BỘ GIÁO DỤC VÀ ĐÀO TẠO

TRƯỜNG ĐẠI HỌC KINH TẾ QUỐC DÂN

Bài giữa kì môn dự báo kinh tế xã hội

Sinh viên thực hiện:

Trần Quốc Tuấn : 47
Nguyễn Thị Phương Thảo: 45
Nguyễn Thu Phương : 39

Hà nội,tháng 10 năm 2023

EXAMINATION ECONOMIC FORECASTING 1

Take-home exam
(ODD number)
Question 1: Give some comments on the application of forecasting methods in
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enterprises in Vietnam,
The application of forecasting methods in enterprises in Vietnam can be beneficial in
many ways. Forecasting is the process of making predictions about future events or trends
using historical data and statistical models. It can help businesses in Vietnam make better
decisions about their operations, resources, and investments, ultimately leading to increased
profitability and competitiveness.
One common application of forecasting in Vietnam is in supply chain management.
Accurately forecasting demand for products can help companies optimize their inventory
levels, minimize stockouts, and reduce wastage. This can be particularly important in
industries such as manufacturing and retail, where supply chain disruptions and
inefficiencies can have significant cost implications.
Another area where forecasting can be useful is in financial planning and budgeting.
By forecasting future revenue and expenses, businesses in Vietnam can better plan their
cash flow and ensure they have the resources to meet their financial obligations. This can
be especially important for small and medium-sized enterprises (SMEs), which may have
limited access to capital.
Finally, forecasting can also be used in marketing and sales. By forecasting
customer demand and trends, businesses in Vietnam can tailor their marketing strategies
and product offerings to meet the needs of their target audience. This can help them
increase customer loyalty and gain a competitive edge in their industry.
However, there are also challenges to using forecasting methods in enterprises in
Vietnam. These include issues with data quality and availability, as well as a lack of

0
technical expertise and resources. Additionally, economic and political instability can
make it difficult to accurately forecast business conditions and trends.
Overall, the application of forecasting methods in enterprises in Vietnam can
provide significant benefits, but it is important for businesses to carefully consider
their data sources and methodologies to ensure the accuracy and reliability of their
forecasts.

Question 2: By using annual Exports of Goods and Services (EXPGSA) of

America from 1929 to 2022 at https://fred,stlouisfed,org/series/EXPGSA, studen
ts have to answer all the following questions:
1. Based on the graph form, it is possible that the definitions are non-linear
trend, Specifically, it is a Sigmoidal graph.

2. In this exercise, we work on mathematical and statistical databases. This series

of data is collected and statistically based on the time series from 1929 to 2022.
According to the chart above, we can see that in general, the data in the series does
not fluctuate very much and the data collected in the time series is evenly spaced.
Therefore, we think of the “moving average” method to be able to smooth out the

0
irregular fluctuations in the time series, then put in the moving average data, we will
forecast the demand in the next period.
Besides, it can be seen that the data and data are quite a lot, so for the convenience
of calculations, we should use a calculator (excel). Therefore, the “exponential
smoothing” method is also a method that can be used in this exercise. This method has a
fairly strict formula for calculating future demand, so its forecast can be trusted.
In this exercise, the forecast amount is relatively large (exports of goods and
services), and this is also a major turnover, related to the economic development of a
country. Therefore, “extrapolation” is also a method to be considered in this
situation.
In short, moving average method, exponential moving average method
and extrapolation method can be used to forecast the movement of the variable.

3. Forecast values of EXPGSA in 2023 and 2024 by using:

 5-period moving average

1
With m=5

∑m yt − i
Using the recipe: Ft+1 = .

m i=0

We have the data table

below:

