilimd 714.61 d[ti ULUTL г).п[шрпи[:
UT|n2fili puinuiL|ni.uuijfili 2br\nLdp huii|uiuuip t 786.27-|n, t^w^wLirud t' 2uippfi jrupuipuitiyrup uipdbp dfigfili -1537.90 uipdbpfig тшррЬрфш! t df^h^nui 786.27-пф
4mpfiujghujjh qnp&ujL|hgp L|uiqdnLd t 51.13%, qmbu[nLd t [30%;70%] dfiguiLiuijprud, li2LU^LU'-lnL^ t' n^ huiduiuhn 2ШРР t, L|uipfiuigfiuiti ^ui-фии|пр t:
<uipuipt¡puiL|uiti qôuijfiti 2br\nLdp huii|uiuuip t -46.47%-fi, li2LU^LU'-lnL^ f « UL< 2LUPßh duiL|uipr|.uiL|titipti rutibli dfigfilirnd -46.47%-nu[ puiguip-ÖuiL| 2br\nLd dfigfilifig:
Ougfi[juigfiuijfi qnpôuiL|figp L|UjqdnLd t -173.48%, li2LU^LU'-lnL^ t' 2ШПРЬ ôujjpujL|bLnujjfili ujpdbplibpp dfigfilifig 2Ьгц|ш6 bli -173.48%-пф -Ri[ujpui[i[ 1-p Иши[шишр t -2194.82-fi, li2LU^LU'-lnL^ t' hmJmfuiipnLpjmlj dfili^U 25%-li qIjr(.nlIjnlü bli -2194.82 d[li ULUL r).n[ujpfig дшбр uipcttig-libp: -Ri[ujpui[i[ 3-p Иши[шишр t -713.89-|n, li2UjliujL|nLd 2ШР^Ь 75%-ti pliri.nLbnLd t -713.89 d[li ULUTL r|.n|uipfig дшбр ujpdbplibp: 8 ULufidtiinpfiuili Иши[шишр t -3.99-fi, li2LU^jai'-lnL^ t' mliblip ÖujfuujL|nrLd-jujb ujufidbmpfiuj: ULufidtiinpfiuijfi dfigfili pujnujL|nLuujjfili ufuuj[p L|mq-drud t 0.47: bpb r).pujlig huipuiphpnLpjnLlip фпрр t Зфд, ujufidbm-pfiiuli n^ tujLiujli t: UTbp r).ba|pnLd li2LlLU^ hujpujpbpnLpjnLlip Иши[шишр t 8.46-fi, НЬтишрир1 ujufidbmpfiujli I;ujL|ujIi t: ^[îpunlifi qnpôujLjfigp
l|uiqdnLií t 0.15, ti2Lutiuil|nLii t 2LUPßh l|btiinpntiuil|uiti duiurud uiufi-dbinpfiui 1|ш:
tgugbup Иши[шишр t -1 2-fi, фгфр t 0-fig, ti2Lutiuil|nLii t' rutibtip linp-Ju[ pu^furudfig uii|b|ji huip|auiôuijp pu^furud: <ш2ф unlib[nu[ 2ШРСФ 2шПс''С^1эш9Ь ^ |-|.шРЬш9Ьп^ L^tjp^пL&nLfajriLtitJtipq1 l|unnLgu[b[ t CC UK 2ШПС''С^1ЭШ9Ь 2ШР£Ш hbmliju[ Jnr).b[p.
