(Tiểu luận FTU) orecasting vietnam’s export value from october 2019 to december 2020 by time series analysis method and box jenkins method using seasonal ARIMA model

FOREIGN TRADE UNIVERSITY FACULTY OF INTERNATIONAL ECONOMICS -*** ECONOMIC FORECAST MID-TERM ASSIGNMENT Forecasting Vietnam’s export value from October 2019 to December 2020 by time series analysis method and Box-Jenkins method using seasonal ARIMA model Lecturer: Class: PhD Chu Thi Mai Phuong KTEE 418.1 Students: Nguyễn Quang Hiếu 1614450022 Nguyễn Ngọc Minh 1614450035 Nguyễn Mạnh Hùng 1614450024 Hanoi, December 12, 2019 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com Contents Abstract Introduction Methods and processes 2.1 Time series analysis method 2.2 Box-Jenkins method and seasonal ARIMA model Data and forecast results 3.1 Data description: 3.2 The process of forecasting Conclusion 17 References 18 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com Abstract In this report, we use time series analysis method and Box-Jenkins method using ARIMA model with seasonal component (SARIMA) to forecast the total export value of Vietnam from October 2019 to December 2020 The forecast results provided by both methods is reliable Between two methods, we find that time series analysis is more preferable Introduction Nowadays, in the era of globalization, trade is dispensable in the economy of each nations and territories It plays a crucial role therefore not only statistics, analysis and evaluation but also the forecasting of import and export is a permanent work of economists, especially policymakers In addition to the state, firms also pay close attention to and forecast import & export situation to facilitate business, in line with the global trend To understand why economic forecasting plays such an important role, first of all we need to understand what is forecasting? Forecasting is a prediction based on statistical data and analysis by scientific methods The object of forecasting is the situation and development trend of a future business, science or social activity The forecast is probabilistic but also reliable because the forecasters base on real data to find trends Vietnam is a country with a favorable geographical position, located in the tropical monsoon climate, with the advantage of diverse agricultural products and rare minerals The export of agricultural products and minerals is a crucial activity, bringing advantages to Vietnam's economy This is the main source of foreign currency revenue, promoting production, bringing jobs and significant external relations meaning However, it seems that the lack of complete control of production and quality of agricultural products abroad as well as the dependence on some importing countries are hindering Vietnam's export industry The exporting products are always closely related by climate, crop, and production patterns throughout the territory of Vietnam Understanding the relationship between these products and the situation of export value will help the government and firms in planning future production and business plans for the most efficient export activities This is the mission of economic forecasting With the purpose of clarifying the forecasting method for export activities of Vietnam, our research team uses the econometric software Eviews to run a model to forecast the total export value of Vietnam from October 2019 to December 2020 based on valuable data collected from General Statistic Office of Vietnam Methods and processes 2.1 Time series analysis method Forecasting process: Step 1: Identifying the data LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com Testing whether the sequence is multiplicative or additive by observing the fluctuation trend of the sequence Step 2: Excluding the seasonal factor from the sequence The seasonal factor is adjusted by using the MA ratios: Calculate the CMA4 if the sequence is sorted by quarter, or CMA12 if the sequence is sorted by month Calculate the ratio of the observations equaling the ratio between the original series and the moving average series: Series of ratios: 𝒀𝒕 𝒀𝑴𝑨 𝒕 = 𝒀 𝟏 𝟑 𝒀 𝟏 𝟒 𝒀𝑴𝑨 𝟏 𝟑 , 𝒀𝑴𝑨 𝟏 𝟒 ,…, 𝒀 𝒎 𝟐 𝒀𝑴𝑨 (𝒎)𝟐 Calculate the ratios for each quarter / month Adjust the original series by seasonal indexes: there is a seasonal index every quarter / month that reflects the impact of the