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Moh Fiqri Nurwahidin
Universitas Negeri Gorontallo
Mathematics

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ARIMA Modeling With Expectation–Maximization Kalman Imputation for Missing Values in Gorontalo Red Chili Prices Moh Fiqri Nurwahidin; Isran K. Hasan; Muhammad Rezky Friesta Payu
Journal of Mathematics, Computations and Statistics Vol. 9 No. 3 (2026): Volume 09 Issue 03 (September 2026)
Publisher : Jurusan Matematika FMIPA UNM

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35580/kfasnm79

Abstract

The price of red chili peppers at Gorontalo City Central Market fluctuates considerably and is classified as a volatile food commodity that can contribute to regional inflation. Accurate forecasting is therefore important for supporting price monitoring and planning. However, daily price records contain missing values, particularly on holidays when price recording was not conducted. This study applies the Expectation-Maximization Kalman (EM-Kalman) algorithm to impute missing observations before modeling the price series using ARIMA. The analysis uses daily price data from January 2023 to December 2025, consisting of 1,096 observations, of which 355 (32.39%) were missing. The data were divided into 80% training and 20% testing sets. The EM-Kalman algorithm successfully produced a continuous time series and converged at the 98th iteration. The ARIMA(0,1,2) model was selected based on the smallest AIC and BIC values, with statistically significant MA parameters and residuals satisfying the white-noise assumption based on the Ljung-Box test. The resulting model achieved a MAPE of 7.56% for the training data and 4.96% for the testing data, indicating highly accurate forecasting performance based on the adopted MAPE classification. These results indicate that the EM-Kalman and ARIMA combination can be used to reconstruct the incomplete price series and generate accurate forecasts of red chili pepper prices. However, this study does not compare EM-Kalman with alternative imputation methods or ARIMA with benchmark forecasting models, which should be considered when interpreting the forecasting performance.
Co-Authors Isran K Hasan