UCt = c1 + c2x t + c3x t2 + c4d01t + £t, (1)
npinbq
UK-li шшрЫ|ш1| « UCli t,
сi, C'¿, Сз, с4 -р* Jnr).b[fi uitihuijin u|uipuidbinpbpp, s -p1 Jnr).b[fi ufuuiLp, t -IT |эрЫ|Г).р,
ciOl-p1 l|bqô фпфп[иш1|ш1|р, npti uipinuihuijinrud t ф^ш^иш1|ш1| óqtiui-duidfi uqr).bgnL|3jnLlip 2008
Unr).b[fi qtiuihuiinduiti шргцги1ф1|Ьрр hbinlLjui[ti ЫГ
UQ = 4736433 - 47067 x t + 12 x t2 - 1414dÔ1t: (2)
Unr).b[fi npuil|fi Li ptiinpi|uiô qnpôntitibpfi li2Lutiuil|ui|jinL|3juiti gruguitif^lih-pp tibpl|uijuigi|uiô bli uirunLuuil|libp 1-rud U 2-rud:
liruriLumlj 1
LTnij.b¿fi npuilfli gmguibfcbbp
1bmbpJ|ibmg|imj|i q.npôujl||ig 0.73
62q.pmi|uJÔ r|.bmbpJ|ibmg|imj|i q.npôml||ig 0.68
bh2bph гфил. 14.32
3>h2bph ^2. 0.00
LnpJrn[ рш2[т|ш0 RS ^шфшЬ|л2 3.33
1]ш1ршрф[ f R3.6.0 dpiuqpiujjib фшрЬрп^:
UrunLuuilj 2
If пг}Ьф nbqpbunpbbpfi Ь2шЬш1/шфп^тЬ
Фпфп^ии^шЬ Q-npóiuljfig Тцр ip. P-value
Cuiuinuiinniti 47366432.86 3.29 0.0046
Гд-pbtii} -47066.67 -3.29 0.0046
fïpbtin2 11.69 3.28 0.0047
ЦЬцд -1414.39 -2.92 0.0101
1^шц1шрф1 f R3.6.0 ópuiqpuijfiti фшрЬрпь[:
li.runluuil|tibp 1-hg I-1 2-fig bpLrud t, np Jnr).b[p 72.86%-ni[ puiguiinprud t uiprurulipuijfiti фпфп[иш1|ш1ф i|uipfiuigfiuiti: íbf^ph ^шфш1ф2П1( uinruqiiuiti aiprynLliplibpp фшитгш! bli, np Jnr).b[li ш Jpnr^nLpjai Jp ti2Lutiuil|ui|ji Ь Uq|nL-uail| 2-rud pbpi|uiö hti dnr|.b|ji uinuitiöfiti qnp&ntitibpfi li2Lutiuil|ui|jinL|3juiti gru-giutif^lihpp: hti^u|bu bpLrud t, pn[np qnpôntitibpp li2Lutiuil|ui|ji bli 99% ti2ui-liail|ai[finL|3jaili Juil|uipr|.uil|nLd: Unr|.h|ji hhinhpnul|hr|.aiuinfil|nL|3juili duiufiti hfi-a|n|abqp umnLqi|b[ t 2 рЬишп^1 Uu|fipdbtifi nuitiquijfiti l|nnb[juigfiuijfi qnpôai-L|figlibpni| Il 9-n[$pbr|.--Pi(uitiinfi |эЬитпи[: 2 |abuinbpli t[ i|l|aijb[ bli Jnr).b[nLJ hb-
inbpnul|br|.uiuinfil|nL|3juiti puiguil|uijnL|3juiti duiufiti: Unr|.b|ji dtiuignpr|.fi linpdu[ pm2fui|uônL|3juli duiufiti hfiu|n|abqp Ишишшши[Ь[ t RS ^шфш1ф2Ь Jfi2ngnu[:
Uinuigi|nLd t ptiinpijuiô dnr|.b[ti шг).Ы|и[шш t, npfi hfiduiti и[рш 1|шшшри[Ь[ t l|uitifuuiinbuni.d: Cum dnr|.h|ji.
« UK(2020) = -2797 d^ UUL г>п[шр (uinuilig COVID-19-h фЫцгф):
о -200 --Ю0 -600 -800 -1000 -1200
4-öuiu|uiinljbp 2 « LLC bnuidujuiljuijlib ¿lupdpbpmgp 2000-2019 pp.'1
Я-0ша|шш1|Ьр 2-rnd libplirnjugilmö' « UK tmuidujuil|uijfiti 2wpdpti|aui-gfig bplirnd t, np 2wpgli rutifi ubqntiuijtinLpjnLti: UbqntiuijtinLpjuiti ui|ji£>fi pui-tiiul|uil|uiti qtiuihuiinuil|uiti[] uinuitiui|nL huiduip Иш21|шр1|и[Ь[ bti ubqntiuijlinL-pjuiti huidui|ai|bpli puin bnuidujuil|tibpfi (qôuiu|uiinl|bp 3):
-Л 1.295
1.2 .......................................