season The adjusted series values are:  Multiplicative model:𝒀𝑺𝑨𝑹 𝒋 𝒊 = 𝒀 𝒋 𝒊 𝑺𝑹 𝑺𝑨𝑹  Additive model: 𝒀𝑺𝑨𝑫 𝒋 𝒊 = 𝒀 𝒋 𝒊 - SDi Step 3: Estimating the trend function and forecasting Estimate the trend function Violation tests:  Omitted variables test  Autocorrelation test  Variance test  Normal distribution of noise test Forecast in the sample Step 4: Combining the trend and seasonal factors to get final forecast result From the forecast result in the sample with the lowest MAPE, we can conduct the forecast outside of the sample to get YSAF The adjusted series values are:   Multiplicative model: Yf =𝒀𝑺𝑨𝑭 SR Additive model: Yf = 𝒀𝑺𝑨𝑭 +SD 2.2 Box-Jenkins method and seasonal ARIMA model Box-Jenkins method, or ARIMA(p, d, q) model, consisting of:  AR(p): the p-order autoregressive model  Y(d): the stationary sequence with the d-order difference  MA(q): the q-order moving average model has the equation: Y d = c + Φ1 Y(d)t-1 + … + Φp Y d t-p + θ1 ut-1 + … + θq ut-q + ut LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com The SARIMA model was developed from the ARIMA model to fit any seasonal time series data, whether they are quarters, 12 months in a year or days a week If the observed data series is seasonal, then the general ARIMA model is now called SARIMA(p, d, q)(P, D, Q), with P and Q respectively is the order of AR and MA, and D is the seasonal difference Forecasting process: Step 1: Excluding the seasonal factor from the sequence Step 2: Applying SARIMA model for the adjusted sequence Step 2.1 Stationarity test A time series is stationary if the mean, the variance, and the covariance (at different lags) stay the same over time The sequence must be stationary in order to be used to predict the trend in future periods Average: E (Yt) = μ = const Variance: Var (Yt) = const Covariance: Cov (Yt, Yt-p) = To see whether the sequence is stationary or not, we can use the auto regression model Yt = ρYt-1 Ut with the hypothesis: 𝐻0 : ρ = 1, Yt is non − stationary 𝐻1 : ρ < 1, 𝑌𝑡 𝑖𝑠 𝑠𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑟𝑦    If the sequence is stationary at level, we have I (d = 0) If the first difference of the sequence is stationary, we have I (d = 1) If the second difference of the sequence is stationary, we have I (d = 2) Step 2.2 Determining the p, q values of ARIMA model After stationarity test, we determine the order of components AR and MA through AutoCorrelation Function (ACF) and Partial Auto-Correlation Function (PACF)  The p-order regression model, AR(p) is written as follows: 𝑝 𝑌𝑡 = ∅0 + ∅𝑖 𝑌𝑡−𝑖 + 𝑢𝑡 𝑖=1 The value of p is determined through the PACF correlation scheme  The q-order moving average model, MR(q) is written as follows: 𝑞 𝑌𝑡 = 𝜃0 + 𝜃𝑖 𝑢𝑡−𝑗 + 𝑢𝑡 𝑗 =1 The value of q is determined through the PACF correlation scheme Step 2.3 Testing the hypothetical conditions of the model  Stability and invertibility test  White noise test LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com  Forecast quality test Step 2.4 Forecasting outside of the sample The model is suitable if it passes all of the above tests, and will be used for forecasting Step 3: Forecasting the original data series After getting the forecasted results of the adjusted series, multiply or add the seasonal factors to get the forecasted results of the original series Data and forecast results 3.1 Data description: - The data used in this research is the total export value of Vietnam per month (unit: billion USD) from January 2011 to September 2019, provided by GENERAL STATISTICS OFFICE of VIETNAM on their website https://www.gso.gov.vn/ in Vietnam, and forecasted using EVIEWS programme - Resize data The very first step to when forecasting by EVIEWS is to expand the observations to add the periods that you want to forecast In our case, as we attempt to forecast Vietnam’s export value from October 2019 to December 2020, we click on Workfile window, Range: 2011M01 2019M09 – 105 observations at the Date specification, we change the End date to 2020M12 Now the model have 120 observations, with 15 forecast observations from 2019M10 to 2020M12 - To check whether the data have seasonal factor or not, we click on the data exportView Graph  Seasonal Graph EXPORT by Season 28,000 24,000 20,000 16,000 12,000 8,000 4,000 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Means by Season Look at