Observation date Year t Y Ŷ |Y-Ŷ|/Y

1929-01-01 1929 1 5,939

1930-01-01 1930 2 4,444

1931-01-01 1931 3 2,906

1932-01-01 1932 4 1,975

1933-01-01 1933 5 1,987

0
1934-01-01 1934 6 2,561 3,450 0,347

0
1935-01-01 1935 7 2,769 2,775 0,002

1936-01-01 1936 8 3,007 2,440 0,189

1937-01-01 1937 9 4,039 2,460 0,391

1938-01-01 1938 10 3,811 2,873 0,246

1939-01-01 1939 11 3,969 3,237 0,184

1940-01-01 1940 12 4,897 3,519 0,281

1941-01-01 1941 13 5,482 3,945 0,280

1942-01-01 1942 14 4,375 4,440 0,015

1943-01-01 1943 15 4,034 4,507 0,117

1944-01-01 1944 16 4,880 4,551 0,067

1945-01-01 1945 17 6,781 4,734 0,302

1946-01-01 1946 18 14,156 5,110 0,639

1947-01-01 1947 19 18,740 6,845 0,635

1948-01-01 1948 20 15,547 9,718 0,375

1949-01-01 1949 21 14,484 12,021 0,170

1950-01-01 1950 22 12,350 13,942 0,129

1951-01-01 1951 23 17,099 15,055 0,120

0
1952-01-01 1952 24 16,459 15,644 0,050

1953-01-01 1953 25 15,313 15,188 0,008

1954-01-01 1954 26 15,836 15,141 0,044

1955-01-01 1955 27 17,677 15,411 0,128

1956-01-01 1956 28 21,284 16,477 0,226

1957-01-01 1957 29 24,017 17,314 0,279

1958-01-01 1958 30 20,560 18,825 0,084

1959-01-01 1959 31 22,725 19,875 0,125

1960-01-01 1960 32 27,045 21,253 0,214

1961-01-01 1961 33 27,602 23,126 0,162

1962-01-01 1962 34 29,066 24,390 0,161

1963-01-01 1963 35 31,074 25,400 0,183

1964-01-01 1964 36 35,019 27,502 0,215

1965-01-01 1965 37 37,146 29,961 0,193

1966-01-01 1966 38 40,920 31,981 0,218

1967-01-01 1967 39 43,467 34,645 0,203

1968-01-01 1968 40 47,906 37,525 0,217

0
1969-01-01 1969 41 51,922 40,892 0,212

1970-01-01 1970 42 59,709 44,272 0,259

1971-01-01 1971 43 62,963 48,785 0,225

1972-01-01 1972 44 70,843 53,193 0,249

1973-01-01 1973 45 95,269 58,669 0,384

1974-01-01 1974 46 126,650 68,141 0,462

1975-01-01 1975 47 138,706 83,087 0,401

1976-01-01 1976 48 149,515 98,886 0,339

1977-01-01 1977 49 159,349 116,197 0,271

1978-01-01 1978 50 186,883 133,898 0,284

1979-01-01 1979 51 230,129 152,221 0,339

1980-01-01 1980 52 280,772 172,916 0,384

1981-01-01 1981 53 305,239 201,330 0,340

1982-01-01 1982 54 283,210 232,474 0,179

1983-01-01 1983 55 276,996 257,247 0,071

1984-01-01 1984 56 302,380 275,269 0,090

1985-01-01 1985 57 303,211 289,719 0,044

0
1986-01-01 1986 58 320,998 294,207 0,083

1987-01-01 1987 59 363,943 297,359 0,183

1988-01-01 1988 60 444,601 313,506 0,295

1989-01-01 1989 61 504,289 347,027 0,312

1990-01-01 1990 62 551,873 387,408 0,298

1991-01-01 1991 63 594,931 437,141 0,265

1992-01-01 1992 64 633,053 491,927 0,223

1993-01-01 1993 65 654,799 545,749 0,167

1994-01-01 1994 66 720,937 587,789 0,185

1995-01-01 1995 67 812,810 631,119 0,224

1996-01-01 1996 68 867,589 683,306 0,212

1997-01-01 1997 69 953,803 737,838 0,226

1998-01-01 1998 70 952,979 801,988 0,158

1999-01-01 1999 71 992,910 861,624 0,132

2000-01-01 2000 72 1096,111 916,018 0,164

2001-01-01 2001 73 1026,812 972,678 0,053

2002-01-01 2002 74 997,979 1004,523 0,007

0
2003-01-01 2003 75 1035,165 1013,358 0,021

2004-01-01 2004 76 1176,363 1029,795 0,125

2005-01-01 2005 77 1301,580 1066,486 0,181

2006-01-01 2006 78 1470,170 1107,580 0,247

2007-01-01 2007 79 1659,295 1196,251 0,279

2008-01-01 2008 80 1835,280 1328,515 0,276

2009-01-01 2009 81 1582,774 1488,538 0,060

2010-01-01 2010 82 1857,247 1569,820 0,155

2011-01-01 2011 83 2115,864 1680,953 0,206

2012-01-01 2012 84 2217,700 1810,092 0,184

2013-01-01 2013 85 2286,981 1921,773 0,160

2014-01-01 2014 86 2377,408 2012,113 0,154

2015-01-01 2015 87 2268,651 2171,040 0,043

2016-01-01 2016 88 2232,110 2253,321 0,010

2017-01-01 2017 89 2388,260 2276,570 0,047

2018-01-01 2018 90 2538,089 2310,682 0,090

2019-01-01 2019 91 2538,450 2360,904 0,070

0
 2020-01-01 2020 92 2148,616 2393,112 0,114

2021-01-01 2021 93 2539,648 2369,105 0,067

2022-01-01 2022 94 2975,843 2430,613 0,183

Sum 4465 17,588

Forecast value:
F₂₀₂₃ = 1 . (y₂₀₁₈ + y₂₀₁₉ + y₂₀₂₀ + y₂₀₂₁ + y₂₀₂₂) = 2548,129
5

Can’t forecast the value for 2024 because we don’t have y2023
 5-period exponential moving average
With m=5 ⇒ = 2/(m+1) = ⅓ = 0,333
Using recipe: Ft+1 = α.yt + (1-α).Ft
We have the data table below:

Observation date Year t t*t Y Y mũ |Y-Ŷ|/Y

1929-01-01 1929 1 1 5,939 5,939 0

1930-01-01 1930 2 4 4,444 5,939 0,336

1931-01-01 1931 3 9 2,906 5,4407 0,872

1932-01-01 1932 4 16 1,975 4,5958 1,327

1933-01-01 1933 5 25 1,987 3,7222 0,873

1934-01-01 1934 6 36 2,561 3,1438 0,228

1935-01-01 1935 7 49 2,769 2,9495 0,065

0
1936-01-01 1936 8 64 3,007 2,8894 0,039

1937-01-01 1937 9 81 4,039 2,9286 0,275

1938-01-01 1938 10 100 3,811 3,2987 0,134

1939-01-01 1939 11 121 3,969 3,4695 0,126

1940-01-01 1940 12 144 4,897 3,6360 0,258

1941-01-01 1941 13 169 5,482 4,0563 0,260

1942-01-01 1942 14 196 4,375 4,5315 0,036

1943-01-01 1943 15 225 4,034 4,4794 0,110

1944-01-01 1944 16 256 4,880 4,3309 0,113

1945-01-01 1945 17 289 6,781 4,5139 0,334

1946-01-01 1946 18 324 14,156 5,2696 0,628

1947-01-01 1947 19 361 18,740 8,2318 0,561

1948-01-01 1948 20 400 15,547 11,7345 0,245

1949-01-01 1949 21 441 14,484 13,0053 0,102

1950-01-01 1950 22 484 12,350 13,4982 0,093

1951-01-01 1951 23 529 17,099 13,1155 0,233

1952-01-01 1952 24 576 16,459 14,4433 0,122

0
1953-01-01 1953 25 625 15,313 15,1152 0,013

1954-01-01 1954 26 676 15,836 15,1811 0,041

1955-01-01 1955 27 729 17,677 15,3994 0,129

1956-01-01 1956 28 784 21,284 16,1586 0,241

1957-01-01 1957 29 841 24,017 17,8671 0,256

1958-01-01 1958 30 900 20,560 19,9171 0,031

1959-01-01 1959 31 961 22,725 20,1314 0,114

1960-01-01 1960 32 1024 27,045 20,9959 0,224

1961-01-01 1961 33 1089 27,602 23,0123 0,166

1962-01-01 1962 34 1156 29,066 24,5422 0,156

1963-01-01 1963 35 1225 31,074 26,0501 0,162

1964-01-01 1964 36 1296 35,019 27,7247 0,208

1965-01-01 1965 37 1369 37,146 30,1562 0,188

1966-01-01 1966 38 1444 40,920 32,4861 0,206

1967-01-01 1967 39 1521 43,467 35,2974 0,188

1968-01-01 1968 40 1600 47,906 38,0206 0,206

1969-01-01 1969 41 1681 51,922 41,3157 0,204

0
1970-01-01 1970 42 1764 59,709 44,8512 0,249

1971-01-01 1971 43 1849 62,963 49,8038 0,209

1972-01-01 1972 44 1936 70,843 54,1902 0,235

1973-01-01 1973 45 2025 95,269 59,7411 0,373

1974-01-01 1974 46 2116 126,650 71,5837 0,435

1975-01-01 1975 47 2209 138,706 89,9392 0,352

1976-01-01 1976 48 2304 149,515 106,1948 0,290

1977-01-01 1977 49 2401 159,349 120,6349 0,243

1978-01-01 1978 50 2500 186,883 133,5396 0,285