Q1
4-&uiu|uiinljbp 3 CC LLC ubqnbuijbnipjuib huirfuifailbp
Я-0шо|шт1|Ьр Зфд bplimd t, np 1-fiti, 2-prj. U 3-pr). bnuidujuil|tibpni.d ub-qntiuijtinLpjuiti huidui|afii(p фпрр t t ubqntiuijtinLpjuiti qnp-
ôntiti uijr|. bnuidujuil|tibpfi pti|auig£>ni.d uinuigLugtirud t 2ШПС''С^1ЭШ9Ь 2ШРРЬ duil|uipr|.uil|tibpfi lii|uiqnLd: hul| 4-prj. bnuidujuil|ni.d dbô t h^iD
l|nLd t, np ubqntiuijtinLpjnLtip inuitirud t 2ШРРЬ duil|uipr|.uil|tibpfi uiöfili: <Ш2~ 1[шр1|Ыф uipinuihuitiduiti U libpdruôduiti ubqntiuijtinLpjuiti huidui|ai|bpp L гф-
21 https://www.cba.am/am/SitePages/statexternalsector.aspx ¿¿ <Ш2ь|шр1|[1 1|штшрЬ[ t" ИЬгфЪш^р:
in hi p L| i[n dwdwljwl|uihuiini|ui&ni.d « uiriLinpu^pgwliuinnLpjuili dbg r|.puilig mtiuail|aipaip l^hntibpp (q&uiu|uiinl|bp 4, airynLuailj 3):
0 4
01
UpLnUjhuj'ULSLU'U U tjC n'(J UJj'U. 0 034 Jni^LSLu'tj lihcn'uLLIj'tl. 0.?44
^-duiujuiinljbp 4. « luptpuihuibifuib U bbpifm&ifuib ubqnbuijbmpjuib hiuiSiupilbp23
ULrijnLUUll) 3
« lupipiuhiuiiJiuii U bbpilni&iluib ipbuiulfiupiup fcfrnbbpQ umUtppui2P2wbuinnip]uib ifb£
bniuiiujiulf Upipuihiubniif ipbu. If2hn' (%) bbpifnidnitf ipbu. If2hn' (%)
I 36.5 63.5
II 37.5 62.5
III 38.7 61.3
IV 35.4 64.6
1-fili II 2-prj. bnuidujuil|libpni.d uipinuihuiliduili U libpdru&duili ubqnliuijlinL-pjuili haidui|ai|bpp dnin till, 3-prj. bnuidujuil|ni.d uipinuihuiliduili ribujgrud db& t 4-pr).fig, fiul| libpdru&duili hail|ainaiL|p, puilifi np libpdru&duili inbuui-
L|aipaip t^h^ti uii|b|ji db6 I;: <bmUaipaip, « Ul< ubqnliuijlinLpjnLlip 3-pr). bn-aidujail|nLd uii|b|ji 2win lidiuliuil|bL t libpdru&duili ubqnliuijlinLpjuilip: « IK ilbpinidnipjniiic SARI MA - ifnr>b|ni(
U.i|b|ji 62qpfiLn aipryrnliplibp U ainaiu[b[ plir|.huilipuil|uili a|aiml|bp uinw-liai[nL lia|aimail|nu[ SARIMA dnr).b[p L|fipainu[b[ t n^ pb « UK duiduiliuil|uijfili 2Luppfi i|pai, lujl uujrj. gruguilif^p l|uiqdnrL uipinuihuiliduili U libpdru&duili diu-diuliuil|uijfili 2wppbpfi u[pai uinuiliSfili-iuniuliSfili, fiul| u[bp2fili £>uij|ni[ uinuig-u[ai6 l|iulifuiuinbunLdiujfili uipdbplibpli rur|r|uil|fi hailiu[b[ bli fipuipfig1 uujrj. l|bpu| umailiai[nu[« UK l|uilifuuunbui|nrL uipdbpp:
UpwuihuitiiHii: ULpmaihailidaili 2wpdpli|auigfi 2wppfi uinuigfinliuiprupjuili u[bp[nL6nL|3jaidp plimpu[b[ t I PLurlLurl-Phih ^wpqp: ULi|mn'-lnri':iUai9hn^ ^ ^wu-liuil|fi uu|innl|nnb[juigfinli ^ruliligfiuilibpfi qpwi|>fil|libpfi hfiduili u[pai plimpu[b[ bli huiduiu|uunuiufuuili AR, ubqnliuijfili AR li MA puir|uir|.pfi£libpp: hul| uu|b|ji 62qphm dninwpl|daili uiuinfifiuilip npn2b[m haidaip hfidp bli 6ainaijb[ lll|uifi-l|bfi (AIC), Paijbujaili (BIC) li dnmaipl|daili npail|p grujg Lnu[nr\ uijl ¿uii|iuilifi2lib-pp (dnmaipl|daili dfigfili ufuai[, dfigfili puiguip5uil| ufuai[, dfigfili puiguip5uil| rnn-
