(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 t

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: PhD Chu Thi Mai Phuong Class: KTEE 418.1

Students:

Hanoi, December 12, 2019

Contents

Abstract 3

1 Introduction 3

2 Methods and processes 3

2.1 Time series analysis method 3

2.2 Box-Jenkins method and seasonal ARIMA model 4

3 Data and forecast results 6

3.1 Data description: 6

3.2 The process of forecasting 7

4 Conclusion 17

5 References 18

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

1 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

2 Methods and processes 2.1 Time series analysis method Forecasting process:

Step 1: Identifying the data

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: 𝒀𝒀𝒕

𝒕

𝑴𝑨 = 𝒀 𝟏 𝟑𝒀

𝟏 𝟑

𝑴𝑨 ,𝒀 𝟏 𝟒𝒀

𝟏 𝟒

𝑴𝑨 , … ,𝒀 𝒎 𝟐𝒀

(𝒎)𝟐

𝑴𝑨 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:𝒀 𝒋 𝒊𝑺𝑨𝑹 = 𝒀 𝒋 𝒊𝑺𝑹

 Additive model: 𝒀 𝒋 𝒊𝑺𝑨𝑫 = 𝒀 𝒋 𝒊𝑺𝑨𝑹 - 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 + Φ 1 Y(d) t-1 + … + Φ p Y d t-p + θ 1 u t-1 + … + θ q u t-q + u t

The SARIMA model was developed from the ARIMA model to fit any seasonal time series data, whether they are 4 quarters, 12 months in a year or 7 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) = 0

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 Auto-Correlation Function (ACF) and Partial Auto-Auto-Correlation Function (PACF)

 The p-order regression model, AR(p) is written as follows:

𝑌𝑡 = ∅0 + ∅𝑖𝑌𝑡−𝑖

𝑝

𝑖=1

+ 𝑢𝑡

The value of p is determined through the PACF correlation scheme

 The q-order moving average model, MR(q) is written as follows:

𝑌𝑡 = 𝜃0+ 𝜃𝑖𝑢𝑡−𝑗

𝑞

𝑗 =1

+ 𝑢𝑡 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

 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

3 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 do 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

4,000 8,000 12,000 16,000 20,000 24,000 28,000

Means by Season

EXPORT 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

3.2 The process of forecasting

- Step 1: Identify the data

By using the command line export, we have the following graph:

4,000 8,000 12,000 16,000 20,000 24,000 28,000

2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

EXPORT

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 do 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:

8 1.088853

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 6673.193 197.0313 33.86870 0.0000

T 142.5878 3.273565 43.55734 0.0000 R-squared 0.948506 Mean dependent var 14087.76 Adjusted R-squared 0.948006 S.D dependent var 4458.812 S.E of regression 1016.704 Akaike info criterion 16.70538 Sum squared resid 1.06E+08 Schwarz criterion 16.75594 Log likelihood -875.0327 Hannan-Quinn criter 16.72587 F-statistic 1897.242 Durbin-Watson stat 1.169695 Prob(F-statistic) 0.000000

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 H

1: The model omits variable

On the estimation window, we click View  Stability Diagnostics Ramsey RESET Testwe chooseNumber of fitted terms = 1

Specification: EXPORTSA C T Omitted Variables: Squares of fitted values

Value df Probability t-statistic 6.641224 102 0.0000 F-statistic 44.10586 (1, 102) 0.0000 Likelihood ratio 37.73265 1 0.0000

According to this result, we haveP-value = 0.0000 <α = 5%Reject H0, accept H1

The model has omitted variable(s)

After adding variables t^2, t^3, the model is statistically significant,but still not pass the Omitted variable test

Specification: EXPORTSA C T T^2

Omitted Variables: Squares of fitted value

Value df Probability t-statistic 2.188769 101 0.0309

F-statistic 4.790708 (1, 101) 0.0309

Likelihood ratio 4.865928 1 0.0274

Specification: EXPORTSA C T T^2 T^3 Omitted Variables: Squares of fitted values

Value df Probability t-statistic 3.320142 100 0.0013 F-statistic 11.02335 (1, 100) 0.0013 Likelihood ratio 10.97988 1 0.0009

We decide to run the least square model of log(exportsa): ls log(exportsa) c t

Dependent Variable: LOG(EXPORTSA) Method: Least Squares

Date: 12/11/19 Time: 23:06 Sample (adjusted): 2011M01 2019M09 Included observations: 105 after adjustments Variable Coefficient Std Error t-Statistic Prob

C 8.962084 0.012285 729.5251 0.0000

T 0.010392 0.000204 50.91531 0.0000 R-squared 0.961786 Mean dependent var 9.502473 Adjusted R-squared 0.961415 S.D dependent var 0.322716 S.E of regression 0.063391 Akaike info criterion -2.660123 Sum squared resid 0.413898 Schwarz criterion -2.609571 Log likelihood 141.6565 Hannan-Quinn criter -2.639638 F-statistic 2592.369 Durbin-Watson stat 1.743267 Prob(F-statistic) 0.000000

As T has very big T-statistic and P-value =0.0000 <α= 5%  the model is statistically significant at significance level 5%

On the estimation window, we click View  Stability Diagnostics Ramsey RESET Test Number of fitted terms = 1

Specification: LOG(EXPORTSA) C T Omitted Variables: Squares of fitted values

Value df Probability t-statistic 1.315627 102 0.1912 F-statistic 1.730874 (1, 102) 0.1912 Likelihood ratio 1.766833 1 0.1838

As P-value >α = 5% not reject H0 the model has no omitted variable Testing Heteroskedasticity

We have the hypothesis:

H0: the model does not suffer from Heterokedasticity

H1: the model suffers from Heteroskedasticity

On the estimation window, we clickView Residual Diagnostics

HeteroskedasticityTestwechoose Breusch – Pagan – Godfrey

Heteroskedasticity Test: Breusch-Pagan-Godfrey F-statistic 4.422442 Prob F(1,103) 0.0379 Obs*R-squared 4.322714 Prob Chi-Square(1) 0.0376 Scaled explained SS 7.775218 Prob Chi-Square(1) 0.0053

It can be seen that P-value = 0.0379 <α = 0.05Reject H0

The model suffers from Heteroskedastictyat significance levelα = 5%

Testing Autocorrelation

We have the hypothesis: H0: The model does not have autocorrelation

H1: The model has autocorrelation

On the estimation window, we clickView Residual Diagnostics Serial Correlation

LM testwe choose Lags to include = 1

Breusch-Godfrey Serial Correlation LM Test:

F-statistic 1.629849 Prob F(1,102) 0.2046 Obs*R-squared 1.651399 Prob Chi-Square(1) 0.1988

It can be seen that P-value = 0.2047 >α = 0.05  Not reject H0

 The model does not have autocorrelation Normality Test

We have the hypothesis: H0: Data are normally distributed

H1: Data are not normally distributed

On the estimation window, we clickView Residual Diagnostics Histogram Normality Test

0 4 8 12 16 20 24

Series: Residuals Sample 2011M01 2019M09 Observations 105

Mean -3.56e-16 Median 0.011236 Maximum 0.203016 Minimum -0.217700 Std Dev 0.063086 Skewness -0.350692 Kurtosis 4.738439 Jarque-Bera 15.37422 Probability 0.000459