1979-01-01 1979 51 2601 230,129 151,3207 0,342

1980-01-01 1980 52 2704 280,772 177,5901 0,367

1981-01-01 1981 53 2809 305,239 211,9841 0,306

1982-01-01 1982 54 2916 283,210 243,0691 0,142

1983-01-01 1983 55 3025 276,996 256,4494 0,074

1984-01-01 1984 56 3136 302,380 263,2983 0,129

1985-01-01 1985 57 3249 303,211 276,3255 0,089

1986-01-01 1986 58 3364 320,998 285,2873 0,111

0
1987-01-01 1987 59 3481 363,943 297,1909 0,183

1988-01-01 1988 60 3600 444,601 319,4416 0,282

1989-01-01 1989 61 3721 504,289 361,1614 0,284

1990-01-01 1990 62 3844 551,873 408,8706 0,259

1991-01-01 1991 63 3969 594,931 456,5381 0,233

1992-01-01 1992 64 4096 633,053 502,6690 0,206

1993-01-01 1993 65 4225 654,799 546,1304 0,166

1994-01-01 1994 66 4356 720,937 582,3532 0,192

1995-01-01 1995 67 4489 812,810 628,5478 0,227

1996-01-01 1996 68 4624 867,589 689,9686 0,205

1997-01-01 1997 69 4761 953,803 749,1754 0,215

1998-01-01 1998 70 4900 952,979 817,3846 0,142

1999-01-01 1999 71 5041 992,910 862,5827 0,131

2000-01-01 2000 72 5184 1096,111 906,0251 0,173

2001-01-01 2001 73 5329 1026,812 969,3871 0,056

2002-01-01 2002 74 5476 997,979 988,5287 0,009

2003-01-01 2003 75 5625 1035,165 991,6788 0,042

0
2004-01-01 2004 76 5776 1176,363 1006,1742 0,145

2005-01-01 2005 77 5929 1301,580 1062,9038 0,183

2006-01-01 2006 78 6084 1470,170 1142,4625 0,223

2007-01-01 2007 79 6241 1659,295 1251,6984 0,246

2008-01-01 2008 80 6400 1835,280 1387,5639 0,244

2009-01-01 2009 81 6561 1582,774 1536,8026 0,029

2010-01-01 2010 82 6724 1857,247 1552,1264 0,164

2011-01-01 2011 83 6889 2115,864 1653,8333 0,218

2012-01-01 2012 84 7056 2217,700 1807,8435 0,185

2013-01-01 2013 85 7225 2286,981 1944,4623 0,150

2014-01-01 2014 86 7396 2377,408 2058,6352 0,134

2015-01-01 2015 87 7569 2268,651 2164,8928 0,046

2016-01-01 2016 88 7744 2232,110 2199,4789 0,015

2017-01-01 2017 89 7921 2388,260 2210,3559 0,074

2018-01-01 2018 90 8100 2538,089 2269,6573 0,106

2019-01-01 2019 91 8281 2538,450 2359,1345 0,071

2020-01-01 2020 92 8464 2148,616 2418,9063 0,126

0
 2021-01-01 2021 93 8649 2539,648 2328,8096 0,083

2022-01-01 2022 94 8836 2975,843 2399,0890 0,194

Sum 4465 281295 19,975

Forecast value:
F₂₀₂₃ = α.y2022 + (1-α).F2022 = 2591,3404
Can’t forecast the value for 2024 because we don’t have y2023