02 03 04
0.96 1.13? 1.059
ili. 1.056 1144
- <W2i|wpl|[i L|wmwpb[ t" hbryibwlip:
24 <W2i|wpl|[i l|wmwpb[t" hbr\|nbujL|p:
25 Sb'u CryerJ. D., Chan K.S., Time Series Analysis, Springer, Texts In Statistics, 2008 (Second Edition, ISBN-978-0-387-759558-6), tg 503, Chapter 9,10, tg 191-245, https://link.sprlnger.com/content/pdf/10.1007%2F978-0-387-75959-3.pdf:
l|nuaij|nli ufuai[ II luj^Ij): UprynLlignLJ, « wpinwhwtiduiti tinuidujuil|uijfiti dai-diutiuil|uijfiti 2wpph liliwpwqpdwti haiJaip ptiinpi[tjL t SARIMA(1,0,0)(1,1,2)[4] r).pfi^)Lnnu[ Jnr).ti[p: Unr).ti[fi q.tiwhuiinduiti uiprurutiptitipp II npuil|fi gnLgaili^titr-pp titipl|uijuigi|w& bli airuriLuail| 4-rud:
ULrijnLUUll) 4
CC lupipiuhiuiiJiuii 2wpd[]lipiugli ¿wpph SARIMA iini}b[nil qiiiuhiuipJiuii
uipt}jniliglibpp
Series: U|Hiiwhwbni.J
ARIMA (1,0,0) (1,1,2) [4] with drift Coefficients:
ar1 sari smal sma2 drift
0.8638 0.8470 -1.6687 0.8470 20.0913 s.e. 0.0620 0.0896 0.1899 0.2168 9.0513
sigmaA2 estimated as 2404: log likelihood=-405.61
AIC=823.22 AICc=824.43 BIC=837.2_
Training set error measures:
_ME RMSE MPE MAPE MASE_
Training set 1.87 46.19 -1.38 7.44 0.43
_ACF1_
Training set -0.095 z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
ar1 0.8638 0.0620 13.9323 < 2.2e-16 ***
sar1 0.8470 0.0896 9.4484 < 2.2e-16 ***
sma1 -1.6687 0.1899 -8.7895 < 2.2e-16 ***
sma2 0.8470 0.2168 3.9063 9.372e-05 ***
drift 20.0913 9.0513_2.2197 0.02644 *_
Signif. codes: 0 0.001 0.01 '*' 0.05 '.' 0.1 ' ' 1
Box-Pierce test
X-squared = 3.5914, df = 4, p-value = 0.4641
Box-Pierce test
X-squared = 10.913, df = 20, p-value = 0.9484
Box-Pierce test
X-squared = 0.72285, df = 1, p-value = 0.3952
<uv?i/uv/7//£ Ljujipujpilh[ £ R 3.6.0 dpuiqpuijlib i/juv/a/i/ant/,
arl -p Lunuj2fiti ljujpq[i Luilipnnbqpbufinb qnpduul^lig, sarl-p' ubqnbuijfib Lunuipfib L/Lupqfi imlipnnbqpbulinb qnpduul^lig, smal-p' ubqnbuijfib uuthnq dfe/ib/i uinuJ2lib L/uipqfi qnpduil^fig, sma2-p' ubqnbuijfib uuihnq dfe/ib/i bpL/pnpri L/uipqfi qnpduilffig, drift-p' ripfttyip feuipdpbpuigfi 2LUP^h huiuipuiipnLbji qnpduiL/[ig):
UqjIHUUll] 5
« bbpifmâifiub ¿uipdpbpuigfi ¿uipgfi SARIMA i/nrçfc/ni/ qbuihuitpifuib
uiprymbgbbpi7
Series: "bbpJnLÔnLJ
ARIMA (1,0,1)(0,1,2)[4| with drift
Coefficients:
ar1 mal smal sma2 drift
0.6786 0.4753 -0.2696 -0.2097 21.6238
s.e. 0.1061 0.1179 0.1300 0.1177 6.8163
sigmaA2 estimated as 9658: log likelihood = -455.01 AIC=922.02 AICc=923.24 BIC=936.01
Training set error measures:
_ME RMSE_MPE MAPE MASE
Training set -0.0796 92.5800 -1.1101 6.9761 0.4266