the graph, it is clearly apparent thatthe means by season between the periods has a fluctuated difference, so this data series has a seasonal factor Therefore, when running the model for forecasting, we have to extract the seasonal factor from the data series in order to have our forecast at high accuracy LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 3.2 The process of forecasting - Step 1: Identify the data By using the command line export, we have the following graph: EXPORT 28,000 24,000 20,000 16,000 12,000 8,000 4,000 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 Looking at the graph, it is given that the amplitude is widening over time Thus, we conclude that the data is suitable for multiplicative model - Step 2: Seasonal Adjustment (Detach the seasonal component) To detach the seasonal component of this data, we as follows:    Open file exportProc  Seasonal Adjustment  Moving Average Methods At the Adjustment Method box, we choose Ratio to moving average – Multiplicative At the Series to calculate box, we name the Adjusted series as exportsa, and the seasonal factoras sr Sample: 2011M01 2020M12 Included observations: 105 Ratio to Moving Average Original Series: EXPORT Adjusted Series: EXPORTSA Scaling Factors: 0.989336 0.755655 1.036596 0.991417 1.024735 1.015298 1.044989 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 10 11 12 1.088853 1.001135 1.056739 1.034498 1.004594 Since the third steps, each method has different approaches:  Time series analysis method with multiplicative model - Step 3: Estimate the exportsa series based on the trend function On theCommand window, we type the commands: genr t=@trend(2011m01)to create trend variable t ls exportsa c t để estimate exportsa in accordance to trend variable t Dependent Variable: EXPORTSA Method: Least Squares Date: 12/11/19 Time: 22:22 Sample (adjusted): 2011M01 2019M09 Included observations: 105 after adjustments Variable Coefficient Std Error t-Statistic Prob C T 6673.193 142.5878 197.0313 3.273565 33.86870 43.55734 0.0000 0.0000 R-squared Adjusted R-squared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.948506 0.948006 1016.704 1.06E+08 -875.0327 1897.242 0.000000 Mean dependent var S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 14087.76 4458.812 16.70538 16.75594 16.72587 1.169695 As T has very big T-statistic and P-value =0.0000 < 5%  the model is statistically significant at significance level 5% Omitted Variable Test: We have the hypothesis: H0 : The model does not omit any variable H1 : The model omits variable On the estimation window, we click View  Stability Diagnostics Ramsey RESET Testwe chooseNumber of fitted terms = Specification: EXPORTSA C T Omitted Variables: Squares of fitted values t-statistic F-statistic Likelihood ratio Value 6.641224 44.10586 37.73265 df 102 (1, 102) Probability 0.0000 0.0000 0.0000 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com According to this result, we haveP-value = 0.0000 5% ->The variable is non-stationary at Level We test whether the model is stationary or not at first differenceby choosing1st differenceIntercept Null Hypothesis: D(EXPORTSA) has a unit root Exogenous: Constant Lag Length: (Automatic - based on SIC, maxlag=12) Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level t-Statistic Prob.* -12.49605 -3.495677 -2.890037 -2.582041 0.0000 *MacKinnon (1996) one-sided p-values Because P-value = 0.0000 < 5% -> the data is stationary at first difference - Testing statistical significance of trend component in the model: choosing View → Unit Root Test → 1st difference, Trendand Intercept, we have: Variable Coefficient Std Error t-Statistic Prob D(EXPORTSA(-1)) -2.191374 D(EXPORTSA(1),2) 0.324109 C 204.0766 @TREND("2011M 01") 2.696672 0.174815 -12.53538 0.0000 0.096284 165.1755 3.366176 1.235514 0.0011 0.2196 2.697111 0.999837 0.3199 It is clear that the trend factor @TREND(“2011M01”) has the P-value much bigger than 5%, which means that it has no statistical significance Therefore, we can exclude the trend factor to run the model using seasonal ARIMA method - Step 4: Find p and q by PACF and ACF LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com We open file exportsaView  Correlogram On the above PACF and ACF charts, correlation coefficients are statistically significantat lag 1, then gradually reduce to Coefficient