Analysis and forecasting of the consumer price index for food and catering services in Vietnam using an ARIMA model

Introduction

The consumer price index (CPI) is a central measure of changes in household living costs and inflation. In Vietnam, food and catering services form a major CPI group because they cover staple food, other food products, and meals consumed away from home. Their prices directly affect household purchasing power and can transmit supply, transport, fuel, weather, disease, and seasonal shocks to headline inflation. In 2024, prices in this group rose by 3.87% and contributed 1.30 percentage points to overall CPI growth. 1 Autoregressive integrated moving-average (ARIMA) models are widely used for short-term macroeconomic forecasting because they exploit the serial dependence in a variable's own history. International applications have forecast CPI in China, Jordan, and Zambia, as well as food-price inflation in Malaysia. 2 -5 Vietnamese studies have also applied ARIMA to headline CPI and inflation, obtaining different lag structures across sample periods. 6 -9 These studies confirm the usefulness of the Box-Jenkins framework, but most concern aggregate CPI or inflation rather than the food and catering services component. This article addresses that narrower empirical gap using monthly data for 2010-2024. Its objectives are to describe the series, determine its order of integration, select a parsimonious ARIMA specification, evaluate residual behaviour and forecast accuracy, and generate a 12-month baseline for 2025. The contribution is practical: food-related CPI is both socially salient and exposed to shocks that may not be visible in an aggregate price index.

Materials and Methods

Data

The study uses 180 monthly observations on Vietnam's CPI for food and catering services from January 2010 through December 2024, obtained from the General Statistics Office of Vietnam (GSO). The CPI is compiled from a representative basket and fixed expenditure weights for a specified base period. 10,11 The sample spans post-crisis recovery, the COVID-19 disruption, global food and energy-price volatility, and changes in domestic price administration. Estimation and diagnostic testing were performed in EViews.

ARIMA specification and model selection

For a time series 𝑦 𝑡 , an ARIMA(𝑝, 𝑑, 𝑞) model applies 𝑑 differences and represents the resulting stationary series using 𝑝 autoregressive and 𝑞 moving-average terms. In compact form,

𝜙(𝐵)(1 -𝐵) 𝑑 𝑦 𝑡 = 𝑐 + 𝜃(𝐵)𝜀 𝑡 ,

where 𝐵 is the backshift operator, 𝜙(𝐵) and 𝜃(𝐵) are the autoregressive and moving-average polynomials, and 𝜀 𝑡 is an innovation. Model construction followed the Box-Jenkins cycle of identification, estimation, diagnosis, and forecasting. 12,13 Stationarity was tested with the augmented Dickey-Fuller (ADF) test. The autocorrelation function (ACF) and partial autocorrelation function (PACF) then guided candidate lag selection. Specifications with statistically insignificant principal coefficients were removed, and the remaining models were compared using adjusted 𝑅 2

, regression standard error, Akaike information criterion (AIC), Schwarz criterion (SC/BIC), and Hannan-Quinn criterion (HQ). Lower information criteria and standard error were preferred, subject to diagnostic adequacy. Residual assessment comprised: (i) correlogram and Ljung-Box Qstatistics for serial correlation; (ii) an ADF test for residual stationarity; (iii) an ARCH test for conditional heteroskedasticity; and (iv) the Jarque-Bera test for normality. Forecast performance was evaluated from June to December 2024 using the absolute percentage error,

The reported errors are complemented by qualitative comparison of actual and fitted movements; this avoids presenting in-sample fit as definitive evidence of performance under future structural shocks.

Results and Discussion

Stationarity and model identification

Visual inspection showed monthly fluctuations around a stable level rather than a persistent deterministic trend. The ADF result in Table 1 rejects the unit-root null at the 1% level. The series was therefore modelled in levels, so 𝑑 = 0.

The PACF was prominent at lags 1 and 13, while the ACF was strongest at lag 1, decayed over lags 2-3, and displayed additional seasonal signals around lags 12 and 18. These patterns motivated combinations involving autoregressive lags 1, 12, and 13 and moving-average lags 1, 2, 3, 12, and 18. After excluding candidates with insignificant principal terms, five specifications remained.

Model estimation and selection

Residual diagnostics

The diagnostics give mixed evidence (Table 4). The residual ADF statistic is -12.22900 (𝑝 < 0.001), confirming residual stationarity.

The ARCH test does not reject constant conditional variance: the Ftest probability is 0.3769 and the Obs. × 𝑅 2 probability is 0.3687. These results support the stability of the residual variance.

However, correlogram Q-statistic probabilities at lags 3, 4, and 5 are 0.005, 0.014, and 0.031, respectively. Thus, short-lag dependence has not been eliminated completely, although probabilities exceed 0.05 from lag 6 onward. Residuals are also non-normal: skewness is 0.706656, kurtosis is 6.394018, and the Jarque-Bera statistic is 101.3761 (𝑝 < 0.001). ARIMA(12, 0, 1) is therefore useful as a compact forecasting baseline, but it is not a fully adequate stochastic description of extreme or asymmetric price movements.

Forecast evaluation and 2025 outlook

The holdout-style comparison for June-December 2024 is shown in Table 5. Absolute percentage errors range from 0.01% in October to 0.56% in November. The mean of the seven reported absolute per-centage errors is approximately 0.30%. The fitted series follows normal month-to-month movements closely, but it tends to understate abrupt peaks and troughs, as expected from a univariate model that has no direct information on harvest conditions, fuel and transport costs, disease outbreaks, or policy interventions. The 2025 baseline forecasts remain near 100 throughout the year (Table 6). The maximum is 100.74 in February and the minimum is 100.12 in March, a range of 0.62 index points. This profile implies no sustained acceleration under historical dynamics. It should not be read as a structural inflation projection because the model cannot anticipate exogenous supply disruptions. The results are broadly consistent with prior evidence that ARIMA can provide accurate short-horizon CPI baselines. 2,3,8 Nevertheless, the remaining residual autocorrelation and heavy-tailed errors are consequential for food prices, which are especially exposed to shocks. Future work should compare seasonal ARIMA, intervention models, and multivariate specifications incorporating fuel prices, transport costs, weather, exchange rates, and food-supply indicators. Forecast evaluation should also use a longer rolling-origin test period.

Conclusion

Monthly food and catering services CPI in Vietnam is stationary in levels over 2010-2024 according to the reported ADF test. Of five retained candidates, ARIMA(12, 0, 1) provides the strongest combination of fit and parsimony, with AIC of 2.449391, SC of 2.520345, and HQ of 2.478160. Forecast errors for June-December 2024 are small, and the 2025 baseline remains in a narrow 100.12-100.74 interval.

The model is informative but not definitive. Residual stationarity and the absence of ARCH effects support its use, whereas autocorrelation at lags 3-5 and pronounced non-normality limit statistical inference and the treatment of extreme shocks. Authorities may therefore use the forecasts as one input to monthly monitoring, accompanied by real-time information on crop supply, inventories, transport and fuel costs, weather, disease, and seasonal demand. For policy and business planning, the central implication is preparedness rather than mechanical reliance on a point forecast. Public agencies can strengthen early-warning systems and coordinate essentialfood supply around holidays and adverse weather. Food producers, distributors, and catering firms can use the baseline for procurement and inventory planning while maintaining contingency suppliers and financial buffers. These measures would reduce the pass-through of temporary supply disruptions to household living costs.

References

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