_ACF1_
Training set 0.0258807
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
ar1 0.67864 0.10613 6.3945 1.611e-10 ***
ma1 0.47527 0.11791 4.0308 5.558e-05 ***
sma1 -0.26965 0.12999 -2.0743 0.038049 *
sma2 -0.20968 0.11774 -1.7809 0.054929
drift 21.62380 6.81627 3.1724 0.001512 **
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Box-Pierce test X-squared = 0.053585, df = 1, p-value = 0.8169_
Box-Pierce test X-squared = 2.4618, df = 5, p-value = 0.7822
Box-Pierce test X-squared = 3.3882, df = 10, p-value = 0.9708
Box-Pierce test X-squared = 4.0279, df = 15, p-value = 0.9976
<£lu2l[lupLi[7 LjLULpLupilb[ £" R 3.6.0 ôpuiqpuij[ib Lfiui[ab[ani[, npipbq '
arl-p uinuipfib L/uipqfi uiL[ipnnbqpbulinb qnpôuiL/fig,
mal-p uLuhnri dfefibfi uinuipfib L/uipqfi qnpduil^fig,
smal-p' ubqnbuijfib uuihnq dfe/ib/i uinui2fib L/uipqfi qnpduil^fig,
sma2-p' ubqnbuijfib uuihnri dfe/ib/i bpLipnpr} L/uipqfi qnpduilffig,
drift-p' ijpfi^iip feuipdpbpuigfi 2LUpj2fi huiuipuiipnLbji qnpôuiLj[ig):
Unr).b[fi qtiuihuiinduiti mprynLtiptibpQ фшитгш! bti, np dnr|.h|ji dninuipl|-duiti прш1|р puipöp t, guibfi np df^fiti, tihsh^1 Lrml|nuuijfiti u[uui|tihpp (ME, MPE) фпрр bti 5%-fig, fiul| Jfigfili puiguipÖuil| innl|nuuijfiti, dfigfili ршдшр0ш1| £>uinuil|nLuuijfiti ufuui[tibpp (МАРЕ, MASE)1 10%-|ig: Pn[np qnpôntitibpp li2uiliui-l|ui|f) bli 99% hui(uitiuil|uitinL|3juidp: Ufi guibfi u|uiinuihuil|uiti |uiqbpni( uipi|uiô Рпри-'т1 |при|п |эЬишр gnLjg t шшфи, np dnr|.h|ji dtiuignpr|.uijfiti ршг\шг).р^р u|uiinuihuil|uiti pui2funLií ги1ф: hti^u|bu hpUrud t, dnr|.b|ji npuil|p puipöp t, uij-ufitiptf htiuipuii|np t П-Пш hfiduiti и[рш l|uitifuuiinbunLiRjbp 1|шшшрЬ[.
4
UpmшhшünLd (2020) = ^ Ьпшйщш^ = 1282.04 + 1337.42 + 1622.67 + 1468.55 =
= 5710.28: (3)
Lduiti Ölinu[ libpdnLÔduiti duiduitiuil|uijfiti 2ШРРЬ til|iupiuq.pdiutj huiduip plimpu[bL t SARIMA(1,0,1)(0,1,2)[4] r>p^inni[ dnr>t¡Lp: 1Гпг>Ьф qliuihuiindiuli шр-rynLliplibpp Li npuil|fi gnLguitjfi2tihpp libpl|uijuigi|uiô bli uirunLuuil| 5-rud:
Unr).b[fi qtiuihuiinduiti uiprurutiptibpp фшuLnnLJ bli, np dnr|.h|ji dninuipl|-duiti прш1|р puipöp t, np Jfigfili, dfigfili innl|nuuijfiti ufuui|tibpp фпрр tili
5%фд, fiul| Jfigfili ршдшр0ш1| innl|nuuijfiti, dfigfili ршдшр0ш1| puiпшL|nluuijfill и^ш^Ьрр1 10%фд: Рп|пр qnpôntitibpp 1|2Ш^Ш'-1Ш1Ь ^ti 95% huii|uitiuil|uilinL-pjuidp: Ufi рш1ф u|uiinuihuil|uiti [aiq.bpni| uipi|uiô Pnpu-'Tlfipufi |эЬитр gnLjg t ипшфи, np Jnr).b[fi dtiuignpr|.uijfiti ршг\шг).р^1| пЛф u|uiinuihuil|uiti pui2furud: Uiniugi|nLd t, np Jnr).b[|i npail|p puipöp t Ll 1|шрпг[ blip г).рш hfiduiti и[рш l|uiti-fuuiinbunLdtibp 1|штшрЬ[.