p is statistically significant at PCF lag 1and lag (exceed the boundaries) Similarly, qis statistically significant at ACF lag and lag (exceed the boundaries).After testing various models, we decide that the model ARIMA (3,1,2) is the best fit We run the command ls d(exportsa) c ar(1) ar(3) ma(1) ma(2) and get the result as follows: Dependent Variable: D(EXPORTSA) Method: Least Squares Date: 12/09/19 Time: 23:07 Sample (adjusted): 2011M05 2019M09 Included observations: 101 after adjustments Convergence achieved after 10 iterations MA Backcast: 2011M03 2011M04 Variable Coefficient Std Error t-Statistic Prob C AR(1) AR(3) MA(1) MA(2) 151.4307 -1.136863 0.223737 0.278084 -0.700130 24.27451 0.064109 0.067404 0.079470 0.078483 6.238260 -17.73319 3.319367 3.499243 -8.920844 0.0000 0.0000 0.0013 0.0007 0.0000 R-squared Adjusted Rsquared S.E of regression Sum squared resid Log likelihood F-statistic Prob(F-statistic) 0.518225 Mean dependent var 155.4159 0.498151 785.5056 59233831 -814.0479 25.81580 0.000000 S.D dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter Durbin-Watson stat 1108.825 16.21877 16.34823 16.27118 1.963457 Inverted AR Roots Inverted MA Roots 38 71 -.76-.07i -.99 -.76+.07i LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com At the significance level of 5%, all coefficients are statistically significant as their Pvalues are much smaller than 0.05 - Step 5: Checking presumative conditions Stability and Invertibility of model From the table above, we see that all the roots are 0.38; -0.76 ± 0.07i; 0.71 and 0.99, respectively, which are bigger than -1 and smaller than 1, thus they all lie inside the unit circle Therefore, this model is stable and invertible White noise test At the estimation window, we click View → Residual Diagnostics → Serial Correlation → Correlogram - Q-statistics → chooseLags to include = 12, we have the Correlogram of Residuals Table: All coefficients not surpass the margin  There is no autocorrelation at 12 consecutive lags Therefore, the model passes the white noise test Forecast quality test Continued at the estimation window, we click Estimate Forecast We set the Forecast name as exportsaf1 (to distinguish with another in time series analysis test) We choose the sample from 2013m08 to 2015m08 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 20,000 Forecast: EXPORTSAF1 Actual: EXPORTSA Forecast sample: 2013M08 2015M08 Included observations: 25 Root Mean Squared Error 729.3714 Mean Absolute Error 601.1484 Mean Abs Percent Error 4.727802 Theil Inequality Coefficient 0.028449 Bias Proportion 0.466427 Variance Proportion 0.123663 Covariance Proportion 0.409910 18,000 16,000 14,000 12,000 10,000 8,000 III IV I II 2013 III IV 2014 I II III 2015 EXPORTSAF1 ± S.E It can be seen that Mean Absolute Percent Error = 4.727802 < 5% the model has good forecast quality and is reliable - Step 6: Outside Sample Forecast In the Forecast box, we choose the sample from 2019m10 to 2020m12 and get the results: 28,000 27,000 26,000 25,000 24,000 23,000 22,000 21,000 M10 M11 M12 M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 M11 M12 2019 2020 EXPORTSAF1 2019M10 2019M11 2019M12 2020M01 2020M02 2020M03 2020M04 2020M05 2020M06 2020M07 2020M08 2020M09 2020M10 2020M11 2020M12 23546.32 22903.26 23839.69 23113.09 24084.96 23479.29 24294.99 23874.81 24506.70 24260.53 24736.08 24626.53 24985.70 24973.48 25252.57 ± S.E We combine the seasonal component to get the final forecast results On the Command window, we typeGenr exportf1 = exportsaf1 * sr 2019M10 2019M11 2019M12 2020M01 2020M02 2020M03 2020M04 2020M05 2020M06 2020M07 2020M08 2020M09 2020M10 2020M11 2020M12 24882.30 23693.39 23949.21 22866.62 18199.92 24338.55 24086.46 24465.35 24881.59 25351.99 26933.96 24654.47 26403.36 25835.02 25368.59 LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com 3.3 Compare the forecast results between two methods 30,000 25,000 20,000 15,000 10,000 5,000 2011 2012 2013 2014 EXPORTF1 2015 2016 2017 EXPORTF2 2018 2019 2020 EXPORT Looking at the graph, both forecast methods show the tendency of export value to overally increase in comparation with previous years; exponentially decline in the first quarter, then increase for the last three quarters Both forecast results are fit with the data Because time series analysis method has smaller MAPE, we choose this