Application of ARIMA model in forecasting Vietnam’s black pepper export price to the U.S. market

Introduction

Pepper is Vietnam's main perennial crop, totaling over 131,8 thousand hectares of cultivated land, 95% of which is situated mainly throughout the Southeast and Central Vietnam. With high economic value, pepper is Vietnam's main agricultural exports, reaching 267 thousand tons, worth 912 million USD in 2023 (Nguyễn Hạnh, 2024) [2] . At present, Vietnam has exported black pepper to over 105 countries and territories (General Statistic Office of Vietnam, 2021), with U.S.A, China, Germany, Netherlands, India and Saudi Arabia having been Vietnam's main and biggest markets. In which, exports to the U.S. In which, exports to the US have always accounted for about 20% of Vietnam's total black pepper export volume to the world. Furthermore, Vietnam is able to utilize opportunities from global trade agreements such as CPTPP and EVFTA, which promote exports to new potential markets (Nông Hữu Tùng and Phạm Công Toản, 2022) [3] . Vietnam is the world's largest producer and exporter of black pepper, accounting for 40% of global production and 60% of market share (followed by Brazil and Indonesia).However, Vietnam Import-Export Report by the Ministry of Industry and Trade (Ministry of Industry and Trade, 2023) indicates that pepper exports are facing a sharp decline in output. More specifically, in 2022, Vietnam's black pepper output decrease by 12.4% compared to 2021, to 228,7 thousand tons, but the average export value recorded a growth of 3.5% compared to the previous year. In 2022, the U.S. remained the largest export market for Vietnamese pepper, with an export volume of 57,809 tons, down 2.5% from the previous year. While China, Vietnam's pepper second largest export market, recorded the sharpest decline, with a decrease of 46.4% (equivalent to 17,761 tons), down to 20,498 tons compared to 2021. And in several major export markets, black pepper export turnover had been declining, including: Pakistan (-45.4%); France (-23.6%); Egypt (-45.4%); Turkey (-26.1%); and Saudi Arabia (-83.1%). Additionally, Vietnam has been losing black pepper market share to Brazil and Indonesia that have much more competitive pricing, a lower export price as these markets apply a lower shipping rates compared to Vietnam. At the same time, political volatility, especially the tensions between Russia and Ukraine, are continuing to affect pepper consumption demand. Furthermore, geopolitical tensions are driving up inflation, leading to a global trend of consumer tightened spending. These are all negatively impacting import and export of many goods, including that of pepper. Therefore, global pepper prices will continue to fluctuate in the coming period as pepper demand continues to rise and fall erratically (Phan Thị Xuân Huệ, 2023) [4] . Consequently, forecasting Vietnam's black pepper price to the U.S. market is of great importance for producers, exporters throughout the country, and to the Vietnamese pepper industry as a whole. ARIMA (Autoregressive Integrated Moving Average) model is widely known and widely used in the field of forecasting time series for its outstanding strengths. ...

Moving-average model of order q (MA(q)), is a process describe through linear weighted equation of random errors and its lagged values. The model is written as follows. ...

Autoregressive integrated moving average model (ARIMA (p,d,q)) is built upon the integration of two processes: (1) and ( 2). The general equation for the ARIMA (p, d, q) model is.

The Box-Jenkins method consists of four iterative steps: (i) Model identification, (ii) Estimation, (iii) Diagnostic and checking, and (iv) Forecast, as presented below:

Step 1: Model identification Identifying ARIMA (p, d, q) model involves finding the appropriate values for p, d, and q. Where d represents the differencing order of the time series, p represents the autoregressive order, and q represents the moving average order. Determining p and q depends on the SPAC = f(t) and SAC = f(t) plots, with SAC being the sample autocorrelation function (SACF) and SPAC being the sample partial autocorrelation function. Selecting an AR(p) model relies on the SPAC plot if it exhibits high values at lags 1, 2, ., p and declines abruptly afterward, while the SAC gradually dies out.

Similarly, choosing an MA(q) model is based on the SAC plot if it shows high values at lags 1, 2, ., q and drops sharply after q, while the SPAC gradually dies out.

Step 2: Estimate the parameters of ARIMA (p, d, q) model: Parameters of the ARIMA model will be estimated using least squares method.

Step 3: Diagnostic and checking After identifying the parameters of the ARIMA model, then a diagnostic need to be done to test for white noise characteristic in error term e t , homoscedasticity of residuals, normality of residuals and stationarity of the ARIMA model.