4
"ühptfnLÖnLtf (2020) = ^ ЬпшйщшЦ; = 1797. 94 + 1870.83 + 2167.87 + 2430.22 =
= 8266.87:
UC (2020) = UpmшhшünLtf (2020) - "bhptfnLÖnLtf (2020)
2556.59:
(4)
(5)
•Huitifuuiinbunuí: <binuiqninnL|3juiti hfiduiti и[рш r^mpu t pbpi|b[ uipinui-gfili ainUmpnLJ uiu|puiti£>tibpfi II ôuinuijnLpjnLtitibpfi uinLinpfi l|uitifuuiinbui|nrL hшpшpЬpшL|gnL|ЭJnLllp, tdu|fipfil| тЬиш1|шршр l|2hntibpp puin bnuidujuil|tib-pfi, uipinuihuitiduiti II tibpdru&duiti haiJaip uinuitiöfiti-uinuitiöfiti (uirunLuuil| 6): Tpailig hfiduiti и[рш hai2i|iiipl|i|b[ tili uiu|puiti£>tibpfi II ôuinuijnLpjnLtitibpfi шр-inuihuitiduiti II tibpdru&duiti l|uitifuuiinbui|nrL aipdbplibpp puin bnuidujuil|tibpfi (airunLuail| 7): U.u|puiti£>uijfiti hai2i|bl|2nfi huiduip шп1|ш t lunaigfili hnaidujail|fi hujJaip huidbduiinduiti фшитшд[1 paiqai: <uidbduiinduiti uiprurutiprud aipöai-tiuiqpi|ui& uitil|nLdp C0VID-19-fi 1;фЫ|т1| t: ULjti maipaiôi|b[ t uidpnri2 l|uipuiti-mfiliaijfili a|aipaia|nLpr).fi daidailiail|ai2P2iiilifi и[рш: ÜainaijnLpjnLlilibpfi г).Ьа|-pmd, airiai2linpr|.i|h|ni( bpl|plibpfi a|ai2Lnnliail|aili haijLnaipaipnL|3jnLlilibpni|, шри[Ь[ bli haidaia|aimaiufuaili bli|aair).pnL|3jnLlilibp II r).pailig hfidaili и[рш hai2-i|aipl|i|b[ t, |эЬ, C0VID-19-fi uшhdшllшфшL|nLdllЬpnl| a|aijdailiaii|npi|aiô, fili^-gaili L|L|npglifi ôainaijnLpjnLlilibpfi ainUmnLpp (1цэЬрш1|штшрф l|ailifuaiinhu-u[nq linpdai[ a|aijiîaililibpfi aipdbpp):
[=1
U.qjni.uuil{ 6
« uiuipiubjjbbpïi U âumutjnipjnibbbpft lunlupp/i l;iSui¡ip¡il] fofrnbbp 2020 р.2ь
bnuiiîujuil/ Uuipuihg ipbu. l]2hn tJurnuijnipjnih ipbu. l]2hn
ШПШШШШШЯ
1 0.56 0.68 0.44 0.32
2 0.56 0.68 0.44 0.32
3 0.49 0.61 0.51 0.39
4 0.57 0.67 0.43 0.33
UrynLumlj 7
CC uiujpuitigbbpfi U óiuniujnipjmbbbpli uinbipp¡i gnigmbfabbp, 2020 p.
bnuiiSujuili ИщршЬд (d[b Ulfb цщшр) Ütuntujnipjnib (d[b Ulfb цщшр)
UpipiuhiubmtS bbnilniàniil UpipiuhiubmtS bbpiSmômiS
1 724.22 1222.60 435.89 467.46
2 754.44 1272.16 187.24 187.08
3 798.52 1322.40 210.95 216.8
4 837.37 1628.25 234.97 243.02
Otlf}UllIktlQ 3114.55 5445.4 l069.05 lll4.36
<ui2i|iupl|i|uiô gruguibf^bbpfi U dnr|.h|tihpfi hfiduiti и[рш l|uitifuuiinhuni.d-tihpp lihpl|uijuigi|uiô hti шгипшш1| 8-nLií:
UrynLumlj 8
« U< IpubfvuiipbumiSbbp 2020 p
Ifbpnij «U< «U<
(шпшЬд COVID-19-h) (COVID-19-h №bbipni)
РшдшрЙш1| Ишь[Ь[шб|1 mbJujnil -2047.15 -2333.7
ß-pbbr|.mj|ib Jnr|.b[nL[ -2797.00 -3188.58
SARIMA Jnr>b[nLl -2556.59 -2915.06
Ujua|fiunu[, u|uipq t r^unlirnJ, np huiduii|uipuil|fi 1;фЫ|1пр « UK-fi и[рш 2mp2 14%-nu[ a|uil|uiunLpr|.fi uii|h|uignLdti t, fiul|, plir^hulirup uinduidp, 2019 p. huidhduiin, « UK u|uil|uiunLpr|.p ршдшр0ш1| huii|h|ui6fi hfiduiti и[рш l|uiti[uui-inhudiuti r).ba|pnLJ l|uii|h|uitiui 18.3%-nu[, |aphtir|.uijfiti dnr|.h|ji hfiduiti ilpuT 61,7%-nu[, hul| SARIMA dnr>h[|i hfiduili и[ршл 48%-nu[:
