The Consumer Price Index (CPI) is a core indicator for measuring inflation levels and changes in the cost of living within an economy. Traditional aggregate modeling struggles to distinguish between the high volatility of food prices and the structural drivers of non-food prices, leading to insufficient forecasting accuracy and policy explanatory power. This study utilizes 175 months of monthly data from December 2011 to June 2026, employing a "food – non-food" layered SARIMAX framework.

By incorporating exogenous variables such as pork, vegetables, refined oil, PPI, and industrial value-added, and through lag extension, VIF collinearity filtering, and significance testing, separate year-on-year equations for food and non-food CPI were estimated. These were then combined using official weights to form the overall CPI. Out-of-sample 24-period rolling one-step-ahead forecasts showed that the non-food layer SARIMAX had an RMSE of 0.237, a slight improvement over the pure SARIMA's 0.239. The food layer faced greater forecasting difficulty during periods of sharp pork price fluctuations, with MAPE being impacted by the near-zero denominator effect.

Baseline projections indicate that the composite CPI year-on-year rate will fluctuate between 0.70% and 1.12% over the next 12 periods, maintaining a generally mild inflation outlook. Scenario stress tests suggest that a refined oil policy shock would impact the forecast for the first half of 2027 by approximately 0.02 to 0.03 percentage points, while a deflationary pressure scenario would result in a path slightly below the baseline.

Key Aspects of the Research Design

The study's core objective was to build a robust forecasting model. This involved constructing separate SARIMAX models for the food and non-food components to identify their unique drivers and seasonal structures. The methodology included a rigorous variable selection process, using VIF to eliminate multicollinearity and only retaining variables with p<0.1 significance. The models were validated through a rolling window back-test, comparing their performance against pure SARIMA models. The final step was to produce a 12-period baseline forecast and conduct multi-scenario stress tests, including an analysis of the contribution of each chosen factor.

Data Sources and Variable Selection

The data for the CPI and related variables was sourced from the National Bureau of Statistics and iFinD, covering the sample period from December 2011 to June 2026. For the food layer, candidate exogenous variables included pork, vegetable, and fruit prices, sow inventory, and holiday dummies. The non-food layer considered variables like Brent crude oil, domestic refined oil price adjustments, PPI, the Nannan Commodity Index, the USD/CNY exchange rate, manufacturing PMI, industrial value-added, and monetary aggregates.

After the comprehensive selection process, nine regressors were retained for the food layer, including current and lagged pork prices, vegetable prices, and various holiday effects. For the non-food layer, six regressors were selected, including lagged refined oil price adjustments, PPI, and industrial value-added. The stationarity of the series was confirmed, and the final model orders were selected based on the AIC criterion, with Ljung-Box tests confirming the residuals were white noise.

Model Estimation and Performance

The final food SARIMAX model was SARIMAX(0,1,2)×(1,0,1,12), with an AIC of 433.31, a significant improvement over the pure SARIMA's 554.69. The non-food model was SARIMAX(1,1,0)×(0,0,1,12), with an AIC of -29.46. The estimated coefficients provided clear economic interpretations. For example, the current pork price had a significant positive pull on food CPI, while the 12-period lag had a negative coefficient, reflecting the mean-reversion effect of the pig cycle. The non-food model showed that the lagged refined oil price adjustment was negatively correlated with non-food CPI, and industrial value-added had a positive effect.

Out-of-Sample Back-Test Results

The 24-period rolling one-step-ahead forecast (July 2024 to June 2026) provided a clear picture of the model's performance. For the non-food layer, the SARIMAX model achieved a slightly lower RMSE (0.237) and MAE (0.188) compared to the SARIMA. The food layer proved more challenging, with the SARIMAX RMSE (1.210) being slightly higher than the SARIMA's (1.148), though its MAE was slightly better. The composite CPI, when weighted together, showed very similar performance between the two models, demonstrating that the layered approach is effective but the overall forecast is constrained by the high volatility of the food component.

Beyond point accuracy, the study also examined directional accuracy. The food layer SARIMAX achieved a direction hit rate of 95.8%, the non-food layer 87.5%, and the composite CPI 83.3%, demonstrating the model's strong ability to identify trend changes, particularly for core inflation.

Baseline Forecast and Scenario Analysis

The baseline forecast for the next 12 periods (July 2026 to June 2027) suggests a mild inflation environment. The composite CPI year-on-year rate is projected to peak at around 1.12% in March 2027 and reach a trough of about 0.70% in December 2026, ending at roughly 0.95%. The food CPI is expected to remain in negative territory, continuing to be a drag on the headline figure, while non-food CPI is projected to stay positive, acting as the primary support.

Four scenarios were stress-tested: a baseline, an inflation scenario (Brent crude oil ×1.30), a deflationary pressure scenario (Nannan Commodity Index ×0.80, industrial value-added -2%), and a refined oil policy shock scenario. The results showed that the refined oil policy shock had the most significant, albeit still modest, impact, lowering the forecast by 0.02-0.03 percentage points from January 2027. The deflationary scenario produced a slightly lower path, while the inflation scenario's impact was negligible as Brent crude oil was not a direct significant variable in the final model, its influence only being indirect through domestic refined oil prices.

Study Limitations and Future Directions

The study acknowledges several limitations. The baseline assumption of flat future paths for exogenous variables may underestimate the cyclical volatility of commodities like oil and pork. The selection of significant variables, based on p<0.1, can change with a rolling sample window, affecting model stability. The linear SARIMAX model has difficulty capturing the non-linear turning points of the pig cycle, leading to larger forecast errors during periods of sharp price swings. Finally, the scenario stress tests were single-factor shocks and did not account for the correlated structure of multiple simultaneous shocks.

Future research could address these limitations by introducing time-varying parameters or Markov switching models to handle structural breaks. Using MIDAS or mixed-frequency data could improve the timeliness of high-frequency price indicators. Finally, employing a machine learning model like XGBoost to fit the residuals from the SARIMAX model could further enhance overall forecasting accuracy.