YALPI ICHKI MAHSULOT TENDENTSIYASINI EKONOMETRIK TADQIQ ETISH

ETISH

G.X. Egamnazarova

Termiz davlat universiteti o’qituvchisi

X.B. Mamataliyev

Muzrabot xizmat ko’rsatish texnikumi direktori

Annotatsiya: Maqolada O’zbekiston Respublikasi yalpi ichki mahsulot hajmining choraklar bo’yicha o’zgarishi vaqtli qatori modellashtirilgan. Multiplikativ model tuzish orqali YaIM hajmi kelgusi 3 yil uchun prognoz qilingan.

Kalit so’zlar: Vaqtli qator, multiplikativ model, trend, mavsumiylik.

ЭКОНОМЕТРИЧЕСКОЕ ИЗУЧЕНИЕ ТЕНДЕНЦИЙ ВАЛОВОГО

ВНУТРЕННЕГО ПРОДУКТА

Аннотация: В статье моделируется временной ряд изменения объема валового внутреннего продукта Республики Узбекистан по кварталам. Путем создания мультипликативной модели был спрогнозирован объем ВВП на ближайшие 3 года.

Ключевые слова: Временной ряд, мультипликативная модель, тренд, сезонность.

AN ECONOMETRIC STUDY OF GROSS DOMESTIC PRODUCT TRENDS

Abstract: The article models the time series of changes in the volume of the gross domestic product of the Republic of Uzbekistan by quarters. By creating a multiplicative model, the volume of GDP was forecast for the next 3 years.

Key words: Time series, multiplicative model, trend, seasonality.

Ma’lumki, yalpi ichki mahsulot (YaHM) mamlakat iqtisodiyoti holatini belgilovchi eng muhim ko'rsatkichdir. Agar u barqaror o'sib borsa, bu mamlakat iqtisodiyoti rivojlanayotganini anglatadi. 2023 yil yakunlari bo’yicha O’zbekiston Respublikasi YaHM hajmi1 066 569 mlrd so’mni tashkil etgan. Aholi jon boshiga 29291,4 ming so’m, YaHMning o’sish surati esa 106 foiz bo’lgan. Choraklar kesimida YaHM darajalari 1-jadvalda berilgan.

1-jadval

O’zbekiston Respublikasi yalpi ichki mahsulot hajmi (mlrd so’m)1 Yillar Chorak YaIM Yillar Chorak YaIM 2016 I 47 816 2020 I 117 981

2016 II 114 568 2020 II 267 680

2016 III 185 110 2020 III 429 489

2016 IV 255 422 2020 IV 605 515

2017 I 53 985 2021 I 136 054

2017 II 131 713 2021 II 323 037

2017 III 221 431 2021 III 523 670

2017 IV 317 476 2021 IV 738 425

2018 I 77 923 2022 I 167 932

2018 II 187 168 2022 II 398 875

2018 III 305 271 2022 III 640 355

2018 IV 426 641 2022 IV 896 618

2019 I 98 744 2023 I 201 680

2019 II 233 452 2023 II 473 731

2019 III 380 930 2023 III 757 604

2019 IV 532 713 2023 IV 1 066 569

YaIM iqtisodiy faoliyatda eng ko'p qo'llaniladigan ko'rsatkichidir. U ma'lum bir mamlakatning iqtisodiy holatining o'sishi yoki pasayishini aniqlash, jahon iqtisodiyotini baholash va mamlakatlar iqtisodiyotini bir-biri bilan solishtirish uchun ham qo'llaniladi. Shu sababdan uning kelajakdagi qabul qilishi mumkin bo’lgan qiymatlarini prognozlash mamlakat iqtisodiyoti uchun muhim ma’lumotlarni olishga zamin yaratadi.

1-jadvalda keltirilgan vaqtli qator darajalari choraklik tendentsiyani tashkil etmoqda. Bunday vaqtli qatorlar additiv, multiplikativ, SAR, SMA, SARMA, SARIMA va boshqa turdagi regressiya tenglamalari bilan modellashtiriladi. Odatda model turini tanlashda vaqtli qator chizmasi ko’zdan kechiriladi (1-rasm). 1 www.stat.uz - O’zbekiston Respublikasi Prezidenti huzuridagi Statistika agentligi ma’lumotlari

1-rasm. O’zbekiston Respublikasi yalpi ichki mahsulot hajmi2

1-rasmda vaqtli qator tebranish amplitudasi kengayib borayotganligini ko’rish mumkin. Demak, ushbu holatda quyidagi ko’rinishdagi multiplikativ vaqtli qator tenglamasini baholash maqsadga muvofiq:

𝑌 = 𝑇 ∙ 𝑆 ∙ 𝐸 (1)

bu yerda, 𝑇 – trend; 𝑆 – mavsumiylik tarkibiy qism; 𝐸 – tasodifiy xatolik.