method’s forecast results The forecasted export values of Vietnam are represented in the graph below: 2019M10 2019M11 2019M12 2020M01 2020M02 2020M03 2020M04 2020M05 2020M06 2020M07 2020M08 2020M09 2020M10 2020M11 2020M12 24528.00567989306 24260.87865835643 23803.97246366137 23685.61444725987 18278.73805844323 25334.62440459529 24481.78077614624 25567.04360738367 25594.36366688558 26616.11848975313 28021.04738294389 26030.92104063317 27761.74000664676 27459.39537180636 26942.25137118548 Conclusion In our research, we use time series analysis method and Box-Jenkins method using ARIMA model with seasonal component to forecast the export value of Vietnam in the period of 15 months, and choose the former method as it has the most fit forecast result According to the forecast,Vietnam’s total export value will slightly increase with considerable fluctuation due to seasonal factor However, in reality there may be more exogenous factors that affect the total export value of Vietnam which we did not include, which could lead to certain errors in the forecast In addition, during the process of running models, we have some slight errors such as the analysis method model still LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com does not have normal distribution As this is the first time we forecast data series, mistakes are inevitable We are terribly sorry for such inconvenience, and we promise to improve in the future forecasts Nevertheless, this research may providepractical information for investors as well as policymakers in finding appropriate solutions to improveVietnam’s export and economic growth Therefore, we have some suggestions to increase Vietnam’s total export value as follows:  Expand scale of production In order to boost exports, export enterprises must utilize their production capacity to expand production scale, increasing production output to meet market demand Enterprises should invest in facilities and input materials, thus they can immediately respond to the fluctuatuons in their export products’ market which are occuring and will be available  Improve product quality To promote exports, enterprises must focus on improving the quality of their products to be able to compete with products of other countries Currently, the direction for export enterprises is to apply an international quality standard system to affirm the quality of their products, and strictly control their costs of production in order to offer the most reasonable prices to satisfythe demand of international consumers  Increase investment in technological innovation.Enterprises can invest in the import or transfer of new technologies, in order to improve the quality of export products and the competitiveness of Vietnamese products in the international market  Diversification in exportproducts Enterprises should diversify their products by creating different designs or using various materials to make their products distinguish And to this, businesses should focus more to the capacity of their product design department.Therefore, the most effective investment for exporters is training and developing their design team in combination with investigating and researching market, identifying the trends of consumption to help their products satisfy customers’ demand, applying production processes according to international standards, etc References 1, “PHÂN TÍCH CHUỖI THỜI GIAN”, Nhu Phong, Quản lý sản xuất NXBĐHQG 2013 ISBN: 978-604-73-1640-3 2, Box, George; Jenkins, Gwilym (1970) Time Series Analysis: Forecasting and Control San Francisco: Holden-Day 3, TỔNG CỤC THỐNG KÊ, Số liệu thống https://www.gso.gov.vn/default.aspx?tabid=629 kê, Giá trị xuất nhập LUAN VAN CHAT LUONG download : add luanvanchat@agmail.com ... time series analysis method and Box- Jenkins method using ARIMA model with seasonal component (SARIMA) to forecast the total export value of Vietnam from October 2019 to December 2020 The forecast... box, we choose the sample from 2019m10 to 2020m12 and get the results: 27,000 2019M10 2019M11 2019M12 2020M01 2020M02 2020M03 2020M04 2020M05 2020M06 2020M07 2020M08 2020M09 2020M10 2020M11 2020M12... total export value of Vietnam from October 2019 to December 2020 based on valuable data collected from General Statistic Office of Vietnam Methods and processes 2.1 Time series analysis method Forecasting