bqpuil|uignLpjmtitihp Ц.2К|штш^фП1^ £>btiuipl|i|hgfiti « UK 2ШПС''С^1ЭШ" gfi u[bp[nLÔnL|3juli, Jnr|.h|uii|npdLuli U l|uitifuuiinhuduiti huipghpp: Сшрс^рЬрш-gfi gruguibf^tibpnil u[bp[nLÔnL|3jnLlip gnyg ini|hg, np pb' inuiphl|uiti, ph' hnuid-ujuil|iujfili 1|три[ш0рпи[ « UK u|uil|uiunLpr|.p, hhinuiqnir^nq duiduiliuil|iu-2P2LulinLJ, r).puUnpb[ t w6fi JfimmJ, plir). nprnJ1 inuiphl|uiti lifigfilirud 7.1%-nu[, fiul| Ьпш Jujul|fig bnuJujul)1 JfigfilirnJ 2.5%-пф '-Luipfiuigfinti i|hp|nLÔnL|Bjni.lip фшш-nnLd t, np « UK duduiliuil|uijfili 2ШРРР ni huiduiuhn t, nibfi uipinui-huijini|uiô ppblir). U l|pb[ t 2008-2011 dqtiuiduidfi uiqr|.hgnL|3jnLtip: Читгид-и[ш6 l|bqô фпфп[иш1|ш1|пи[ u|uipuipn|uijfiti ррЬЬгф dnr|.h|ji qtiuihuiinduiti шр-ryriLliplibpp gnyg bb тшфи, np í|>fitiuitiuuil|uiti óqliuid'unjfi uiqr|.hgnL|3jnLtip «
ib <ш21|шр1|[1 1|шипшрЬ[ t ИЬгфЬшЬцп:
11 <Ш2ь|шр1|[1 1|штшр1|Ь[ t R 3.6.0 ôpmq.pmj|nb фш[эЬ[эпь[:
UK-fi и[рш -1414 J[li ULUL г|.п[шр t L|uid, 2007 p. huidbduim, 64%-nu[ u|uil|ui-unLpri.fi uii|b|uignLd: UbqnliuijlinLpjuili huidui|ai|ji i|bp|nL&nL|3jnLlip gnLjg t Lnw-фи, np ubqnliuijfili qnp&nlilibpp 2ШРРЬ dhmnL^D l|p6aiinnLd bli 1-fig 3-prj. bn-шdujail|lihpnuj, fiul| 4-pqnLif uii|h|uiglinLd: « aipmaihailiJaili haidaip ubqn-liuijfili qnp&nlifi umuii|b|uiqnLjli qpuil|uili uiqqbgnLpjnLlip 3-pq hnaidujail|nLd t, fiul| libpdnL&duili haiJaip1 4-pqnLii: 4ainnLgu[ai6 SARIMA dnr|.b|libpfi hfiduili u[pai r|mpu pbpu[ai6 « UK l|uilifuuiinbunLduijfili aipdbpp 2020 |э. haiJaip, ainailig COVID-19-fi l$bl|inh, l|uiqdnLii t -2556.59 UU1-" фпцир, huLl C0VID-19-h 1;фЫ|тр Иш2ф шпшб1 -2915.06 i^li ULUTL г>п[шр:
Clir|.huilinLp ainJaiJp, uinaigi|ui& pn[np l|uilifuuiinbunLduijfili qliuihuiinui-L|aililibpp ifiuiuinrud bli, np pliail|ailinli u|uijduililibpnLd « UK-li uipqbli fiul| mlibp u[aim|aaipaigJaili dfiinrndlibp: Ujua|fiuni|, l|uipnq blip bqpaihailiqb[, np C0VID-19 Llu Jbl| LpuignLgfi^ puiguiuuil|uili 2nl| « UK-fi haiJaip:
Oquiuiqnp6i[ui6 qpuil|uitinLpjmti
1. ГЭ-ш1[шгушЬ Ii. U mp^bbp, «lTiul|pninbinhuiul|iub L^bp^nL&nLfa-jnlIj, dnr|.h|iu4npnLd U l|iub|xiiuinhunLd»/U188, bp., «Iidphpr|.» diuinhbiu2iup, «Sbinhuiuqhin» hpiuin., 2014, 76 tg:
2. ГЭ-ш1[шгушЬ Ii. L mp^bbp, «<Lujiuuiniub|i <iubpiuii|hinnL|ajiub inbinhuiul|iub qiupqiugdiub qhpiul|iujnL|3jni.bhp|i qbiuhiuinnLdp U l|iub(uiuinhuni.dp», bp., «Iidpbpr|.» dujinhbiu2UJp, «Sbinhuiuqhin» hpiuin., 2015, 115 tg:
3. <iujiuuiniub <P (umdp, ТсН^шр^Ь piupl^n(unLdbbp|i hiur|piuhiup-diub ii|iuinbh hbiupiui|npnL|3jnLb, lTiul|pninbinbuiuq|'iinnL|3jnLb, lunLinrup Li bbpr|.pnLdbbp, bpl|p|i inbinhuiul|iub qiupqiugnLdbhp|i о^фпфтЛ, Ü2nLb/3dbn, 2017-2018:
4. CC 4P, Ч-Ьшб^ hiu2i|hLni|nL|3jnLb (T'-L-ß 6ршд|лр, 1фЬ hniudujiul|, 2020, TM.-ß 2019 |э., 4-pq. hniudujiul|, Spiuqp|i l|iuiniupdiub hiu2-i[bini[nL[3jnLb), 2020:
5. Кремер H.lil., Путко Б.А. Эконометрика: учебник, М., ЮНИТИ-ДАНА, 2002, 311 е., Глава 6.
