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Sains Malaysiana 54(10)(2025): 2539-2551
http://doi.org/10.17576/jsm-2025-5410-16
Multiplicative Error Model Based on Robust Estimation:
Evidence from (Model Ralat Pendaraban Berdasarkan Keteguhan Anggaran: Bukti daripada
TING LI* & SAIFUL IZZUAN HUSSAIN
School of Mathematical
Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia,
Received: 20
December 2024/Accepted: 28 August 2025
Abstract
This
study presents a robust estimation approach for the Multiplicative Error Model
(MEM), developed for analyzing non-negative,
high-frequency financial time series data. Although maximum likelihood
estimation (MLE) is widely used, it is very sensitive to outliers and shows
poor results for small sample sizes. To address this problem, we propose a
self-weighted M-estimation method that accounts for infinite variance and
weights outliers downwards, thereby improving the stability and robustness of
the estimation. Simulation studies with four distributions confirm the superior
performance of this method compared to MLE and LAD estimators. An empirical analysis
using five-minute price spread data of eight major Chinese commodity futures -
gold, petroleum asphalt, soybean, iron ore, soybean oil, corn, sugar, and
rapeseed oil - demonstrates the practical advantages of this method. The
results show a consistent improvement in model fit, which translates into lower
AIC values and confirms the effectiveness of self-weighted M-estimation for
noisy, high-frequency financial data.
Keywords: Empirical analysis; high-frequency data;
Multiplicative Error Model; self-weighted M-estimation
Abstrak
Penyelidikan ini memperkenalkan pendekatan penganggaran teguh bagi Model Ralat Pendaraban (MEM) yang dibangunkan untuk menganalisis data siri masa kewangan frekuensi tinggi yang bukan negatif. Walaupun kaedah penganggaran kebolehjadian maksimum (MLE) digunakan secara meluas, namun ia sangat sensitif terhadap nilai terpencil dan menunjukkan prestasi yang lemah apabila saiz sampel kecil. Bagi mengatasi masalah ini, kajian ini mencadangkan kaedah penganggaran berpemberat-kendiri-M yang mengambil kira varian tak terhingga dan memberikan pemberat lebih rendah kepada nilai terpencil, sekali gus meningkatkan kestabilan dan keteguhan anggaran. Kajian simulasi yang melibatkan empat taburan menunjukkan prestasi kaedah ini lebih baik berbanding anggaran MLE dan
LAD. Analisis empirik yang menggunakan data harga lima-minit bagi lapan kontrak niaga hadapan komoditi utama China - emas, asfalt petroleum, soya, bijih besi, minyak soya, jagung, gula dan minyak biji rapa - membuktikan kelebihan praktikal kaedah ini. Hasil kajian menunjukkan peningkatan tekal dalam kesesuaian model yang diterjemahkan kepada nilai AIC yang lebih rendah, sekali gus mengesahkan keberkesanan penganggaran berpemberat-kendiri-M bagi data kewangan frekuensi tinggi yang bising.
Kata kunci: Anggaran berpemberat-kendiri-M; analisis empirik; data frekuensi tinggi; Model Ralat Pendaraban
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