Step 4: Forecast Based on the equation of ARIMA model, analyze point forecast and forecast confidence interval in ARIMA model.

Estimated results and discussion

Stationarity test: In mathematics, stationarity is used as a tool in time series analysis. In time series analysis, stationarity testing is a crucial step to ensure the statistical validity to form a model. A stationary process is a random process where the mean and variance of the errors remain constant over time. In reality, most economic time series (original series) are non-stationary. This implies that the mean and variance of these time series change over time. However, differencing data often transforms non-stationary time series into stationary ones. Data series used in ARIMA model is assumed to be stationary. Therefore, to forecast the amount of international travelers to Vietnam with ARIMA model, we have to identify whether the input data are stationary. To confirm this, it is possible to first rely on direct observation of the graph of the time series, and then test it. We utilize a widely used testing method, Augmented Dickey-Fuller (ADF), a method, which in econometrics is known as unit root test for root and differenced time series. Figure 1 shows that the monthly export price of black pepper from Vietnam to the US (denoted as GIA) is unstable and has an increasing trend. Specifically, its mean tends to increase over time periods. This suggests that the export price of black pepper from Vietnam to the US is non-stationary. However, when the first-order difference of this series is taken, the new series, the change in the export price of black pepper from Vietnam to the US (abbreviated as dgia), does not have a clear trend and fluctuates around a certain average value (Figure 3). This is considered a characteristic of a stationary series. To confirm these speculations, we use the ADF and PP test methods to see if the results are consistent.

Source: Calculated with Eviews 12 by authors with statistics Stationary characteristic test results using ADF and PP is given below in table 1. From table 1, values at the 1%, 5% and 10% conclude dgia is stationary series. Therefore, both of the testing methods are uniformed and we can conclude that dgia is stationary series.

Building an ARIMA Model for the Time Series of Vietnamese Black Pepper Export Price Volatility to the US Market:

To construct the ARIMA model, we utilize a time series dataset comprising 62 observations from January 2019 to February 2024. The original data is represented by the gia series, and the first-order differenced data is represented by the dgia series.

Step 1: Identification (identify the values of p, d and q):

The gia series test above indicates that the series is stationary at first-order differencing, implying that d=1. By using autocorrelation and partial autocorrelation function plots of dgia time series, we determined the order of the ARIMA model (p,1,q) to be p = 2 and q = 0.

Step 2: Estimate ARIMA (2,1,0) model: Estimating the model using maximum likelihood method and test to retain regression coefficients that were statistically significant at 5% significance level. The results are as follows.

Source: Calculated with Eviews 12 by authors with statistics.

Step 3: Model testing and diagnostics *Test that the residual is stationary series Results from testing residual series (e) with ADF and PP testing methods are shown in table 3 below. From Table 4, we have all Prob (probability) larger than 5%, so we accept H o , the residuals in model ( 4) have white noise characteristics.

Homoscedasticity test

We use ARCH test to identify model's homoscedasticity.

Null hypothesis Ho: the model does not have homoscedasticity.

Alternative hypothesis H1:

The model has homoscedasticity. With  = 5%, test done with Eviews 12 give the results show in table 4. The stability test conducted using Eviews 12 software yielded the results shown in Figure 6. From figure 6, we can see that all the inverse roots lie within the unit circle. From the tests above, the ARIMA (2,1,0) model meets the stability conditions and the residual term is white noise, with a constant variance of the error.

Step 4: Forecast: From model (4), we identify. 5 shows that the forecasted values for Vietnamese black pepper export price to the U.S from March to April 2024 is close to reality. This states that ARIMA (2,1,0) model is able to explain fluctuations of black pepper prices However, future forecast points involve larger errors. Therefore, it is necessary to update the data regularly to provide more realistic forecasts.

Conclusion

The fluctuations in the price of Vietnamese pepper exports to the US market is a time series follow an ARIMA model (2,1,0). Base on this model we can give short-term forecast Vietnam's black pepper export price to the U.S. market. Results for months from March 2024 to August 2024, indicates little error compared to reality, with up to 0,22 units, which is considerable in a volatile global economy at present. Nevertheless, the ARIMA model can be used to forecast, while not being optimal as the dependencies in the model are assumed to be linear. Therefore, forecast results from ARIMA model (2,1,0) export price of Vietnamese black pepper to the US market can serve as a reference for management agencies, policymakers and businesses to implement guidelines, strategies, and propose solutions and recommendations for developing black pepper

Acknowledgement

cultivated areas across the country, especially for applying technology in production to improve productivity and sustainability in the future.

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