(1) modelni baholash uchun dastlab mavsumiylikni aniqlanishimiz talab etiladi (2-jadval).

2-jadval

Mavsumiylik bahosini aniqlash bo’yicha hisob-kitoblar3 Yillar Chorak YaIM

(𝒀)

Sirg'aluvchi

o'rtacha

Markazlashgan

sirg'aluvchi

o'rtacha

Mavsumiylik

bahosi 2016 I 47816,2 - - - 2016 II 114568,0 150729,0 - -

2016 III 185109,8 152271,2 151500,1 1,2

2016 IV 255421,9 156557,3 154414,3 1,7 2017 I 53985,2 165637,6 161097,5 0,3 2017 II 131712,5 181151,2 173394,4 0,8

2017 III 221430,7 187135,7 184143,5 1,2

2017 IV 317476,4 200999,7 194067,7 1,6 2 Muallif ishlanmasi. 3 Muallif ishlanmasi

2016 I

2016 II

2016 III

2016 IV

2017 I

2017 II

2017 III

2017 IV

2018 I

2018 II

2018 III

2018 IV

2019 I

2019 II

2019 III

2019 IV

2020 I

2020 II

2020 III

2020 IV

2021 I

2021 II

2021 III

2021 IV

2022 I

2022 II

2022 III

2022 IV

2023 I

2023 II

2023 III

2023 IV 2018 I 77923,4 221959,8 211479,8 0,4 2018 II 187168,2 249251,0 235605,4 0,8

2018 III 305271,3 254456,2 251853,6 1,2

2018 IV 426641,0 266027,1 260241,6 1,6 2019 I 98744,4 284941,8 275484,4 0,4 2019 II 233451,5 311459,7 298200,7 0,8

2019 III 380930,2 316268,8 313864,2 1,2

2019 IV 532712,5 324825,9 320547,3 1,7 2020 I 117981,0 336965,6 330895,7 0,4 2020 II 267679,7 355166,2 346065,9 0,8

2020 III 429489,1 359684,4 357425,3 1,2

2020 IV 605514,9 373523,6 366604,0 1,7 2021 I 136053,8 397068,7 385296,2 0,4 2021 II 323036,6 430296,3 413682,5 0,8

2021 III 523669,6 438265,9 434281,1 1,2

2021 IV 738425,2 457225,6 447745,8 1,6 2022 I 167932,1 486396,9 471811,3 0,4 2022 II 398875,5 525945,1 506171,0 0,8

2022 III 640354,9 534382,1 530163,6 1,2

2022 IV 896617,9 553096,0 543739,0 1,6 2023 I 201680,0 582408,2 567752,1 0,4 2023 II 473731,1 624896,0 603652,1 0,8

2023 III 757604,0 - - -

2023 IV 1066569,0 - - -

2-jadvalda keltirilgan mavsumiylik baholari o’rtacha qiymatlarini to’g’rilovchi koeffitsiyentga bo’lish orqali mavsumiylikni aniqlash mumkin (3-jadval)

3-jadval

Choraklar bo’yicha mavsumiylik tarkibiy qismi darajalari4 Choraklar I II III IV

JAMI 2,5 5,5 8,5 11,5

4 Muallif ishlanmasi O'rtachasi 0,354691 0,780581 1,209344 1,648744 To’g’rilovchi koeffitsiyent 0,99834 Mavsumiylik (𝑺) 0,355281 0,781879 1,211355 1,651485

𝑌 natijaviy belgini (yoki (1) modelni) 𝑆 ga bo’lish orqali 𝑇 ∙ 𝐸 bahosi aniqlanadi:

𝑌

𝑆 = 𝑇∙𝑆∙𝐸

𝑆 = 𝑇 ∙ 𝐸 (1)

Natijalar 4-jadvalda keltirilgan (4-jadval).

4-jadval

𝑻 ∙ 𝑬 qiymatlari5 Yil Chorak 𝑻 ∙ 𝑬 Yil Chorak 𝑻 ∙ 𝑬 2016 I 134 586,96 2020 I 332 078,29

