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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
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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:
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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/
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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:
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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-
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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
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drift-p' ijpfi^iip feuipdpbpuigfi 2LUpj2fi huiuipuiipnLbji qnpôuiLj[ig):
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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)
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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).
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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
