Forecasting the Consumer Price Index in Bandar Lampung Using the Autoregressive Integrated Moving Average (ARIMA) Model: An Applied Statistics Context for Mathematics Education

Abstract

The Consumer Price Index (CPI) is a key economic indicator for monitoring changes in household consumption prices and supporting inflation assessment, making accurate short-term forecasting important for regional economic planning. This study aims to analyze the historical pattern of the CPI in Bandar Lampung, identify the most appropriate Autoregressive Integrated Moving Average (ARIMA) model, and forecast CPI values for March 2026 to February 2027. A quantitative time-series design was employed using 100 monthly CPI observations from November 2017 to February 2026 obtained from Statistics Indonesia (BPS). The analysis followed the Box-Jenkins procedure, including stationarity testing, first-order differencing, model identification using ACF and PACF, parameter estimation, residual diagnostics, model comparison, and forecasting. The results showed that the original CPI series was non-stationary but became stationary after first-order differencing. Among the candidate models, ARIMA(1,1,1) was selected because its parameters were statistically significant and its residuals satisfied the white-noise assumption, with a Ljung-Box p-value of 0.9999. The model produced RMSE = 3.75, MAE = 0.94, MAPE = 0.85%, and MAD = 0.94. Forecasts indicated a gradual increase in CPI from 108.6605 in March 2026 to 109.6443 in February 2027. Therefore, ARIMA(1,1,1) provides an interpretable short-term forecasting model for supporting regional price monitoring and demonstrating an applied use of time-series analysis in mathematics education.