2016 II 146 529,11 2020 II 342 354,38

2016 III 152 812,17 2020 III 354 552,64

2016 IV 154 661,91 2020 IV 366 648,68

2017 I 151 950,83 2021 I 382 947,09

2017 II 168 456,36 2021 II 413 154,18

2017 III 182 795,89 2021 III 432 300,78

2017 IV 192 236,88 2021 IV 447 127,97

2018 I 219 329,10 2022 I 472 674,24

2018 II 239 382,58 2022 II 510 149,78

2018 III 252 008,20 2022 III 528 627,02

2018 IV 258 337,73 2022 IV 542 916,08

2019 I 277 933,37 2023 I 567 663,55

2019 II 298 577,54 2023 II 605 887,92

2019 III 314 466,24 2023 III 625 418,74

2019 IV 322 565,71 2023 IV 645 824,13

𝑇 ∙ 𝐸 bu trend va tasodifiy xatoliklardan iborat qator hisoblanadi. Odatda bunday qatordan trendni ajratish uchun eng kichik kvadratlar usulini qo’llash etarli hisoblanadi. Shu maqsadda 𝑇 = 𝑎 + 𝑏𝑡 ko’rinishidagi chiziqli model tuzamiz (5-jadval). 5 Muallif ishlanmasi

5-jadval

Regression tahlil natijalari6

ВЫВОД

ИТОГОВ

Регрессионная статистика Множественный R 0,988 R-квадрат 0,977 Нормированный R-квадрат 0,976 Стандартная ошибка

268,285 Наблюдения 32 Дисперсионный анализ

df SS MS F Значимость

F Регрессия 1 7,3654E+11 7,3654E+11

250,606 5,131E-26 Остаток 30 1,7668E+10 588949659 Итого 31 7,5421E+11

Коэффи-

циенты

Стан-

дартная

ошибка

t-ста-

тистика

P-Зна-

чение

Нижние

95% Y-пересечение

785,166 8 785,266 8,399 0,000 55 843,259 6 Muallif ishlanmasi Переменная X 1

431,498 464,640 35,364 0,000 15 482,575

5-jadvalga ko’ra, Fisherning F mezoni hisoblangan qiymati 𝐹ℎ𝑖𝑠 = 1250,606 ga teng. Bu esa 𝑑𝑓1 = 𝑚 = 1 va 𝑑𝑓2 = 𝑛 − 1 − 1 = 30 erkinlik darajasida hamda, 𝛼 = 0,05 ahamiyatlilik darajasidagi Fisherning jadval qiymati 𝐹𝑗𝑎𝑑 = 4.17 dan katta. Shuningdek (3) modelning parametrlari bo‘yicha Styudentning t mezoni qiymatlari 𝑡𝑎 = 8,399 va 𝑡𝑏 = 35,364 ga teng. Bu esa 𝛼 = 0,05 ahamiyatlilik darajasi hamda 𝑑𝑓 = 𝑛 − 1 = 31 erkinlik darajasida Styudentning t mezoni jadval qiymati 𝑡𝑗𝑎𝑑 = 2,04 dan katta. Shu sababli model statistik ahamiyatga ega hisoblanadi.

Shunday qilib, trend tenglamasini quyidagicha yozish mumkin:

𝑇 = 73785,166 + 16431,498𝑡 (2)

Shunday qilib, 𝑆 mavsumiylik tarkibiy qism darajalari hamda 𝑇 trend tarkibiy qismi modeli baholandi. Ulardan foydalanib, kelgusi 3 yil uchun prognoz qiymatlar ishlab chiqildi (6-jadval). Shuni aytib o’tish kerakki, vaqtli qatorning haqiqiy darajalari hamada tekislangan darajalari o’rtasidagi approksimatsiya hatoligi 6,61 foizni tashkil etdi.

6-jadval

Yalpi ichki mahsulot hajmining 2024-2026 yillar uchun prognoz qiymatlari7 T/r Yillar Chorak Mavsumiylik

tarkibiy qismi, 𝑺

Trend tarkibiy

qismi, 𝑻

Yalpi ichki

mahsulot, 𝒀̂ 1 2024 I 0,355281 616 024,6 218 862 2 2024 II 0,781879 632 456,1 494 504

3 2024 III 1,211355 648 887,6 786 033

4 2024 IV 1,651485 665 319,1 1 098 765 5 2025 I 0,355281 681 750,6 242 213 6 2025 II 0,781879 698 182,1 545 894

7 2025 III 1,211355 714 613,6 865 651

8 2025 IV 1,651485 731 045,1 1 207 310 9 2026 I 0,355281 747 476,6 265 564 10 2026 II 0,781879 763 908,1 597 284 7 Muallif ishlanmasi

11 2026 III 1,211355 780 339,6 945 268

12 2026 IV 1,651485 796 771,1 1 315 856

Prognoz qiymatlarning chizmasi 2-rasmda berilgan:

2-rasm. O’zbekiston Respublikasi yalpi ichki mahsulot hajmi (mlrd so’m)8

Shunday qilib, 2027 yilga kelib, O’zbekiston Respublikasi yalpi ichki mahsulot hajmi 1 315 856 mlrd so’mni, o’sish esa 123% ni tashkil etishi taxmin qilinmoqda.

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