 Extrapolation with an appropriate trend

T = 2022 - 1929 + 1 = 94

Using OLS: T. lnα + β. t= Y

α. t + β. t2 = Y.t
Giải hệ phương trình ta được: lnα = 0,746  α = 2,108

β = 0,083

Using the recipe: Yt = α.eβ.t

We have the data table
below:

Observation date Year t t*t Y Y mũ |Y-Ŷ|/Y

1929-01-01 1929 1 1 5,939 2,291 0,614

1930-01-01 1930 2 4 4,444 2,490 0,440

1931-01-01 1931 3 9 2,906 2,707 0,068

1932-01-01 1932 4 16 1,975 2,943 0,490

1933-01-01 1933 5 25 1,987 3,199 0,610

0
0
1934-01-01 1934 6 36 2,561 3,477 0,358

1935-01-01 1935 7 49 2,769 3,780 0,365

1936-01-01 1936 8 64 3,007 4,109 0,366

1937-01-01 1937 9 81 4,039 4,466 0,106

1938-01-01 1938 10 100 3,811 4,855 0,274

1939-01-01 1939 11 121 3,969 5,278 0,330

1940-01-01 1940 12 144 4,897 5,737 0,171

1941-01-01 1941 13 169 5,482 6,236 0,138

1942-01-01 1942 14 196 4,375 6,779 0,549

1943-01-01 1943 15 225 4,034 7,369 0,827

1944-01-01 1944 16 256 4,880 8,010 0,641

1945-01-01 1945 17 289 6,781 8,707 0,284

1946-01-01 1946 18 324 14,156 9,465 0,331

1947-01-01 1947 19 361 18,740 10,288 0,451

1948-01-01 1948 20 400 15,547 11,184 0,281

1949-01-01 1949 21 441 14,484 12,157 0,161

1950-01-01 1950 22 484 12,350 13,215 0,070

0
1951-01-01 1951 23 529 17,099 14,365 0,160

1952-01-01 1952 24 576 16,459 15,615 0,051

1953-01-01 1953 25 625 15,313 16,974 0,108

1954-01-01 1954 26 676 15,836 18,451 0,165

1955-01-01 1955 27 729 17,677 20,057 0,135

1956-01-01 1956 28 784 21,284 21,802 0,024

1957-01-01 1957 29 841 24,017 23,700 0,013

1958-01-01 1958 30 900 20,560 25,762 0,253

1959-01-01 1959 31 961 22,725 28,004 0,232

1960-01-01 1960 32 1024 27,045 30,441 0,126

1961-01-01 1961 33 1089 27,602 33,091 0,199

1962-01-01 1962 34 1156 29,066 35,970 0,238

1963-01-01 1963 35 1225 31,074 39,101 0,258

1964-01-01 1964 36 1296 35,019 42,503 0,214

1965-01-01 1965 37 1369 37,146 46,202 0,244

1966-01-01 1966 38 1444 40,920 50,223 0,227

1967-01-01 1967 39 1521 43,467 54,594 0,256

0
1968-01-01 1968 40 1600 47,906 59,345 0,239

1969-01-01 1969 41 1681 51,922 64,509 0,242

1970-01-01 1970 42 1764 59,709 70,123 0,174

1971-01-01 1971 43 1849 62,963 76,226 0,211

1972-01-01 1972 44 1936 70,843 82,859 0,170

1973-01-01 1973 45 2025 95,269 90,070 0,055

1974-01-01 1974 46 2116 126,650 97,909 0,227

1975-01-01 1975 47 2209 138,706 106,429 0,233

1976-01-01 1976 48 2304 149,515 115,691 0,226

1977-01-01 1977 49 2401 159,349 125,759 0,211

1978-01-01 1978 50 2500 186,883 136,704 0,269

1979-01-01 1979 51 2601 230,129 148,600 0,354

1980-01-01 1980 52 2704 280,772 161,532 0,425

1981-01-01 1981 53 2809 305,239 175,590 0,425

1982-01-01 1982 54 2916 283,210 190,871 0,326