6. Статистическое моделирование и прогнозирование: учеб. Пособие, Е.М. Марченко и др., Владим. гос. ун-т им А. Г. и Н. Г. Столетовых, Владимир, Изд-во ВлГУ, 2018, 100 с.
7. Cryer J.D., Chan K.S., Time Series Analysis, Springer, Texts in Statistics, 2008 (Second Edition, ISBN-978-0-387-759558-6), Chapter 9,10.
8. Burgert M., Dees S., Forcasting World Trade Direct Versus "Bottom-up" Approaches, European Central Bank (Working Paper Series no882), March, 2008.
9. Keck A., Raubold A., Truppia A., Forecasting International Trade: A Time Series Approach, OECD Journal: Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2009(2).
10. Rafiq S., Yun L, Ali G., Forecasting the Trend Analysis of Trade Balance of Pakistan: A Theoretical and Empirical Investigation, International Journal of Academic Research in Business and Social Sciences, 2016, vol.6, No. 7 (ISSN:2222-6990).
11. Khan T., Identifying an Appropriate Forecasting Model for Forecasting Total Import of Bangladesh, International Journal of Trade, Economics and Finance, Vol. 2, No 3, June 2011.
12. https://www.wto.org/english/news_e/pres20_e/pr855_e.htm
13. https://www.cba.am/am/SitePages/statexternalsector.aspx
14. https://tradingeconomics.com/armenia/exports
15. https://tradingeconomics.com/armenia/imports
16. https://armstat.am/en/
17. https://www.microsoft.com/en-us/
18. https://www.r-project.org/
19. https://univer-nn.ru/statistika/pokazateli-dinamiki-temp-rosta-i-prirosta/ ДИАНА МАТЕВОСЯН
Аспирант кафедры международных экономических отношений АГЭУ
Анализ и прогнозирование динамики торгового баланса РА,- Данная статья посвящена анализу и прогнозированию трендов торгового баланса РА. Был проведен комплексный анализ и моделирование динамики исследуемого явления с использованием статистических инструментов. В частности, был использован подход временных рядов. На основе моделей были сделаны прогнозы относительно будущих тенденций торгового баланса РА, что доказывает, что даже в нормальных условиях торговый баланс имеет значительную тенденцию к ухудшению, a C0VID-19 будет иметь лишь надбавочный эффект, углубляя существующий дефицит.
Ключевые слова: торговый баланс, баланс товаров, баланс услуг, эмпирические удельные веса, C0VID-19, модель SARIMA.
JEL: F17, Н62
DIANA MATEVOSYAN
PhD Student at the Chair of International Economic Relations at ASUE
Analysis and Forecasting of the Dynamics of the Armenian Trade Balance. - The paper is devoted to the analysis and forecasting of the trade balance trends of the Republic of Armenia. A comprehensive analysis and modeling of the dynamics of the studied phenomenon were carried out using statistical tools. In particular, the time series approach was used. Based on the models, forecasts were made regarding future trends in RA trade balance, which proves that even under normal conditions, the trade balance has a significant tendency to worsen, and COVID-19 will only have an extra effect, deepening the existing deficit.
Key words: trade balance, balance of goods, balance of services, empirical densities, COVID-19, SARIMA model. JEL: F17, H62
