Sains Malaysiana 44(7)(2015): 1033–1039

A Comparison between Bayesian and Maximum Likelihood Estimations in Estimating

Finite Mixture Model for Financial Data

(Perbandingan antara Bayesian dan Anggaran Kebolehjadian Maksimum dalam Menganggar

Model Campuran Terhingga untuk Data Kewangan)

SEUK-YEN PHOONG* & MOHD TAHIR ISMAIL

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

Received: 22 May 2013/Accepted: 5 February 2015

ABSTRACT

Over the years, maximum likelihood estimation and Bayesian method became popular statistical tools in which applied to fit finite mixture model. These trends begin with the advent of computer technology during the last decades. Moreover, the asymptotic properties for both statistical methods also act as one of the main reasons that boost the popularity of the methods. The difference between these two approaches is that the parameters for maximum likelihood estimation are fixed, but unknown meanwhile the parameters for Bayesian method act as random variables with known prior distributions. In the present paper, both the maximum likelihood estimation and Bayesian method are applied to investigate the relationship between exchange rate and the rubber price for Malaysia, Thailand, Philippines and Indonesia. In order to identify the most plausible method between Bayesian method and maximum likelihood estimation of time series data, Akaike Information Criterion and Bayesian Information Criterion are adopted in this paper. The result depicts that the Bayesian method performs better than maximum likelihood estimation on financial data.

Keywords: Akaike information criterion; Bayesian information criterion; Bayesian method; finite mixture model; maximum likelihood estimation

ABSTRAK

Sejak beberapa tahun, anggaran kebolehjadian maksimum dan kaedah Bayesian menjadi alat statistik popular yang sesuai digunakan untuk model campuran terhingga. Trend ini bermula dengan adanya teknologi komputer sejak sedekad yang lalu. Selain itu, sifat asimptot bagi kedua-dua kaedah statistik juga menjadi salah satu daripada faktor utama dalam meningkatkan populariti kaedah ini. Perbezaan antara kedua-dua kaedah ini adalah parameter untuk anggaran kebolehjadian maksimum adalah tetap tetapi tidak diketahui manakala parameter bagi kaedah Bayesian bertindak sebagai pemboleh ubah rawak dengan taburan yang dikenali sebelum ini. Dalam kertas ini, kedua-dua anggaran kebolehjadian maksimum dan kaedah Bayesian digunakan untuk mengkaji hubungan antara kadar pertukaran wang dan harga getah bagi Malaysia, Thailand, Filipina dan Indonesia. Untuk mengenal pasti kaedah yang paling munasabah antara kaedah Bayesian dan anggaran kebolehjadian maksimum untuk data siri masa, kriteria maklumat Akaike dan kriteria maklumat Bayesian diguna pakai dalam kertas ini. Kesimpulannya, keputusan menunjukkan bahawa kaedah Bayesian mempunyai prestasi yang lebih baik daripada anggaran kebolehjadian maksimum dalam menganalisis data kewangan.

Kata kunci: Anggaran kebolehjadian maksimum; kaedah Bayesian; kriteria maklumat Akaike; kriteria maklumat Bayesian; model campuran terhingga

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*Corresponding author; email: yen_phoong@hotmail.com