1983-01-01 1983 55 3025 276,996 207,481 0,251

1984-01-01 1984 56 3136 302,380 225,537 0,254

0
1985-01-01 1985 57 3249 303,211 245,165 0,191

1986-01-01 1986 58 3364 320,998 266,501 0,170

1987-01-01 1987 59 3481 363,943 289,693 0,204

1988-01-01 1988 60 3600 444,601 314,904 0,292

1989-01-01 1989 61 3721 504,289 342,308 0,321

1990-01-01 1990 62 3844 551,873 372,098 0,326

1991-01-01 1991 63 3969 594,931 404,480 0,320

1992-01-01 1992 64 4096 633,053 439,680 0,305

1993-01-01 1993 65 4225 654,799 477,944 0,270

1994-01-01 1994 66 4356 720,937 519,537 0,279

1995-01-01 1995 67 4489 812,810 564,750 0,305

1996-01-01 1996 68 4624 867,589 613,898 0,292

1997-01-01 1997 69 4761 953,803 667,322 0,300

1998-01-01 1998 70 4900 952,979 725,396 0,239

1999-01-01 1999 71 5041 992,910 788,525 0,206

2000-01-01 2000 72 5184 1096,111 857,146 0,218

2001-01-01 2001 73 5329 1026,812 931,740 0,093

0
2002-01-01 2002 74 5476 997,979 1012,825 0,015

2003-01-01 2003 75 5625 1035,165 1100,967 0,064

2004-01-01 2004 76 5776 1176,363 1196,779 0,017

2005-01-01 2005 77 5929 1301,580 1300,930 0,000

2006-01-01 2006 78 6084 1470,170 1414,144 0,038

2007-01-01 2007 79 6241 1659,295 1537,210 0,074

2008-01-01 2008 80 6400 1835,280 1670,987 0,090

2009-01-01 2009 81 6561 1582,774 1816,406 0,148

2010-01-01 2010 82 6724 1857,247 1974,479 0,063

2011-01-01 2011 83 6889 2115,864 2146,310 0,014

2012-01-01 2012 84 7056 2217,700 2333,093 0,052

2013-01-01 2013 85 7225 2286,981 2536,132 0,109

2014-01-01 2014 86 7396 2377,408 2756,841 0,160

2015-01-01 2015 87 7569 2268,651 2996,756 0,321

2016-01-01 2016 88 7744 2232,110 3257,551 0,459

2017-01-01 2017 89 7921 2388,260 3541,041 0,483

2018-01-01 2018 90 8100 2538,089 3849,202 0,517

0
 2019-01-01 2019 91 8281 2538,450 4184,181 0,648

2020-01-01 2020 92 8464 2148,616 4548,312 1,117

2021-01-01 2021 93 8649 2539,648 4944,131 0,947

2022-01-01 2022 94 8836 2975,843 5374,397 0,806

Sum 4465 25,592

Forecast value:
F₂₀₂₃ = α.eβ.95= 5842,107
Can’t forecast the value for 2024 because we don’t have y2023

4. Calculate MAPE
Using the
recipe:

MAPE =

Moving average method: 17,588 = 19,762

Exponential moving average: 19,975 = 21,250

Extrapolation (exponential trend): 25,592 = 27,225

5. In the long-term, we should use extrapolation forecasting because this is a

relatively simple method that can be done quickly and with little cost and can be used
when the number of forecasts is very large.

0
 In the short-term, we see that the MAPE value of the moving average method
is the lowest, so this is the most optimal method that we should choose to use for
forecasting.